THE BEHAVIOR OF BEAMS OF RELATIVISTIC NONTHERMAL ELECTRONS UNDER THE INFLUENCE OF COLLISIONS AND SYNCHROTRON LOSSES

For many astrophysical situations, such as in solar flares or cosmic gamma-ray bursts, continuum gamma rays with energies up to hundreds of MeV have been observed and can be interpreted to be due to bremsstrahlung radiation by relativistic electrons. The region of acceleration for these particles is not necessarily the same as the region in which the radiation is produced, and the effects of the transport of the electrons must be included in the general problem. Hence it is necessary to solve the kinetic equation for relativistic electrons, including all the interactions and loss mechanisms relevant at such energies. The resulting kinetic equation for nonthermal electrons, including the effects of Coulomb collisions and losses due to synchrotron emission, has been solved analytically in some simple limiting cases and numerically for the general cases including constant and varying background plasma density and magnetic field. New approximate analytic solutions are presented for collision-dominated cases, for small pitch angles and all energies, synchrotron-dominated cases, both steadystate and time dependent, for all pitch angles and energies, and for cases when both synchrotron and collisional energy losses are important, but for relativistic electrons. These analytic solutions are compared to the full numerical results in the proper limits. These results will be useful for calculation of spectra and angular distribution of the radiation (X-rays, γ-rays, and microwaves) emitted via synchrotron or bremsstrah-lung processes by the electrons. We shall examine these properties and their relevance to observations in subsequent papers.