Adil B. Hassam

The centrifugal mirror confinement scheme incorporates supersonic rotation of a plasma into a magnetic mirror device. This concept has been shown experimentally to drastically decrease parallel losses and increase plasma stability as compared with prior axisymmetric mirrors. MCTrans++ is a dimensionless (0-D) scoping tool which rapidly models experimental operating points in the Centrifugal Mirror Fusion Experiment (CMFX) at the University of Maryland. In the low-collisionality regime, parallel losses can be modelled analytically. A confining potential is set up that is partially ambipolar and partially centrifugal. Due to the stabilizing effects of flow shear, the perpendicular losses can be modelled as classical. Radiation losses such as bremsstrahlung and cyclotron emission are taken into account. A neutrals model is included, and, in some circumstances, charge-exchange losses are found to exceed all other loss mechanisms. We use the SUNDIALS ARKODE library to solve the underlying equations of this model; the resulting software is suitable for scanning large parameter spaces, and can also be used to model time-dependent phenomena such as a capacitive discharge. MCTrans++ has been used to verify results from prior centrifugal mirrors, create an experimental plan for CMFX and find configurations for future reactor-scale fusion devices.

Thermal electron Bernstein emission has been observed at the second harmonic of the electron cyclotron frequency at the mid-plane of the Maryland Centrifugal eXperiment. The emission is received in the X-mode polarization and coupled to the Bernstein wave by the B-X mode conversion process. The average B-X coupling efficiency is approximately 20%. The observed emission indicates thermal electron temperatures an excess of 100 eV in the core of the rotating plasma. The measured electron temperature is consistent with recent ion temperature measurements and indicates that the total energy confinement time exceeds 500 μs.

Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.

Toroidal magnetohydrodynamic (MHD) simulations demonstrate that sheared poloidal flows in tokamaks can be generated by the resonant excitation of the geodesic acoustic mode (GAM). Poloidal flows are generated by two resonant excitation methods: oscillating currents in an external coil and an oscillating heat source. The coil current and the heat source oscillate in time at the local GAM frequency. The sheared poloidal flow generated by the excitation of the GAM may be useful for the suppression of plasma instabilities.

The stabilizing effect of velocity shear on the macroscopic, broad bandwidth, ideal interchange instability is studied in linear and nonlinear regimes. A 2D dissipative magnetohydrodynamic (MHD) code is employed to simulate the system. For a given flow shear, V′, linear growth rates are shown to be suppressed to below the shear-free level at both the small and large wavelengths. With increasing V′, the unstable band in wavenumber-space shrinks so that the peak growth results for modes that correspond to relatively high wavenumbers, on the scale of the density gradient. In the nonlinear turbulent steady state, a similar turbulent spectrum obtains, and the convection cells are roughly circular. In addition, the density fluctuation level and the degree of flattening of the initial inverted density profile are found to decrease as V′ increases; in fact, unstable modes are almost completely stabilized and the density profile reverts to laminar when V′ is a few times the classic interchange growth rate. Moreover, the turbulent particle flux diminishes with increasing velocity shear such that all the flux is carried by the classical diffusive flux in the asymptotic limit. The simulations are compared with measurements of magnetic fluctuations from the Maryland Centrifugal Experiment, MCX, which investigated interchange modes in the presence of velocity shear. The experimental spectral data, taken in the plasma edge, are in general agreement with the numerical data obtained in higher viscosity simulations for which the level of viscosity is chosen consistent with MCX Reynolds numbers at the edge. In particular, the residual turbulence in both cases is dominated by elongated convection cells. Finally, concomitant Kelvin-Helmholtz instabilities in the system are also examined. Complete stability to interchanges is obtained only in the parameter space wherein the generalized Rayleigh inflexion theorem is satisfied.

A drift instability of a collisional magnetized plasma, unstable due to the Braginskii thermal force but not requiring any direct dissipation such as resistivity or electron inertia, is examined. Unlike conventional drift-modes, the maximum growth rate of the thermal force drift wave (TFDW) is of order the drift frequency, making for a strongly turbulent nonlinear state. A 3D, magnetized two-fluid code is developed to allow the study of both ideal MHD modes as well as lower frequency drift modes. The governing equations are essentially the ideal MHD equations with the inclusion of Hall and thermal force terms in Ohm’s law. This set of equations is reduced in a finite β, long parallel wavelength, and small but significant Larmor radius ordering and tested for shear Alfven waves, parallel sound waves, and drift modes. The code is employed to recover the TFDW instability, to verify the code against the mode’s analytic linear characteristics, and to study the nonlinear behavior of the TFDW. The TFDW growth is strongly suppressed by parallel thermal conduction and thus this mode is more likely to be observed in low temperature plasmas.

The Maryland Centrifugal Experiment (MCX) Project has investigated the concepts of centrifugal plasma confinement and stabilization of instabilities by velocity shear. The basic requirement is supersonic plasma rotation about a shaped, open magnetic field. Overall, the MCX Project attained three primary goals that were set out at the start of the project. First, supersonic rotation at Mach number up to 2.5 was obtained. Second, turbulence from flute interchange modes was found considerably reduced from conventional. Third, plasma pressure was contained along the field, as evidenced by density drops of x10 from the center to the mirror throats.

The stability of the ideal magnetohydrodynamic (MHD) interchange mode at marginal conditions is studied. A sufficiently strong constant magnetic field component transverse to the direction of mode symmetry provides the marginality conditions. A systematic perturbation analysis in the smallness parameter, |b₂/B_c|^1/2, is carried out, where B_c is the critical transverse magnetic field for the zero-frequency ideal mode and b₂ is the deviation from B_c. The calculation is carried out to third order including nonlinear terms. It is shown that the system is nonlinearly unstable in the short wavelength limit, i.e., a large enough perturbation results in instability even if b₂/B_c > 0 (linearly stable). The normalized amplitude for instability is shown to scale as |b₂/B_c|^1/2. A nonlinear, compressible, MHD simulation is done to check the analytic result. Good agreement is found, including the critical amplitude scaling.