1. Modeling the Askaryan signal (in dense dielectric media) Jaime Alvarez-Muñiz Univ. Santiago de Compostela, Spain In collaboration with: J. Bray, C.W. James, W. R. Carvalho Jr., A. Romero-Wolf, R.J. Protheroe, M. Tueros, R.A. Vazquez, E. Zas

2. Outline Motivation& quick reminder of radio technique Methods to model the signal – Monte-Carlo (microscopic) simulations – Finite Difference Time Domain methods – Very simple models – Semi-analytical models Comparisons: MC-MC, MC-models, MC-FDTD,… Conclusions

3. Motivation: UHE detection Expected events (Ahlers model) Auger IceCube 0.6 0.4

4. Small fluxes of cosmogenic neutrinos: ≈ 0.5 per km 2 per day over 2π sr above EeV Small neutrino interaction probability: ≈ 0.1 - 0.2 % per km of water at EeV Small budget … typically these days… Fix rate at ≈ 20 – 40 events/ km 2 / year (say) ≥ 100 km 3 of instrumented volume of water How big a detector is needed ? How to achieve this?. Detection of coherent Cherenkov radiation in dense media.

5. Reminder: Basics of radio-emission in dense media

6. MOON REGOLITH RICE - ARA - ARIANNA GLUE ANITA2 LORD LUNASKA NuMoon The radio technique in dense media Many experimental initiatives & hopefully more to come (see this meeting) LOFAR dense →  ≈ 1 g cm -3

7. The source: -induced showers Hadronic showers ≈ 20% E @ EeV “Mixed” showers ≈ 80% E @ EeV ≈ 20% E n @ EeV EM or Hadronic

8. Dimensions & speed of the source Longitudinal spread (Radiation length X 0 ≈ 39 m in ice) Ultra-relativistic electrons above K ≈100 keV v > c/n (n=1.78) Zas-Halzen-Stanev (ZHS) MC, PRD 45, 362 (1992) 1 TeV electron shower ice Lateral spread (Moliere radius r M ≈ 10 cm in ice) Longitudinal spread in ice increases as: log E E < 1 PeV E 0.3-0.5 E > 1 PeV can reach ≈ 100 m (LPM) Lateral spread varies slowly with E

9. atomic “Entrainment” of electrons from the medium as shower penetrates Excess negative charge develops (electrons) → Main interactions contributing: Net negative charge: Askaryan effect G. Askar´yan, Soviet Phys. JETP 14, 441 (1962) Askaryan effect present in any medium with bound electrons (for instance in air). G.A. Askaryan Compton Moeller Bhabha e + annhilation Askaryan effect confirmed in SLAC experiments atomic “Low” energy processes ~ MeV

10. Modeling the signal

11. Basic idea: – Obtain signal from 1 particle track from 1st principles (Maxwell). – Simulate shower & add contributions from individual particle tracks. Advantages: – Full complexity of shower development accounted for. Shower-to-shower fluctuations – Accurate calculation of radiation from different primaries: e, p, Disadvantages: – Time consuming – “Thinning” techniques @ ≈ EeV and above Main codes & refs.: – ZHS (Zas-Halzen-Stanev et al.), GEANT3.21 & 4, ZHAireS (ZHS+Aires) (1) Monte Carlo simulations J. A-M, W. R. Carvalho, M. Tueros, E. Zas, Astropart. Phys. 35, 287-299 (2012) Zas, Halzen, Stanev PRD 45, 362 (1992) Razzaque et al. PRD 65, 103002 (2002) Hussain & McKay PRD 70, 103003 (2004)

12. Radiation single particle track: Frequency domain 1.E(ω,x) increases with frequency 2.E(ω,x) ≈ length of particle track perpendicular to direction of observation 3.E(ω,x) 100% polarized (perpendicularly to observer´s direction) 4.E(ω,x) : diffraction pattern exhibiting central peak around cos θ C = 1/nβ (  =0) & angular width Δθ ~ (ω δt) -1 Maxwell´s equations → Fourier-components of Electric field E(ω,x) emitted by charged particle traveling along finite straight track at constant speed v: frequency diffraction tracklength phase factor global phase v v┴v┴ θ t1t1 t 1 +  t k track v ┴  t far-field observer

