Radar detection of ultra high energy cosmic rays

TARA (Telescope Array Radar) is a cosmic ray radar detection experiment co- located with Telescope Array, the conventional surface scintillation detector (SD) and fluorescence telescope detector (FD) near Delta, UT. The TARA detector combines a 40 kW transmitter and high gain transmitting antenna which broadcasts the radar carrier over the SD array and in the FD field of view to a 250 MS/s DAQ receiver. Data collection began in August, 2013. TARA stands apart from other cosmic ray radar experiments in that radar data is directly compared with conventional cosmic ray detector events. The transmitter is also directly controlled by TARA researchers. Waveforms from the FD-triggered data stream are time-matched with TA events and searched for signal using a novel signal search technique in which the expected (simulated) radar echo of a particular air shower is used as a matched filter template and compared to radio waveforms. This technique is used to calculate the radar cross-section (RCS) upper-limit on all triggers that correspond to well-reconstructed TA FD monocular events. Our lowest cosmic ray RCS upper-limit is 42 cm^2 for an 11 EeV event. An introduction to cosmic rays is presented with the evolution of detection and the necessity of new detection techniques, of which radar detection is a candidate. The software simulation of radar scattering from cosmic rays follows. The TARA detector, including transmitter and receiver systems, are discussed in detail. Our search algorithm and methodology for calculating RCS is presented for the purpose of being repeatable. Search results are explained in context of the usefulness and future of cosmic ray radar detection.

RADAR DETECTION OF ULTRA HIGH ENERGY COSMIC RAYS by Isaac J. Myers A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Department of Physics and Astronomy The University of Utah August 2015 Copyright © Isaac J. Myers 2015 All Rights Reserved The Uni v e r s i t y of Utah Gradua te School STATEMENT OF DISSERTATION APPROVAL The dissertation of Isaac J. Myers has been approved by the following supervisory committee members: John Belz Douglas Bergman Behrouz Farhang Mikhail Raikh Gordon Thomson , Chair , Member , Member , Member , Member May 6, 2015 Date Approved May 6, 2015 Date Approved May 5, 2015 Date Approved May 1, 2015 Date Approved May 14, 2015 Date Approved and by Carleton Detar , Chair/Dean of the Department/College/School of _____________ Physics and Astronomy and by David B. Kieda, Dean of The Graduate School. ABSTRACT TARA (Telescope Array Radar) is a cosmic ray radar detection experiment co­located with Telescope Array, the conventional surface scintillation detector (SD) and fluorescence telescope detector (FD) near Delta, UT. The TARA detector combines a 40 kW transmitter and high gain transmitting antenna which broadcasts the radar carrier over the SD array and in the FD field of view to a 250 MS/s DAQ receiver. Data collection began in August, 2013. TARA stands apart from other cosmic ray radar experiments in th a t radar data is directly compared with conventional cosmic ray detector events. The transmitter is also directly controlled by TARA researchers. Waveforms from the FD-triggered data stream are time-matched with TA events and searched for signal using a novel signal search technique in which the expected (simulated) radar echo of a particular air shower is used as a matched filter template and compared to radio waveforms. This technique is used to calculate the radar cross-section (RCS) upper-limit on all triggers that correspond to well-reconstructed TA FD monocular events. Our lowest cosmic ray RCS upper-limit is 42 cm2 for an 11 EeV event. An introduction to cosmic rays is presented with the evolution of detection and the necessity of new detection techniques, of which radar detection is a candidate. The software simulation of radar scattering from cosmic rays follows. The TARA detector, including transmitter and receiver systems, are discussed in detail. Our search algorithm and methodology for calculating RCS is presented for the purpose of being repeatable. Search results are explained in context of the usefulness and future of cosmic ray radar detection. CONTENTS A B S T R A C T ..................................................................................................................... iii L IST OF F IG U R E S ....................................................................................................... vii A C K N OW L E D G M E N T S ...........................................................................................xviii C H A P T E R S 1......IN T R O D U C T IO N TO CO SM IC RA Y P H Y S IC S ............................... 1 1.1 Energy S p e c trum ................................................................................................ 4 1.2 Sources and P ro p ag a tio n ................................................................................. 5 1.3 Composition......................................................................................................... 11 1.4 Detection Methods ............................................................................................. 15 1.4.1 Surface D e te c to r ...................................................................................... 16 1.4.2 Fluorescence D e te c to r............................................................................ 16 1.4.3 Air Shower Radio Emission................................................................... 17 1.4.4 Cosmic Ray R ad a r.................................................................................... 18 2. EAS R A D A R ECH O E S .................................................................................... 22 2.1 Bi-static Radar .................................................................................................. 22 2.2 Properties of EAS-Induced Ionization Columns ......................................... 23 2.2.1 Air Shower Properties ............................................................................ 23 2.2.2 Ionization in EAS .................................................................................... 24 2.3 Plasma Physics .................................................................................................. 26 2.3.1 Neglecting Electron-neutral Collisions ................................................ 26 2.3.2 Including Electron-neutral Collisions .................................................. 28 2.4 Forward Enhancement ...................................................................................... 35 2.5 Simulation ........................................................................................................... 36 2.5.1 Frequency Modulation ............................................................................ 36 2.5.2 Received Power ........................................................................................ 42 2.6 Case Study: TARA ........................................................................................... 46 2.6.1 Detector Design ........................................................................................ 46 2.6.2 Chirp Characteristics ............................................................................... 48 3. TARA D E T E C T O R ............................................................................................. 54 3.1 Telescope Array De tec to rs............................................................................... 55 3.1.1 Surface D e te c to r ...................................................................................... 55 3.1.2 Fluorescence D e te c to r............................................................................ 58 3.2 T ra n sm itte r......................................................................................................... 59 3.2.1 Hardware.................................................................................................... 59 3.2.2 Remote Monitoring and C o n tro l......................................................... 61 3.2.3 Performance................................................................................................ 62 3.3 Transmitting A n te n n a ...................................................................................... 64 3.3.1 Physical D e sig n ........................................................................................ 64 3.3.2 Theoretical Perfo rman ce ........................................................................ 67 3.3.3 Measured Performance .......................................................................... 6 8 3.4 Receiver Antenna................................................................................................ 71 3.5 Receiver Front-end............................................................................................. 72 3.6 Receiver D A Q .................................................................................................... 79 3.6.1 DAQ Structure ........................................................................................ 79 3.6.2 Design Challenges.................................................................................... 81 3.6.3 DAQ Implementation ............................................................................ 81 3.6.3.1 Amplitude Limiter.......................................................................... 8 6 3.6.3.2 Band-Pass Filtering........................................................................ 8 6 3.6.4 Performance Evaluation.......................................................................... 8 6 3.6.4.1 Linear Chirp Signal........................................................................ 8 8 3.6.4.2 Simulated Air Sh ow e r................................................................... 89 3.7 Conclusion........................................................................................................... 90 4. DATA D E S C R IP T IO N AND ANALYSIS T E C H N IQ U E S ............ 94 4.1 FD-triggered Data ............................................................................................. 95 4.2 Waveforms ........................................................................................................... 98 4.3 N o is e ..................................................................................................................... 103 4.4 FIR F i l t e r ........................................................................................................... 109 4.4.1 LTI Systems ............................................................................................. 111 4.4.2 Fourier Analysis........................................................................................ 113 4.4.3 Implementation ........................................................................................ 114 4.5 Matched Filter .................................................................................................... 116 5. RCS C A L C U L A T IO N ........................................................................................ 121 5.1 Data Preparation ................................................................................................ 124 5.1.1 Trigger Time Range ................................................................................. 126 5.1.2 Transmitter Logs ...................................................................................... 128 5.1.3 Snapshots Selection ................................................................................. 128 5.2 Matched Event Simulation ............................................................................... 129 5.3 Matched Event MF Response and Threshold ........................................... 132 5.4 Scale Factor r .................................................................................................... 133 6 . R E S U L T S ...................................................................................................................136 6.1 Positive Detection Events ............................................................................... 138 6.2 Individual Event Scale F a c to r ........................................................................ 138 6.3 Systematic E r r o r ................................................................................................ 141 6.3.1 Effect of Uncertainty in Reconstructed Shower Parameters......... 144 6.3.2 Effect of Fixed Frequency Receiver Antenna Model in Echo Sim ulation..................................................................... 150 6.4 RCS Upper L im its ............................................................................................. 153 v 7. C O N C L U S IO N .......................................................................................................161 7.1 Comparison with Other Experiments ......................................................... ..162 7.1.1 Atmospheric Radars .................................................................................162 7.1.2 MARIACHI..................................................................................................163 7.2 Comparison with Other Theoretical R e s u lts ............................................. ..168 7.3 CR Radar V ia b ility .............................................................................................169 R E F E R E N C E S ................................................................................................................ 171 vi LIST OF FIGURES 1.1 The cosmic ray energy spectrum for all particles as seen from a several experiments. 1 Reprinted figure with permission from E. Barcikowski, copyright 2011. .................................................................................................... 3 1.2 The cosmic ray energy spectrum for all particles multiplied by E 3 to expose spectral features. 1 Reprinted figure with permission from E. Bar­cikowski, copyright 2011....................................................................................... 5 1.3 The TA SD cosmic ray energy spectrum2 for all particles multiplied by E 3 to expose spectral features. A broken power line has been fit to the data. © AAS. Reproduced with permission................................................... 6 1.4 Hillas plot. 1 ,3 The product of an astrophysical object's size and typical magnetic field is a major factor in the Fermi shock acceleration model. Diagonal lines mark the minimum limit of th a t product necessary to accelerate protons to 1020 eV, under the assumption that [ s = Vs/c is 1 and 1/300, respectively. Vs is the shock front velocity. Reprinted figure with permission from E. Barcikowski, copyright 2011.................................. 8 1.5 Significance skymaps4 in equatorial coordinates of Telescope Array event clustering, known as the "hotspot." Seventy-two events were detected with E0 > 57 EeV (a). The maximum number of events th a t occurred in a 20° radius circle is 19 (b), with 5.1a statistical significance. Back­ground expectation from geometrical exposure to an isotropic sky in the same circle size (c) and a significance map (d) of events (b) occurring in the simulated sky are shown. © AAS. Reproduced with permission. 10 1.6 Element abundances of cosmic rays and the solar system, 1 both relative to Si. Nuclei lighter than C are and some nuclei lighter than Fe are over-abundant in the cosmic ray flux. Reprinted figure with permission from E. Barcikowski, copyright 2011................................................................. 