Henry Strauss

Wall forces produced during ITER disruptions

Nonlinear simulations with the M3D code [W. Park et al., Phys. Plasmas 6, 1796 (1999)] are performed of disruptions produced by large scale magnetohydrodynamic instabilities. The toroidally asymmetric wall forces produced during a disruption are calculated in an ITER [T. Hender et al., Nucl. Fusion 47, S128 (2007)] model. The disruption is produced by a vertical displacement event and a kink mode. Expressions are derived for the wall force, including the sideways force, using a thin conducting wall model. The scaling of wall force with γτw is obtained, where γ is the kink growth rate and τw is the wall penetration time. The largest force occurs with γτw≈1. A theory is developed of the wall force produced by kink modes. The theory is in qualitative agreement with the simulations and Joint European Torus [V. Riccardo et al., Nucl. Fusion 49, 055012 (2009)] experiments. In particular, the theory and simulations give dependence of the sideways on γτw, correlation of sideways force with sideways plasma displac...

Extended MHD simulation of resonant magnetic perturbations

Resonant magnetic perturbations (RMPs) have been found effective in suppressing edge localized modes (ELMs) in the DIII-D experiment (Evans et al 2006 Phys. Plasmas 13 056121, Moyer et al 2005 Phys. Plasmas 12 056119). Simulations with the M3D initial value code indicate that plasma rotation, due to an MHD toroidal rotation or to two-fluid drifts, has an essential effect on the RMP. When the flow is below a threshold, the RMP field can couple to a resistive mode with a helical structure, different from the usual ELM, that amplifies the non-axisymmetric field. The magnetic field becomes stochastic in the outer part of the plasma, causing density and temperature loss. At higher rotation speed, the resistive mode is stabilized and the applied RMP is screened from the plasma, so that the stochastic magnetic layer is thinner and the temperature remains similar to the initial unperturbed state. The rotational flow effects, along with the remnants of the screened RMP, cause a density loss which extends into the plasma core. The two-fluid model contains intrinsic drift motion and axisymmetric toroidal rotation may not be needed to screen the RMP nor stabilize the resistive mode.

3D MHD VDE and disruptions simulations of tokamaks plasmas including some ITER scenarios

Tokamaks vertical displacement events (VDEs) and disruptions simulations in toroidal geometry by means of a single fluid visco-resistive magneto-hydro-dynamic (MHD) model are presented in this paper. The plasma model is completed with the presence of a 2D wall with finite resistivity which allows the study of the relatively slowly growing magnetic perturbation, the resistive wall mode (RWM), which is, in this paper, the main drive of the disruption evolution. Amplitudes and asymmetries of the halo currents pattern at the wall are also calculated and comparisons with tokamak experimental databases and predictions for ITER are given.

Tokamak toroidal rotation caused by AVDEs and ELMs

Toroidal rotation can be produced by disruptions, as observed in several experiments. There is a concern that rotating asymmetric forces during an ITER disruption might resonate with the blanket and other structures surrounding the plasma. Here it is shown, both computationally using the M3D code, and analytically, that toroidal rotation is produced by magnetohydrodynamic turbulence. In particular, rotation is produced during an asymmetric vertical displacement event (AVDE) disruption. Toroidal and poloidal rotation are also produced during edge localized modes (ELMs), and may be consistent with a scaling law found for intrinsic toroidal rotation in H-mode tokamaks.

MHD simulations with resistive wall and magnetic separatrix

Abstract A number of problems in resistive MHD magnetic fusion simulations describe plasmas with three regions: the core, the halo region, and the resistive boundary. Treating these problems requires maintenance of an adequate resistivity contrast between the core and halo. This can be helped by the presence of a magnetic separatrix, which in any case is required for reasons of realistic modeling. An appropriate mesh generation capability is also needed to include the halo region when a separatrix is present. Finally a resistive wall boundary condition is required, to allow both two dimensional and three dimensional magnetic perturbations to penetrate the wall. Preliminary work is presented on halo current simulations in ITER. The first step is the study of VDE (vertical displacement event) instabilities. The growth rate is consistent with scaling inversely proportional to the resistive wall penetration time. The simulations have resistivity proportional to the −3/2 power of the temperature. Simulations have been done with resistivity contrast between the plasma core and wall of 1000 times, to model the vacuum region between the core and resistive shell. Some 3D simulations are shown of disruptions competing with VDEs. Toroidal peaking factors are up to about 3.

Response to 'Comment on 'Wall forces produced during ITER disruptions'' [Phys. Plasmas 17, 124703 (2010)]

We offer a response to the claims of L. E. Zakharov.We offer a response to the claims of L. E. Zakharov.

Global Hybrid Simulations of Energetic Particle-driven Modes in Toroidal Plasmas

Global hybrid simulations of energetic particle-driven MHD modes have been carried out for tokamaks and spherical tokamaks using the hybrid code M3D. The numerical results for the National Spherical Tokamak Experiments (NSTX) show that Toroidal Alfven Eigenmodes are excited by beam ions with their frequencies consistent with the experimental observations. Nonlinear simulations indicate that the n=2 mode frequency chirps down as the mode moves out radially. For ITER, it is shown that the alpha-particle effects are strongly stabilizing for internal kink mode when central safety factor q(0) is sufficiently close to unity. However, the elongation of ITER plasma shape reduces the stabilization significantly.

An efficient method for solving elliptic boundary element problems with application to the tokamak vacuum problem

Abstract A method for regularizing ill-posed Neumann Poisson-type problems based on applying operator transformations is presented. This method can be implemented in the context of the finite element method to compute the solution to inhomogeneous Neumann boundary conditions; it allows to overcome cases where the Neumann problem otherwise admits an infinite number of solutions. As a test application, we solve the Grad–Shafranov boundary problem in a toroidally symmetric geometry. Solving the regularized Neumann response problem is found to be several orders of magnitudes more efficient than solving the Dirichlet problem, which makes the approach competitive with the boundary element method without the need to derive a Green function. In the context of the boundary element method, the operator transformation technique can also be applied to obtain the response of the Grad–Shafranov equation from the toroidal Laplace n = 1 response matrix using a simple matrix transformation.

Plasmas beyond MHD: two-fluids and symmetry breaking

Extended MHD effects are important in the nonlinear behavior of magnetically confined plasmas, even at the simplest level represented by the self-consistent diamagnetic (B × ∇p) drifts. Allowing the electrons and ions to move independently, even as fluids, breaks certain geometrical symmetries preserved by the MHD equations that can be important for toroidal fusion burning plasmas. These symmetries are also broken by certain experimental designs and high temperature plasma conditions. Results are shown from the two-fluid and hybrid particle/fluid models in the M3D MPP code, part of the SciDAC CEMM (Center for Extended Magnetohydrodynamic Modeling) project.

Nonlinear Simulation Studies of Tokamaks and STs

The multilevel physics, massively parallel plasma simulation code, M3D, has been used to study spherical tori (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX [National Spherical Torus Experiment] under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-beta disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g., through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion-driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.