COMBINED 1ST-ORDER AND 2ND-ORDER FERMI ACCELERATION IN RADIO GALAXY HOT-SPOTS

We investigate the transport of relativistic particles in radio galaxy hot spots using the diffusion approximation and including both first and second order Fermi acceleration. Our intention is to determine the effect Fermi acceleration of the second order may have on synchrotron spectra of hot spots. This seems useful due to the high Alfven velocities therein. At least in the case of flat spectrum hot spots, i.e. with a power-law index above 1/2, pure first-order acceleration is inconsistent with recently derived physical parameters, particularly the high Alfven velocities. This opens the possibility of interpreting the observed radiation of hot spots as created by combined first and second-order Fermi acceleration. A difference between the forward and backward wave intensities, often considered as deciding, can not change this result, except for an almost complete absence of one wave type. If we assume a compression ratio of approximately r = 2.5 consistency is restored for the spectra of recently investigated hot spots without need for changing the formerly derived physical parameters.