Analytical model of wall forces produced by kink perturbations in tokamaks

Abstract

Analytical model of the electromagnetic forces produced by kink modes on the tokamak wall [H. R. Strauss et al., Phys. Plasmas 17, 082505 (2010)] is revisited. One of the main conclusions of the mentioned paper is that the largest force occurs at cs w % 1, where c is the kink growth rate and s w is the wall penetration time. In the present study, a similar approach is developed under less restrictive assumptions on the plasma and dynamics of perturbation, and a different result is obtained: the force increases with c and must be maximal at cs w ! 1. Additionally, the dependence of its amplitude on the plasma parameters is clarified. All distinctions and their reasons are explained in detail. The analysis is performed in the cylindrical model incorporating a resistive wall treated without traditional thin-wall constraints and covering therefore a full range in cs w . It is applicable to either locked or rotating modes. Estimates of the sideways force are presented and compared with earlier forecasts. V C 2015 AIP Publishing LLC. [http://dx.

General approach to the problem of disruption forces in tokamaks

“…No independent corroboration of the main result of [13] has appeared since then, but only disproving arguments. In [13], an analytical model of the wall force produced by kink modes was proposed to explain the discovered force maximum, but this was contested in [14]. This might be ignored as reflecting the model deficiencies, but there is a severe criticism in [25][26][27], where one of the boundary conditions used in the M3D simulations is directly called unphysical.…”

“…In tokamaks with different wall geometries the effects must be different. The extrapolations to ITER based on the dimensional rescaling suggested by ( 1) and ( 2) or similar expressions in [12][13][14] may be misleading until the relation of the sideways force in the JET to the wall properties is established. With clear physics and strict mathematics behind (11) and ( 12), these equalities can be a reliable basis for such studies.…”

“…When pointed out, the latter seems the most natural. However, equality (7) has never been employed (or even noticed) in the studies devoted to the calculation of the sideways and/or vertical forces on the vacuum vessel [4,5,9,[12][13][14]. With definition (3), extending the integration to infinity, which is allowed because = = j j 0 p w outside of = + i p w, this is a direct consequence of…”

“…To be precise, the 'theory' was an analysis within a cylindrical (single helicity mode) model of a plasma with a circular cross-section and uniform current density. Other analytical attempts have also been based on similarly simplified approaches [13,14].…”

Sideways force due to coupled rotating kink modes in tokamaks

“…of the plasma centroid, and ζ is the toroidal angle; see also equation (11) in [29]. The efficiency of a kink mode as a driver of F X was later evaluated and confirmed in [30][31][32][33][34][35][36], and the Noll's formula (1) was announced [33] to be theoretically justified as the upper estimate of the sideways force. With approx-imate J ITER = 5J IET , B ITER 0 = 2B JET 0 and minor radii b ITER = 2b IET , the scaling F ITER X ≈ 20F JET X from JET to ITER proposed in [33] and mentioned in [15] gives an unacceptable 80 MN for ITER at F JET X = 4 MN reported in [4-6, 9, 15, 29], and therefore attracts attention.…”