An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field
arXiv:2212.02654 · doi:10.1017/S0022377823000077
Abstract
Starting from the equations of collisionless linear gyrokinetics for magnetised plasmas with an imposed inhomogeneous magnetic field, we present the first known analytical, closed-form solution for the resulting velocity-space integrals in the presence of resonances due to both parallel streaming and constant magnetic drifts. These integrals are written in terms of the well-known plasma dispersion function (Faddeeva & Terentev 1954; Fried & Conte 1961), rendering the subsequent expressions simpler to treat analytically and more efficient to compute numerically. We demonstrate that our results converge to the well-known ones in the straight-magnetic-field and two-dimensional limits, and show good agreement with the numerical solver by Gürcan (2014). By way of example, we calculate the exact dispersion relation for a simple electrostatic, ion-temperature-gradient-driven instability, and compare it with approximate kinetic and fluid models.
arXiv comment35 pages, 13 figures
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