Kinetic Theory of Strongly Magnetized Plasmas

Abstract

Coulomb collisions in plasmas are typically modeled using the Boltzmann collision operator or its variants. These apply to weakly magnetized plasmas in which the typical gyroradius of particles significantly exceeds the Debye length. Conversely, O'Neil has developed a kinetic theory to treat plasmas that are so strongly magnetized that the typical gyroradius of particles is much smaller than the distance of closest approach in a binary collision. This dissertation presents a generalized collision operator that applies across the full range of magnetization strength and which asymptotes to the traditional Boltzmann collision operator in the weakly magnetized limit and O'Neil's theory in the extremely magnetized limit. The theory also spans the weak to strong Coulomb coupling regimes by incorporating the mean force kinetic theory concept. To demonstrate novel physics associated with strong magnetization, it is used to compute the friction force on a massive test charge and the ion-electron temperature relaxation rate.

Recent works studying weakly coupled plasmas have shown that strong magnetization leads to a transverse component of the friction force that is perpendicular to both the Lorentz force and velocity of the test charge, in addition to the stopping power component. Recent molecular dynamics simulations have also shown that strong Coulomb coupling, in addition to strong magnetization, gives rise to a third ``gyrofriction'' component of the friction force in the direction of the Lorentz force. The generalized kinetic theory captures these effects and agrees well with the molecular dynamics simulations over a broad range of Coulomb coupling and magnetization strengths. The transverse force strongly influences the average motion of a test charge by changing the gyroradius, and the gyrofriction force is found to slightly change the gyrofrequncy of the test charge resulting in a phase shift.

Strong magnetization is also shown to break a fundamental symmetry of independence of the collision rate on the sign of the charges of the interacting particles, commonly known as the ``Barkas effect". It is found that the friction force changes dramatically depending on the sign of the interacting charges. The magnitude of the Bragg peak of the stopping power component for oppositely-charged particles decreases in magnitude compared with like-charged particles, and the perpendicular components increase in magnitude. Moreover, the difference between the two cases increases with increasing magnetization strength. On computing the electrical resistivity from the friction force, it is found that strong magnetization in conjunction with oppositely-charged interactions significantly decreases the parallel resistivity and increases the perpendicular resistivity.

Ion-electron temperature relaxation in strongly magnetized plasma is also found to exhibit novel properties. Strong magnetization is generally found to increase the temperature relaxation rate perpendicular to the magnetic field and to cause the temperatures parallel and perpendicular to the magnetic field to not relax at equal rates. This, in turn, causes a temperature anisotropy to develop during the equilibration. The temperature relaxation rate is also found to depend strongly on the sign of the charge of the interacting particles. It is found that the combination of oppositely charged interaction and strong magnetization causes the ion-electron parallel temperature relaxation rate to be significantly suppressed, scaling inversely proportional to the magnetic field strength.