13. Radiation from a shower: frequency domain Contributions to E-field from all charged particles tracks Phase factors (different for each particle) If θ ≈ θ C or obs >> shower dimensions (small enough ω) at θ → Phase factors ≈ equally small → COHERENCE (@ MHz-GHz) E ≈ ω Σ (-e) v i δt i + ω Σ (+e) v i δt i ≈ ω Σ (-e) v i δt i electronspositronscharge excess Charge of each particle

14. 50 % of excess track due to electrons with K e < 6 - 7 MeV [E. Zas, F. Halzen, T. Stanev PRD 45, 362 (1992)] keV-MeV electrons contribute most to radio emission Excess negative tracklength: T(e-) – T(e+) vs K threshold Modeling with MC: Low energies matter…

15. v v┴v┴ θ t1t1 t2t2 track See also “end-points” algorithm: T. Huege et al., PRE 84, 056602 (2011) C. James talk at this meeting Vector potential E-field Time [J. A-M, A. Romero-Wolf, E. Zas, PRD 81, 123009 (2010)] Radiation single particle track: Time domain Maxwell´s equations → Radiation comes from instantaneous acceleration at start & deceleration at end of particle track Acceleration DecelerationAcceleration

16. A. Romero-Wolf & K.Belov (Proposal to test geosynchrotron in SLAC) A-M, Romero-Wolf, Zas, PRD 81, 123009 (2010)] Comparison algorithm with Jackson

17. ZHS-”multi-media” – Based on ZHS (1993). – Electromagnetic showers only (E up to 100 EeV – “thinned”) All EM processes included (bremss, pair prod., Moeller, Compton, Bhabha, e+ annhilation, dE/dX,…) – Multi-media: (Almost) any dense, dielectric & homogeneous medium can be used: Ice, sand, salt, Moon regolith, alumina,… – Tracking of particles in small linear steps + ZHS algorithm – E-field can be calculated in: Time-domain & Frequency-domain. Far-field (Fraunhofer) and “near”-field (Fresnel – see later). The Zas-Halzen-Stanev (ZHS) code [J. A-M, C.W. James, R.J. Protheroe, E. Zas, Astropart. Phys. 32, 100 (2009)] [J. A-M, A. Romero-Wolf, E. Zas, PRD 81, 123009 (2010)] Also GEANT 3.21 & 4 Razzaque et al. PRD 65, 103002 (2002) Hussain & McKay PRD 70, 103003 (2004) ~ 1 m from shower axis

18. ZHAireS = ZHS + Aires – Shower simulation with Aires – Electrom., hadronic &  showers (E up to 100 EeV – thinned sims) All relevant processes included. Different low & high-E hadronic interaction models available. – Ice only (so far). Can be extended to other dense media. Works in air (see Washington R. Carvalho talk – this meeting) – Tracking of particles in small linear steps + ZHS algorithm – E-field can be calculated in: Time-domain & Frequency-domain. Far-field (Fraunhofer) and “near”-field (Fresnel). The ZHAireS code Also GEANT4 Hussain & McKay PRD 70, 103003 (2004) J. A-M, W. R. Carvalho, M. Tueros, E. Zas, Astropart. Phys. 35, 287-299 (2012) J.A-M, W.R. Carvalho, E.Zas, Astropart. Phys. 35, 325-341 (2012)

19. Basic idea: – Discretize space-time into lattice – Calculate electric field approximating Maxwell´s differential equations by difference equations Advantages: – Very flexible: effects of dielectric boundaries, index of refraction gradients, far & near field,… – 1 single run produces field “everywhere” in space-time – Can be linked to shower MC simulation predicting excess charge Disadvantages: – Computationally intensive: grid size < lateral dimension/10 So far only radiation from unrealistic “shower” was obtained (?) Main refs.: – Talks by C.-C. Chen et al. this meeting C.-Y. Hu, C.-C. Chen, P. Chen, Astropart. Phys. 35, 421-434 (2012) (2) Finite Difference Time-Domain (FDTD) techniques

