1. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Theory Notes on Shower and Radio Pulse

2. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Outline Basic mechanism for Radio Cherenkov Coherence issues and pulse characteristics Types of showers EM shower characteristics (low E) EM showers at high energy Hadronic showers Codes Some Results Assessment

3. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Basic mechanism 5 m  c = 56 o +/- 3 o Details depend on a)length of shower b)charge excess c)radial profile Askaryan: Q s = N e- - N e+ ~ (E s /GeV)

4. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Coherence issues Consider five cases – all with the same “projected track length”   ~  /d Z = 1, d = 10, r = 0P = 10 Z = 1, d = 10, r = 0P = 10 Z = 10, d = 1, r = r 0 P = 10(  – 100(  inf)  ~  0 Z = 10, d = 1, r = 0P = 100 Z = 10, d = 1, r = r 0  ~  0 P ~ 10

5. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Longitudinal and radial profiles Avg. shower profiles from 100 GeV e’s in ice FLUKA (Clem). red: e - blue: e + black: sum green: excess Radial Profiles. Determined by multiple scattering, Moliere radius. Energy dependence. r(E) ~ 1/E (m.s. dominated by end of track)

6. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Frequency/angle correlation

7. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Shower Types Charged current events –lepton + recoil shower –electron, mu, tau Neutral current events –hadronic shower Recoil fraction

8. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 LPM effect – lengthens shower, by say f, then Hadronic showers    interactions compete with decay High energy showers, above a few PeV Z = 10, d = 1, r = r 0  ~  0 /f P ~ 10/f With LPM Without LPM “Hadronic” E s = 20% E

9. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Codes Zas, Halzen, Stanev “Santiago” group, Zas, Alvarez-Muniz,… (LPM, Hadronic), high energy sampling techniques. GEANT 3.2.1 (under estimates track length, unless special care is taken) GEANT 4 FLUKA

10. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Simulation issues Normalization (ok, now (10%), at low energies) Spectrum – some disagreement between ZHS analytic form and preliminary GEANT results Fluctuations – dominated by first few interactions (or LPM effects) Do we really understand LPM? Summing hadronic and EM showers? Magnetic fields ?

11. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Spectrum S. Seunerine: preliminary by eye. ZHS by eye.

12. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Spectrum II From Francis From Zed

13. Shower & RF theory David Seckel, ANITA Collab. Mtg. Nov. 24-25, /2002 Fluctuations Also: interference between hadronic and electromagnetic