UW-CPTC 08-4 A kinetic equation for unstable plasmas in a finite space-time domain

S. D. Baalrud,∗ J. D. Callen, and C. C. Hegna Department of Engineering Physics, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706-1609, USA (Dated: September 16, 2008) Abstract A generalization of the Lenard-Balescu equation is derived that includes wave-particle scattering by collective instabilities in finite space-time domain plasmas. It is shown that wave-particle interactions can dominate conventional particle-particle Coulomb scattering when finite times are considered or convective instabilities are present in a medium of finite spatial extent before the instabilities grow to nonlinear or turbulent amplitudes. The modified Lenard-Balescu operator retains important physical properties including particle, momentum and energy conservation laws and the Boltzmann H-theorem. To demonstrate it’s utility, the theory is applied to the simple example of convectively growing ion-acoustic instabilities in a finite spatial domain.