20. Basic idea: – Simple models of charge development (line current, “box” current, constant charge,…) Advantages: – Gain insight into features of radio-emission in time & freq-domains – Help understanding complex Monte Carlo simulations Disadvantages: – Too simplistic… but a necessary “academic” exercise… Main refs.: – See this talk. (3) (Very) simple models

21. Far-field observer at Cherenkov angle θ C t 1 → 2 = L/v = t 1 → 3 = L cosθ C / (c/n) Wavefronts in phase Time-domain:  Observer sees whole shower “at once” (sensitivity to longitudinal profile lost…) Frequency domain:  Constructive interference at ALL wavelengths  Spectrum increases linearly with frequency: NO frequency cut-off 1D “line” model of shower development Time Assumptions: a.1D line of current (excess charge Q) spreading over length L. b.Charge travels at v > c/n radiation wavefronts in phase θ c ≈ 56 o ice L 1 2 3 z J(z,t) = v Q  (z - vt) “Huygens approach” Far-field observer

22. 1D “line” model of shower development Far-field observer at θ ≠ θ C Wavefronts NOT in phase (due to longitudinal shower spread L) Time-domain  Observer sees radiation in a finite interval of time depending on angle (sensitivity to long profile): Δt ( θ ) ≈ L (1 – n cosθ) / c ≈ few 10 ns Frequency domain  Spectrum increases linearly with frequency up to: Frequency cut-off ω cut ( θ ) ≈ Δt -1 ≈ few 100 MHz radiation wavefronts out of phase L 1 2 3 θ < θcθ < θc Time z J(z,t) = v Q  (z - vt) Far-field observer

23. 2D “box” model of shower development Assumptions: 1.2D current: longitudinally over L & laterally over R. 2.Uniform excess charge & travels at v > c/n Far-field observer at Cherenkov θ C Wavefronts NOT in phase (due to lateral spread R of shower). Time-domain:  Observer sees radiation in a finite interval of time: Δt ≈ R sinθ c / (c/n) < ns Frequency domain:  Spectrum increases linearly with frequency: Frequency cut-off ω ≈ Δt -1 ≈ GHz L R wavefronts in phase out of phase θcθc radiation R sinθ c Time z Far-field observer

24. 2D “box” model of shower development Far-field observer at θ ≠ θ C Wavefronts NOT in phase (due to longitudinal L & lateral spread R of shower) Time-domain:  Observer sees radiation in finite interval of time: Δ t = max [R sinθ/ (c/n), L (1 – n cosθ)/c] Frequency domain:  Spectrum increases linearly with frequency: Frequency cut-off ω ≈ Δ t -1 ≈ few 100 MHz - GHz L R wavefronts out of phase radiation R sinθ θ < θcθ < θc Time z Far-field observer

25. Far-field observer at Cherenkov angle ( θ c ) : – Spread in time of pulses and frequency cut-off determined by lateral spread of shower (R). Far-field observer at θ ≠ θ c : – Spread in time of pulses and frequency cut-off (mainly) determined by longitudinal spread of shower (L). Conclusions from “box” model

26. Basic idea: – Obtain charge distribution from complex MC simulations. – Use them as input for analytical calculation of radio pulses. Advantages: – Accurate & computationally efficient. – Full complexity of charge distributions (LPM effect,…) – Shower-to-shower fluctuations. – Different primaries (e, p, n) – Gain insight into features of radio-emission in time & freq-domains Disadvantages: – None ! (well maybe that they need input from MC) Main refs.: – This talk. (4) Semi-analytical models J.A-M, R.A. Vazquez, E.Zas, PRD 61, 023001 (1999) J. A-M, A. Romero-Wolf, E. Zas, PRD 81, 123009 (2010) J. A-M, A. Romero-Wolf, E.Zas, PRD 84, 103003 (2011)

27.  Diffraction by a slit Δ θ ≈ ( ω L) -1 L Angular distribution of E-field θcθc 1D “line” model with variable Q(z) [J. A-M & E. Zas, PRD 62, 063001 (2000)] Frequency domain: E-field can be obtained Fourier- transforming the longitudinal profile Q(z) of excess charge Assumptions: a.1D line of current (excess charge Q) spreading over length L. b.Charge varies with depth & travels at v > c/n (obtained from MC) J(z,t) = v Q(z)  (z - vt) Shower slit Far-field observers

