Eur. Phys. J. D (2012) 66: 28
https://doi.org/10.1140/epjd/e2011-20477-4

Regular Article

Radial drift invariant in long-thin mirrors

¹ Uppsala University, Ångström laboratory, Box 534, SE 751 21 Uppsala, Sweden
² Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and Technology”, 61108 Kharkiv, Ukraine

^a e-mail: olov.agren@angstrom.uu.se

Received: 15 August 2011
Received in final form: 29 November 2011
Published online: 31 January 2012

Abstract

In omnigenous systems, guiding centers are constrained to move on magnetic surfaces. Since a magnetic surface is determined by a constant radial Clebsch coordinate, omnigeneity implies that the guiding center radial coordinate (the Clebsch coordinate) is a constant of motion. Near omnigeneity is probably a requirement for high quality confinement and in such systems only small oscillatory radial banana guiding center excursions from the average drift surface occur. The guiding center radial coordinate is then the leading term for a more precise radial drift invariant I_r, corrected by oscillatory “banana ripple” terms. An analytical expression for the radial invariant is derived for long-thin quadrupolar mirror equilibria. The formula for the invariant is then used in a Vlasov distribution function. Comparisons are first made with Vlasov equilibria using the adiabatic parallel invariant. To model radial density profiles, it is necessary to use the radial invariant (the parallel invariant is insufficient for this). The results are also compared with a fluid approach. In several aspects, the fluid and Vlasov system with the radial invariant give analogous predictions. One difference is that the parallel current associated with finite banana widths could be derived from the radial invariant.