Plasma stability theory including the resistive wall effects

Abstract

Plasma stabilization due to a nearby conducting wall can provide access to better performance in some scenarios in tokamaks. This was proved by experiments with an essential gain in${\it\beta}$and demonstrated as a long-lasting effect at sufficiently fast plasma rotation in the DIII-D tokamak (see, for example, Straitet al.,Nucl. Fusion, vol. 43, 2003, pp. 430–440). The rotational stabilization is the central topic of this review, though eventually the mode rotation gains significance. The analysis is based on the first-principle equations describing the energy balance with dissipation in the resistive wall. The method emphasizes derivation of the dispersion relations for the modes which are faster than the conventional resistive wall modes, but slower than the ideal magnetohydrodynamics modes. Both the standard thin wall and ideal-wall approximations are not valid in this range. Here, these are replaced by an approach incorporating the skin effect in the wall. This new element in the stability theory makes the energy sink a nonlinear function of the complex growth rate. An important consequence is that a mode rotating above a critical level can provide a damping effect sufficient for instability suppression. Estimates are given and applications are discussed.

Analysis of Electromagnetic Loads on the Vacuum Vessel during Thermal Quench in the TRT Tokamak

“…The force of 73.8 MN, obtained after multiplying this value by nine to get an estimate for ITER, differs from the force of 70 MN calculated in [22] by less than 5.5%. This confirms that simple scaling (9) with can be used for extrapolations even without taking into account the changes in the inductance .…”

“…In this approximation, the total plasma volume is and , therefore, for the TQ proceeding at the constant current J, Eq. ( 7) can be reduced to (9) In Eqs. ( 7) and ( 9), the force is the sum of two forces: (10) where two terms correspond to the following partition:…”

“…It is assumed that after the TQ, the temperature drops to 10 eV with uniform distribution over the radius, while the density and its profile do not change. On the considered time axis, the TQ starts at 0.6 ms and lasts for 0.1 ms. For comparison, the response time of the TRT wall, which is usually estimated [8,9] as (6) ( is the wall minor radius), is approximately 60 ms, which is 600 times longer that the given TQ duration. The vacuum vessel wall should respond to the changes in the magnetic field caused by such a TQ as an ideal conductor.…”

“…In fact, the beta values are at the level of a few percent (less than 3% in the TRT project), but they are called high because of dangerous vicinity to the limits, exceeding which results in the development of instabilities. The stability problems still remain critical for the toroidal systems [6][7][8][9][10], although the considerable progress has been achieved in tokamak studies [6,7,[11][12][13][14][15][16]. However, with increasing scales of experiments, new problems arise, because the instabilitygenerated releases of heat and magnetic energy result in damage of the wall and in-vessel elements.…”

Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER highQscenarios

“…The growth rate of the mode increases with increasing wall resistivity, i.e. in this case the instability can also be identified as a resistive wall mode [30]. The resistive wall is more important in this particular case because the initial equilibrium is ideal MHD stable in the presence of a ideally conducting wall.…”