28. Time domain: [J. A-M, A. Romero-Wolf, E. Zas, PRD 81, 123009 (2010)] J(z´,t´) = v Q(z´)  (z´ - vt´) Current A(t obs, θ) ≈ v Q(ζ) / R Vector potential E(t obs, θ) = dA(t obs, θ)/d tobs Electric field ζ → Retardation + time-compression effects: Source position (z) mapped to observer time (t obs ) via θ –dependent relation: t obs = z(1 - ncosθ)/c + t 0 t obs = t 0 @ θ c E-field Bipolar pulses Vector potential = Re-scaling of longitud. profile Longitudinal development from MC sims. Far-field observers Coulomb gauge

29. Relativistic effects Source position (z) mapped to observer time (t obs ) via θ –dependent relation: t obs = z(1 - ncosθ)/c + t 0 When observing shower at angles: θ = θ c → observer sees shower at t=t 0 As observer moves from θ c shower appears to last longer in time. θ > θ c observer sees first the start of shower and then the end (causality) θ < θ c observer sees first the end of the shower and later the start (non-causality) (Many more interesting effects if observer is in the near-field… see later in this talk) Far-field observers

30. Modelling signal away from Cherenkov simple & straightforward – Time-domain: vector potential = rescaling & time- transforming longitudinal profile. – Freq.-domain: Electric field = Fourier transform of longitudinal profile. (Longitudinal profile easy/fast to obtain with MC simulations) Conclusion from 1D line model

31. 3D model with variable Q(z) Current: J(r´, φ´,z´,t´) = v(r´,φ´,z´) f(r´,z´) Q(z´)  (z´ - vt´) Lateral spread Longitudinal spread 1D model fails close to Cherenkov angle where lateral spread is of utmost importance for radio emission [J. A-M, A. Romero-Wolf, E. Zas, PRD 84, 103003 (2011)]

32. Dealing with the lateral spread Convolution of longitudinal & lateral contributions LateralLongitudinal Lateral spread is difficult to model & deal with when obtaining vector potential. However if 2 assumptions are made: (a) Shape of lateral density depends weakly on depth: f(r´,z´) ≈ f(r´) (b) Radial velocities depend weakly on depth´: v(r´,  ´,z´) ≈ v(r´,  ´) [J. A-M, A. Romero-Wolf, E. Zas, PRD 84, 103003 (2011)]

33. A(  Cher t) quasi-universal function Scales with primary energy Dependence with primary: e, p Asymmetryc due to observer´s position & radial components of velocity Existing parameterisation. “Trick” to obtain form factor: At Cherenkov angle only lateral spread is relevant (all shower depths z´are seen at the same time – remember box model ?) Vector potential at θ C : obtained in MC sims. Form factor Shower tracklength: obtained in MC sims. Integrals decouple at  Cher Observer´s time [ns] R x Vector potential [V s] [J. A-M, A. Romero-Wolf, E. Zas, PRD 84, 103003 (2011)]

34. contribution to A due to lateral spread at  z weighted by  Q(z)/4  R  t obs =  z (1 - ncos θ)/c zz  t obs Time reverses  <  Cher Depth z [m]  Cher - 20 o Electron 1 EeV

35.  t obs =  z (1 - ncos θ)/c Large compression in time when  is close to  Cher Depth z [m] zz  t obs  Cher + 0.1 o Electron 1 EeV

36. Modelling signal at any  is simple & straightforward – Vector potential = convolution longitudinal & lateral contributions, with appropriate rescaling & time-compression. – Lateral contribution = form factor (easily obtained in MC sims. from vector potential at Cherenkov angle) – Longitudinal profile modeled with MC sims. (fast !) Procedure works in the far-field & “near”-field (near-field = distances > lateral shower dimensions i.e. > 1 m ) Procedure works also for p, showers – Simply use lateral contribution corresponding to hadronic showers or a mixture in case of e Charged Current Conclusion from 3D model

