Ideal MHD stability limits of low aspect ratio tokamak plasmas

Abstract

The ideal magnetohydrodynamic (MHD) stability limits of low aspect ratio tokamak plasmas are computed numerically for plasmas with a range of cylindrical safety factors q*, normalized plasma pressures beta , elongations kappa and central safety factors q(0). Four distinct regimes are optimized, namely: (a) low-q* plasmas with q(0)=1.1 with and without a stabilizing wall, (b) low-q* plasmas with no wall and 1.1<q(0)<2, (c) high- beta , high bootstrap fraction plasmas at moderate kappa requiring a wall and edge current drive and (d) high- beta , very high bootstrap fraction plasmas with moderate to high kappa requiring a stabilizing wall but little external current drive. A stable equilibrium is found at an aspect ratio of A=1.4 and an elongation of kappa =3.0, with 99.3% of the current provided by the plasma pressure and beta =45%. Special attention is paid to the issues of numerical convergence and the proper definition of bootstrap current fraction

Physics basis for a spherical torus power plant

“…[4] and [5] for high bootstrap fraction equilibria optimized for ballooning stability was that the marginally stable b increased very rapidly with increasing k . However, it is also necessary to determine what upper limit the n0/0 vertical instability and low-n kink modes impose on k and hence b .…”

“…Ideal MHD stability analysis of low-aspect-ratio tokamak plasmas has already been carried out by several authors [4,5] and the relevant scalings for the maximum stable b that might be achievable in an ST power plant are reasonably well understood. Combining Troyon b and bootstrap current scalings, the relationship between the achievable plasma toroidal b and the dimensionless parameters relevant to a power plant design can be expressed as:…”

“…The first method, described in Ref. [4], specifies a linear profile of the flux-surface-averaged parallel current density ratio j ×/B / B ×/9f between the magnetic axis and the radius of tangency to the bootstrap current profile. The value of the current density on axis is determined by the specified q(0) value.…”

“…The functional forms used for the shape and pressure and temperature profiles in the following analysis are described in Refs. [4] and [5] and are not repeated here.…”

“…These physics features included such desirable features as large natural elongation, strong magnetic helical pitch, and the existence of a large near-omnigeneous region in the plasma cross section which suggests improved confinement. More recent theoretical studies by Menard [4], Miller [5], and coworkers have shown that for certain specific classes of plasma equilibrium with close fitting conducting walls, there exist stable solutions to the plasma equilibrium equations with very large values of the plasma b and with essentially all of the plasma current self-provided by the bootstrap effect. The large b and high bootstrap fraction compensate for the low TF strength and the high value of plasma current, making this concept competitive with that based on the advanced tokamak.…”