Dependence of ideal MHD kink and ballooning modes on plasma shape and profiles in tokamaks

Abstract

Extensive numerical studies of ideal MI'P instabilities have been carried out to gain insight into the parametric dependence of critical p's in tokamaks. The .large numrt .;; i r. tor related equilibrium quantities involved in establishirq a critir-al '.' has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the par, meter regimes appropriate for both current and reactor-sized plasmas. A :indr>vc!Lo 'InnondencR on the pressure profile and a stronc variation with the current pro Tile is found. The principal resul t is that for aspect ratio P.''a '•>, critical (3' s are of the order of r% for circular cross sections and 5% for plasmas with elongation i, "-' 2; sorewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analyzed to compare critical i' as a function of toroidal mode number n. We conclude that the infinite-n analytic ballooning theory provides a sufficient condition for ideal MHD internal node stability. Low-n free boundary modes appear to set a lower limit.

Simple, general, realistic, robust, analytic tokamak equilibria. Part 1. Limiter and divertor tokamaks

“…actually credit the profile to an earlier paper (Todd et al. 1979). For the actual surface coordinates , plus the corresponding normalized surface coordinates , the Miller profile is defined in terms of an angle-like parameter , , as follows: Here, is the elongation, is the triangularity and .…”

Special topics in plasma confinement

“…Critical β as a function of 1/n for a configuration with (a) R/a = 3.5, κ = 1.65, δ = 0.25, α = 1.4 and 1.0 < q < 3.0 and (b) R/a = 4.6, κ = 1.0, δ = 0, α = 2 and 1.04 < q < 1.58. (Reproduced with permission from Todd et al (1979).) modes -as in a straight cylinder (Connor & Taylor 1987)?…”

“…The effect of changing cross-section on ballooning modes was investigated by Todd et al. (1979) for plasma in a torus with the idealised D-shaped cross-section shown in figure 60. The parameters and , respectively, define the triangularity and ellipticity of the boundary, , , and describes the peaking of the pressure profile, .…”

Tokamak D-T neutron source models for different plasma physics confinement modes

“…MS shapes have been expressed from their reduced plasma horizontal minor radius a and their poloidal angle˛(see Fig. 1) [6,[9][10][11][12]:…”