12 1.7 High Resolution Fly's Eye (HiRes) composition for E 0 > 1018 eV. 5 The lines are the result of CORSIKA6 air shower simulations using the dif­ferent hadronic interaction models. Data are shown with the points and clearly indicate a light composition at high energies. Reprinted figure with permission from R. Abbasi, et al., Phys. Rev. Lett. 104, 161101 (2010). http://dx.doi.org/10.1103/PhysRevLett.104.161101. Copyright 2010 by the American Physical Society............................................................ 13 1.8 Pierre Auger Observatory (PAO) composition result. 7 The lines are the result of CORSIKA6 Monte Carlo shower simulation studies us­ing different hadronic models. The points are data. Note the error bars. These data indicate th a t the composition is increasingly protonic before E 0 = 1 0 18-25 eV, and increasingly heavier beyond. This result in in stark contrast to the earlier HiRes result 8 (Figure 1.7) which showed a protonic composition up to the highest energies. Reprinted figure with permission from J. Abraham, et al., Phys. Rev. Lett. 104,091101 (2010). h ttp ://d x .d o i.o rg /1 0 .1 1 0 3 /P h y sR e v L e tt.1 0 4 . 091101. Copyright 2010 by the American Physical Society....................... 14 1.9 Telescope Array hybrid five-year composition result. 9 The red and blue lines represent different hadronic models used in simulating proton (blue) and iron (red) extensive air showers. Reprinted from Astroparti-cle Physics, 64, R.U. Abbasi, et al., Study of Ultra-High Energy Cosmic Ray Composition Using Telescope Array's Middle Drum Detector and Surface Array in Hybrid Mode, 49-62, Copyright (2015), with permis­sion from Elsevier. ............................................................................................. 15 1.10 Picture of a single Telescope Array surface detector (SD), composed of a communications tower, solar panel for providing power to electronics and plastic scintillator enclosed in sheet metal.............................................. 17 1.11 Picture of Black Rock Mesa (BRM) FD building with the telescope doors open showing the segmented focusing mirrors.................................... 18 2.1 A CORSIKA (histogram) vs. Gaisser-Hillas and NKG (curve) compari­son of ionization electron density as a function of radius near Xmax for a 1019 eV vertical shower. Agreement is good near the core where electron density is highest.................................................................................................... 26 2.2 Plasma frequency as a function of radius at Xmax for a 1019 eV shower calculated using Gaisser-Hillas and NKG parameterizations. Gaisser- Hillas parameters were averages of values obtained by CORSIKA sim­ulations. The horizontal black line corresponds to the TARA radar carrier frequency at 54.1 MHz............................................................................ 29 2.3 Survey of estimates of electron-neutral collision frequency as a function of altitude. Data points are from Vidmar, 10 Itikawa, 11 Lovell, 12 Suga, 13 Stasielak et al. , 14 and the mean free path points are calculated by dividing mean electron speed by the mean free p a th ................................... 31 2.4 Real and imaginary parts of the index of refraction (n = ^ - i \ ) with 1011 Hz collision frequency each with u e = (10-3 , 10-2 , 10-1) v. The TARA radar frequency is 54.1 MHz. Note th a t the red and black curves in the top plot are very close to one................................................................. 34 2.5 Relative scattered electric field 15 magnitude for several different cylinder radii, expressed as fractions of the incident wavelength, as a function of angular deviation from the forward scattering direction............................. 36 2.6 Contributions from paths of varying lengths (red), TX ^ target ^ RX, summed at the receiver result in a chirp signal (bi-static configuration). 37 viii 2.7 Simulated chirp spectra fits to highest amplitude frequency component for four different geometries. Each simulation represents a vertical, 10 EeV CR shower located midway between transmitter and receiver. TX ^ RX separation distances are shown on the legend. Both the time offsets and absolute frequency ranges have been justified for direct chirp rate comparison...................................................................................................... 39 2.8 Spectrograms showing simulated radar echoes for a shower midway between transmitter and receiver and inclined 30° out of the TX/RX plane. Top: Electron lifetime is fixed at 1 ns and antenna gain is held constant. This configuration simulates a small scattering object travelling at the speed of light toward the ground. Middle: Electron lifetime is fixed at 100,000 ns and antenna gain is held constant. This configuration simulates a scattering rod beginning high in the atmo­sphere and growing toward the ground at the speed of light. Bottom: Electron lifetime is determined from empirical models and RCS comes from the thin-wire approximation (Section 2.5.2) and shower evolution models. Antenna gain is determined from lookup tables generated by NEC. 16 This configuration simulates a cosmic ray radar echo................... 41 2.9 Plot showing Fmax vs. time for the three simulated echo waveforms shown in Figure 2.8. Black points represent Fmax for the short lifetime waveform. Red and blue points represent Fmax for the long lifetime and full simulation waveforms, respectively............................................................. 42 2.10 Radar echo spectrogram from a 1019 eV shower located midway between transmitter and receiver inclined 30° out of the plane connecting the two. TX ^ RX separation is 39.5 km, the TARA separation distance............ 47 2.11 Received power vs. time for a simulated radar echo assuming a ge­ometry th a t maximizes signal (black). The same received power curve is shown multiplied by a damping factor of 1 0 - 6 (green) to account for collisional damping. Note th a t the damping factor is calculated assuming a collision frequency of 1011 Hz, which is likely overestimated due to the assumption of near-thermal ionization electron energies (see Section 2.3.2). The red line is integrated background noise power in the TARA passband (see Chapters 3 and 4). Simulated received power has been adjusted by +30 dB to account for front end amplifiers, through which background noise has passed................................................................... 50 2.12 Radar echo chirp slope distribution for 10,000 simulated radar echoes. Chirp slope is determined by a linear fit to an Fmax vs. time plot with each point weighted by its Fourier amplitude. The sounding wave polarization does not affect the slope. Near Fmax the chirp rate is actually slightly concave. Linear chirp rates are used for easy comparison. 51 2.13 Radar echo duration distribution from 10,000 simulated echoes. Echo duration is defined as the time difference between the Pmax - 10 dB points. 52 ix 2.14 Fmax distribution for 10,000 simulated radar echoes. The different histograms are for no cuts (black), Pmax > -1 0 0 dBm (red) and Pmax > -8 0 dBm (green). Fmax is the frequency component th a t occurs with the highest power. Peaks in Fmax correspond to fluctuations in aTW, which can be seen in Figure 2.10, and which were discussed in Section 2.5.2. 53 3.1 Map of TARA Observatory sites (transmitter and receiver) along with the Telescope Array (TA) detector facilities. The transmitter broad­casts as station WF2XZZ near Hinckley, Utah, towards a receiver site located at the TA Long Ridge Fluorescence Detector (FD). The sound­ing radiation illuminates the air over the central portion of the TA Surface Detector array, shown with dashed blue lines th a t indicate the beamwidth 3 dB below the peak gain............................................................... 56 3.2 Map of Telescope Array9 showing fluorescence detectors (FD) as blue triangles, with their approximate detection angle, overlooking surface detectors (SD) represented by small black squares. Reprinted from Astroparticle Physics, 64, R.U. Abbasi, et al., Study of Ultra-High Energy Cosmic Ray Composition Using Telescope Array's Middle Drum Detector and Surface Array in Hybrid Mode, 49-62, Copyright (2015), with permission from Elsevier. ........................................................................ 57 3.3 Schematic of surface detector plastic scintillator........................................... 58 3.4 Schematic of the transmitter hardware configuration. A computer con­nected to RF sensor equipment, an arbitrary function generator and transmitter control electronics orchestrates the two distinct transmitters and provides remote control and logging. RF power from each transmit­te r's two amplifier cabinets is combined with out of phase power rejected into a 50 Q load. A hybrid combiner sums the combined output of each transmitter and sends tha t power to the antenna. Power reflected back into the hybrid combiner is directed to a third RF load. ........................ 60 3.5 Transmitter forward power (black) and room temperature (red) during April 2013. Poor air conditioning calibration resulted in daily temper­ature fluctuations which caused large output power modulation. ......... 63 3.6 Transmitter forward power (black) and room temperature (red) during December 2013. A well-calibrated air conditioning system keeps room temperature stable and increased automatic gain control minimizes for­ward power fluctuations........................................................................................ 64 3.7 Transmitter on-time in days (black, left vertical axis) and forward and reflected power in units of kW (red and blue, right vertical axis) during 2013. Total duty cycle during this period is 83%.......................................... 65 3.8 Configuration of the eight Yagi antennas and mounting poles which comprise the TARA transmitting antenna array........................................... 67 x 3.9 Simulated horizontal (top) and vertical (bottom) radiation patterns of the eight-Yagi TARA antenna array shown in blue. Red points are measured data th a t have been uniformly scaled to best fit the model. Forward gain is 22.6 dBi, beamwidth is 12° horizontal, 10° vertical, and the F /B ratio is 11.8 dB....................................................................................... 69 3.10 Reflection coefficient ($ n ) for the eight-Yagi array...................................... 70 3.11 Dual polarized TARA Log Periodic Dipole Antenna (LPDA)................... 72 3.12 SWR of a horizontally polarized TARA LPDA as measured in an ane-choic chamber.......................................................................................................... 73 3.13 Simulated horizontal (top) and vertical (bottom) radiation pattern of a horizontally polarized TARA LPDA at the transmitter sounding fre­quency of 54.1 MHz. Beamwidths ( - 3 dB below peak gain) are shown with red lines. Peak gain is 12.6 dBi................................................................ 74 3.14 Effective height in meters vs. frequency in MHz of the TARA receiver LPDA. The Sn parameter and gain of the receiver antenna are inserted into Equation 3.1 and plotted vs. frequency using the anechoic chamber data (solid line), simulated data from NEC (fine dashed), and simulated data with the 54.1 MHz values of Sn and gain held constant (dot-dashed line). ....................................................................................................................... 75 3.15 Beamwidth of a single channel LPDA as measured in an anechoic cham­ber at the University of Kansas.......................................................................... 76 3.16 S2i (transmission coefficient) of the filter and amplifier bank connected to the triggering channel of the DAQ............................................................... 77 3.17 Snapshot (forced trigger) Power Spectral Density (PSD) at 80.0 MHz averaged over eight days versus Local Mean Sidereal Time (LMST). Top: Data taken in December, 2013. Bottom: Data taken in May, 2014. There is strong correlation in peak PSD and sidereal time which indicates the signal is galactic in origin. Horizontal error bars show bin width. Vertical error bars are std. dev. in the mean................................... 78 3.18 Average receiver system (black) Power Spectral Density (PSD) in dBm/Hz superimposed with a fit to measured galactic background noise and its associated error 17 (red band). System attenuation, filters and amplifiers were accounted for to determine absolute received power. No other calibration or scaling was applied to the receiver d a ta ................................ 80 3.19 Elements of the radar receiver station.............................................................. 80 3.20 Spectrogram of background noise at the receiver site. Frequency and time are on the vertical and horizontal axes, respectively, with color representing the power in a particular frequency component. The carrier signal is represented by the horizontal line at 54.1 MHz. Broadband transients are the vertical lines and stationary noise sources are the horizontal band near 30 MHz.............................................................................. 82 3.21 Position of the triggering pulse within the data window th a t is written to disk........................................................................................................................ 83 xi 3.22 Linear down-chirp signal. (a) Signal in time-domain. (b) Signal in time-frequency domain.......................................................................................... 84 3.23 Block diagram of the matched-filter-type detector........................................ 85 3.24 False alarm rate versus relative threshold (nY units of the standard deviation at each filter output) for different amplitude limiter levels. . . 8 8 3.25 Time-frequency (spectrogram) representation of a linear, -1 MHz/^s, -10 dB SNR received chirp signal as recorded by the DAQ system.......... 89 3.26 Probability of detection for the matched-filter-type detector with nY = 6 . 90 3.27 Spectrogram of simulated air shower radar echo with 5 dB ASNR. The radar echo is from a simulated shower inclined 30° out of the T X ^ R X plane and located midway between the transmitter and receiver............. 91 3.28 Probability of correct detection for the matched-filter detector using nY = 6 for a simulated air-shower echo th a t is scaled and emulated with a function generator............................................................................................... 91 3.29 Minimum detectable radar cross section (RCS) as a function of dis­tance perpendicular to the plane connecting the transmitter and re­ceiver. The transmitter antenna main lobe points along this plane. For simplicity, the minimum RCS is calculated from the bi-static radar equation (Equation 2.1) for a cosmic ray air shower midway between transmitter and receiver with maximum transmitter and receiver gains. The 5 MHz FlexRIO passband trigger scheme (Section 3.6.3.2) was assumed to detect a constant amplitude radar echo with chirp rate in [-3,-1] MHz/^s (Section 3.6.3) and signal-to-noise (SNR) ratio 7 dB (Section 3.6.4.2) below background noise (Figure 3.18, Section 3.4), the empirical detection performance for the 5 MHz DAQ passband. Further assumptions are ground-level detection and constant wavelength A. Vertical dashed red lines show the -3 dB beamwidth of the transmitter antenna. ................................................................................................................ 