Coulomb Scattering in a Very Strong Magnetic Field

Abstract

The spiralling of charged particles in an intense magnetic field is taken into account in the description of their collisions involving small fractional momentum transfer. The transition probability to the continuum of possible states is given. In addition, the transition probability is given for a particle's orbit center to be displaced from one magnetic line of force to another, with accompanying momentum change, as a result of scattering by a fixed charge. The equivalent results are derived for the scattering of two identical particles in their relative coordinate system.As the result of scattering, the momentum change along the magnetic field in a uniform, collimated beam of spiralling particles is found to be very much smaller than the sum of the magnitudes of the individual momentum changes in that direction. In contrast to ordinary Coulomb scattering, one finds that there is a lower limit to the momentum transfer to individual particles and that there is an adiabatic cutoff distance associated with the interaction which, in some plasma situations, can be shorter than the value of the Debye distance.The WKB approximation for generalized Laguerre polynomials is appended.