Dalton D. Schnack

Magnetohydrodynamics of plasma relaxation

What is relaxation, and why is it important? connection to dynamo theory theoretical framework experimental observations - laboratory systems astrophysical systems characteristic phenomena observed in magnetically confined plasmas Taylor relaxation theory - the minimization procedure applicability of the invariants comparison with observations nonlinear MHD description - numerical simulation the basic dynamo mechanism helical ohmic state MHD fluctuations nonlinear mode coupling nonideal boundaries magnetic helicity balance sawtooth oscillations finite plasma pressure effects effects of relaxation on plasma heating and transports - transport in stochastic magnetic fields topological dissipation ion healing critique - discussion of MHD results limitations of the MHD model outstanding issues.

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.

Calculating electron cyclotron current drive stabilization of resistive tearing modes in a nonlinear magnetohydrodynamic model

A model which incorporates the effects of electron cyclotron current drive (ECCD) into the magnetohydrodynamic equations is implemented in the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)] and used to investigate the effect of ECCD injection on the stability, growth, and dynamical behavior of magnetic islands associated with resistive tearing modes. In addition to qualitatively and quantitatively agreeing with numerical results obtained from the inclusion of localized ECCD deposition in static equilibrium solvers [A. Pletzer and F. W. Perkins, Phys. Plasmas 6, 1589 (1999)], predictions from the model further elaborate the role which rational surface motion plays in these results. The complete suppression of the (2,1) resistive tearing mode by ECCD is demonstrated and the relevant stabilization mechanism is determined. Consequences of the shifting of the mode rational surface in response to the injected current are explored, and the characteristic short-time responses of resistive te...

SATURATION OF MAGNETOROTATIONAL INSTABILITY THROUGH MAGNETIC FIELD GENERATION

The saturation mechanism of magnetorotational instability (MRI) is examined through analytical quasi-linear theory and through nonlinear computation of a single mode in a rotating disk. We find that large-scale magnetic field is generated through the α-effect (the correlated product of velocity and magnetic field fluctuations) and causes the MRI mode to saturate. If the large-scale plasma flow is allowed to evolve, the mode can also saturate through its flow relaxation. In astrophysical plasmas, for which the flow cannot relax because of gravitational constraints, the mode saturates through field generation only.

Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics

Relaxed states of a plasma column are found analytically in single-fluid and Hall magnetohydrodynamics (MHD). We perform complete minimization of the energy with constraints imposed by invariants inherent in the corresponding models. It is shown that the relaxed state in Hall MHD is a force-free magnetic field with uniform axial flow and/or rigid azimuthal rotation. In contrast, the relaxed states in single-fluid MHD are more complex due to the coupling between velocity and magnetic field. Cylindrically and helically symmetric relaxed states are considered for both models. Helical states may be time dependent and analogous to helical waves, propagating on a cylindrically symmetric background. Application of our results to reversed-field pinches (RFP) is discussed. The radial profile of the parallel momentum predicted by the single-fluid MHD relaxation theory is shown to be in reasonable agreement with experimental observation from the Madison symmetric torus RFP experiment.

Numerical simulation of laminar plasma dynamos in a cylindrical von Kármán flow

The results of a numerical study of the magnetic dynamo effect in cylindrical von Karman plasma flow are presented with parameters relevant to the Madison Plasma Couette Experiment. This experiment is designed to investigate a broad class of phenomena in flowing plasmas. In a plasma, the magnetic Prandtl number Pm can be of order unity (i.e., the fluid Reynolds number Re is comparable to the magnetic Reynolds number Rm). This is in contrast to liquid metal experiments, where Pm is small (so, Re⪢Rm) and the flows are always turbulent. We explore dynamo action through simulations using the extended magnetohydrodynamic NIMROD code for an isothermal and compressible plasma model. We also study two-fluid effects in simulations by including the Hall term in Ohm’s law. We find that the counter-rotating von Karman flow results in sustained dynamo action and the self-generation of magnetic field when the magnetic Reynolds number exceeds a critical value. For the plasma parameters of the experiment, this field satu...

Magnetohydrodynamic computation of feedback of resistive shell instabilities in the reversed field pinch

Magnetohydrodynamic computation demonstrates that feedback can sustain reversal and reduce the loop voltage in resistive shell reversed field pinch (RFP) plasmas. Edge feedback on approximately 2R/a tearing modes resonant near the axis is found to restore plasma parameters to nearly their levels obtained with a close fitting conducting shell. When original dynamo modes are stabilized, neighbouring tearing modes grow to maintain the RFP dynamo more efficiently. This suggests that the experimentally observed limits on RFP pulse lengths to the order of the shell time can be overcome by applying feedback to a few helical modes