92 4.1 FD-triggered data rate on a night in August, 2013. The rate is averaged over 5 sec time bins. High rate periods occur primarily at the beginning and end of data acquisition and at several periods throughout the run when the detector is calibrated. Typical trigger rates over many runs are between 3 and 5 Hz........................................................................................ 96 4.2 Event display for an FD-trigger chosen at random from the August, 2013 FD run. The top plot is the time domain waveform with voltage on the vertical axis and time on the horizontal axis. The bottom plot is a spectrogram of the waveform created using a 512 sample window size, and 256 sample overlap. Power spectral density (PSD) is shown on the z or color axis.......................................................................................................... 99 4.3 Time domain of Figure 4.2 on a smaller scale. The primary frequency component of the total waveform is the 54.1 MHz radar carrier............... 100 xii 4.4 Event display for an FD-trigger chosen at random from the August, 2013 FD run. This plot is the same as th a t in Figure 4.2 but with 54.1 MHz notch and 30 MHz high pass digital filters applied....................................... 101 4.5 Event display for a snapshot chosen at random from the August, 2013 FD run with both 54.1 MHz notch and 30 MHz high pass digital filters applied. The waveform and spectrogram are very similar to the FD-triggered event display shown in Figure 4.4.................................................... 102 4.6 Voltage RMS distribution of 249 matched FD-triggered events in red overlayed with th a t of snapshots in black. All FD-triggered, matched events from the August, 2013 FD run are included in the red histogram. Only values from the first 249 snapshots from the set used for estimating backgrounds in August, 2013 data are included for comparison. FD-triggered data and snapshots have been filtered by a set of cuts described in Section 5.1.3........................................................................................................ 103 4.7 Event display for low amplitude, transient broadband noise. This type of noise can give high MF response................................................................... 104 4.8 Event display for high VRMS, broadband transient noise. MF response is always high for any noise with large amplitude relative to the standard background............................................................................................................... 106 4.9 Event display showing an intermittent carrier at 120 MHz. Intermittent carriers are typically present in most spectra, but at much lower power. When carrier power increases spuriously, it can interfere with detection by raising the MF response................................................................................. 107 4.10 Event display showing an artificial high amplitude impulse caused by applying the notch filter to a waveform with dropped samples. A bug in the DAQ occasionally causes two dropped samples. When the notch filter, which is adapted to a specific phase and amplitude, passes over the region with dropped samples it briefly loses the ability to notch the frequency of interest before readapting............................................................ 108 4.11 Notch filtered snapshot VRMS distribution for a selection of snapshots taken during the August, 2013 FD run............................................................ 109 4.12 Event display showing the FlexRIO DAQ quantization noise. These data were taken with a 50 Q terminator on the channel input. Quan­tization noise at ~ -150 dBm/Hz is over two orders of magnitude higher than room temperature thermal noise at -174 dBm/Hz. Note that quantization noise cannot be compared directly to previous event displays because RF input for this plot has not passed through the frontend amplifiers and filters............................................................................. 1 1 0 4.13 Frequency response H , which has been reflected about frequency 0 MHz, or DC. These data are the transmission coefficient S21 data taken from filter bank 3 which we desire to emulate with a digital filter. ................. 115 4.14 Frequency response H has been extended to fill the range [0, 2n), sam­pled (decimating by 6 ) and converted to linear values................................. 116 xiii 4.15 Spectrograms showing simulated Gaussian noise (top) and the same noise filtered with an FIR filter designed from the frequency response shown in Figure 4.13. Amplitude features can be directly compared between the spectrogram and the desired response. ................................. 117 4.16 Three examples of test waveform (left plots) and their Matched Filter (MF) responses (right plots). In each case a 10 ^s sine wave is superim­posed on Gaussian noise. The absolute value of the MF response using a template identical to the superimposed sine wave is plotted versus the time where the MF is applied. Peak response occurs at 20 ^s where the superimposed sine wave and the template are aligned. The top, middle and bottom plots show results from superimposing the sine wave at 1 0 , 0 and -20 dB SNR in power.............................................................................. 119 4.17 Matched filter detection efficiency as a function of ASNR using a canon­ical simulated radar echo. This detection scheme is described in Sec­tion 5.3. Selected snapshots from the August, 2013 FD run are used both to determine the 3a response threshold and as backgrounds on which scaled echo waveforms are superimposed. In contrast with the FlexRIO self-triggering test conducted at the receiver site which resulted in a -7 dB ASNR 100% detection efficiency, this postprocessing scheme has 100% efficiency at -11 dB ASNR....................................................................... 120 5.1 Transmitter forward power during the months in 2013/2014 when the analysis data set were recorded. The transmitter was turned off in January and February, 2014 due to power supply overheating and a failing power splitter. Power was reduced in March and April to avoid damaging the KTVN transmitter, which needed upgraded power ampli­fiers.................................................................................................................... ........ 123 5.2 Time difference between FD reconstructed events and the TARA FD-triggered events to which they are matched for the entire data set (see Table 5.1). The 33 ^s delay is caused by FD DAQ trigger formation, cable delay and TARA DAQ delay in signaling an event to the GPSY18 GPS event logger.................................................................................................... 125 5.3 Time domain of notch-filtered snapshot taken in August, 2013 showing DAQ trigger time (96 ^s, solid red line) and adjusted trigger range (48 ^s and 101 ^s, dashed red lines). This snapshot has both a phase shift at 22 ^s and high VRMS noise at 87 ^s. The phase shift occurs outside the trigger range under consideration, and therefore would not be excluded from the set of snapshots used in the analysis (discussed in Section 5.1.3). High VRMS noise near the end of the trigger range will cause large MF response, placing this snapshot in the tails of the MF response distribution............................................................................................. 127 5.4 Simulated radar echo from a cosmic ray air shower located midway between the transmitter and receiver, inclined 30° out of the TX/RX plane. Top: Time domain waveform. Bottom: Spectrogram..................... 130 xiv 5.5 Simulated radar echo th a t has been filtered according to the RF frontend transmission coefficients S21. Top: Time domain waveform. Bottom: Spectrogram............................................................................................................. 131 5.6 Peak MF response distribution for an August, 2013 FD-triggered matched event using 400 snapshots with a simulated radar echo MF template. The 3 RMS threshold is 32.6 + 3 ■ 6.4 = 51.8................................................. 133 6.1 Power spectral density (PSD) of 1292 radar echoes (red) simulated from matched event parameters and 1292 snapshots (black) selected for analysis from the August, 2013 FD run using a 512 sample window size. Radar echo PSD is the maximum value in the [40, 80] MHz passband. Snapshot PSD is the un-filtered value at 65 MHz for comparison with the noise floor in Figure 3.18. The blue line is approximate noise floor level at 65 MHz. The simulation includes full TX/RX antenna radiation patterns, transmitter power at detection time and air shower geometry and energy reconstructed by Telescope Array. The thin-wire approximation (Equation 2.26) is used to calculate the RCS.................... 137 6.2 Distribution of Nsnap>exc, number of snapshots whose peak MF response exceeds threshold. One entry per matched FD-triggered event................. 139 6.3 r 90 (color scale) for all negative detection (FD-triggered waveform peak MF response did not exceed threshold) events shown at reconstructed core locations in Telescope Array CLF (referenced to Central Laser Facility) coordinates. Red dashed lines mark the primary beam -3 dB beamwidth. This histogram format can be misleading because events with similar core locations can fall into the same bin.................................. 140 6.4 r 90 distribution of all negative detection events. Large r 90 occurs when matched-event geometry specifies an EAS that occurs outside the an­tenna main lobe...................................................................................................... 141 6.5 r 90 (color scale) for negative detection events with r 90 < 0.1 shown at reconstructed core locations in Telescope Array CLF coordinates. Red dashed lines mark the primary beam -3 dB beamwidth.............................. 142 6 . 6 r 90 (color scale) negative detection events restricted to those with 90° < azimuth < 180° shown at reconstructed core locations in Telescope Array CLF coordinates. Red dashed lines mark the primary beam -3 dB beamwidth................................................................................................................ 143 6.7 54.1 MHz notch and 30 MHz high pass filtered FD trigger waveform sample histogram. Red line is a Gaussian fit.................................................. 146 6 . 8 Distribution of peak matched filter responses from 400 snapshots su­perimposed with a simulated radar echo using scale factor r 90. The simulated radar echo is from a low r 90 August, 2013 event. A Gaussian is fitted to the d a ta ................................................................................................ 147 xv 6.9 Distribution of peak matched filter responses from 400 snapshots su­perimposed with a simulated radar echo using scale factor r 90. The simulated radar echo is from a low r 90 August, 2013 event th a t has been modified by increasing the ^ angle 7.7°. A Gaussian is fitted to the d a ta ..................................................................................................................... 148 6.10 Behavior of detection probability and mean peak MF response /3 as a function of scale factor r . r range is chosen such th a t it includes r 90, which is 0.00088...................................................................................................... 150 6 . 1 1 r 90 (color scale) for negative detection events with r 90 < 0 .1 , similar to Figure 6.5. Additionally, green arrows begin at the core location of the five lowest r 90 events and point in the direction of each event's azimuth. Arrow length is proportional to zenith angle.................................................. 151 6 . 1 2 Spectra of the first entry in Table 6.1 corresponding to on of the five lowest r 90 events detected in the present analysis. Top: Spectrogram of simulated radar echo created using FD event reconstructed parameters with o tw RCS. Gaussian noise has been added to emphasize only the primary expected received signal. Frequency at maximum power Fmax is 57.6 MHz, very close to the assumed 54.1 MHz receiver radiation pattern used in the simulation. Bottom: Spectrogram of matched radar waveform which has been 54.1 MHz notch-filtered and 30 MHz high pass-filtered.............................................................................................................. 152 6.13 Spectra of the second entry in Table 6.1 corresponding to one of the five lowest r 90 events detected in the present analysis. Top: Spectrogram of simulated radar echo created using FD event reconstructed parameters. Gaussian noise has been added to emphasize only the primary expected received signal. Fmax is 55.7 MHz. Bottom: Spectrogram of matched radar waveform which has been 54.1 MHz notch-filtered and 30 MHz high pass-filtered.................................................................................................... 154 6.14 Spectra of the third entry in Table 6.1 corresponding to one of the five lowest r 90 events detected in the present analysis. Top: Spectrogram of simulated radar echo created using FD event reconstructed parameters. Gaussian noise has been added to emphasize only the primary expected received signal. Fmax is 55.7 MHz. Bottom: Spectrogram of matched radar waveform which has been 54.1 MHz notch-filtered and 30 MHz high pass-filtered.................................................................................................... 155 6.15 Spectra of the fourth entry in Table 6.1 corresponding to one of the five lowest r 90 events detected in the present analysis. Top: Spectrogram of simulated radar echo created using FD event reconstructed parameters. Gaussian noise has been added to emphasize only the primary expected received signal. Fmax is 55.7 MHz. Bottom: Spectrogram of matched radar waveform which has been 54.1 MHz notch-filtered and 30 MHz high pass-filtered.................................................................................................... 156 xvi 6.16 Spectra of the fifth entry in Table 6.1 corresponding to one of the five lowest r 90 events detected in the present analysis. Top: Spectrogram of simulated radar echo created using FD event reconstructed parameters. Gaussian noise has been added to emphasize only the primary expected received signal. Fmax is 57.6 MHz. Bottom: Spectrogram of matched radar waveform which has been 54.1 MHz notch-filtered and 30 MHz high pass-filtered.................................................................................................... 157 6.17 Integrated thin-wire approximation to RCS for a simulated radar echo according to reconstructed shower parameters. Phase factors are in­cluded in the sum of the total RCS to properly account for each longi­tudinal shower segment......................................................................................... 159 6.18 Received power vs. time for the event with r 90 = 0.00077 (black). The same received power curve is shown multiplied by r 90 (blue) and the damping factor 10- 6 (green) calculated in Section 2.3.2 to account for collisional damping. Note th a t the damping factor is calculated assuming a collision frequency of 1011 Hz, which is likely overestimated due to the assumption of near-thermal ionization electron energies (see Section 2.3.2). The red line is integrated background noise power in the TARA passband (see Chapters 3 and 4). Simulated received power has been adjusted by +30 dB to account for front end amplifiers, through which background noise has passed................................................................... 160 7.1 Event display of a 36 dB ASNR MARIACHI radar echo candidate tha t was time-matched to a scintillator detector event. The passband DAQ was tuned to 67.26 MHz and used 2.8 kHz sample ra te .............................. 