John B. McBride

Theory and Simulation of Turbulent Heating by the Modified Two-Stream Instability.

Results of an analytical and numerical study of the nonresonant, modified plasma two‐stream instability, which is driven by relative streaming of electrons and ions across a magnetic field B0 are presented. The instability has characteristic frequency and growth rate comparable to the lower‐hybrid frequency. The linear theory is discussed both in the electrostatic and fully electromagnetic cases, and a detailed numerical study of the dependence of the unstable roots of the dispersion relation for a wide range of plasma parameters is presented. The nonlinear theory includes discussions of (1) quasilinear theory, (2) trapping, which is responsible for nonlinear stabilization, (3) a derivation of a fully nonlinear scaling law which shows how results scale with electron‐ion mass ratio, and (4) the effect of cross‐field vortex‐like motion caused by turbulence induced E × B drifts. One‐and two‐dimensional computer simulations with dense k‐space spectra are presented in support of this theory. The simulations sh...

Theory and Simulation of the Beam Cyclotron Instability

A detailed theory in conjunction with the results of computer simulation experiments is presented for the beam cyclotron instability. The main results are (1) After a period of exponential quasilinear development, turbulent wave‐particle interactions cause cross‐field diffusion of the electrons which smears out the electron gyroresonances. This occurs at a level of turbulence which scales as Σκ(| Eκ |2/4πN0Te)∼(Ωe/ωe)2(Ωe/kve), where Ωe and ωe are the electron cyclotron and plasma frequencies, and results in a transition to ordinary ion sound modes that would occur in an unmagnetized plasma. The magnetic field serves to reduce the effects of electron trapping. (2) This level of turbulence appears to have virtually no effect on long wavelength fluid modes. (3) At this level the instability stabilizes if ordinary ion sound is stable due to ion Landau damping. For cold ions it continues to develop at the slower ion acoustic growth rate until the fields become strong enough to trap the ions. After the fields ...

Electromagnetic and finite βe effects on the modified two stream instability

Abstract Electromagnetic effects are found to stabilize the modified two stream instability under certain given conditions. The importance of this result to several classes of experiments is discussed.

Radio frequency stabilization of electrostatic interchange modes

It is shown theoretically that long‐wavelength, rf fields in the ion cyclotron frequency range can stabilize low‐frequency, electrostatic interchange modes. Stabilization does not require specified gradients in the spatial distribution of rf energy. This offers an appealing alternative to ponderomotive stabilization of curvature driven modes, and may help explain recent observations on the Phaedrus tandem mirror experiment.

Low‐frequency parametric instabilities of magnetized plasmas with two ion species

A theoretical and computer simulation treatment is presented of the response of magnetized plasmas with two ion species to low‐frequency, electric fields oscillating at ω0 near the lower‐hybrid frequency ωlh that shows the existence of parametric instabilities. A new decay instability involving the Buchsbaum two ion resonance occurs for ω0>ωlh, and a purely growing instability occurs for ω0<ωlh. The analysis is valid even when the masses of the ion components are comparable and applies, for example, to deuterium‐tritium plasmas. Computer simulation experiments demonstrate the potential importance of these instabilities as ion heating mechanisms.

Anomalous Resistance due to Cross‐Field Electron‐Ion Streaming Instabilities

New computer simulations show that the nonlinear stage of the beam cyclotron instability is stabilized if Ti/Te≳υd/υe, similar to ion sound, as has been predicted theoretically. In this case, the instability makes no significant contribution to anomalous resistance, for the conditions of typical laboratory resistive shocks. In the opposite case, a theoretical study of the later development shows that after the onset of ion trapping, both wave energy and electron temperature grow linearly with time, and the anomalous electron‐ion collision frequency becomes constant at ∼0.02 times the electron plasma frequency. These conclusions are supported by simulation studies.

Microwave heating of the ELMO Bumpy Torus relativistic electron ring

A model for microwave heating of electron rings in the ELMO Bumpy Torus configuration is analyzed using a relativistically correct quasi‐linear formulation. The spatial locations of heating by the different electron‐cyclotron harmonics are calculated. The steady‐state ring energy and the microwave power required to sustain the rings are determined by balancing the line‐averaged heating rate against classical collisional and radiative energy loss processes. Although ring formation is generally attributed to the second harmonic electron‐cyclotron resonance, the calculations show that fundamental heating also plays a critical role in ring start‐up and steady state. The model predicts ring power requirements for EBT which are consistent with previous estimates.

THEORY OF TURBULENT PLASMA HEATING BY ANOMALOUS ABSORPTION OF MAGNETOSONIC WAVES.

Theory and computer simulation experiments have shown the potential importance of the fluid-like, modified two-stream instability as an ion heating mechanism in low-β plasmas. To take advantage of the strong ion heating which it can produce, we consider inducing the instability with large-amplitude waves in order to convert the energy in the wave fields into ion thermal energy. Since the instability is driven by relative electron-ion drifts across a magnetic field 0, and has a frequency comparable to the lower hybrid frequency ωLH, a natural choice for the driver wave is a magnetosonic wave which propagates across 0 near the Alfven speed. As a specific example, we demonstrate that for the parameters of the Princeton ST-Tokamak it is theoretically possible to achieve thermonuclear temperatures by anomalously absorbing these waves via the modified two-stream instability.

On the theory of the beam cyclotron instability in plasmas

Abstract Important new aspects of the linear theory of the beam cyclotron instability in a magnetized plasma are discussed.

Persistence of magnetohydrodynamic stability in field reversed pinches against microinstability

The question of the persistance of magnetohydrodynamic stable profiles in reversed field Z pinches is addresses, considering the probability of enhanced transport due to various microinstabilities. It is found that Suydam’s criterion for magnetohydrodynamic stability usually requires sufficient magnetic shear to prevent microinstabilities throughout most of the radial profiles.