37. Comparison of methods

38. MC vs MC

39. Frequency spectrum – EM showers Electron 1 PeV ice θCθC θ C - 10 o θ C - 20 o shower observer θ E-field

40. Frequency spectrum – EM showers shower observer θ E-field Electron 1 TeV ice

41. Semi-analytical models vs MC

42. Electron 1 EeV Time-domain: away from  Cher Vector potential traces shape of longitudinal profile Time reversal

43. Time-domain: close to  Cher Electron 1 EeV Vector potential traces shape of longitudinal profile Time reversal

44. Time-domain: even closer to  Cher Electron 1 EeV Sensitivity to longitudinal profile lost

45. Time-domain: proton showers A(  Cher t) proton- showers (obtained in MC sims. with ZHAireS) A(  Cher t) proton vs electron-showers ZHAireS MC Proton – 100 TeV

46. Time-domain: -induced showers A(  Cher,t) ( e ) = 0.83 A(  Cher,t) (e @ 1 EeV) + 0.17 A(  Cher,t) (p @ 1 EeV) e + N → e + jet E( e ) = 1 EeV E(electron) = 0.83 EeV E(hadronic jet) = 0.17 EeV ZHAireS MC e – 1 EeV

47. FDTD vs MC

48. Quantitative comparisons not possible… – FDTD → radiation for unrealistic shower dimensions (memory limitations - size of space-time lattice) Q(z) ≈ exp(-z 2 /2  z 2 ) symmetric (instead of Greisen-like)  lateral (r) ≈ exp(-r 2 /2  r 2 ) with  r =1 m (instead of ≈ 0.1 m) – Different dimensions alter coherence of emission in FDTD compared to MC (ZHS, ZHAireS, G4). MC & FDTD predict same effects in the “near” field: – Fields decreasing as 1/sqrt(R) (cylindrical symmetry) – Dependence on frequency of transition 1/sqrt(R) → 1/R (given by Fraunhofer condition: R > L 2 sin 2  /  – More assymmetric waveforms than in far-field – Transition from more bipolar waveform in near-field to more multi-peaked in far-field (LPM showers)

49. “Near-field” in MC & FDTD More asymmetric waveform as R decreases Observer sees different slices of shower at different distances, angles,… 1/sqrt(R) in near-field 1/R in far-field Electron 10 TeV - ZHS MC  ~  Cher

50. Near-field in MC & FDTD Shower (≈ 20 m long) Observers Shower max. seen at  Cher → time compression → “single” bipolar pulse Shower NOT seen at  Cher → NO time compression → multi-peaked bipolar pulse ZHAireS Monte Carlo vs 3D model

51. Near-field effects in MC & FDTD Compression effects very important Observer may see 2 distinct slices of shower longitudinal development at once Polarization depends on time. Mixing of 2 polarizations

52. Data vs MC

53. Experiments at SLAC: sand, salt & ice Askaryan effect seen !!! Linearly polarized signal Power in radio waves goes as E 0 2 Bipolar pulses in time-domain Agreement with theoretical expectations Bunches of ~ GeV bremss. photons dumped in sand & salt & ice: E 0 ~ 6 x 10 17 – 10 19 eV. D. Saltzberg et al. PRL 86 (2001); P.Miocinovic et al. PRD 74 (2006), P. Gorham et al. PRL 99 (2007) Angular distribution of electric field Frequency spectrum ICE target ANITA More attempts: K. Belov, A. Romero-Wolf @ this meeting

54. – MC simulations: Achieved maturity Agree between each other : ZHS & ZHAireS & GEANT3.21 & 4 – ZHAireS most complete: time & freq. – far & “near” – e & p & Validated by data ! – more tests – air in proposal stage. – FDTD: More flexible than MC. Need to be applied to more realistic cases: comparison to MC – Semi-analytic models: Reproduce complex MC simulations (get input from them) One of the best compromises: accuracy/fastness Summary: Modeling Askaryan signal

55. Quantitative comparison of FDTD & MC – Validation of algorithms (FDTD does not implicitely use any algorithm) Propagation effects not included. – Absorption other than 1/R or 1/sqrt(R) – Effect of variable refractive index Curved paths from shower to observer Time delays NOTE: Other MC using params. of signal include propagation effects (UDel MC, Ohio MC,…) – Tailored to specific expts. (ANITA, ARA,…) Some things to-do