166 xvii ACKNOWLEDGMENTS Planning and building of the TARA detector spanned nearly five years, followed by two years of data collection. During this period many people took part in advancing our experiment, and helped me in a personal way to meet the challenges of science research. Several people stand out in my mind as having made outstanding contribu­tions. I have had many invaluable discussions with Helio Takai, a co-founder of the MARIACHI experiment, about radar echo simulation and air shower physics. Ben Stokes, Gordon Thomson, Stan Thomas, Jeremy Smith, and Dmitri Ivanov provided assistance on numerous occasions. Tom Stroman deserves special thanks for providing fluorescence detector events for comparison with TARA data. All of my friends in TA and TARA have offered a helping hand at some point, whether through physics or programming discussions or career advice and encouragement. Dave Barr, Gary McDonough, Stanton Thomas, and Patrick Wright assisted in numerous hardware and facilities tasks tha t kept our experiment functioning. Support from Frank Misak has been indispensable in keeping TARA affairs in order. John Matthews has offered his knowledge about the fine details of operating a large experiment, including navigating the University of Utah bureaucracy and working with private contractors. Bill Ramsey not only helped procure the television transmitters used in the exper­iment, but assisted several times in the field to prepare the transmitters for operation. For the last several years Bill Gillman has been our to go-to guy for his transmitter expertise and broad electronics knowledge. He directed us in commissioning our final high power transmitter system in Hinckley, UT and he serviced the transmitters while we pushed them beyond the commercial specification. Most importantly, I would like to thank my advisor John Belz for many physics and research discussions and his constant availability and willingness to help me understand and learn new things. TARA is a group effort, but the analysis presented in this dissertation is primarily the work of John and me. Without John's assistance and experience in experimental physics, I wouldn't have been able to produce such a clear and appropriate methodology. Finally, I want to express my appreciation to my family for their support, both financial and moral. Early TARA funding was a seed grant from VP for Research Tom Parks. U.S. National Science Foundation grants NSF/PHY-0969865 and NSF/MRI-1126353 and a special grant from the W.M. Keck Foundation carried our experiment for its duration. On a personal level, these grants supported my research assistantship which allowed me to spend my time doing research. I would also like to acknowledge the gener­ous donation of analog television transmitter equipment by Salt Lake City KUTV Channel 2 and ABC Channel 4, and the general cooperation of the Telescope Array collaboration. xix CHAPTER 1 INTRODUCTION TO COSMIC RAY PHYSICS The title "cosmic ray" is misleading because cosmic rays are single highly energetic particles th a t propagate through space both within and outside of our galaxy. Gamma rays and electrons are sometimes included in the definition. In this text the term will primarily denote hadronic particles, from single protons to atomic nuclei as heavy as iron and higher. In 1912 Victor Hess conducted research 19 th a t showed evidence of cosmic origins of previously observed charged particles in the atmosphere, work about which he later wrote a book20 (translated to English) and won the Nobel prize. From measurements taken with an electroscope while aboard a balloon, Hess showed tha t the rate of discharge in an electroscope increases with altitude. An electroscope is a device th a t shows a net charge by the separation between charged foils. Energetic charged particles bombarding the instrument create trails of ionization electrons th a t allow leakage current from the charged foil, allowing discharge which decreases deflection. Prior to Hess's discovery, the radiation th a t discharged electroscopes was thought to originate in the earth. Pierre Auger is credited with the discovery of atmospheric particle cascades called air showers, which are initiated by a single cosmic ray primary particle. 21 Interest grew from the realization that energetic secondary particles indicate a highly energetic primary. With a basic understanding of the atmospheric phenomenology of cosmic rays, the scientific community turned its attention to the question of their origin. The answer to this question is still being pursued today. Theoretical frameworks for acceleration sources are abundant, but arrival direction and possible astronomical objects haven't been correlated with high probability. 2 Cosmic Ray (CR) research has led to the discovery of new fundamental particles such as the positron22 (e+), muon23 (^ - ) and pion 24 (n± ,n 0), which opened the door to particle physics. In the decades since the early discoveries, the range of detected cosmic ray energies has increased by over eleven orders of magnitude, from 1 0 9 to 1020 eV. Ultra high energy cosmic rays (UHECR) are classified as those th a t have energies greater than 1018 eV (Exa-eV, EeV) and exceed the most powerful particle accelerators in single-particle energy made by humankind by a factor of roughly 100,000 (1 EeV cosmic ray primary proton compared to 7 TeV LHC proton beam25). The primary question of CR physics still remains. There is no strong evidence of correlations between CR and known astronomical structures. Galactic and extra-galactic magnetic fields smear CR arrival directions. UHECRs are the best candidates for source correlation because the Larmor radius is proportional to energy, so the random component of the arrival direction is minimized. Unfortunately, the UHECR flux is very low. Section 1.1 contains an explanation of the measured energy spectrum (Figure 1.1) which indicates, e.g., th a t one can expect a single 1020 eV cosmic ray particle per square kilometer per century. Therefore, detectors are large; Pierre Auger Observatory (PAO, southern hemisphere) surface detector covers over 3000 km2 and Telescope Array (TA, northern hemisphere) covers nearly 700 km2. Large detectors are expensive to build and maintain, and funding agencies have been hesitant to fund substantial expansions of the current large de­tectors. Investigation of alternate detection methods is driven by the desire for better statistics. The CR energy spectrum dictates th a t UHECR event rates are low. Any new technique th a t measures energy, composition and geometry in a large fiducial volume at lesser cost will be successful. Cherenkov,26 molecular bremsstrahlung, 27 and geomagnetic synchrotron28 are passive detection methods currently being inves­tigated. Radar detection of cosmic rays29 is the only active technique being pursued. CR physics needs new tools and detection methods which will allow better statistics at the highest energies. Radar detection of cosmic rays is one possible solution that would allow remote detection at 1 0 0 % duty cycle. What follows in this chapter is a brief description of the CR spectrum, possible 3 Cosmic Ray Spectra of Various Experiments ^ 104 cT ® 2 w 102 > a> O w 1 0 -1 2 X A 2 10-4 u_ 10-7 10-10 10-13 10-16 10-19 10-22 10-25 10-28 1 0 9 1 0 10 1 0 11 1 0 12 1 0 13 1 0 14 1 0 15 1 0 16 1 0 17 1 0 18 1 0 19 1020 1021 E n e r g y (eV ) F ig u re 1.1: The cosmic ray energy spectrum for all particles as seen from a several experiments. 1 Reprinted figure with permission from E. Barcikowski, copyright 2011. i 1 1 m u i m i n i i 1 1 m u i i i i i i i i i i n t+, (1 particle/m -sec) ..x. (1p + LEAP - satellite X Proton - satellite ☆ Yakustk - ground array * Haverah Park - ground array o Akeno - ground array A AGASA - ground array □ Fly's Eye - air fluorescence X HiRes1 mono - air fluorescence 0 HiRes2 mono - air fluorescence X HiRes Stereo - air fluorescence □ Auger - hybrid ....... > X Knee X (1 particle/m2-yea Ankle articJe/km2-year) (1- -partic4e/k-m-2-century)- : ----= i i i i i i i i i i mini i m i n i i ini i i i l i mini i i i i i i i i i i i i i i i i i i m i 4 source acceleration mechanisms, and primary particle composition and propagation. Air shower footprint and novel radio emission detection techniques are introduced. Cosmic ray radar detection is proposed as a method of detection which may have advantages over other channels. Chapter 2 gives an explanation of air showers including the cascade processes of electromagnetic and hadronic components, and the longitudinal profile and lateral distribution of particles. Plasma physics and scattering models relevant to radar echo simulation is discussed in Section 2.3. Chapter 3 gives a complete description of the Telescope Array Radar (TARA) detector, including transmitter, receiver antennas and DAQ, and performance estimates. Chapter 4 introduces the data, experimental challenges, and processing techniques. Chapter 5 describes the analysis procedure in which I search waveforms for evidence of radar echoes and calculate the radar cross-section (RCS). Analysis results and conclusion follow in Chapters 6 and 7. 1.1 Energy Spectrum An energy spectrum plot (flux vs. energy) is shown in Figure 1.1. Notice the nearly constant E - 3 power law and the large range of detected energies. The low and high energy ends of the spectrum require dramatically different detection and measurement techniques because of orders of magnitude difference in flux. For example, above 1018' 9 eV the TA detector has an aperture of 890 km2 sr. 30 Using the figure, the rate of 1019 eV primaries detected by TA is calculated to be slightly less than one per day. Note th a t TA is the world's second largest UHECR detector, covering approximately 680 km2 . 30 At the other end of the spectrum, consider a 1 0 0 cm2, 2 n steradian detector flown on a high-altitude balloon or satellite. Its count rate would reasonably be greater than 50 s- 1 for 10 GeV particles. A spectral index of -3 indicates a nonthermal acceleration source because the spectrum is not peaked as in, e.g., Planck's Law. Spectral features can be seen more readily if the featureless Figure 1.1 ordinate is multiplied by E 3. Figure 1.2 shows this modification. Three prominent spectral features at 1015 eV, - 4 x 1017 eV and - 4 x 1018 eV are known as the knee, second knee and ankle. Above - 6 x 1019 eV the spectrum 5 Cosmic Ray Spectra of Various Experiments 102 M 11m i l i 111m i l i 11 M i n i i 11 M i n i i 11 i i i i i i i 11 M i n i i 1111m i - i 11 1 1 1 1 1 1 - 1 1 1 1 1 1 1 1 1 - 1 1 1 1 1 1 1 1 1 - 1 1 1 1 1 1 1 1 1 - 1 1 1 1 1 1 1 1 1 - 1 1 1 m oo (0 (0 CM E 10 CM> CM 0 uT 1 oL U 10-1 10- 10" + + ☆ Yakustk - ground array * Haverah Park - ground array o Akeno - ground array A AGASA - ground array □ Fly's Eye - air fluorescence * HiRes1 mono - air fluorescence 0 HiRes2 mono - air fluorescence X HiRes stereo - air fluorescence □ Auger - hybrid 11 m ill_ _ 1 1 Mini_ _ 1 11 m ill_ _ 1 1 m ini_ _ 1 1 m ini_ _ 1 1 m ini_ _ 1 1 m ini_ _ 1 1 m ini_ _ 1 11 mill_ _ 1 111 mil_ _ 1 1 m ini_ _ 1 1 m ini 1 11111 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 Energy (eV) F ig u re 1.2: The cosmic ray energy spectrum for all particles multiplied by E 3 to expose spectral features. 1 Reprinted figure with permission from E. Barcikowski, copyright 2 0 1 1 . falls rapidly due to the Greisen-Zatsepin-Kuzmin (GZK) cut-off. 31 Figure 1.2 best shows the knee. A third spectrum plot, shown in Figure 1.3, is a scaled version of Figure 1.2 th a t best shows the ankle and second knee. These features are evidence of specific source mechanisms and propagation models (Section 1.2). The spectral index changes from -2 .7 to -3 .1 after the knee, a softening of the spectrum. After the second knee the spectrum steepens again and finally becomes less steep at the ankle. 1.2 Sources and Propagation The knee is often associated with the upper limit of galactic acceleration sources. It is near the maximum energy th a t can be obtained by protons accelerated at supernova shock fronts (see the following paragraph) and below the critical energy E c at which the galactic magnetic field (B ~ 3 ^ G32) domain correlation length 6 F ig u re 1.3: The TA SD cosmic ray energy spectrum2 for all particles multiplied by E 3 to expose spectral features. A broken power line has been fit to the data. © AAS. Reproduced with permission. l ~ 0.1 kpc is comparable to the Larmor radius rL = 1.08pc E [PeV] ZB [^G] ' (1 .1 ) Z is atomic number. CRs with energy less than the critical energy take a very long time to leave the galaxy, and thus are more likely to encounter the earth. Substituting l for rL and solving, E c ~ 3 x 1017 eV for protons, two orders of magnitude greater than the energy of the knee. Therefore, it is a natural assumption tha t the decreasing flux is related to acceleration limits of galactic sources. Furthermore, all experiments agree in a steepening of the spectrum above several times 1015 eV. 3 4 ,35 One popular model for a galactic CR source is acceleration at supernova shock fronts associated with supernova remnants. 3 6 ,37 According to the Fermi theory, 38 CR acceleration is a diffusive process in which a particle gains energy by interacting with 7 the supernova remnant's magnetic field each time the particle crosses the shock front. There is some probability th a t each crossing of the shock front by the particle can be its last. Additionally, shock acceleration predicts a power law spectrum, which has been shown to be supported by experimental data such as th a t in Figure 1.3. The maximum kinetic energy achieved is Emax = Ze [ s B T V s, where [ s = Vs/c is the velocity of the shock in units of c, and T is the time the particle remained in the shock front. For typical values, Emax = Z x 1014 eV, 39 much less than the knee energy, - 1015 eV for protons. Figure 1.4 is a Hillas plot 3 th a t shows magnetic the field and size of astrophys-ical objects. It demonstrates th a t certain species of astrophysical objects have the necessary size, magnetic field strength and live long enough to boost nuclei to large energies. Diagonal lines show the minimum product of field strength and size that can produce a 1020 eV proton primary. The steepening of the slope above the knee can be explained by a combination of the maximum energy th a t can be obtained by specific nuclei and propagation losses. It has already been shown th a t Emax is proportional to Z , which implies th a t the maximum energy obtained by a species with atomic number Z is equal to Z times the energy obtained by a proton, E Z = Z E p. As low-Z nuclei reach their acceleration limits after the knee, higher Z nuclei take over. Propagation losses cause spectrum steepening by leakage from the galaxy40 - 4 2 or interaction with background photons or massive particles. 4 3 ,44 The second knee is often related to a loss of the heaviest remaining galactic primaries. An extragalactic population of CR sources stiffens the spectrum above the ankle. The spectrum at energies greater than the ankle may be buoyed by an excess of proton primaries th a t originated with higher energies but suffered electron-pair production losses on cosmic microwave background (CMB) photons or result from an originally light source composition.45 More protons are detected with energies lower than their original maximum energies which increases the spectral index over the region above the ankle. 5 The proton pair production process is p + y ^ p + e + e+ (1 .2 ) 8 F ig u re 1.4: Hillas plot. 1 ,3 The product of an astrophysical object's size and typical magnetic field is a major factor in the Fermi shock acceleration model. Diagonal lines mark the minimum limit of that product necessary to accelerate protons to 102 0 eV, under the assumption th a t fis = Vs/c is 1 and 1/300, respectively. Vs is the shock front velocity. Reprinted figure with permission from E. Barcikowski, copyright 2011. 