On the stability of the $m=1$ rigid ballooning mode in a mirror trap with high-beta sloshing ions

TL;DR

This paper investigates the stability of the m=1 ballooning mode in mirror traps with high-beta sloshing ions, exploring suppression methods and the effects of various physical parameters on stability.

Contribution

It provides a detailed analysis of the stability conditions for the m=1 ballooning mode in mirror traps with oblique NBI and high-beta ions, including suppression strategies.

Findings

Suppression of the m=1 ballooning mode is possible with wall shape and NBI angle adjustments.

Finite Larmor radius effects stabilize small-scale modes with m>1.

Various stabilization methods like conducting walls and end MHD anchors are analyzed.

Abstract

Stability of the ``rigid'' $m = 1$ ballooning mode in a mirror axisymmetric trap is studied for the case of oblique neutral beam injection (NBI), which creates an anisotropic population of fast sloshing ions. Since small-scale modes with azimuthal numbers $m>1$ in long thin (paraxial) mirror traps are easily stabilized by finite Larmor radius (FLR) effects, suppression of the rigid ballooning and flute modes would mean stabilization of all MHD modes, with the exception of mirror and fire-hose disturbances, which are intensively studied in geophysics, but have not yet been identified in mirror traps. Large-scale ballooning mode can, in principle, be suppressed either by the lateral perfectly conducting wall, or by the end MHD anchors such as cusp, or by biased limiters, or by combination of these two methods. The effect of the wall shape, vacuum gap width between the plasma column and the lateral wall, angle of oblique NBI, radial profile of the plasma pressure, and axial profile of the vacuum magnetic field are studied.