56. End

57. Backup slides

58. Why dense media & why radio? Observation wavelength >> shower dimensions Coherent emission → Power ≈ (Excess charge) 2 ≈ (Shower energy) 2 (In dense media ex. ice, L ≈10 m, R ≈ 0.1 m → coherence up to MHz – GHz) Broad bandwidth ( MHz → GHz ) Excess charge (Askaryan effect) due to keV-MeV electrons. MeV electrons travel at v > c/n in dense media interaction probability scales with density Large vols. of dense, radio “transparent” media exist in Nature: ice, moon regolith, salt, … Cheap detectors: antennas (dipoles, etc…) Information on energy, direction, flavour,… preserved

59. Electromagnetic showers at high-E dominated by:  pair production:  → e + e -  bremsstrahlung: e +/- + N → e +/- + N +  “electrically neutral interactions” → no net charge Charge separation due to geomagnetic field unimportant in dense media: 10 MeV e- traveling L=1 m deviates R≈ 0.05 cm laterally (irrelevance of this mechanism checked in simulations). Net charge in dense media produced by “Askaryan effect” Net charge

60. Excess negative charge Δq scales with shower E. Δq increases slowly with depth. Δq depends on medium. ZHS Monte Carlo simulations e-induced showers in ice

61. Frequency spectrum – EM showers E. Zas, F. Halzen, T. Stanev, PRD 45, 162 (1992), J. A-M & E. Zas, PLB 411, 218 (1997) shower observer

62. Angular distribution ZHS ice E-field/E 0 V MHz -1 TeV -1 E. Zas, F. Halzen, T. Stanev, PRD 45, 162 (1992), J. A-M & E. Zas, PLB 411, 218 (1997) Angle w.r.t. shower axis [deg] Cherenkov peak Δ θ ≈ (L ) -1 ΔθΔθ

63. 1 PeV 10 PeV 100 PeV 1 EeV 10 EeV LPM effect in EM showers Screening effect on electron & photon interaction reduces bremsstrahlung & pair-production cross sections w.r.t. Bethe-Heitler predictions Electromagnetic showers having E > E LPM (~ 2 PeV in ice – medium dependant): Long. dimension L increases faster than ~ log E, typically as E β, β ~ ⅓ – ½ Produces multiple lumps in long. development at highest energies. Lateral dimension R does not change much with shower energy. Above EeV other processes (photoproduction) dominate

64. θCθC θ C - 10 o θ C - 20 o Frequency spectrum in “LPM showers” Elongated profiles at EeV induce smaller cut-off frequencies at θ≠θ c Cut-off frequency at Cherenkov angle unaffected. Large shower-to-shower fluctuations Field normalized to primary energy

65. Freq. spectrum – Hadronic showers Contribution to radio-emission from: protons + charged pions + muons + charged kaons < 2% above PeV Slow elongation with energy → small cut-off frequencies at θ≠θ c Cut-off frequency at Cherenkov angle increases slowly with energy

68. Radio emission in several dense dielectric media

69. Ice vs Moon regolith vs Salt Medium Density [g/cm 3 ] Radiation length [cm] R Moliere [cm] Excess Tracklength/E 0 [m/TeV] Ice0.939.311.41980 Moon1.813.06.91190 Salt2.010.85.91105

70. Salt vs Ice vs Regolith Longitudinal development of excess charge (length units) Radiation lengths: L 0 ≈ 39.3 cm L 0 ≈ 10.8 cm L 0 ≈ 13.0 cm Lateral spread of excess charge @ shower max. Moliere radii: R M ≈ 11.5 cm R M ≈ 5.9 cm R M ≈ 7.0 cm

71. Salt vs Ice vs Moon regolith Medium E field V/MHz/TeV @ 1 MHz Cut-off frequency @ θc [GHz] Cut-off frequency @ θc – 5 0 [MHz] Ice2.1 x 10 -10 ≈ 2≈ 200 Moon9.2 x 10 -11 ≈ 5≈ 600 Salt8.6 x 10 -11 ≈ 4≈ 500

72. Frequency spectrum – EM showers shower observer θ E-field