M. Phillips

MHD stability properties of bean-shaped tokamaks

A study of the MHD stability properties of bean-shaped tokamak plasmas is presented. For ballooning modes, while increased indentation gives larger stable-beta configurations, the existence and accessibility of the second stable region are sensitive to the pressure and safety factor profiles. The second stable region appears at lower beta values for large aspect ratio and moderately high q-values. Finite-Larmor-radius kinetic effects can significantly improve the stability properties. For low-q ( 1) operation, long-wavelength (n ~ 2, 3) internal-pressure-driven modes occur at modest βp values and accessibility to higher beta operation is unlikely. Indentation modifies the nature of the usually vertical axisymmetric instability, but the mode can be passively stabilized by placing highly conducting plates near the tips of the plasma bean. At constant q, indentation has a stabilizing effect on tearing modes.

A magnetohydrodynamic stability study of reverse shear equilibria in the Tokamak Fusion Test Reactor

A study is presented of the low‐n (n=1,2,3) magnetohydrodynamic stability of equilibria with reverse shear safety factor profiles. The low‐n stability boundaries are found to be characterized by resonance structures due to internal so‐called ‘‘infernal’’ mode types of instabilities. The parametric dependence of shear reversal width and depth, current, and pressure gradient on the beta limit are determined by using profile models that allow each parameter to be varied independently. Reverse magnetic shear is found to have a stabilizing influence for modes with toroidal mode numbers n≥2 leading to the possibility of improved β limits in the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Res. 26, 11 (1984)].

Transition to the second region of ideal MHD stability

Transition to the second region of MHD stability has been examined in circular cross-section boundary tokamak geometry. Values of β and βp, corresponding to equilibria which are marginally stable in the second region on each flux surface, are presented. The aspect ratio scaling of these functions is shown to be sensitive to the value of the on-axis safety factor qo. Equilibria evolving from the first to the second region of stability have been generated by a transport code which calculates the two-dimensional evolution of the magnetic configuration self-consistently with the thermal and particle diffusion. The transport model enhances the diffusion coefficients on flux surfaces which are unstable to high-n modes, thereby altering the pressure profile locally. The q-profile, modified by neutral beam driven current so that q0 > 1, reduces the size of the unstable region sufficiently to allow transition to the second region. Auxiliary power requirements for this transition are estimated. Stability of the transition equilibria to low-n external and internal modes is also examined. All ideal modes restabilize as βp approaches and exceeds unity. A close fitting conducting wall is needed to stabilize low-n external kink modes.

MHD stability properties of a high current, high beta tokamak

Various aspects of MHD stability are studied for a high current, high beta tokamak. Included is a study of kink and ballooning mode beta limits as a function of current and safety factor at the plasma edge (qs). These studies were carried out with pressure profiles optimized with respect to ballooning and ohmically consistent current profiles whereby the ⋅/⋅∇ profile is specified. The effect of current profile shaping is studied. Current profiles with steep edge gradients are more unstable to kink instabilities at high beta. This is particularly true for values of qs near an integer value on edge where the kink mode beta limit can fall off steeply. For a less steep edge current gradient, the ballooning modes are more unstable at high beta. The effect of elongation and triangularity are also considered. Improvement in the beta limit is observed for increasing elongation, up to κ = 2.0, after which beta drops off. A modest increase in triangularity does not improve the overall beta limits.

Effect of current profile shape on second region access in high‐beta tokamak plasmas

The effect of current density distribution in tokamak plasmas is examined on the access to the second stability regime of high‐n ballooning modes. The main factor in determining access to the second stability regime is to lower shear sufficiently on each flux surface. This is achieved by broadening the current profile. A general method of finding equilibria with access to the second region of stability is presented. The value of on‐axis safety factor q0 is found not to be a good measure of the type of profile required for second region access.

Magnetohydrodynamic stability studies of supershot plasmas

Slowly growing magnetohydrodynamic (MHD) instabilities are usually detected experimentally in supershot plasmas in the Tokamak Fusion Test Reactor [in Plasma Physics and Controlled Nuclear Fusion Research 1986, Kyoto (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 75] (TFTR). These instabilities, when they occur, result in deterioration of the confinement and limit the attainable β. Using initial profile data from transport analysis of specific high β supershot plasmas, the predictions of the single fluid, linear MHD stability model are studied and compared with the experimental observations. It is shown that, in the highest β plasmas achieved, the pressure gradients in the interior are such that the absence of the 1/1 mode is difficult to reconcile with the single fluid MHD model if the safety factor, q<1. On the assumption that q exceeds unity everywhere, it is found that supershot plasmas are predicted to be unstable or near marginal to small toroidal mode number, pressure‐driven instabi...