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Context. In powerful cosmic nonthermal radiation sources with a dominant magnetic field self generation, partition between the energy densities in magnetic fields and relativistic electrons is expected. As the electrons cool by synchrotron emission, the magnetic field strength becomes time-dependent and adjusts itself to the actual kinetic energy density of the radiating electrons. Aims. For the case of instantaneous injection of power law distributed electrons with a flat power law spectral index, the nonlinear synchrotron fluence is calculated. Methods. Results. For flat (spectral index 1 < s < 2) injected power laws the nonlinear synchrotron fluence at small frequencies approaches a power law ∝v ―0.6 , independent of the value of s, which is identical to the synchrotron fluence behaviour for steep injected power laws.

Synchrotron fluence of nonlinearly cooled relativistic electrons with instantaneous flat power law injection