Converter acceleration mechanism in GRB
sources of extremely high-energy cosmic rays
Vl.V. Kocharovsky1, E.V. Derishev1, V.V. Kocharovsky1,2

1 Institute of Applied Physics, RAS, Nizhny Novgorod, Russia
2 Department of Physics and Astronomy, Texas A&M University,College Station, USA

Fermi-type acceleration• I, II, and I & II
• Shocks and shear flow
• Supernovae• Problems• Relativistic flows
For refs see an introductory review Physics-Uspekhi 50 (3), 308 (2007)
and original papers Phys.Rev. D 66, 023005 (2002); 68, 043003 (2003)Accompanying radiation vs. diffuse γ-backgroundActive galactic nuclei (AGN) – possible.

Limitation of diffusive shock acceleration

Advantages of converter mechanisme-/e+ - γ cycle

p - n cycle

Deflection angles,
critical energies

Shock wave

Shear flow

Homogenious
magnetic fieldθ ~ (3l0/rgГ2)1/3
ε1= Гε2= ГeBR

θ ~ (2l0/rgГ2)1/2
ε1= ε2= ГeBR

Chaotic
magnetic fieldθ ~ (2lcl0/rg2Г2)1/4
θ ~ (3lcl0/2rg2Г)1/3
ε1= ε2= ГeB(Rlc)1/2 ε1= Г-1/2ε2= ГeB(Rlc)1/2

One can see that in GRBs and AGN inner jets
protons can in principle be accelerated up to 1021eV. At such energies,acceleration is likely to be radiative-loss limited in both cases. Above1021eV GRBs fail because of their insufficient duration and AGN innerjets -- because of insufficient Poynting-flux luminosity. Hot spots, radio
lobes and galaxy clusters can still work to 3-5*1021eV undervery speculative assumption that the magnetic field is ordered on all scales
and the acceleration efficiency is about 1. In this case, acceleration
is escape-limited.
At the energies greater 1022eV the cosmic ray primaries have to beheavy nuclei. In all the sources listed above the heavy nuclei areaccelerated in the escape-limited regime, so that the attainable energy isroughly Z times more than for protons. However, the nuclei of such energy
are fragmented through interaction with the microwave backgroundphotons after traveling a distance of less than 1Mpc, that means they must
be produced within the local group of galaxies, and GRBs would be theonly possibility to do this. Although the nuclei are easily fragmented inradiation-reach environments of GRBs, we have to conclude that formallythe primaries with energy up to 2-3*1022eV can be produced within theframework of acceleration scenario.

see, e.g., ApJ 655, 980See,e.g.,(2007)

Luminosity

Conclusions
We compare different acceleration mechanisms and show that theconverter mechanism, suggested recently, is the least sensitive to thegeometry of the magnetic field in accelerators and can routinely
operate up to cosmic-ray energies close to the fundamental limit. The
converter mechanism utilizes multiple conversions of charged particles
into neutral ones (protons to neutrons and electrons/positrons tophotons) and back by means of photon-induced reactions or inelastic
nucleon-nucleon collisions.
It works most efficiently in relativistic shocks or shear flows
under the conditions typical for Active Galactic Nuclei, Gamma-Ray
Bursts, and microquasars, where it outperforms the standard diffusive
shock acceleration. The main advantages of the converter mechanism
in such environments are that it greatly diminishes particle losses
downstream and avoids the reduction in the energy gain factor, which
normally takes place due to highly collimated distribution ofaccelerated particles.
We also analyze the properties of gamma-ray radiation, whichaccompanies acceleration of particles via the converter mechanism andcan provide an evidence for the latter. In particular, we point out thefact that the opening angle of the radiation beam-pattern is different atdifferent photon energies, which is relevant to the observability of thecosmic-ray sources as well as to their timing properties.