Nonlinear cooling of relativistic particles under equipartition conditions

Abstract

Aims. In powerful cosmic nonthermal radiation sources with dominant magnetic-field self generation, the plasma physical processes generating these magnetic fields by relativistic plasma instabilities are closely related to the processes energising ultra-high energy radiating electrons in these sources. Then the magnetic field strength becomes time-dependent and adjusts itself to the actual kinetic energy density of the radiating electrons. As a consequence, the synchrotron radiation cooling of individual relativistic electrons exhibits a nonlinear behaviour because of the dependence of the magnetic energy density on the actual time-varying kinetic energy density. Methods. The nonlinear kinetic equation for the intrinsic temperoral evolution of relativistic electrons is solved for the case of instantaneous injection of power-law distributed electrons. Results. The properties of the resulting approximate, nonlinear electron density show significant differences compared to the standard linear solution for constant non-equipartition magnetic-field energy density as, for instance, the different time behaviour of the upper and lower cut-offs of the electron distribution. Also the differential electron fluence as a function of electron energy differs from the linear fluence. For large spectral indices s > 2 of the injected power law, the nonlinear fluence exhibits a weaker break at the lower injected electron cut-off γ1 than the linear fluence. For small spectral indices 1 2) injected power laws, the nonlinear synchrotron fluence at low frequencies approaches a power law ∝ν −0.6 , independent of the value of s, which is identical to the synchrotron fluence behaviour from monoenergetically injected relativistic electrons.