Adiabatic compression of ion rings

Abstract

A study has been made of the compression of collisionless ion rings in an increasing external magnetic field, Be = ẑBe(t), by numerically implementing a previously developed kinetic theory of ring compression. The theory is general in that there is no limitation on the ring geometry or the compression ratio, λ≡Be (final)/Be (initial)⩾1. However, the motion of a single particle in an equilibrium is assumed to be completely characterized by its energy H and canonical angular momentum Pϑ with the absence of a third constant of the motion. The present computational work assumes that plasma currents are negligible, as is appropriate for a low-temperature collisional plasma. For a variety of initial ring geometries and initial distribution functions (having a single value of Pϑ), it is found that the parameters for ’’fat’’, small aspect ratio rings follow general scaling laws over a large range of compression ratios, 1⩽λ≲103: The ring radius varies as λ−1/2; the average single particle energy as λ0.72; the root mean square energy spread as λ1.1; and the total current as λ0.79. The field reversal parameter is found to saturate at values typically between 2 and 3. For large compression ratios the current density is found to ’’hollow out’’. This hollowing tends to improve the interchange stability of an embedded low β plasma. The implications of these scaling laws for fusion reactor systems are discussed.