9 Opposing the bolstering effects are red-shift losses from Hubble expansion and ulti­mately the GZK cut-off (described below). There are two categories of theories th a t seek to describe natural phenomena th a t result in extremely high-energy particles. The first category consists of so-called bottom-up models, which involve accelerating existing particles to highly relativistic energies. As can be inferred from the Hillas plot (Figure 1.4), either very large acceleration regions or very energetic shock fronts are necessary to accelerate particles above 1 EeV. Compact objects such as gamma ray bursts (GRB) have been favored recently because of analyses which suggest th a t the kinetic energy released in such events is sufficient to produce 100 EeV charged particles.46 GRB sources would not be seen because the GRB would have occurred long before the arrival of the cosmic ray. Radio galaxies are another example of a bottom-up CR source. The second category consists of top-down models which avoid the acceleration mechanism debate. Instead, they suggest currently unknown super-massive particles whose decay cascades produce relativistic protons and neutrons. 47 Other top-down sources include relics from the Big Bang48 and dark matter th a t are outside the scope of this work. Above 50 EeV most experiments observe a strong decrease in flux, with the exception of the Akeno Giant Air Shower Array (AGASA) 49 which observes an increase. This suppression was predicted in 1966 by Greisen, 50 and independently Zatsepin and Kuzmin31 in the same year. Although predicted independently, the energy loss mechanism uses all three names, thus GZK. It represents the interaction of CR hadrons with the cosmic microwave background (CMB) 2.7 K photons. Proton interactions with the CMB form a A+(1232) resonance (center of mass) which quickly decays: p + Y ^ A+ [ ++ pn . (1.3) A 2.7 K = 7 x 10- 4 eV CMB photon interacting with a CR proton achieves this center of mass energy if the proton has energy - 1020 eV. However, the position of the cut-off can be detected at lower energies because of the interaction of protons with higher energy photons, i.e., those in the tail of the distribution. The cut-off was first 10 observed with 5 .1 a significance by the HiRes collaboration51 and later observed with 5 .5 a significance by Telescope Array. 2 Spectral features above GZK could help narrow possible sources. The hope is th a t UHECRs, detected with good statistics and minimal magnetic field blurring, will point at their sources. The Telescope Array collaboration has published encouraging evidence of a an arrival direction "hot spot" with a statistical maximum significance of 5 .1 a in a 20° radius circle for CR with energies above 57 EeV.4 The significance of such a cluster occurring on an isotropic sky (modified for detector acceptance) is 3.6a. Figure 1.5 shows plots of the significance on a skymap in equatorial coordinates. Definitive source discovery requires th a t the next generation of CR detectors have much larger apertures. (a) (b) F ig u re 1.5: Significance skymaps4 in equatorial coordinates of Telescope Array event clustering, known as the "hotspot." Seventy-two events were detected with E0 > 57 EeV (a). The maximum number of events th a t occurred in a 20° radius circle is 19 (b), with 5 .1 a statistical significance. Background expectation from geometrical exposure to an isotropic sky in the same circle size (c) and a significance map (d) of events (b) occurring in the simulated sky are shown. © AAS. Reproduced with permission. 11 1.3 Composition The chemical composition of cosmic rays combined with spectrum information allows for the most accurate construction of source and propagation models. Tech­niques have been developed to measure composition directly for low energy primaries and statistically for high energy primaries th a t are detected by their extensive air shower initiated in the atmosphere. At the highest energies, HiRes and PAO disagree about the trend toward heavier mass composition (see5 and7). At low energies, typically below the knee, CR mass and charge (and thus com­position) can be measured directly. At the knee and higher, surface detector arrays determine composition by observing the electron to muon ratio near Xmax, which is proportional to ln A,3 2 ,52 the log of the mass number. Xmax is depth in the atmosphere in units of g/cm2 where the shower reaches its maximum. After X max the shower decreases in size. The relative abundance of CR particles to that found in the solar system is high for low atomic number nuclei. Figure 1.6 shows both CR and solar system abundances (each relative to Si). Elements lighter than carbon and several elements lighter than iron show a large discrepancy with the solar system counterpart. This is consistent with spallation from CMB photons as CR propagate through the galaxy. The High Resolution Fly's Eye experiment (HiRes) found a trend in CR compo­sition with energy using FD telescopes which shows th a t cosmic rays become more protonic as primary energy increases above 1018 eV. 5 ,8 Figure 1.7 shows mean Xmax as a function of E0 for CORSIKA6 Monte Carlo shower simulations using several different hadronic interaction models. Also shown are the HiRes data points. These data indicate protonic composition above 1 EeV. Contrasting the HiRes result is the PAO UHECR composition, 7 Figure 1.8. Unlike HiRes, PAO data suggest an increasingly heavy composition at the highest energies. TA has recently published a five-year hybrid (SD and FD) composition result 9 (see Figure 1.9). With systematic uncertainty, this result is consistent with protons at the highest energies. There is speculation th a t the disparity is evidence of a northern-southern hemisphere source or propagation asymmetry. TA/PAO working groups are trying to resolve this discrepancy. 53 12 Relative Chemical Abundances of the Elements F ig u re 1.6: Element abundances of cosmic rays and the solar system, 1 both relative to Si. Nuclei lighter than C are and some nuclei lighter than Fe are over-abundant in the cosmic ray flux. Reprinted figure with permission from E. Barcikowski, copyright 2 0 1 1 . 13 F ig u re 1.7: High Resolution Fly's Eye (HiRes) composition for E 0 > 1018 eV. 5 The lines are the result of CORSIKA6 air shower simulations using the different hadronic interaction models. Data are shown with the points and clearly indicate a light compo­sition at high energies. Reprinted figure with permission from R. Abbasi, et al., Phys. Rev. Lett. 104, 161101 (2010). http://dx.doi.org/10.1103/PhysRevLett.104.161101. Copyright 2010 by the American Physical Society. 14 E [eV] F ig u re 1.8: Pierre Auger Observatory (PAO) composition result. 7 The lines are the result of CORSIKA6 Monte Carlo shower simulation studies using different hadronic models. The points are data. Note the error bars. These data indicate th a t the composition is increasingly protonic before E0 = 1 0 18-25 eV, and increasingly heavier beyond. This result in in stark contrast to the earlier HiRes result 8 (Figure 1.7) which showed a protonic composition up to the highest energies. Reprinted figure with permission from J. Abraham, et al., Phys. Rev. Lett. 104, 091101 (2010). h t t p : / / d x .d o i.o rg /1 0 .1 1 0 3 /P h y sR evL e tt.1 0 4 .0 9 1 1 0 1 . Copyright 2010 by the American Physical Society. 15 F ig u re 1.9: Telescope Array hybrid five-year composition result. 9 The red and blue lines represent different hadronic models used in simulating proton (blue) and iron (red) extensive air showers. Reprinted from Astroparticle Physics, 64, R.U. Abbasi, et al., Study of Ultra-High Energy Cosmic Ray Composition Using Telescope Array's Middle Drum Detector and Surface Array in Hybrid Mode, 49-62, Copyright (2015), with permission from Elsevier. 1.4 Detection Methods Surface detection (SD) and fluorescence detection (FD) techniques currently dom­inate cosmic ray physics experiments. There are drawbacks to each technique, high cost being common to both. Experiments th a t host both SD and FD apparatus can record hybrid measurements in an approach th a t exploits the best qualities of each technique. FD data precisely determine energy scale and shower evolution and SD data constrain core location and timing. 54 There are several emerging detection methods, one of which is radar detection, which may allow low-cost CR detection or increased detection ability over large areas. 16 Cherenkov, geo-magnetic synchrotron, and molecular bremsstrahlung emission offer three types of potential passive detection channels which involve radio emission from air showers. Section 1.4.3 briefly introduces shower radio emission detection methods. In contract, radar is an active detection method. Radar detection of cosmic rays has the possibility of being remote sensing with 100% duty cycle. Depending on the magnitude of scattering by extensive air showers (EAS), radar detection could allow extremely large apertures by using broad antenna beamwidths th a t detect CR showers tens or hundreds of kilometers away, such as in meteor detection by radar. 55 Section 1.4.4 includes a brief history of radar detection of cosmic rays and an overview of TARA. 1.4.1 S u rfa c e D e te c to r An array of surface detectors (SD) allows multipoint sampling of shower products at one plane in shower longitudinal development. Shower reconstruction relies on model-dependent Monte Carlo simulations and Xmax is not observed directly. The duty cycle of surface detector arrays is 100%, good for extremely low flux UHECR, but the cost of instrumenting and maintaining an array covering hundreds of square kilometers is high. Figure 1.10 shows a TA scintillator-type SD with solar panel and radio communications tower. SDs measure several quantities th a t are used to calculate X max. Shower front curvature will be less for those th a t evolve earlier in the atmosphere (low X max), and the time distribution of particle arrival, often called width, will be less if the shower occurs lower in the atmosphere (large Xmax). Also, the logarithm of the electron-to-muon ratio at the ground level is a function of ln A,3 2 ,52 where A is the primary particle atomic mass number. The ratio can be measured to give information about composition and thus X max. 1.4.2 F lu o re s c en c e D e te c to r Fluorescence telescopes detect air showers remotely via fluorescence light emitted by atmospheric N2 molecules th a t have been excited by collisions with passing shower products. TA fluorescence telescopes (Figure 1.11) have a range of about 40 km at the highest energies. Unlike surface detector measurements the fluorescence technique 17 F ig u re 1 .1 0 : Picture of a single Telescope Array surface detector (SD), composed of a communications tower, solar panel for providing power to electronics and plastic scintillator enclosed in sheet metal. captures the longitudinal and lateral development of the shower with mirrors that focus the light on cameras with photomultiplier tube pixels. Atmospheric calorimetry also gives an absolute energy scale. Because the intensity of UV fluorescence light is low relative to sky noise backgrounds, the fluorescence method only works on clear, moonless nights. The average duty cycle for the TA FD is ~ 10% . 56 FDs offer the best measurement of Xmax because the brightest part of the shower can be seen directly, but lack the exposure of SDs because of a 10% duty cycle. The fluorescence method is viable on cloudless, moonless nights when faint UV signal can pass through the atmosphere without attenuation and light pollution is minimal. 1.4.3 A ir Shower R ad io Em issio n Charge excess in co-moving secondary particles (20-30% negative charge excess57) near the shower front can produce Cherenkov radiation known as the Askaryan ef­fect. 58 Askaryan radiation is expected to be coherent, polarized and in the microwave band. Low cost light cones on the ground and in the path of the shower will collect Cherenkov radiation in a direct measurement of Xmax a composition dependent parameter59 (see Section 1.3). Primary geometry can be determined from timing 18 F ig u re 1.11: Picture of Black Rock Mesa (BRM) FD building with the telescope doors open showing the segmented focusing mirrors. and energy can also be calculated by comparison to Monte Carlo studies. Geo-magnetic synchrotron emission is another type of radiation produced as air showers propagate through the atmosphere. Shower electrons interact with the E a rth 's magnetic field to form relativistically forward beamed low VHF signals. 28 Shower front thickness is comparable to the emission wavelength so the benefit of coherent signals are expected. Ionization electrons in the shower path may emit bremsstrahlung radiation during rapid thermalization by interactions with neutral molecules. Molecular bremsstrahlung radiation (MBR) is incoherent and unpolarized. 27 Just as in fluorescence light emis­sion, MBR is proportional to the number of shower products and therefore directly sensitive to primary energy. Recent measurements of the total microwave emission of air showers indicate polarized waves, which discredits an explanation in terms of molecular bremsstrahlung emission. 60 1.4.4 Cosmic R ay R a d a r The idea of radar detection of cosmic rays was first mentioned in the literature in 1941.29 Anomalous radar events seen by T.L. Eckersley61 were the impetus for the investigation. This was the first time radar was suggested as a high energy CR 19 detection technique. Blackett and Lovell later used pulsed military radar mounted in air planes (see Ref.12). Although they were ultimately unsuccessful proving the technique, their efforts spurred nearly 70 years of similar attempts. Their subsequent ground based radar investigations at Jodrell Bank evolved into the Jodrell Bank radio astronomy observatory. In 1962 K. Suga proposed 13 searches for ultra-high energy cosmic rays (UHECR) using the radar echo method. This suggestion directly followed his statement th a t the observable range of CR particles should extend above 1020 eV. He determined that a scintillator array th a t could detect such high energies with a reasonable count rate would have to cover an area of 1000 km2, a prescient observation given the size of TA and PAO observatories' large ground arrays. He concluded, "the method of density sampling by large plastic scintillators is basically unsuitable for observing these large events and th a t essentially different methods must be used for this purpose." In 2003 a radar experiment was proposed to search for radar echoes alongside the Large Area Air Shower (LAAS) array (see62). Unfortunately, no results were reported. The Jicamarca Radio Observatory used pulsed radar in an attempt to detect CR air showers. 