Coherent radio-wave emission from extensive air showers. Olaf Scholten KVI, University of Groningen +Krijn de Vries + Klaus Werner: Astropart. Phys. 29, 94 (2008). Astropart. Phys. 29, 393 (2008), arXiv:0712.2517 [astro-ph] Proceedings Arrena ’08 conference ARENA 2010, Nantes June 29 - July 2, 2010

Multiple Approaches Microscopic: Follow orbit of each electron & positron Add fields of individual particles Macroscopic, Emphasize collective aspect Average motion of individual particles Add charges & currents and calculate fields Talk: Marianne Ludwig Easier to understand basic structure radio signal Competing length scales Talk: Tim Huege ARENA 2010, Nantes June 29 - July 2, 2010

General features coherent signal Observation: Currents and charges confined to limited space-time volume Typical coherent length scale: L Pancake thickness Shower length Consequence: Response at large wavelength vanishes E=0 @ n=0 Response vanishes for wavelength < L E=0 @ n> c/L Physics determined by length & time scales ARENA 2010, Nantes June 29 - July 2, 2010

General features II L =0  cancelation Frequency Time Issues for models competing length scales magnitude (distance) ARENA 2010, Nantes June 29 - July 2, 2010

Coherence Charges within wavelength (λ) cannot be distinguished  contribute coherently L<λ : I = E2 ≈ Nc2 where Nc ≈ 106 Far-apart charges add incoherently E ≈ √Nc L>λ : I = E2 ≈ Nc Difference is factor ≈ 106 ARENA 2010, Nantes June 29 - July 2, 2010

Coherent GeoMagnetic Radiation  Geomagnetic Current Lorentz force pulls charges apart induces net current Shower core photons  Moving Dipole net separation of charges Static Dipole Separated charges slowly diffuse Charge excess Coherent radiation D Stopped positrons Stopped electrons Efficient model: Assume all charges concentrated near shower core e- e+ vd c e- vd c j BE D ARENA 2010, Nantes June 29 - July 2, 2010

Induced Electric Current Lorentz force: accelerated Air density: deceleration. Net result: equilibrium, almost constant perp. drift velocity. Induced electric current Jx=e vd Nc = J0 ρ(z) strongly varies Classical E&M: Electric field = derivative (vector) potential Potential = sum charge (current) / distance 3 km ARENA 2010, Nantes June 29 - July 2, 2010

Macroscopic GeoMagnetic Radiation > The Basic picture < Air shower Horizontal drift velocity of electrons creates current Pancake = e+ e- plasma Electric current develops when plasma moves through magnetic field of the Earth Radiation emitted by time varying electric current Pulse sensitive to shower development prior to maximum ARENA 2010, Nantes June 29 - July 2, 2010

Complete study Conclusion: Interesting Physics in Radio signal Dominant Transverse current D Usually Moving Dipole ~15 % e- Static Dipole D ~2 % >25 % Charge Excess Harm Schoorlemmer Krijn de Vries Conclusion: Interesting Physics in Radio signal Pulse shape reflects shower profile before maximum ARENA 2010, Nantes June 29 - July 2, 2010

Recent developments Chemical composition Azimuth dependence Close proximity to shower core Talk Krijn de Vries: Coherent Charge excess radiation = Askaryan Cherenkov effects ARENA 2010, Nantes June 29 - July 2, 2010

Competing scales pulse shape: tmax shifts as d2 Emax prop to d-4 long. shower structure: Zero X-ing <-> shower Max pulse shape: tmax shifts as d2 Emax prop to d-4 d=300 m d=700 m Pulse broadens with increasing distance Pancake thickness important at short distances ARENA 2010, Nantes June 29 - July 2, 2010

pancake at small d At short distance pulse shape is stable Result independent on Convergence parameter Only top part shower is sampled by pulse ARENA 2010, Nantes June 29 - July 2, 2010

Pulse shape in frequency Low frequencies dominate at large distances ARENA 2010, Nantes June 29 - July 2, 2010

Lateral dependence Ratio Power above 25 MHz ARENA 2010, Nantes June 29 - July 2, 2010

Chemical composition p Peaks lower than Fe E=1017 eV proton & iron Longitudinal profile E=1017 eV proton & iron 40 showers each Pancake distribution p Peaks lower than Fe ARENA 2010, Nantes June 29 - July 2, 2010

Chemical composition II power ratio v.s. cut-off frequency 40 proton and 40 Fe showers Why have protons a faster drop? Peak closer to ground  lower frequency  sooner out of juice with increasing d C:\Documents and Settings\Olaf Scholten\My Documents\Attachments\2009\ldf.jpg ARENA 2010, Nantes June 29 - July 2, 2010

Polarizations at different observer positions Geomagnetic polarization ~ β x B Charge excess polarization: Depending on observer position. Pointing inwards Moving dipole polarization: Depending on observer position. ARENA 2010, Nantes June 29 - July 2, 2010 17

Azimuth dependence of signal strength I Vertical shower, 00 = East 900 = North Disentangle contributions ARENA 2010, Nantes June 29 - July 2, 2010

Conclusions Pulse can be understood based on simple geometrical arguments Interesting Physics in Radio signal Pulse shape reflects shower profile before maximum Competing shower thickness & profile Sensitive to chemical composition Signal is Phi-dependent Disentangle contributions ARENA 2010, Nantes June 29 - July 2, 2010