C.R. Sovinec

Formation and sustainment of electrostatically driven spheromaks in the resistive magnetohydrodynamic model

The nonlinear time-dependent equations of resistive magnetohydrodynamics are solved in simply connected domains to investigate spheromak formation and sustainment with electrostatic current drive. Spheromak magnetic fields are generated in three-dimensional computations as the nonlinear state resulting from an unstable pinch. Perturbations convert continuously supplied toroidal magnetic flux into poloidal magnetic flux, leading to “flux amplification” of field embedded in the electrodes. Relaxation of the axisymmetric component of the parallel current profile can be substantial, and the final nonlinear state is steady over a wide range of parameters. However, for sufficiently large values of Lundquist number or sufficiently large applied potential, nonsteady final states are observed with periodic relaxation events in some cases. Under most conditions, the saturated configuration exhibits chaotic scattering of the magnetic field lines. Conditions just above the marginal point of pinch instability sustain ...

Compact toroid formation, compression, and acceleration

Research on forming, compressing, and accelerating milligram‐range compact toroids using a meter diameter, two‐stage, puffed gas, magnetic field embedded coaxial plasma gun is described. The compact toroids that are studied are similar to spheromaks, but they are threaded by an inner conductor. This research effort, named marauder (Magnetically Accelerated Ring to Achieve Ultra‐high Directed Energy and Radiation), is not a magnetic confinement fusion program like most spheromak efforts. Rather, the ultimate goal of the present program is to compress toroids to high mass density and magnetic field intensity, and to accelerate the toroids to high speed. There are a variety of applications for compressed, accelerated toroids including fast opening switches, x‐radiation production, radio frequency (rf) compression, as well as charge‐neutral ion beam and inertial confinement fusion studies. Experiments performed to date to form and accelerate toroids have been diagnosed with magnetic probe arrays, laser interf...

Overview of quasi-single helicity experiments in reversed field pinches

We report the results of an experimental and theoretical international project dedicated to the study of quasi-single helicity (QSH) reversed field pinch (RFP) plasmas. The project has involved several RFP devices and numerical codes. It appears that QSH spectra are a robust feature common to all the experiments. Our results expand and reinforce the evidence that the formation of self-organized states with one dominant helical mode (Ohmic SH state) is an approach complementary to that of active control of magnetic turbulence to improve confinement in a steady state RFP.

The NIMROD code: a new approach to numerical plasma physics

NIMROD is a code development project designed to study long-wavelength, low-frequency, nonlinear phenomena in toroidal plasmas with realistic geometry and dynamics. The numerical challenges of solving the fluid equations for a fusion plasma are discussed and our discretization scheme is presented. Simulations of a resistive tearing mode show that time steps much greater than the Alfven time are possible without loss of accuracy. Validation tests of a resistive interchange mode in a shaped equilibrium, a ballooning mode and nonlinear activity in reversed-field pinches are described.

NIMROD: A computational laboratory for studying nonlinear fusion magnetohydrodynamics

Nonlinear numerical studies of macroscopic modes in a variety of magnetic fusion experiments are made possible by the flexible high-order accurate spatial representation and semi-implicit time advance in the NIMROD simulation code [A. H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)]. Simulation of a resistive magnetohydrodynamics mode in a shaped toroidal tokamak equilibrium demonstrates computation with disparate time scales, simulations of discharge 87009 in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] confirm an analytic scaling for the temporal evolution of an ideal mode subject to plasma-β increasing beyond marginality, and a spherical torus simulation demonstrates nonlinear free-boundary capabilities. A comparison of numerical results on magnetic relaxation finds the n=1 mode and flux amplification in spheromaks to be very closely related to the m=1 dynamo modes...

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

Strongly magnetized plasmas are rich in spatial and temporal scales, making a computational approach useful for studying these systems. The most accurate model of a magnetized plasma is based on a kinetic equation that describes the evolution of the distribution function for each species in six-dimensional phase space. High dimensionality renders this approach impractical for computations for long time scales. Fluid models are an approximation to the kinetic model. The reduced dimensionality allows a wider range of spatial and∕or temporal scales to be explored. Computational modeling requires understanding the ordering and closure approximations, the fundamental waves supported by the equations, and the numerical properties of the discretization scheme. Several ordering and closure schemes are reviewed and discussed, as are their normal modes, and algorithms that can be applied to obtain a numerical solution.

Nonlocal closures for plasma fluid simulations

The application of fluid models in studies of transport and macroscopic stability of magnetized, nearly collisionless plasmas requires closure relations that are inherently nonlocal. Such closures address the fact that particles are capable of carrying information over macroscopic parallel scale lengths. In this work, generalized closures that embody Landau, collisional and particle-trapping physics are derived and discussed. A gyro/bounce-averaged drift kinetic equation is solved via an expansion in eigenfunctions of the pitch-angle scattering operator and the resulting system of algebraic equations is solved by integrating along characteristics. The desired closure moments take the form of integral equations involving perturbations in the flow and temperature along magnetic field lines. Implementation of the closures in massively parallel plasma fluid simulation codes is also discussed. This implementation includes the use of a semi-implicit time advance of the fluid equations to stabilize the dominant ...

Conductive electron heat flow along magnetic field lines

In this work, a unified closure for the conductive electron heat flux along magnetic field lines is derived and examined. Both free-streaming and collisional pitch-angle scattering of electrons are present in the drift kinetic equation which is solved using an expansion in pitch-angle eigenfunctions (Legendre polynomials). The closure takes the form of a generic integral operator involving the electron temperature variation along a magnetic field line and the electron speed. Derived for arbitrary collisionality, the heat flux closure may be written in forms resembling previous collisional and collisionless expressions. Electrons with two to three times the thermal speed are shown to carry heat for all collisionalities and thermal electrons make an important contribution to the heat flow in regimes of moderate to low collisionality. As a practical application, the flow of electron heat along a chaotic magnetic field is calculated in order to highlight the nonlocal nature of the closure which allows for heat to flow against local temperature gradients.

Dynamics of the major disruption of a DIII-D plasma

The dynamics of the major disruption of DIII-D discharge 87009 are investigated with the NIMROD code [Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. To explore the time dynamics in a computationally efficient manner, a fixed-boundary equilibrium is used to model the physics of a plasma being heated through an ideal magnetohydrodynamic (MHD) instability threshold. This simulation shows a faster-than-exponential increase in magnetic energy as predicted by analytic theory [Callen et al., Phys. Plasmas 6, 2963 (1999)]. The dynamics of the heat flux loading on the divertor surfaces is explored with an equilibrium that has the plasma beta raised 8.7% above the best equilibrium reconstruction to start above the ideal MHD threshold. The nonlinear evolution of the ideal mode leads to a stochastic magnetic field and parallel heat transport leads to a localization of the heat flux that is deposited on the wall. The structure of the heat flux deposition is dependent upon the magnetic topology that results from th...

Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code

A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1–20). The results use the compressible MHD model and depend on a precise representation of “ideal-like” and “vacuumlike” or “halo” regions within the code. The halo region is modeled by the introduction ...