63 Regarding detected radar signals, they said, "it has not been possible to conclude th a t they are caused by ultra high energy cosmic rays." In Shigaraki, Japan, the atmospheric MU-Radar64 data were searched for short-duration echoes. No convincing evidence has been produced. Each of these experiments used traditional military pulsed radar, which is a poor choice for detecting rare, random CR events. Additionally, early and recent experiments (with the exception of radar experiments at LAAS) had no means of confirming th a t features in the data correspond to actual CR events. It is clear that an investigation into CR radar detection needs a continuous wave (CW) (or otherwise constant) carrier and conventional CR detector in close proximity with which data can be correlated. P. Gorham authored a theoretical paper65 about the prospect of radar detection. He categorized the scattering properties of EAS relative to carrier frequency and offered some practical analysis about EAS parameters tha t may be measurable using the radar technique. As I'll demonstrate in Chapter 2 , Gorham neglected to consider 20 the unique time-frequency signature expected in the received signal and significantly overestimated the scattering magnitude. MARIACHI6 6 ,67 investigated bi-static radar scattering of VHF signals from EAS, making parasitic use of commercial television transmissions in Long Island, New York. They found a correlation between receiver antenna waveform and co-located scintillator detector impulses. Unfortunately, further investigation into MARIACHI results is limited because the carrier source is not known (there are many television and radio transmitter stations in the area) and the amount of data collected during the short MARIACHI operational period is very small. Telescope Array Radar (TARA) 6 8 ,69 is the culmination of decades of CR radar detection experiments. We have further developed the bi-static technique by using a dedicated high power, constant wave (CW), low-VHF transmitter in a radio-quiet area, co-located with Telescope Array, the largest conventional cosmic ray observatory in the Northern Hemisphere. The TARA detector can potentially detect events in coincidence with TA. Positive correlation of radar events with TA data will allow confirmation of the scattering ability of EAS. Nondetection presumably allows only the calculation of upper limits on the scattering magnitude. In August 2012, TARA broke ground on a transmitter facility located just outside the TA surface detector array. High gain transmitting antennas focus the radar signal over the SD array to receiver antennas located at the Long Ridge FD station. Two 20 kW analog TV transmitters operating in CW mode broadcast a 54.1 MHz radar signal. Experimental radio station WF2XZZ went live in March 2013 with initial 25 kW power output. In the following chapters I give a complete description of the challenge of CR radar detection and the solutions (both hardware and software) we have engineered to make the first measurement of the upper limit of the CR radar cross-section. First, I cover EAS evolution and plasma physics pertinent to formulation of the problem, including a description of the CR radar echo simulation I have created. In the next chapter I describe the TARA detector th a t emphasizes co-location with Telescope Array, high gain antennas, continuous wave high power transmitter directly under our control 21 and high sample rate data acquisition (DAQ). Following that, I describe the data and analysis chain. In the last chapter I discuss results in comparison with other experiments and both our brief theoretical expectation and th a t of others. Finally, I offer my perspective on the prospect of future CR radar detection. CHAPTER 2 EAS RADAR ECHOES In this chapter I address issues related to the TARA expected received signal. First, I discuss relevant signal fundamentals and the unique challenges radar echo detection presents. Then I discuss reflection mechanisms in the context of atmospheric simulation incorporates shower evolution, detector parameters and radar cross-section is the foundation of all radar scattering calculations. PR is received power, PT is transmitter power, GR and GT are the receiver and transmitter station antenna gains, respectively, A is the radar wavelength, RT is distance between transmitter and target, Rr is distance between target and receiver, and a is the RCS. Depending on target symmetry, the RCS can be a constant or a function of several parameters. The RCS is defined as where r is distance from target to receiver (RX), Ss is the scattered power density and Si is the incident power density from the transmitter (TX). A limit is included in Equation 2.2 to ensure only the far-field pattern is tested. The RCS is an effective target area whose magnitude depends on the orientation of the target relative to the receiver, target composition and relative size of the target to interrogating signal gases ionized by CR showers and present results from my chirp simulation. The models from literature. Full detail CORSIKA6 simulations are shown to agree with the shower evolution models used in the simulation. I then show distributions of simulation results assuming TARA detector parameters. 2.1 Bi-static Radar The bi-static radar equation = PtGGt _g^ _ a2 R 4nRT 4n RR 4n , (2 .1 ) (2 .2 ) 23 wavelength. As I will show, the primary difficulty in determining the feasibility of radar detection is in quantifying the RCS for CR air showers. 2.2 Properties of EAS-Induced Ionization Columns Radar detection of cosmic rays depends on charged particle production in the atmosphere. A cascade of interactions composed primarily of electrons and muons occurs when the primary cosmic ray particle collides with molecules in the atmo­sphere. This is called an Extensive Air Shower (EAS). For a detailed discussion of EAS see, e.g., Heitler70 or Sokolsky. 71 2.2.1 A ir Shower P ro p e r tie s Some common EAS parameters are primary particle energy E 0 (eV), depth Xmax (g/cm2) in the atmosphere where the maximum number of particles Nmax is reached, and the depth of first interaction X0 (g/cm2). The critical energy E c (eV) is the energy below which the dominant energy loss mechanism is bremsstrahlung radiation rather than pair production. In air E c is 81 MeV. 72 When the average particle energy decreases below Ec, particle production ceases and the EAS starts to decrease in size. Typically, UHECR are considered to be those with E 0 > 1018 eV. We may expect the cosmic ray RCS to depend on E 0 because Nmax is proportional to E 0. Therefore, the received power is related to primary energy. Gaisser-Hillas73 N (X) = Nmax ( , X exp Xmax - X 0 X maxX- (2.3) A is a parameterization of the average shower longitudinal profile, the number of charged shower products as a function of depth X in the atmosphere, where A is interaction length in air. Nmax, X0, X max and A only loosely represent their physical counterparts and are typically determined from Monte Carlo simulations using hadronic interaction models. The majority of particles N (X ) are free electrons th a t do not include ionization electrons. The radial dimension of EAS electrons is given by the Nishimura-Kamata-Greisen (NKG) 74 equation: P(r) = N P f ) , (2.4) X X 24 which gives the number area density as a function of radius, at a specific shower age s. Shower age71 is defined as S = 1 + 2 ln(E0 /E c) / X / \ • (2.5) Also, r 1 is the Moliere multiple scattering unit 7 1 ,75 and the function f in Equation 2.4 is76 f ( < ) = ( r T ( 1 + r 1 ) ~ • <*,) With NKG and the Gaisser-Hillas parameterization one can determine free electron density in three dimensions as the shower evolves. 2.2.2 Io n iz a tio n in EAS Atmosphere ionization by energetic shower particles is the primary plasma pro­duction mechanism. Ionization electrons are quantified by calculating the number of free electrons produced in EAS as a function of shower progress and radius, then using energy deposition models to determine the ionization yield. An electron produced by the shower will ionize atmospheric molecules until its energy is below the mean ionization energy, I = 33.8 eV. 77 The number of ionization electrons Ntot produced over some track length £ is dependent on the number of particles created by the shower N (X ), the mean ionization energy of the atmosphere I , atmospheric density p (X ), and the minimum-ionizing energy loss factor dE (X ), all a function of depth X (g/cm2, typically): dE Ntot(X) = N (X ) - (X ) p (X ) £ I - 1 . (2.7) Energy deposition in the atmosphere |E ( x ) is obtained from Nerling's parameter­ization, 78 shown in Equation 2.8, where a eff(X ) N (X ) = d E (x ). Together with coefficients (Table 2.1), a eff is given as a function of shower age s: a eff(s) = 7 : TC (C + c4 + c5 ■ s • (2.8) 2 + s ) C3 Atmosphere ionization occurs more rapidly in regions where the charged shower products' density is high. Therefore, the distribution of ionization electrons created by shower products should follow the lateral distribution (NKG). 25 T ab le 2.1: Constants in the Nerling parameterization78 (Equation 2.8) of EAS energy deposit in the atmosphere. C1 3.90883 C2 1.05301 C3 9.91717 C4 2.41715 c5 0.13180 To verify NKG at Xmax, we have generated an unthinned CORSIKA6 with QGSJETII79 hadronic interaction model shower at 1019 eV. The ionization electron density is calculated by summing the number of ionization electrons in a given radial bin Nr produced by shower-generated charged particles, which consist primarily of energetic electrons. Each electron has simulated energy and radial distance from the shower axis, which defines an area determined by the radial bin size. This energy/area Ep is multiplied by the ratio of atmospheric density at ground level (roughly the location of Xmax for TA for a 1019 eV shower) to the radiation length in air pair/l (l is in units of g/cm2), which is the inverse of the distance a particle will travel th a t results in an energy reduction of all but 1/e. Resulting energy density is divided by the mean ionization energy per electron pair I and multiplied by 1 - e- 1 to account for the radiation length loss per unit of distance travelled. At Xmax, ionization loss per radiation length is equal to the electron energy. 77 The summation algorithm, with explicit units, th a t produces the total ionization electrons in a radial bin r is Nr~ 1 pion,r [cm ] ^ ^ ^ EP,i i= 0 eV cm2 Pair [cm3] (1 - e ) / / [eV] . (2.9) l LMcm*2 1J It is assumed th a t a radial distance from shower core and area represented by the radius can be computed from simulation output for each charged particle. A com­parison plot showing good agreement between free electron density as predicted by CORSIKA and GH/NKG is shown in Figure 2.1. Ionization electron density can be obtained by substituting the NKG density (Equation 2.4) for N (X ) in Equation 2.7. In the remaining sections, electron quantity and lateral distribution are calculated exclusively with GH and NKG. 26 F ig u re 2.1: A CORSIKA (histogram) vs. Gaisser-Hillas and NKG (curve) compar­ison of ionization electron density as a function of radius near Xmax for a 1019 eV vertical shower. Agreement is good near the core where electron density is highest. 2.3 Plasma Physics 2.3.1 N e g le c tin g E le c tro n -n e u tra l Collisions Natural longitudinal oscillations occur in ionized gases because of Coulomb inter­actions between free electrons. The free electron plasma frequency can be calculated using first principles. Consider a macroscopically neutral plasma whose density is low such th a t collisions are ignored. An incident electromagnetic field with frequency will cause the electrons to oscillate according to the equation of motion d 2 r eE = m d t 2 > (210) where r is the electron displacement vector giving the position caused by the incident field relative to where the electron would be in the absence of a disturbance. Both E 27 and r have the harmonic component e x p ( - iurt). The product of plasma density N , displacement r, and the electron charge e is the polarizability P , which is proportional to permittivity of the medium80 eE = e0E + P . (2.11) Using N e r = P and multiplying both sides of Equation 2.10 by Ne, we have NE e 2 = - U m P . (2.12) The index of refraction n is the ratio of speed of light in free space to th a t in the medium e/e0 = ^J1 + P /(E e 0). Substituting the previous expression solved for P in Equation 2.12, 2 Ne2 u 2 . . n = 1 ----- 2----- u = 1 ------ 2 . (2.13) 2 e0m Neglecting geomagnetic or collisional effects, the plasma frequency is Ne2 u e = \ ----- [rad/s]. (2.14) y e0m The index of refraction in this case is either real or imaginary, but not complex. If the plasma frequency is greater than the wave frequency, n is real. Refraction angle is determined via Snell's law. Plasma frequency greater than the incident wave frequency results in a purely imaginary index of refraction, meaning th a t beyond a certain skin depth the waves cannot penetrate-the electric field is reflected. Such a plasma is called overdense. If the sounding wave frequency is larger, the index of refraction is real so the transmitted wave is refracted in the underdense regime. Maxwell's equations can be manipulated to form the wave equation. For example, ^ + k2 n 2Ex = 0 (2.15) dx2 represents a plane wave travelling in the z direction, with k = u / ca. The so­lution is E x = E0 exp[i(urt - knx)]. When u r < u e, n 2 < 0, the wave Ex = " The constant in the second term is originally j 2 but the assumption can be made for most materials that ^ Permittivity e can be written e0 n2 which gives the constant n2 j 2 eo^o- The speed of light in vacuo c = 1 /^ e 0^0. Therefore, the constant can be written k2n2 where k is the wave number in free space. 28 E0 exp(i^rt) exp(-k|n|x) is attenuated in the plasma and reflected. Otherwise n2 > 0 so the wave can penetrate the ionized gas region in which there may be secondary scattering mechanisms th a t can reflect the signal. This splits the classification of the scattering center into two regimes, underdense and overdense. A plasma is overdense when incident waves are reflected and the index of refraction is purely imaginary. Waves in an underdense plasma are refracted when the index of refraction is real or In the underdense regime, Thomson scattering is a coherent scattering mechanism th a t may interfere constructively or deconstructively at the receiver, depending on the size of the scattering volume relative to the radar wavelength. Radar waves penetrate component of the wave. The Thomson scattering cross-section for an electron is80 UHECR air shower particles exist up to several kilometers from the core, though at very low density following the trend in Figure 2.1. Therefore, Thomson scattering is negligible from large radius parts of the shower. Approximately 80% of shower particles are contained within a 100 m radius, 14 where scattering from a 5.5 m wavelength (54.1 MHz, TARA radar frequency) will interfere, possibly destructively. Above a few centimeters radius from the shower axis u r > u e (see Figure 2 .2 ). Charged particle density near the shower core is accurately described by NKG. This has been measured directly for PeV-level showers. 81 The plasma is overdense only at small radii ( 1 cm). 