Unified Ideal Stability Limits for Advanced Tokamak and Spherical Torus Plasmas

Abstract

Ideal magnetohydrodynamic stability limits of shaped tokamak plasmas with high bootstrap fraction are systematically determined as a function of plasma aspect ratio. For plasmas with and without wall stabilization of external kink modes, the computed limits are well described by distinct and nearly invariant values of a normalized beta parameter utilizing the total magnetic field energy density inside the plasma. Stability limit data from the low aspect ratio National Spherical Torus Experiment is compared to these theoretical limits and indicates that ideal non-rotating plasma no-wall beta limits have been exceeded in regimes with sufficiently high cylindrical safety factor. These results could impact the choice of aspect ratio in future fusion power plants. Introduction -The superconducting advanced tokamak [1, 2] is presently the leading candidate for producing an efficient magnetic fusion reactor. Alternative concepts such as the compact stellarator [3,4] and spherical torus [5][6][7] are also actively being pursued as possible improvements to the advanced tokamak. The advanced tokamak (AT) and spherical torus (ST) reactor concepts have several features in common. In particular, both rely on the neoclassical bootstrap current [8] to sustain nearly all of the plasma current and on stabilization of pressure-driven external kink modes to achieve sufficiently high beta (ratio of plasma kinetic pressure to magnetic pressure) to produce power efficiently. The AT and ST reactor concepts have been independently optimized for various physics and engineering constraints and arrive at notably different plasma aspect ratio and beta. This difference has motivated the present work which seeks to understand how the theoretical ideal magnetohydrodynamic (MHD) stability limits of the AT and ST are linked. More generally, aspect ratio invariants of stability are sought.The first equilibrium regime studied consists of fully self-driven plasmas utilizing a close-fitting conducting wall to stabilize external kink modes. The stability limits of this regime represent the maximum achievable beta for this class of equilibrium at any aspect ratio given the present understanding of the relevant physics. The second regime studied consists of plasmas with a self-driven current fraction of 50% and no conducting wall stabilization of the external kink mode. The stability limits of this regime have largely been experimentally realized in present-day tokamaks [9] but have only recently been realized in relatively new ST experiments. Finally, the no-wall current limit is studied for typical AT and ST configurations. These studies show that the degeneracy

The effects of sheared toroidal rotation on stability limits in tokamak plasmas

“…q min is well above unity) and that the rotation shear is below the threshold for destabilizing a KH mode, as discussed in section 4. To use equation (1) for extrapolation to future devices, an expression for β static N can be taken from scalings with aspect ratio, I p /aB, shaping, pressure peaking, internal inductance and so on, as given in references [19] or [20] for instance. …”

“…At such large sheared rotation velocities, magnetic Kelvin-Helmholtz (KH) instabilities [17] become a concern, as recently observed in a magnetized plasma in the solar corona [18]. In the same way that previous studies have investigated shaping or aspect ratio effects to optimize fusion power plant design [19,20], here we assess the effects of strong rotation on stability limits in tokamak plasmas. In section 2 we provide details of the numerical tools used and the plasma equilibria studied, before describing the effects of rotation on the pressure limit in section 3.…”

Beta-limiting MHD Instabilities in Improved-performance NSTX Spherical Torus Plasmas

“…One of the key results of Reference [22] is the finding that the no-wall stability limit set by ballooning and low-n kink modes is β N ≈ 3.1 ± 0.3 for cylindrical kink safety factor q * ≥ 1.7. The computed limit was found to hold for shaped tokamak plasmas over a wide range of aspect ratios.…”

High beta, Long Pulse, Bootstrap Sustained Scenarios on the National Spherical Torus Experiment (NSTX)

“…Recent theoretical work has shown that β N ∼ 3 describes the no-wall ideal MHD external kink limit for a large range of q * ≡ (1 + κ 2 )πaB t0 /µ 0 I p and aspect ratio, as shown in recent theoretical work [15].…”