May 8-10

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Author: Ilon Joseph
Requested Type: Poster
Submitted: 2023-04-01 10:56:40

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Contact Info:
Lawrence Livermore National Laboratory
7000 East Ave.
Livermore, CA   94551
USA

Abstract Text:
An accurate calculation of the total polarization charge density is important for the determination of the self-consistent electric field in a magnetized plasma. However, there is a paradoxical factor of 1/2 difference between the pressure-driven “diamagnetic” polarization density calculated using real-space gyrokinetic theory versus drift-reduced fluid and drift-kinetic theory that has not been clearly explained in the literature. The results of both approaches are consistent with one another when the probability distribution function is the orbit-average of a real-space function. Half of the diamagnetic polarization is due to the transformation from the guiding center density to the real space density. The other half is due to the difference between the guiding center density and the density in the limit of vanishing Larmor radius. The resolution is closely related to the Spitzer paradox: the way in which the single-particle drifts and collective fluid drifts match after correctly accounting for the magnetization current.
In regions that are well-confined, the equilibrium particle distribution function (PDF) can only depend on the robust constants of the motion. To first order in perturbation amplitude, it can be expressed as the orbit average of the PDF in the limit of zero orbit width. Diamagnetic polarization effects arise due to the finite width of particle orbits, e.g. gyro-motion and parallel circulation/banana motion. Because the energy and angular momentum depend on the combined electric and magnetic potential, they do not generate net polarization and the corresponding electric and diamagnetic polarization must precisely cancel. For example, an isotropic Maxwell-Boltzmann distribution is confined by electrostatic forces and has no perpendicular rotation. In contrast, anisotropic dependance on the magnetic moment and/or parallel invariant does generate net polarization effects proportional to the temperature anisotropy.

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