2.3.2 In c lu d in g E le c tro n -n e u tr a l Collisions As free electrons are jostled by thermal motion of neutral molecules, they are prevented from radiating coherently. Interactions with ions are not considered because of the relatively few ionization electrons and corresponding parent ions compared to neutral molecules. Very near the core, ionization electron density reaches 108 cm- 3 (see Figure 2.2), whereas atmospheric density at 4.5 km above sea level and 300 K is N /V = P / k T = 1017 cm-3 , which gives a neutral molecule to electron ratio of 109. complex. the CR shower and scatter off free electrons by exciting them with the electric field (2.16) 29 r [cm] F ig u re 2.2: Plasma frequency as a function of radius at Xmax for a 1019 eV shower calculated using Gaisser-Hillas and NKG parameterizations. Gaisser-Hillas parame­ters were averages of values obtained by CORSIKA simulations. The horizontal black line corresponds to the TARA radar carrier frequency at 54.1 MHz. Coherent scattering decreases as the effective collision frequency climbs relative to the radar frequency because interactions with neutral particles occur many times each cycle. If one includes collisional effects and assumes th a t all of an electron's excess momentum gained from interaction with the radar wave is lost with each collision with a molecule, the equation of motion is written d 2 r d r eE = - (217) Following the same procedure as before, the equation for the index of refraction becomes M 2 n 2 = 1 - m2n e. , , . (2.18) 2 ( 1 - iV/Mr) When the effect of electron-neutral collisions is included, the index of refraction is complex. In general n = ^ -ix. The absorption coefficient x characterizes exponential 30 plane wave amplitude decay as a function of distance. ^ is the index of refraction. Let A = (ue/ur) 2 and B = v/ur, then 2 A . AB „ . n = 1 - 1 + B 2 - * 1 + B 2 = a + lb. (2.19) By the square root formula for complex numbers82 the real and imaginary components of n are ^ = /(a2 + b2)1/'2+ a x = - / (a2 + b2)1/2 - a ( 2 20) In the case of CR shower plasmas, the free electron density is low compared to neutral molecules, and therefore the collision rate v between electrons and neutral particles is high relative to the radar frequency. Electron scattering is damped by collisions with neutral particles. Collisional damping has often been neglected in the CR radar literature. As will be shown, this effect is large and greatly impacts the viability of CR radar. When collision frequency is large compared to the wave frequency, very little energy is extracted from the wave. From the perspective of the incident field, rapid collisions effectively "pin" free electrons in place, preventing work from being done. 83 Partial scattering is only expected for high plasma frequencies, or when the sounding frequency is the same order of magnitude as the collision frequency. Even near the core, when the plasma frequency exceeds the sounding wave frequency (see Figure 2.2), scattering is highly attenuated. Figure 2.3 shows collision frequency in air at varying altitudes as calculated by several different authors. It also includes a simple mean free path estimate that agrees fairly well with the other results. All collision frequency values beside the mean free path result were calculated using a standard form of the collision frequency which is a function of the momentum transfer cross-sections and electron velocity:84 v(v) = v (n n2C 2 (v) + NO2C 2 (v)) (2.21) where Qm(v) is the momentum transfer cross-section as a function of velocity and N is the mass density. Vidmar's values10 come from a simulation which includes experimental values of air density and temperature as a function of altitude, momentum transfer collision 31 Figure 2.3: Survey of estimates of electron-neutral collision frequency as a function of altitude. Data points are from Vidmar, 10 Itikawa, 11 Lovell, 12 Suga, 13 Stasielak et al. , 14 and the mean free path points are calculated by dividing mean electron speed by the mean free path. rates as a function of altitude, and recombination/attachment rates. Collision rates are reported for electrons with temperatures Te = 300, 400, 500 K. Itikawa11 calculates the collision frequency from experimental values of the momentum transfer cross­section for electron temperatures up to 5000 K. The Lovell values12 are given without justification, and are included mainly for historical significance. Suga's value13 is also given without justification. Stasielak et al. 14 take a different approach that approximates the ionization electron energy distribution as Maxwellian with Te = 1.5 x 105 K (13 eV), then calculates the average collision frequency over the velocity distribution. At similar altitudes the collision frequencies vary over one order of magnitude. 32 At X max the average shower particle energy is Ec = 81 MeV. The average energy of ionization electrons increases with the energy of the incident particle.85 In the limit where the secondary electron distribution has a substantial portion of relativistic en­ergies, the collision frequency may decrease with energy due to decreasing momentum transfer cross-section. Qm decreases nearly two orders of magnitude for each decade increase in electron energy above 1,000 eV.85 High energy momentum transfer data do not exist in the literature. Assuming this trend continues, the product vQm decreases as the relativistic regime is approached. In this case, we overestimate the collision frequency by assuming a near thermal secondary electron energy distribution. Without high energy cross-section data, we estimate the damping magnitude by assuming the electron-neutral collision rate in air is ~ 1011 Hz, large compared to our 54.1 MHz radar wave (see Chapter 3). Plasma frequency is also small compared to v, so we expect significant damping at all shower radii. The large discrepancy in frequencies also justifies the neglect of geomagnetic effects which have been ignored because the cyclotron frequency = e|B|/m - 5 x 106 Hz ^ v = 1011 Hz. A quick comparison between Equations 2.10 and 2.17 elucidates the extreme level of damping caused by such a large discrepancy in radar frequency and effective collision frequency. After substituting terms and taking derivatives the right hand side of the equations become -mwr2r and -mwr2r ^1 - i- p ) . We define an effective mass in the second expression meff = m ^1 - i -^ j . Scattering power is proportional to a = d2r/dt2 and a a 1 /m, so reduction in scattering power from collisional damping is m 1 ( ur \ 2 T - ( ^ ) . (2 .2 2 ) meff For relevant values ur = 108 Hz and v = 1011 Hz, damping in power is of order 10-6. Our result is not consistent with P. Gorham's paper on the subject. 65 There are two fundamental differences between Gorham's assumptions and ours that give disparate results. First, the effect of collisional damping is ignored in Gorham. The second difference is the large electron lifetime used in his calculations. It is stated that t > 1 0 ^s and greater at higher altitudes and possibly as long as 2 0 ms at 1 0 km, which 33 is larger-by a factor of one million-to values found in. 1 0 ,8 6 , 87 His RCS estimate is therefore very large, oEAS = 104 m2 for a 100 EeV shower perpendicular to a 10 m wavelength radar wave. Including collisions, the plasma is never truly overdense, where the index of refraction is purely imaginary. Rather, both refraction and attenuation in plasma will occur. Portions of the shower only approach the overdense regime when ur ~ v and ur > ue. Given TARA transmitter frequency and collision frequency in air (ur ^ v and ur > ue only at small radii), CR showers will never appear overdense. In this case Thomson scattering is the primary scattering mechanism, though it will be strongly damped by collisions. Figure 2.4 shows ^ and x plotted using 1011 Hz collision frequency for three different plasma frequencies ue = ( 1 0 -3 , 1 0 -2 , 1 0 -1) v over a sounding frequency range relevant to our 54.1 MHz radar. The complex index of refraction n shows that the real part of n, the part that affects refraction, never deviates from unity at TARA radar frequency 54.1 MHz and plasma frequency ue equal to 10- 3 v. The imaginary part of n, proportional to absorption in the medium, is only about 1/1000. Scattering is very small even when the plasma frequency meets and exceeds the radar frequency (ue ~ 1 0 - 3 v). The plots in Figure 2.4 contain all the information necessary to conclude that EAS scattering is very small-the real part of the index of refraction never appreciably moves away from unity and the imaginary part is very small so absorption is also negligible. Stasielak et al. first consider absorption from the perspective of electrical conductivity of the plasma medium, from which they derive the refractive index and subsequently determine the absorption coefficient aabs from the imaginary part. Using E0 = 100 EeV and reasonable values for up and vc, plasma frequency and collision frequency (their notation), they estimate aabs < 3 dB/km near the shower core (~ cm diameter) and less than 0.3 dB/km for larger radii. Given the high density radius is small and remaining shower plasma density decreases above that, absorption is ignored. We have also ignored the effect of absorption in the RCS model proposed in Section 2.5.2. Stasielak et al. continue with a calculation of reflected power using the Fresnel 34 Radar Frequency [MHz] |X| (v = 1.0e+05 MHz) Radar Frequency [MHz] Figure 2.4: Real and imaginary parts of the index of refraction (n = ^ - i\) with 1011 Hz collision frequency each with ue = (10-3 , 10-2 , 10-1) v. The TARA radar frequency is 54.1 MHz. Note that the red and black curves in the top plot are very close to one. formula, Rn n n n + np (2.23) Rp for two cases is considered. The first case assumes vc = 2 THz, v 1 MHz (radar frequency), vp = 100 MHz, distance from the shower axis rL is of order a few centimeters and E0 = 100 EeV, for which Equation 2.23 gives Rp = 6 x 10-5. In the second case all parameters are the same except vp, which is much less, and rL = 1 m; 2 35 Rp drops to 10-11. Collisions between electrons and molecules reduce reflection to one part in 1 0 , 0 0 0 even in the case where vp/v = 1 0 0 . Scattering is simulated by Stasielak et al. with the Thomson scattering cross section ot modified by the reduction in power, proportional to particle acceleration, derived from the equation of motion. Their procedure is the same as that in Sec­tion 2.3. I arrive at a damping factor in Equation 2.22 which is equal to the damping factor in their result for the reduction in RCS (2.24) Finally, they give RCS versus time for a 1 EeV shower perpendicular to the direction of a v = 1 MHz radar wave is plotted for several different integration limits. Collision frequency is vc = 4.5 THz, much greater than the value we use (see Figure 2.3), typically 0.1 THz. In the maximum case, all parts of the shower are integrated from very near the shower core to the radius wherein 95% of plasma electrons are located. Only a very small longitudinal portion of the shower is con­sidered, where the plasma density is greatest. At the maximum of the 95% curve, o eAS = 4 x 10- 1 0 cm2, 174 dB below Gorham's result. 2.4 Forward Enhancement Depending on radar frequency and the scattering model, bi-static radar may have a forward scattering enhancement relative to the mono-static case. When a/A ^ 1, no forward scattering benefit is obtained. A conductive thin wire with radius of order one centimeter (the collision-less overdense region radius) is much smaller than the wavelength of VHF radar waves (54.1 MHz inclusive), so no appreciable forward scattering enhancement is expected. Figure 2.5 shows a comparison of metallic cylinder forward scattering radiation patterns as a function of the angle from the forward direction for several different cylinder radii expressed as fractions of the radar wavelength. The diffraction peak vanishes when a/A is below 0.1. Thomson scattering in a region where the majority of shower electrons lie (~ 100 m) would also not be expected to have a scattering enhancement. Forward enhancement is only expected when the characteristic size of the target is the order of the radar wavelength. 36 Figure 2.5: Relative scattered electric field15 magnitude for several different cylinder radii, expressed as fractions of the incident wavelength, as a function of angular deviation from the forward scattering direction. 2.5 Simulation 2.5.1 Frequency Modulation A simple plasma physics model has been discussed which includes collisional effects. In the frequency space under consideration, the model predicts that CR air showers are weak scattering targets. Section 2.3.2 gives a calculation of the order of magnitude of damping based on the radar wave frequency and collision rate in air. Section 2.5 describes the model-independent frequency dynamics of received EAS radar echoes and Section 2.5.2 introduces a RCS model used for simulating the collision-less overdense region. Energetic shower particles travel in a disk coaxial with the EAS direction of propagation. Less energetic products are quickly thermalized. From the perspective 37 of a radar system, an EAS is a disk moving through the atmosphere at the speed of light, leaving a quickly fading plasma trail. I have created a simulation that uses the bi-static radar equation, TARA detector geometry and known EAS dynamics to calculate the received signal based on a scattering model, which will be discussed shortly. From the simulation perspective, the superposition principle indicates that multiple scattering path lengths from different points along the shower track (see Figure 2.6) result in summation of scattered rays of the same frequency but with different phase. 88 Continuing with the simulation perspective, during a given time step St at time ti, the bi-static radar equation is applied to each longitudinal shower segment (each with length cSt) from which light could have reached the receiver. Both the shower particles and radar echo move at the speed of light, so a segment j is included if the shower progress Pi , the distance the shower has travelled since first interaction, is greater than the distance from segment j to the receiver RR,j minus the progress of the shower at segment j , P j . The plasma state of segment j , and thus RCS properties, are that of the segment at retarded time ti,j = (Pi - RR,j - P j)/c. Notice the retarded time is not (Pi - RR,j)/c, which gives the time when scattered light from segment j left the segment, but does not give its age. Segment age must be tracked properly to include plasma dissipation. Consider the EAS to be a chain of longitudinal segments. Each segment has mag­nitude and phase determined by the segment's total path length, radar wavelength, RCS at the current point in the shower, shower geometry relative to the TX and RX and geometrical antenna factors. The integrated contribution of all segments j is the received signal at time ti. Complex phase factors are included in the sum. Figure 2 .6 : Contributions from paths of varying lengths (red), TX ^ target ^ RX, summed at the receiver result in a chirp signal (bi-static configuration). 