1. The endpoint formalism for the calculation of electromagnetic radiation and its applications in astroparticle physics
radiation from „endpoints“
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2. Named radiation mechanisms
many named radiation mechanisms in the literature
Synchrotron radiation
(Vavilov-)Cherenkov radiation
Transition radiation
and many more …
these are idealized concepts for simplified problems
when applied to realistic problems, they can lead to confusion:
„On the Cherenkov threshold associated with synchrotron radiation in a dielectric medium“
„Cherenkov radiation from an Electron Traveling in a Circle through a Dielectric Medium“
etc …
let‘s go back to basics!
ICRC 2011 Beijing #0653, see also arXiv:

3. Charged particle motion: Liénard-Wiechert fields
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delay: R/c r ^ q b
continuous formulation
difficult to apply in Monte Carlo codes
ICRC 2011 Beijing #0653, see also arXiv:

4. Discretization of particle motion: endpoints
discrete formulation for arbitrarily complex motion
radiation only from endpoints r ^ b1
delay: R/c b2
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endpoints: decelerate from b1 to rest
then accelerate from rest to b2
ICRC 2011 Beijing #0653, see also arXiv:

5. Radiation from a single endpoint
time domain formulation
frequency domain formulation
- for deceleration from b* to rest (stopping point)
+ for acceleration from rest to b* (starting point)
ICRC 2011 Beijing #0653, see also arXiv:

6. Reproducing Synchrotron Radiation
discretize circular motion
fineness dictated by Dt, nmax
pairs of stopping and starting points
B-field
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ICRC 2011 Beijing #0653, see also arXiv:

7. Reproducing Synchrotron Radiation
direct calculations in time-domain and frequency-domain
agreement with FFT of the other domain
localized signal: time-domain is better for this problem
ICRC 2011 Beijing #0653, see also arXiv:

8. Reproducing Transition Radiation
beautifully reproduced, for details please see arXiv:
ICRC 2011 Beijing #0653, see also arXiv:

9. Application: Askaryan Radiation
shower particle track near medium surface θC
“Cherenkov” shock wave from “static field”
not reproduced by (current) endpoint formalism
significant in the near-field (E ~ 1/R2)
vanishes in vacuum and thus in “Formation Zone”
Radio emission from acceleration/deceleration (time-variation of charge excess in shower)
modelled by endpoint formalism
dominant in far-field (E ~ 1/R)
arises also in vacuum
No „Formation Zone“: Askaryan emission does not vanish for cosmic ray showers near lunar surface.
ICRC 2011 Beijing #0653, see also arXiv:

10. Application: EAS Radio Emission (REAS3)
earlier Monte Carlos missed radiation due to „creation and destruction“ of particles (time-variation of Nparticles)
REAS3 employs endpoint formalism – consistency!
pulses become bipolar
spectra fall to zero at frequency zero
breakthrough: agreement between microscopic (REAS3) and macroscopic (MGMR) models
ICRC 2011 Beijing #0653, see also arXiv:

11. Application: EAS Radio directly in CORSIKA
simple implementation
very efficient calculation, fast and numerically stable
full CORSIKA information, no information loss
refractive index effects included
ICRC 2011 Beijing #0653, see also arXiv:

12. Conclusions
named „emission mechanisms“ only apply to idealised situations
endpoint formalism works for arbitrarily complex problems
is very well-suited for implementation in Monte Carlo codes
works in time- and frequency domains
successfully applied endpoint formalism in astroparticle physics
Askaryan emission does not vanish near medium surface
reconciliation of microscopic (REAS3) and macroscopic models for radio emission from EAS
ICRC 2011 Beijing #0653, see also arXiv:

13. Backup Slides
ICRC 2011 Beijing #0653, see also arXiv:

14. Radiation from a single endpoint in vacuum
relativistic beaming
in medium disconti-nuity at Cherenkov angle
ICRC 2011 Beijing #0653, see also arXiv:

15. Radiation from a single endpoint in a medium
ICRC 2011 Beijing #0653, see also arXiv:

16. Achievable precision
ICRC 2011 Beijing #0653, see also arXiv:

17. Simulating Transition Radiation
ICRC 2011 Beijing #0653, see also arXiv: