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UBC Theses and Dissertations

Collisional relaxation in plasmas Crossman Statter, Gregory Christopher


The energy relaxation of two types of fully ionized plasma systems are determined with the solution of the Fokker-Planck equation. In both cases the plasma constituents are treated as being point-like and structureless and the plasma relaxes collisionally in the absence of spatial gradients and external electric and magnetic fields. The first plasma system consists of one plasma species dilutely dispersed in a second plasma which acts as a heat bath at equilibrium. The initial energy distribution of the dilute constituent is chosen to be a delta function and the approach to a Maxwellian distribution at the heat bath temperature is determined. The second plasma system consists of just one plasma species which initially possesses a bi-Maxwellian ion velocity distribution function (VDF). The average of the kinetic energy, m<v [2/‖] > /2 for particle motions in some arbitrary z direction serves to define a temperature parameter T‖ =m<v[2/‖]>/k for this degree of freedom. Similarly, the temperature T⊥=m<v[2/⊥]>/2k, where v⊥ is the velocity component in the plane perpendicular to z, parametrizes the average energy for the other two translational degrees of freedom The relaxation of T‖ and T⊥ to a common temperature, T, via self-collisions of the plasma is studied. In both cases the collisional relaxation can be described by a linear collision operator and the expansion of the distribution function in the eigenfunctions of the Fokker-Planck operator is considered. The reciprocals of the corresponding eigenvalues are the characteristic relaxation times for the system. For the first plasma system, the temperature relaxation time determined with the solution of the Fokker-Planck equation is compared with the relaxation time calculated with the assumption that the distribution function remains Maxwellian all the time. For the second plasma system the relaxation time is the characteristic time for the relaxation of one of the temperature components and is comparedwith the relaxation time calculated with the assumption that the distribution function remains bi-Maxwellian all the time. The results are compared with other theoretical and experimental results. A study of the eigenvalue spectrum of the Fokker-Planck operator and the temporal approach to equilibrium is also emphasized.

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