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 tex2html_wrap_inline12, but it has a soft, long-distance, infrared divergence when the spatial dimension tex2html_wrap_inline14 approaches 3 from above. The Lenard-Balescu equation correctly describes the dynamically screened, soft, long-distance interactions when tex2html_wrap_inline16, but it has a short-distance, hard, ultraviolet divergence when tex2html_wrap_inline14 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 tex2html_wrap_inline12 and from the Lenard-Balescu equation for tex2html_wrap_inline16 yields the correct result for the physical limit at tex2html_wrap_inline24 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.

Laurence Yaffe
Tue Nov 23 18:29:04 PST 1999