Richard A. Nebel

Three-dimensional magnetohydrodynamic studies of the reversed-field pinch

Three‐dimensional computational studies of nonlinear resistive megnetohydrodynamic (MHD) instabilities in the reversed‐field pinch are presented. It is found that multihelicity mode coupling effects alter the evolution of m=1 modes from that obtained in single helicity. Strong mode coupling to m=0 and m=2 is observed. Magnetic island overlap results in stochastic field lines. At low values of the pinch parameter this is confined to the central region of the pinch; for larger values the stochasticity may extend to the wall. Healing of outer flux surfaces is observed as modes peak and relax. Decay of positive toroidal flux is retarded. Impact on confinement is discussed, and connection is made with experimental observations.

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.

Global confinement and discrete dynamo activity in the MST reversed field pinch

Results obtained on the Madison Symmetric Torus (MST) reversed‐field pinch [Fusion Technol. 19, 131 (1991)] after installation of the design poloidal field winding are presented. Values of βθe0≡2μ0ne0Te0/B2θ(a)∼12% are achieved in low‐current (I=220 kA) operation; here, ne0 and Te0 are central electron density and temperature, and Bθ(a) is the poloidal magnetic field at the plasma edge. An observed decrease in βθe0 with increasing plasma current may be due to inadequate fueling, enhanced wall interaction, and the growth of a radial field error at the vertical cut in the shell at high current. Energy confinement time varies little with plasma current, lying in the range of 0.5–1.0 msec. Strong discrete dynamo activity is present, characterized by the coupling of m=1, n=5–7 modes leading to an m=0, n=0 crash (m and n are poloidal and toroidal mode numbers). The m=0 crash generates toroidal flux and produces a small (2.5%) increase in plasma current.

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.

Compressibility as a feature of field reversal maintenance in the reversed‐field pinch

Five different codes have been used to simulate the identical problem in reversed‐field pinch (RFP) dynamics using the resistive magnetohydrodynamic (MHD) model in three dimensions with the same set of initial and boundary conditions. Three codes are compressible, while two are incompressible. The assumption of incompressibility was made in the spirit of reducing the model so that, for example, the codes would run faster while retaining the relevant physics. The results show that the three compressible codes agree quite well with each other and the two incompressible codes agree with each other also, but the compressible and incompressible models show qualitatively different behavior. Most importantly, for a certain set of boundary and initial conditions, the compressible codes predict field reversal maintenance while the incompressible codes do not. Thus compressibility is an important feature of RFP physics. This is in contrast to tokamak physics where the strong toroidal field enforces incompressibility at low poloidal beta.

Inertial‐Electrostatic Confinement Neutron/Proton Source

There is considerable demand in the scientific community for a neutron generator with an output of 106–108 neutrons/second (n/s) that can be switched on or off, emit fusion neutrons, be self‐calibrating, and offer portable operation. An Inertial Electrostatic Confinement (IEC)‐based neutron generator is proposed to meet these needs.In an IEC device, ion beams are injected into a spherical vacuum vessel containing one or more sets of spherical wire grids. A high fusion rate is generated in a dense plasma region created in the center of the innermost grid by intersecting ion beams and the associated potential well structure. Here, we describe a unique configuration, termed the IECGD, where a gaseous discharge in a single‐gridded device serves as the ion source. Operation in the newly discovered “Star” discharge mode maximizes the effective grid transmission factor for ions. This configuration, then, provides a simple, rugged, low‐cost fusion neutron source, operating in the 106 D‐D n/s or 108 D‐T n/s range....

The role of m=0 modal components in the reversed-field-pinch dynamo effect in the single fluid magnetohydrodynamics model

The role of the m=0 modal components on the reversed‐field‐pinch (RFP) dynamo effect is examined in the single fluid magnetohydrodynamic (MHD) model by comparing results with and without various nonlinear convolutions of the m=0 spectrum. Results indicate that the dynamo effect comes directly from the m=1 instabilities and the effect of other nonlinear convolutions is small. Scaling studies of δB/B with the Lundquist number (S) are also performed. It is found that δB/B is independent of S (diffusionlike scaling), which is consistent with the view that the dynamo effect arises directly from the m=1 modes.

Stable, thermal equilibrium, large-amplitude, spherical plasma oscillations in electrostatic confinement devices

The problem of large-amplitude spherical oscillations of an ion cloud in an Inertial Electrostatic Confinement (IEC) device is examined. It is shown that ion fluctuations of a Gaussian profile in a spherical, harmonic well are stable to all hydrodynamic modes, and stable oscillations about the oscillating equilibrium state may be damped by continuum damping. It is also shown that the ion state forms a thermal equilibrium, in spite of the orders of magnitude, density, and temperature changes during the oscillation cycle. Finally, a brief discussion of how to experimentally realize the required electron distributions for these oscillations is presented.

The periodically oscillating plasma sphere

A new method of operating an inertial electrostatic confinement (IEC) device is proposed, and its performance is evaluated. The scheme involved an oscillating thermal cloud of ions immersed in a bath of electrons that form a harmonic oscillator potential. The scheme is called the periodically oscillating plasma sphere, and it appears to solve many of the problems that may limit other IEC systems to low gain. A set of self-similar solutions to the ion fluid equations is presented, and plasma performance is evaluated. Results indicate that performance enhancement of gridded IEC systems such as the Los Alamos intense neutron source device is possible as well as high-performance operation for low-loss systems such as the Penning trap experiment. Finally, a conceptual idea for a massively modular Penning trap reactor is also presented.

Production and application of dense Penning trap plasmas

A new paradigm for producing well‐confined, dense‐thermonuclear plasmas is described. The convergence of a radial beam distribution of a Penning‐trap‐confined plasma produces a dense inertially confined non‐neutral plasma. The equilibrium, stability, classical transport, and particle‐handling properties of such a concept are developed. The application of this approach to controlled fusion using a pure electron plasma to form a central virtual cathode in which ions are electrostatically confined is discussed. On one hand, extreme plasma control is required, placing the major uncertainty on issues of machine precision. On the other hand, development is characterized by the manufacture and testing of extremely small and inexpensive systems. Thus, it would seem that a timely experimental test of this concept would be ineluctable. Success at such experiments might indicate an alternate path to practical fusion applications.