38 The dynamical received signal will be a chirp signal,88 which has time-dependent frequency. Furthermore, signal components scattered early in shower evolution when the RCS is small and path length is large will have low amplitude, while signals scattered near Xmax (typically 3-5 km from ground level at the location of the detector) will be from portions with larger RCS and shorter path lengths so the expected received signal later in the shower is large. Section 2.5.2 is devoted to a discussion of the received power. Some of the expected radar echo chirp properties can be understood using geo­metrical arguments. Let L be the total path length RT + Rr and L' = dL/dt the instantaneous rate of change of path length. The magnitude of L' is proportional to chirp rate. If L' > 0 the received frequency is less than the radar frequency and if L' < 0 the received frequency is greater than the radar frequency. Time-dependent frequency is analogous to Doppler shifted light or sound waves, though not identi­cal because the wavelength of scattered radar carrier is fixed at the receiver- only combined phase changes. Typical CR air showers, which start far away and move toward the Earth's surface, albeit with occasionally large incidence angles, produce a down chirp (decreasing frequency) as long as the core location is between TX and RX. One can imagine geometries in which L' approaches zero, then becomes positive as the shower crosses the line connecting TX and RX. In this case, the chirp frequency will first match, then descend below the radar frequency. Neutrino air showers originating close to the earth's surface or low in the atmosphere could produce down chirps that start below the radar frequency and descend to lower frequencies as the shower evolves. Just as signal amplitude gives information about the primary, the chirp signature contains information about the air shower geometry. With the exception of lateral symmetry about a plane perpendicular to the ground and containing the TX and RX points, and a rotational symmetry about a line connecting the transmitter and receiver, chirp signals are unique. Figure 2.7 shows three canonical chirps with different TX ^ RX baselines. Canon­ical chirps are simulated radar echoes from small zenith angle air showers located midway between transmitter and receiver. Unless otherwise stated, the primary 39 Figure 2.7: Simulated chirp spectra fits to highest amplitude frequency component for four different geometries. Each simulation represents a vertical, 10 EeV CR shower located midway between transmitter and receiver. TX ^ RX separation distances are shown on the legend. Both the time offsets and absolute frequency ranges have been justified for direct chirp rate comparison. energy is 10 EeV. The lines are fits to the highest amplitude frequency component in each time bin. Amplitude is neglected on the plot, so the length of the fit line is not proportional to duration. However, I define duration to be the time that received power is within 10 dB of maximum. Likewise, bandwidth is defined as the frequency difference between the above and below maximum -10 dB power points. Duration for the four simulations are 4.7 ^s, 7.1 ^s, 12.4 ^s and 21.7 ^s for the 5 km, 10 km, 20 km and 40 km separation distances, respectively. Their bandwidths are 63 MHz, 59 MHz, 63 MHz and 62 MHz. Bandwidths are similar because the steepness of the chirp slope compensates for short duration. In practice, short-baseline chirps would be difficult to detect because their high frequencies imply correspondingly high bandwidths. A very basic echo simulation that only tracks the phase of a point (determined 40 by total path length L) with speed c will correctly yield the primary component of the chirp signature, frequency as a function of time. As an example, I have generated three different radar echoes using the simulation code with different electron life­times and antenna gains. Figure 2.8 show spectrograms of the simulated waveforms. Spectrograms are three-dimensional: time in ^s on the horizontal axis, frequency in MHz on the vertical axis and Power Spectral Density (PSD) in dBm/Hz on the z or color axis. PSD is the received power in dBm (dB relative to mW) divided by the Fourier transform band used to calculate the spectrogram. It is useful in comparing received power in an absolute way between different measurements and Fourier transform window sizes. Simulated waveforms used in each of the figures have been superimposed on Gaussian noise to hide features caused by aliasing. The first two simulations use constant value cross-section; the third uses a thin-wire approximation model for the RCS (see Section 2.5.2 for more detail) in combina­tion with shower evolution models. The top plot in Figure 2.8 shows a spectrogram for a very short free electron lifetime, which means there is only one scattering path length per time step. It can be thought of as a very small metallic (re: scattering) target that moves at the speed of light. In the second simulation (Figure 2.8, middle plot) a very long lifetime is used such that the shower can be thought of as a thin metallic cylinder that starts high in the sky and grows toward the ground at the speed of light, its scattering properties remaining intact for the duration of the simulation. The last spectrogram (Figure 2.8, bottom plot) is from the full radar echo simulation, which uses antenna radiation pattern, shower evolution models and the thin-wire approximation as the radar cross-section. The frequency at maximum amplitude Fmax vs. time is the same in all three plots. Absolute power varies widely, as expected from different targets. Figure 2.9 shows Fmax vs. time for each of the three simulation results on the same plot. One concludes that the chirp frequency signature is not dependent on RCS model. 41 Time [|j s ] Figure 2.8: Spectrograms showing simulated radar echoes for a shower midway between transmitter and receiver and inclined 30° out of the TX/RX plane. Top: Electron lifetime is fixed at 1 ns and antenna gain is held constant. This configuration simulates a small scattering object travelling at the speed of light toward the ground. Middle: Electron lifetime is fixed at 100,000 ns and antenna gain is held constant. This configuration simulates a scattering rod beginning high in the atmosphere and growing toward the ground at the speed of light. Bottom: Electron lifetime is determined from empirical models and RCS comes from the thin-wire approximation (Section 2.5.2) and shower evolution models. Antenna gain is determined from lookup tables generated by NEC. 16 This configuration simulates a cosmic ray radar echo. 42 N T. 2 140 xCtJ E LL 120 100 80 60 0 5 10 15 20 25 Time [j-is] Figure 2.9: Plot showing Fmax vs. time for the three simulated echo waveforms shown in Figure 2.8. Black points represent Fmax for the short lifetime waveform. Red and blue points represent Fmax for the long lifetime and full simulation waveforms, respectively. 2.5.2 Received Power The principal component of the echo simulation is the bi-static radar equation 2.1, which gives the received power as a function of detector/target geometry, transmit­ter/ receiver antenna parameters, transmitter power and sounding wavelength. A simulation time step 5t is chosen such that c5t ^ A, then the shower is considered to be a string of longitudinal segments of length c 5t as described in the previous section. At time t., the amplitude of each longitudinal segment (including phase) is included in the sum Vr,. = E (t') Z • (2.25) j Pj (t.) is the received power from the bi-static radar equation 2 . 1 calculated at the retarded time and Z is the impedance of the receiving antenna. VR,. is the received voltage at time t.. According to the superposition principle, it is correct to sum the voltage amplitude at the receiver, not the received power. 43 As described, the echo simulation is quite simple. The challenge lies in choosing re­alistic scattering, shower evolution and plasma description models. Several effects are included to make the simulation more accurate. Gaisser-Hillas parameters are coded as functions of primary energy E0 using CORSIKA Monte Carlo data (Zech89). The NKG function combined with Nerling's parameterization78 of a (see Equation 2.8) give the ionization lateral distribution. Atmospheric density as a function of altitude is obtained from the 1976 Standard Atmosphere. 90 Electron lifetime as a function of altitude comes from Vidmar. 10 The collision-less overdense radius is determined from the lateral distribution, which is used in the thin-wire approximation to give the segment cross-section. Transmitter and receiver radiation patterns have been simulated16 and confirmed observationally (see Chapter 3). Shower products recombine or attach quickly in the atmosphere. The electron recombination/attachment lifetime for near-thermal electrons (500 K) t ~ 10 ns. 1 0 ,86 Ionization electrons will have a range of energies, the mean of which will be much greater than thermal energy. At Xmax the mean particle energy is the critical energy Ec = 81 MeV-the typical particle is highly relativistic. As the ionizing particle energy increases, the mean energy of secondary particles increases.85 Those with energies above the mean require additional collisions with neutral particles to reach equilibrium before attachment can occur, so the attachment lifetime is greater than that of thermal electrons. The lower limit signal duration is the time it takes for the EAS to reach the ground. A typical CR proton first interaction depth is 40 g/cm2 ,7 or about 1 2 km above sea level. Assuming the EAS propagates at the speed of light, radar echoes are expected to be 30 ^s in duration. High energy ionization electrons may prolong the plasma lifetime. Even assuming Gorham's high t = 10 ^s, the duration is only increased by 30%. To estimate received power from EAS-scattered radar waves, it is necessary to make assumptions about the RCS of air shower plasmas. Certain types of atmospheric radar91 rely on scattering either by local irregularities in the index of refraction or coherent strata with gradients in the refractive index in the direction parallel to propagation. Air shower free electron density changes rapidly as radius decreases 44 over hundreds of meters. However, the magnitude of electron density is not sufficient to modify the index of refraction in a significant way, even near the high-density core (see Section 2.3.2). Scattering due to plasma irregularities or rapidly changing density is negligible. The overdense region in the collision-less case resembles a thin conducting wire. Though there is no expectation of spectral reflection at this region when collisions are included, it represents a natural boundary where plasma frequency is greatest because electron density is highest near the core. Including collisions, the region where scattering is maximized due to the steep shower density profile is narrow relative to ~ km shower size, likely similar to a ~ 100 m radius cylinder. 14 All forms of scattering from this region will be highly attenuated (see Section 2.3.2). We use the collision-less overdense region in simulation and proceed as if collisions do not occur. This region is treated as a short-lived, conductive thin wire. The model overestimates the RCS because collisions are neglected, but does not affect frequency vs. time as described in Section 2.5.1. In Chapter 5 and, briefly, in this section a strategy is proposed to account for the over-estimated echo power that arises from neglecting collisional damping. The RCS of a perfectly conducting thin wire aTW many wavelengths long but only a fraction of a wavelength in diameter is given by,92 L is the wire length, 9 is the angle between the wire and the direction of incidence, 0 is the angle between the incident wave polarization and the wire axis, a is the radius, A is the wavelength and y is 1.78, e raised to the power of Euler's constant 0.577. Equation 2.26 is prescribed for the case L ^ A, but the reader will see that aTW is not strongly dependent on L. In simulation the thin-wire radius a is dependent on shower lateral distribution, itself a function of shower geometry, primary energy, etc., and the state of the plasma at retarded time t'. Segment j at time step i is described by NKG with N = N0,j e x p ( - t i , j /t ), where N0,j is the initial number of ionization electrons in axw (2.26) 45 segment j and t is electron lifetime. The maximum radius where NKG multiplied by segment length c8t has a free electron density that exceeds the density corresponding to a 54.1 MHz plasma frequency is the thin-wire radius a. I make a few observations about the the thin-wire model and Equation 2.26: • Polarization dependence goes as cos4 0, peaked for polarization parallel to wire axis and zero for polarization perpendicular to wire axis. To maximize received signal, E-field polarization should be parallel to the air shower trajectory. • All dependence on wire radius a is in the denominator where it enters logarith­mically. • Unlike scattering in the a ~ A regime, scattered radiation will not be enhanced in the forward direction (Figure 2.5). Rather, we can treat the short-thin-wire radiation as dipole emission. • A change of ~ 30° in aspect 9 will cause significant oscillations because of amplification in the (sin n/n) 2 term. Known shortcomings of the model: • High electron density air shower core ionization will likely be an imperfect conductor, due again to the high rate of collisions with neutral molecules. We expect significant damping of RCS due to this effect. • Even absent collisional effects, plasmas have an associated "skin depth" given by 8 = c/iMp. If the radius of the wire a ^ 8 only a small part of the incident radiation may be absorbed and re-radiated by the wire. • Radius a is itself linearly dependent on E0 meaning the RCS is only logarith­mically dependent on primary energy. These first two factors will have the effect of reducing the intensity of scattered radiation by an unknown amount, but will not change the geometrical dependence of RCS. This suggests a (somewhat model dependent) way of quantifying the observed RCS of extensive air showers, or placing limits on RCS in the case of nonobservation. 46 We assume a is proportional to aTW, and therefore that each segment of the shower has a radar cross section given by a = r ffxw (2.27) where r is a constant representing the effects of imperfect conductivity and collisional damping. Received power is proportional to the RCS and therefore also to r. The observation of echoes at some power level would thus be a measure of r , and nonob­servation will allow calculation of an upper limit on r. Analysis details regarding this proposition will be discussed in Chapter 5. In the following section, I apply the thin-wire approximation for a particular transmitter/receiver configuration and use transmitter power PT and gain values Gt , Gr specific to the TARA radar detector currently in operation near Delta, UT (Section 2.6). 2.6 Case Study: TARA The TARA detector consists of a VHF transmitter, custom transmitting and receiving antennas, and an intelligent DAQ (described in detail in Chapter 3). The transmitter is a reconfigured analog television transmitter which broadcasts a 54.1 MHz CW radar signal under the FCC's experimental licensing system. It is located near Delta, UT and directs its radar beam south-west across the TA surface detector array toward receiving antennas at the Long Ridge fluorescence detector. Transmitter total power output is 40 kW, typically 25-30 kW. Construction on the transmitter station and antennas began in August, 2012. The complete TARA detector (transmitter site and receiver antennas/DAQ) went online in August, 2013. Figure 2.10 shows the spectrogram of a canonical shower for TARA geometry. Properties relevant to detection are chirp slope, Fmax and chirp duration. I have used simulation results to determine optimal TARA transmitting antenna radiation patterns and in data acquisition system design. 2.6.1 Detector Design TARA's primary goal is to achieve coincidences with Telescope Array. The bi­static radar detector transmits its radar beam over TA fiducial volume. TX RX 47 140 |^120 o 100 80 60 40 r i 1 1 T 1 ( ■ k : ! ■ t; M l i / ' r t V i , ' 1 ' ■' 1 ■III 11 1 1 1 - ■ / . ))'• i 1 ■ ■■ 1 1 1 - ■, 1 - i i y j ■' * ■ , ■ ■ , - u f f l f . Tl . f . j ' . . i , . , n If-1M* 1 11 IN Mil r. T1 I M WT. 1 1 1 1 V V eg 1 ... . - "j1 ' . 1'/ 1 III 1 - _ s n i ! . " 1 ' ■ V1 1 i ,i -h ll 1 1 1 1 1i i i 11 i i i i 11 i i i 1k 1I i i I , 1 , , ,, i ,,, 0 5 10 15 20 25 30 Time [p,s] N -150n= -160 g -17°8C L -180 -190 -200 -210 -220 -230 Figure 2.10: Radar echo spectrogram from a 1019 eV shower located midway between transmitter and receiver inclined 30° out of the plane connecting the two. TX ^ RX separation is 39.5 km, the TARA separation distance. spacing is critical because it strongly influences received signal characteristics. As the separation distance decreases, L' increases so the chirp rate and frequency, relative to transmitted frequency, also increase. Correspondingly, chirp duration decreases. Echoes typically exhibit frequency shifts of order ur (Figure 2.10). This implies that even a low-VHF signal (such as TARA's 54.1 MHz) requires a broadband receiver. Higher frequency radar requires larger bandwidth. A DAQ detection frequency range from 50 MHz to 100 MHz requires a 200 MS/s baseband receiver or 50 MS/s passband receiver by the Nyquist sampling theorem. 93 Large bandwidths are unusual in radar applications, which rarely exceed hundreds of Hz. Noise power PN is proportional to bandwidth PN = kTB [W], where k is Boltzmann's constant and B is the bandwidth in Hz. Therefore, large bandwidth receivers have high noise floors compared to traditional narrow-band radar. In all radar systems the noise floor is limi