Ross L. Spencer

Magnetohydrodynamic equilibrium and stability of field‐reversed configurations

Magnetohydrodynamic equilibrium and stability studies of field‐reversed configurations are presented. Experimentally realistic equilibria are calculated numerically for a plasma inside a conducting cylinder. Stability studies indicate that equilibria ranging from elliptical to highly racetrack‐shaped are all unstable to the internal tilting mode.

Review of the Los Alamos FRX-C experiment

The FRX-C device is a large field-reversed theta pinch experiment with linear dimensions twice those of its FRX-A and FRX-B predecessors. It is used to form field-reversed configurations (FRCs), which are high-beta, highly prolate compact toroids. The FRX-C has demonstrated an R/sup 2/ scaling for particle confinement in FRCs, indicating particles are lost by diffusive processes. Particle losses were also observed to dominate the energy balance. When weak quadrupole fields were applied to stabilize the n = 2 rotational mode, FRC lifetimes >300..mu..s were observed. Detailed studies of the FRC equilibrium were performed using multichord and holographic interferometry. Measurements of electron temperature by Thomson scattering showed a flat profile and substantial losses through the electron channel. The loss rate of the internal poloidal flux of the FRC was observed to be anomalous and to scale less strongly with temperature than predicted from classical resistivity.

Two‐dimensional equilibria of field‐reversed configurations in a perfectly conducting cylindrical shell

Two‐dimensional field‐reversed equilibria bounded by a conducting cylinder are computed. The computation is made possible by using a global constraint and by using a computational algorithm that is protective of the initial guess. A pressure profile is used that has sufficient generality to match experimentally produced configurations. It is found that for some choices of separatrix radius and separatrix beta, no equilibria exist. The reasons for loss of equilibrium are discussed and an example of a configuration near loss of equilibrium conditions is given.

Adiabatic compression of elongated field‐reversed configurations

The adiabatic compression of an elongated field‐reversed configuration (FRC) is computed by using a one‐dimensional approximation. The one‐dimensional results are checked against a two‐dimensional equilibrium code. For ratios of FRC separatrix length to separatrix radius greater than about ten, the one‐dimensional results are accurate within 10%. To this accuracy, the adiabatic compression of FRC’s can be described by simple analytic formulas.

Free boundary field‐reversed configuration (FRC) equilibria in a conducting cylinder

Highly elongated field‐reversed configuration (FRC) equilibria are computed in a straight conducting cylinder for the pressure profile p′(ψ) = cH(ψ), where H(x) is the Heaviside function. The equilibria are found by inverting the Grad–Shafranov equation by means of a Green’s function and by solving the resulting nonlinear integral equation. Long equilibria are obtained only for values of the constant c very near a critical value: the equilibria change from 2:1 elongated to infinitely long as c varies by only 0.3%. This criticial value of c is predicted by the average beta condition.

Numerical calculation of axisymmetric non-neutral plasma equilibria

Efficient techniques for computing axisymmetric non‐neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite‐differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one‐half Debye length to achieve the same accuracy.

Damped diocotron quasi-modes of non-neutral plasmas and inviscid fluids

Computations of damped diocotron oscillations (quasi-modes) are described for non-neutral plasmas and inviscid fluids. The numerical method implements a suggestion made by Briggs, Daugherty, and Levy some 25 years ago [Phys. Fluids 13, 421 (1970)] to push the branch line that forms the continuum into the complex ω-plane by solving the mode equation in the complex r-plane. For the special case of power-law density profiles the calculation finds the same quasi-mode frequencies found recently by Corngold [Phys. Plasmas 2, 620 (1995)]. It is found that the feature of the continuum eigenfunctions which indicates the presence of a nearby quasi-mode is continuity of the derivative of the regular part of the eigenfunctions near the singularity. The evolution of Rayleigh modes, found in density profiles with steps, is also studied as the density steps are smoothed.

Experimental and computational equilibria of field-reversed configurations

Experimental measurements on the field‐reversed configurations produced in the FRX‐C device (Plasma Phys. 26, 991 (1984)]are compared to corresponding measurements on numerically computed magnetohydrodynamic equilibria. Good agreement between experiment and theory is obtained for magnetohydrodynamic (MHD) equilibria with separatrix betas of about 0.6. The experimental measurements indicate that the separatrix is more elliptical and that the flux surfaces are distributed more gently in the axial direction than in the equilibria computed previously. A sharp spike in dp/dψ at the separatrix is found to produce computed equilibria similar to those observed experimentally. The effect of end mirrors and toroidal field on equilibrium properties is also discussed.

Neutral-plasma oscillations at zero temperature

Cold plasma theory is used to calculate the response of an ultracold neutral plasma to an applied rf field. The free oscillation of the system has a continuous spectrum and an associated damped quasimode. This quasimode dominates the driven response and is resonant in the tail of the density distribution. Recent experiments used the plasma response to an applied rf field to determine the plasma density in an expanding ultracold plasma. The comparison between experiment and theory indicates that this method accurately determines the expansion velocity and underestimates the initial plasma density by a factor of 3 in weakly collisional plasmas.

SPHEROMAK FORMATION AND OPERATION WITH BACKGROUND FILLING GAS AND A SOLID FLUX CONSERVER IN CTX

Spheromaks with lifetimes of 1 ms are produced in the CTX experiment. This paper describes the diagnostics and measurements on plasmas which, for CTX-produced plasmas, are the hottest and longest-lived discharges using a solid copper flux conserver. These spheromaks are formed using a static hydrogen background gas filling the entire vacuum system before the discharge. The density rapidly decays in 150–300 μs from an initial value of (1–3) × 1014 cm−3 to a steady-state plateau with a value of (1–4) × 1013cm−3,determine d by the pressure of the gas fill. A multi-point Thomson scattering system measures the radial profiles of electron temperature and density. Peak temperatures of over 40 eV are observed, and the average temperature increases in time by Ohmic heating from 15 eV to over 30 eV. Equilibrium models for the magnetic field structure are used to calculate values of peak local beta (8–13%), volume-averaged beta (3–8%), and engineering beta (10–25%). The operation with a filling gas results in a reduction of the impurity radiation power as measured by spectroscopy. Improved vacuum practices, discharge cleaning and the use of the static gas fill have resulted in discharges in which the radiation power loss is not dominating the energy balance late in time. Particle loss and the associated ionization and heating of the neutral particles required to maintain the density plateau appear to be the major energy loss processes in the spheromak.