An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field. (24th April 2023)

• Record Type: Journal Article
• Authors: Ivanov, P.G.; Adkins, T.
• Is Part Of: Journal of plasma physics. Volume 89:Number 2(2023)
• Publication Date: 2023-04-24
• Subjects: fusion plasma -- plasma instabilities; Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S0022377823000077
• Languages: English
• ISSNs: 0022-3778

Abstract

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 & Terent'ev, Tables of Values of the Function $w(z)=\exp (-z^2)(1+2i/\sqrt {\pi }\int _0^z \exp (t^2) \, \mathrm {d} t)$ for Complex Argument, 1954. Gostekhizdat. English translation: Pergamon Press, 1961; Fried & Conte, The Plasma Dispersion Function, 1961. Academic Press), 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 ( J. Comput. Phys., vol. 269, 2014, p. 156). 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.