On the isotropization of electrons in synchrotron sources

Electrons radiating synchrotron radiation develop a pitch angle anisotropy, and so become unstable to the coherent emission of hydromagnetic waves. The evolution of the coupled system of anisotropic electrons and waves is studied in the absence of any dissipation of the waves in the ambient medium. The anisotropy of the electrons approaches a steady state in which the anisotropy is energy independent and of orderv_A/c (v_A=Alfvén speed). The conditions for this small degree of anisotropy to be maintained are examined.Due to this scattering the bend in the synchrotron spectrum, from an inverse power law with index to one with index 4/3+1, due to an initial or recurrent injection of electrons, could only occur at infrared or higher frequencies.