Influence of the shape of a conducting chamber on the stability of rigid ballooning modes in a mirror trap

Abstract

MHD stabilization of flute and ballooning modes in an axisymmetric mirror trap is studied under the assumption of a strong Finite Larmor Radius effect that suppresses all perturbations with azimuthal numbers m ≥ 2 and makes the m = 1 mode ‘rigid’. The rigid mode can be effectively suppressed using a perfectly conducting lateral wall without any additional means of stabilization or combined with end MHD anchors. Numerical calculations were carried out for an anisotropic plasma produced in the course of neutral beam injection into the minimum of the magnetic field at the right angle to the trap axis. The stabilizing effect of the conducting shell made of a straightened cylinder is compared with a proportional chamber, which, on an enlarged scale, repeats the shape of the plasma column.
 It is confirmed that for convincing wall stabilization of the rigid modes, the plasma beta (β, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value βcr2. When the conducting lateral wall is combined with conducting end plates imitating MHD end anchors, there are two critical betas and, respectively, two stability zones β < βcr1 and β > βcr2 that can merge, making the entire range 0< β <1 of betas allowable for stable plasma confinement.
 The dependence of the critical betas on the plasma anisotropy, mirror ratio, width of the vacuum gap between the plasma column and the lateral wall, radial pressure profile, and axial magnetic field profile is examined.

Wall stabilization of the rigid ballooning m = 1 mode in a long-thin mirror trap

“…earlier used in Refs. [2][3][4], approximates the axial profile of the vacuum magnetic field and which we used earlier. on the graphs as compared to magnetic field in GDT [9] and WHAM [10] devices.…”

“…Continuing the line of Ref. [4], this paper compares, when it is suitable, the stabilizing effect of proportional chamber with a straightened chamber, which is assigned the abbreviation 'St' (Straightened).…”

“…Using notations introduced in Ref. [4], one can specify than the Lw configuration can provide an upper stability zone at a sufficiently large beta that exceeds second critical value, β > β cr2 . In the Cw, Bw (Blind Wall) and Rw (Ring Wall) configurations lower zone β < β cr1 can appear in addition to the upper one.…”

“…In the first article [2], which was followed by the two more papers [3,4], a plasma model with isotropic pressure was implemented. It was assumed that the plasma column is surrounded by a cylindrical perfectly conducting chamber with a variable radius, which is proportional * igor.kotelnikov@gmail.com to the plasma radius with a constant coefficient.…”

“…Calculations published in Ref. [4] made it possible to compare the stabilizing effect of a proportional conducting chamber with the effect of such a "straightened" chamber for a model of a transverse NBI.…”