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Runaway electrons may be generated in a tokamak during the start up, during normal operation and during a plasma disruption. During a disruption, runaway electrons can be accelerated to high energies, potentially damaging the first wall. To predict the consequences of runaway generation during a disruption, it is necessary to consider resonant interactions of runaways with the bulk plasma. Here we consider the interactions of runaways on low mode number tearing modes. We have developed a fluid runaway electron model for the 3D MHD code M3D-C1 (Jardin et al 2012 J. Comput. Sci. Discovery 6 014002). To benchmark, we have reproduced the MHD linear tearing mode results (with runaway electrons) in a circular cylinder presented in previous analytic studies (Helander et al 2007 Phys. Plasmas 14 104142) and have extended them here with a numerical eigenvalue calculation. We find that the low mode number tearing mode has a rotation caused by the MHD - runaways interaction and the perturbed toroidal current scale length is much smaller with runaways than without and decreases as the runaway speed increases. [ABSTRACT FROM AUTHOR]

A benchmark exercise for the modeling of vertical displacement events (VDEs) is presented and applied to the 3D nonlinear magnetohydrodynamic codes M3D-C1, JOREK, and NIMROD. The simulations are based on a vertically unstable NSTX equilibrium enclosed by an axisymmetric resistive wall with a rectangular cross section. A linear dependence of the linear VDE growth rates on the resistivity of the wall is recovered for sufficiently large wall conductivity and small temperatures in the open field line region. The benchmark results show good agreement between the VDE growth rates obtained from linear NIMROD and M3D-C1 simulations and from the linear phase of axisymmetric nonlinear JOREK, NIMROD, and M3D-C1 simulations. Axisymmetric nonlinear simulations of a full VDE performed with the three codes are compared, and an excellent agreement is found regarding the plasma location and plasma currents, as well as eddy and halo currents in the wall. [ABSTRACT FROM AUTHOR]

H-mode plasma operation of the Korea Superconducting Tokamak Advanced Research (KSTAR) device has been expanded to significantly surpass the ideal MHD no-wall beta limit. Plasmas with high normalized beta, βN, up to 4.3 have been achieved with reduced plasma internal inductance, li, to near 0.7, exceeding the computed n=1 ideal no-wall limit by a factor of 1.6. Pulse lengths at maximum βN were extended to longer pulses by new, more rapid control. The stability of the observed m/n=2/1 tearing mode that limited the achieved high βN is computed by the M3D-C¹ code, and the effect of sheared toroidal rotation to tearing stability is examined. As a method to affect the mode stability in high βN plasmas, the non-resonant alteration of the rotation profile by non-axisymmetric magnetic fields has been used, enabling a study of the underlying neoclassical toroidal viscosity (NTV) physics and stability dependence on rotation. Non-axisymmetric field spectra were applied using in-vessel control coils (IVCCs) with varied n=2 field configurations to alter the plasma toroidal rotation profile in high beta H-mode plasmas and to analyze their effects on the rotation. The rotation profile was significantly altered with rotation reduced by more than 60% without tearing activity or mode locking. To investigate the physical characteristics and scaling of the measured rotation braking by NTV, changes in the rotation profile are analytically examined in steady state. The expected NTV scaling with the square of the normalized applied field perturbation agrees with the measured profile change δB2.1-2.3. The NTV is also found to scale as Ti2.1-2.4, in general agreement with the low collisionality "1/ν" regime scaling of the NTV theory (TNTV-(1/v) ∝Ti 2.5). [ABSTRACT FROM AUTHOR]

The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w). For a low beta plasma without external heating, Δ'(w) can be approximately described by two terms, Δ'ql(w), Δ′A(w) [White et al., Phys. Fluids 20, 800 (1977); Phys. Plasmas 22, 022514 (2015)]. In this work, we present a simple method to calculate the quasilinear stability index Δ′ql rigorously, for poloidal mode number m≥2. Δ′ql is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ'0, w, wlnw, and w 2. Δ′A is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δ′ql and Δ′A is consistent with the more accurate expression calculated perturbatively [Arcis et al., Phys. Plasmas 13, 052305 (2006)]. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. It is also confirmed by the simulation that the Δ′A has to be considered in calculating island saturation. [ABSTRACT FROM AUTHOR]