Another Use of Dimensional Continuation for Plasma Physics:
The Rate at Which Different Species Come Into Equilibrium

Lowell S. Brown

Plasmas may be created that contain different species which are at different temperatures. This happens, for example, when a plasma experiences a laser pulse which preferentially heats the light electrons that have the larger scattering cross section. The Coulomb interactions between the two species brings them into equilibrium at a common temperature. To compute the rate at which equilibrium is approached in a dilute plasma , we exploit a novel technique employing dimensional continuation that has been introduced recently. The Boltzmann equation correctly describes the short-distance, hard collision interactions for spatial dimensions , but it has a soft, long-distance, infrared divergence when the spatial dimension approaches 3 from above. The Lenard-Balescu equation correctly describes the dynamically screened, soft, long-distance interactions when , but it has a short-distance, hard, ultraviolet divergence when approaches 3 from below. As explained in detail in previous work, as as reviewed here, the analytical continuation of the sum of the rates computed from the Boltzmann equation for and from the Lenard-Balescu equation for yields the correct result for the physical limit at dimensions. We use this method to compute the rate at which two species come into thermal equilibrium for arbitrary mass ratios and for arbitrary initial temperature ratios.

See [physics/9911056] for all the details.