S. C. Jardin

Numerical study of tilt stability of prolate field-reversed configurations

Global stability of the field-reversed configuration (FRC) has been investigated numerically using both three-dimensional magnetohydrodynamic and hybrid (fluid electron and δf particle ion) simulations. The stabilizing effects of velocity shear and finite ion Larmor radius (FLR) on the n=1 internal tilt mode in the prolate FRCs have been studied. Sheared rotation is found to reduce the growth rate, however a large rotation rate with Mach number of M≳1 is required in order for significant reduction in the instability growth rate to occur. Kinetic effects associated with large thermal ion orbits have been studied for different kinetic equilibria. The simulations show that there is a reduction in the tilt mode growth rate due to FLR effects, but complete linear stability has not been found, even when the thermal ion gyroradius is comparable to the distance between the field null and the separatrix. The instability existing beyond the FLR theory threshold could be due to the resonant interaction of the wave with ions whose Doppler shifted frequency matches the betatron frequency.

Ideal and resistive edge stability calculations with M3D-C1

Growth rates of edge localized modes for various benchmark equilibria, including a diverted equilibrium, are calculated using the nonideal fluid code M3D-C1. Growth rates calculated by M3D-C1 in the ideal limit are found to agree with those calculated by ideal magnetohydrodynamics codes. The effects of nonuniform density and resistivity profiles are explored, as well as the sensitivity of growth rates to the position of the ideal vacuum-plasma interface. Growth rates of the diverted equilibrium are found to be particularly sensitive to moving this interface inward from the separatrix, but less sensitive to extending the plasma region beyond the separatrix. The resistivity profile within the plasma is found not to affect growth rates significantly; however, growth rates may be greatly reduced by treating the outer region as a resistive plasma instead of an ideal vacuum. Indeed, it is found that for typical scrape-off layer (SOL) temperatures, the resistive SOL model behaves more like an ideal plasma than a...

Numerical study of global stability of oblate field-reversed configurations

Global stability of the oblate (small elongation, E 1 these are the interchange and two co-interchange modes with different polarization. It is shown that the n=1 tilt mode becomes an external mode when E<1, and it can be effectively stabilized by close-fitting conducting shells, even in the small Larmor radii (MHD) regime. The tilt mode stability improves with increasing oblateness, however at sufficiently small elongations the radial shift mode becomes more unstable than the tilt mode. The interchange mode stability is strongly profile dependent, and all n⩾1 interchange modes can be stabilized for a class of pressure profile with separatri...

Global extended magnetohydrodynamic studies of fast magnetic reconnection

Recent experimental and theoretical results have led to two lines of thought regarding the physical processes underlying fast magnetic reconnection. One is based on the traditional Sweet–Parker model but replaces the Spitzer resistivity with an enhanced resistivity caused by electron scattering by ion acoustic turbulence. The other includes the finite gyroradius effects that enter Ohm’s law through the Hall and electron pressure gradient terms. A two-dimensional numerical study, conducted with a new implicit parallel two-fluid code, has helped to clarify the similarities and differences in predictions between these two models. The former yields resistivity-dependent reconnection with a thick, moderate-aspect-ratio current sheet. If the sheet thickness is less than or comparable to the ion skin depth, it is verified that the Hall effect will predominate [Shay et al., Geophys. Res. Lett. 26, 2163 (1999)], producing true fast reconnection with a microscopic current sheet of unit aspect ratio and a distorted ...

Finite element implementation of Braginskii’s gyroviscous stress with application to the gravitational instability

A general coordinate-independent expression for Braginskii’s form of the ion gyroviscosity in the two-dimensional potential field representation is presented, and is implemented in a full two-dimensional, two-fluid extended magnetohydrodynamic (MHD) numerical model. The expression for the gyroviscous force requires no field to be differentiated more than twice, and thus is appropriate for finite elements with first derivatives continuous across element boundaries (C1 finite elements). From the extended MHD model, which includes the full gyroviscous stress, are derived linear dispersion relations of a homogeneous equilibrium and of an inverted-density profile in the presence of gravity. The treatment of the gravitational instability presented here extends previous work on the subject [M. N. Rosenbluth, N. A. Krall, and N. Rostoker, Nucl. Fusion Suppl. 1, 143 (1962); K. V. Roberts and J. B. Taylor, Phys. Rev. Lett. 8, 197 (1962)]. Linear and nonlinear simulations of the gravitational instability are present...

Non-existence of Normal Tokamak Equilibria with Negative Central Current

Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal magnetohydrodynamic equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) cannot exist with negative central current. That proof is extended here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated.

The M3D-C1 Approach to Simulating 3D 2-fluid Magnetohydrodynamics in Magnetic Fusion Experiments

A new approach for solving the 3D MHD equations in a strongly magnetized toroidal plasma is presented which uses high-order 2D finite elements with C1 continuity. The vector fields use a physics-based decomposition. An efficient implicit time advance separates the velocity and field advance. ITAPS (SCOREC) adaptivity software and TOPS solvers are used.

Magnetohydrodynamic modeling of two-dimensional reconnection in the Magnetic Reconnection Experiment

A two-dimensional magnetohydrodynamics (MHD) code is used to investigate the dynamical evolution of driven reconnection in the Magnetic Reconnection Experiment (MRX) [M. Yamada et al., Phys. Plasmas 7, 1781 (2000)]. The initial conditions and dimensionless parameters of the simulation are set to be similar to the experimental values. Many features of the time-evolution of magnetic configurations for both co- and counter-helicity reconnection in MRX are successfully reproduced in the framework of resistive MHD. The resistive MHD model is then augmented by the addition of a “model Hall” term to begin to assess the importance of two-fluid physics in the experiment. The effective decoupling of the ion fluid from the reconnecting magnetic field due to the model Hall term is shown to be important during the early dynamic X-phase of MRX reconnection, while effectively negligible during the late “steady-state” Y-phase, when plasma heating takes place. These results are consistent with the available experimental e...

Multi-region approach to free-boundary three-dimensional tokamak equilibria and resistive wall instabilities

Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.

Numerical Calculations Demonstrating Complete Stabilization of the Ideal Magnetohydrodynamic Resistive Wall Mode by Longitudinal Flow

The cylindrical ideal magnetohydrodynamic (MHD) stability problem, including flow and a resistive wall, is cast in the standard mathematical form, ωA⋅x=B⋅x, without discretizing the vacuum regions surrounding the plasma. This is accomplished by means of a finite element expansion for the plasma perturbations, by coupling the plasma surface perturbations to the resistive wall using a Green’s function approach, and by expanding the unknown vector, x, to include the perturbed current in the resistive wall as an additional degree of freedom. The ideal MHD resistive wall mode (RWM) can be stabilized when the plasma has a uniform equilibrium flow such that the RWM frequency resonates with the plasma’s Doppler-shifted sound continuum modes. The resonance induces a singularity in the parallel component of the plasma perturbations, which must be adequately resolved. Complete stabilization within the ideal MHD model (i.e., without parallel damping being added) is achieved as the grid spacing in the region of the re...