Radio Cherenkov Radiation from High Energy Shower in Time Domain w/o Far‐Field approx. Mr. Chih‐Ching Chen LeCosPA & National Taiwan University

Outline The shower source size and detecting region. How much percent events we need consider? – Hadronic/EM shower from Neutrino interaction – lepton signal (e, μ, τ ) Behavior of Cherenkov signal – Assumtion – Finite Difference Time Domain (FDTD) method – Time domain current integral method Conclusion

I. Shower Size and Detection Region

10^19eV Proton in ice simulate the Hardonic Shower 10m

Electron 10^19eV in ice 10^19eV e- 140m

Good shower size summary Arxiv:1005:0552 Jaime Alvarez-Muniz, Washington R. Carvalho Jr., Matıas Tueros, Enrique Zas

Cherenkoov Radiation is single slit interference Far field condition : L >> D^2/λ 200m shower L= 40km 200m shower: 1km faraway Near field : >200m Far field : ~50m

II. How much percent events we need consider?

Neutrino interaction Charge current : Neutral current~ 1:1 (GQRS98) Astrophysics source: π -> μ+ ν μ -> e + ν e +ν μ + ν μ Flavor at source (e:μ:τ) = 1:2:0 ( π decay) Flavor at earth (e: μ:τ) = 1:1:1 lepton energy ~ 80% neutrino energy. ν+ N -> ν + jet neutral current ν+ N -> lepton + jet charge current

Lepton Signal Nu_e Hadronic shower(~10s meter) +EM shower(~100 meter ) Nu_mu or Nu_Tau: Hadronic shower (~10s meter) + mu/Tau propagation decay to electron -> Hardonic/EM shower Hadonic shower EM shower/ Hadonic shower EM shower Hadonic shower

Muon, Tau Propagation μ, τ energy loss in medium (GQRS, Dutta, Bugaev…..) Bremsstrahlung processes e+ e−-pair production processes Photonuclear processes Stocastic caustic energy loss

5x10 18 eV Muon propagate in ice Photonuclear loss Pair production loss Photonuclear loss Pair production loss Photonuclear loss EM shower Hadronic shower

10 19 eV Tau propagate in ice Photonuclear loss Pair production loss Hadronic shower EM shower

Ultrahigh energy muon, tau in ice Hadonic shower EM shower Hadonic shower EM shower With LPM effect

Neutrino Flavor Behavior Electron νMuon νTau ν N.C.Hardornic Shower ~20%E ~10m C.C.Hardornic Shower ~20% ~10m C.C. lepton Electron EM shower Muon Propagation Tau Propagation ~80%E ~100m(LPM)~10s km All charge current neutrino signal with huge shower(s)

III. Behavior of Cherenkov Signal

Assumption 1.The current come from high energy particle. 2. De-charging process without induce current. 3. De-charge process is finished before signal detected. N+ Neutral atom ion electron positron photon

Cherenkov Radiation Simulation by Finite Difference Time Domain Advantage of FDTD: First principle, Time domain, Global simulation. w/o approximation (Near field) Shower is cylindrical symmetry. Radiation is polarized ( Er, Ez,H φ ) Net current

FDTD speedup by GPU FDTD simulation cost a lot CPU power. 4 hours. -> 1min.

FDTD gaussian source

E - R relation of 100MHz speed up

Electron shower signal

III. Behavior of Cherenkov Signal Time- domain integral

Liénard–Wiechert potential Lorentz gauge

For Radiation study… k*E=0; k*B=0 for EM radiation. (Transverse wave) E(x,t)//A(x,t) if ϕ ~ 1/r 2 k*A=0 Total charge have gone to 0 when we detection. ϕ (x,t)( instantaneous ) This is radiation gauge, (transverse, Coulomb)

Radiation Gauge

A(x,t) j(x’,t’) θ J T (x’,t’)

Shower size100 m,R = 600 m Charge A(t) vector potential Electric field y Electric field x Shape of two pol. E-field Is different

Shape is varying with detect angle θ = θc θ = θc-+θ

On Cherenkov angle Shower position Detected time Log(A(t’)) Log(A(t))

Conclusion The shower size from c.c. UHE ν inter. is huge The signal from UHE moun, tau is multi –bang Cherenkov signal in time domain is studied.

varying index n(z) Caustic envelope has formed Travel time is multi-valued in this regain This effect will happen in radio propagation

Varying index of reflation n(z) A(x,t) j(x’,t’) θ J T (x’,t’) n(z)