Axial instability of FRC plasma with non-rigid body displacement

An axial instability criterion for typical FRC plasmas of C-2W device [1] is presented. The criterion is formulated as an eigenvalue problem for the linearized force in z-direction with a self-adjoint operator. The method defines both growth rate and (r,z) structure of unstable plasma displacement (mode); but still being simpler and faster than the full 3D formulation of the linear stability problem. Plasma displacement remains axisymmetrical, two types of 2D plasma flow are considered: in z-direction and incompressible one. Subject of the instability analysis is 2D Grad-Shafranov plasma equilibrium which includes both FRC and Scrape-Off Layer (SOL), free boundary of plasma, vacuum between plasma and conducting wall, and open ends of magnetic lines near mirror magnets. Details about the criterion as well as the equilibrium model and their numerical realizations are also discussed.

[1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).