Near-field Effects in Radiowave Detection of Cosmic Neutrinos

1. Near-field Effects in Radiowave Detection of Cosmic Neutrinos Graduate Institute of Astrophysics, National Taiwan University Leung Center for Cosmology and Particle Astrophysics Center for Theoretical Sciences Chiayu, Hu guided by Prof. Pisin Chen

2. Outline • Cosmic neutrinos • Cherenkov radiation & Askaryan effect • Fresnel & Fraunhofer zone • Calculation technique • Results

3. Cosmic Neutrinos • GZK process: high energy cosmic ray interacting with CMB photons will generate cosmic neutrinos. • Directly point back to the UHECR sources. • Extremely small cross section, difficult to detect. GZK neutrinos !! Cut-off in CR spectrum Targets of km scales are needed

4. Neutrino Interactions • Neutrinos coming from the space would have chance to interact with the earth. • Shower development: hadronicshowers cascade of secondary particles RM shower axis a ( log E)

5. Askaryan Effect • The positive and negative charge would produce radiation in opposite polarizations and cancel out with each other. • Askaryan effect: 20% excess of negative charges in the shower. * Due to e+ annihilation and e- scattering into the shower. * The net charge emits Cherenkov radiation. GurgenAskaryan

6. Coherent Cherenkov Radiation • If the shower is generated in a dense medium, its size would be very localized (meter scale). • Wavelength longer than the shower size are considered to be coherent emitted. N: # of particles in shower For radio wavelength, total power N2

7. Neutrino Detection Cherenkov radiation n shower detector

8. Fraunhofer approximation • The standard way to calculate the radiation is Green’s function method. • Fraunhofer (far-field) approximation: • Parameterization formula: Difficult to integrate P.W. Gorham et al. Phys. Rev. D 72, 023002 (2005)

9. Far Field Result J. Alvarez-Muniz et al., Phys. Rev. D 74. 023007 (2006)

10. Diffraction of Cherenkov Radiation • Shower with finite size will lead to diffraction, which is an analogy to the slit diffraction experiment. • Far field (Fraunhofer) diffraction pattern = Fourier transformation of shower development. • The Fraunhofer condition : a2sin2q/l <R a sinq q a

11. Near-field becomes important • The size (in g/cm2) of the shower scales with log(E) in the low energy range. • But if the energy is high enough (>1015eV), the Landau–Pomeranchuk–Migdal (LPM) effect will suppress the EM cascade, and therefore elongate the shower dramatically. • A shower in ice with E ~ 1018 eV will have its size of 50 m, and a 1020 eV shower can even be ~200 m long. • The Fraunhofer approximation is no longer valid.

12. FDTD method • We adopt the finite-difference time-domain technique, a numerical method of EM wave calculation. EM fields are calculated at discrete places on a meshed geometry. • Does not require to do the difficult integration. • Near field pattern can beproduced directly. z detector Cherenkovradiation shower q R r

13. Simulation Result

14. Distance Dependence Blue: radiation Green: 1/sqrt(r) Red: 1/r 100 MHzat Cherenkov angle Cylindrical behavior for small r Spherical behavior for large r

15. Angular Spread (4m)

16. Spectrum (4m)

17. Angular Spread (32m)

18. Spectrum (32m)

19. Summary • Our method reproduces the radiation pattern in the far field,while it provides straightforward calculation of the near field. • In the near field region, the radiation is a cylindrical wave instead of a spherical wave. • The shape of spectrum and angular spread in the Fresnel zone is r-dependent, the simple scaling does not work in this region. Important for energy reconstruction.

20. Back up Slides

21. FDTD in cylindrical lattice z r-z plane Ez Hφ Er ‧‧‧ ‧‧‧ Same lattice r

22. Maxwell equations in Cylindrical Coordinate σm = 0 Hz = Hr = Eφ = 0 d/dφ = 0