RESEARCH HIGHLIGHTS IN PLASMA PHYSICS
Roy W. Gould
Keyed to the publication list [ ].
Collaborators in ( ), Ph.D. students in italics.
Beam-type Magnetrons and the Diocotron Effect . First to show that space charge effects in planar magnetron oscillators (M Carcinotrons) reduces the start-oscillation current by analyzing a planar electron beam in crossed electric and magnetic fields interacting with a slow wave circuit so as to form a backward wave oscillator. This analysis included the diocotron instability, known then as the "slipping stream instability" of planar beams. This work was selected for inclusion in its entirety in Hutter's book "Beam and Wave Electronics in Microwave Tubes" (Van Nostrand 1960).
Beam Plasma Interaction [3, 9, 16, 19, 29, 42] (Boyd, Field, Allen, Poeschel). This work resulted in the original definitive experiment which demonstrated spatial growth of a wave on an electron beam traversing a plasma when the frequency of the wave was approximately equal to the electron plasma frequency. Later, the non-linear bunching process, the limit to growth, and the efficiency of conversion of beam energy to wave energy was examined.
Plasma Waveguides [5, 6, 10, 44] (Trivelpiece, Mason). This work, in a definitive experiment with accompanying theory, established the propagation of slow waves in cylindrical plasma colunms. These modes have been much studied and used by others and recently shown to be of importance for relativistic beam microwave devices. Later, it was shown that thin superconducting films also support slow waves and that the associated group delay could be important in practical devices.
Tonks-Dattner Resonances [21, 22, 25, 26] (Parker, Nickel, Vandenplas). The explanation of the Tonks-Dattner resonances as Langmuir waves in a warm inhomogeneous plasma column, propagating between the plasma sheath and the radius where the wave frequency is equal to the local plasma frequency, was first proposed by Gould. A series of careful experiments was performed and compared by numerical solutions of the plasma fluid equations (the latter also included calculations of the plasma radial profile). Excellent agreement confirmed the explanation.
Compressional Alfven Waves  (Swanson, Hertel). This work provided the first experimental demonstration of compressional Alfven waves shortly after torsional Alfven waves were observed by another group. It was also shown that, using the measured impulse response of the plasma, the dispersion of the waves could be obtained on a single shot.
Ion Acoustic Waves [14, 27] (Fried). This work gave the first kinetic treatment of ion acoustic waves and the dependence of Landau damping of ion acoustic waves on T /Ti. It discussed the growth of the ion acoustic instability when there is a drift of electrons relative to ions. It also stimulated the tabulation of the plasma dispersion function and its properties. A second paper discussed the excitation of ion acoustic waves by a grid and the resulting spatial decay.
Cyclotron Echoes [31, 31, 35, 39, 42, 43] (Blum, Bauer, Kegel). This work followed the observation of cyclotron echoes by Hill and Kaplan. Their observations were extended to upper hybrid echoes and the various (nonlinear) physical mechanisms which were responsible for the echoes were explored. This work culminated in a review of the processes involved, a comparison with echoes in other types of systems, and a set of criteria for the occurrence of echoes in various physical systems, including a continuum of microscopically reversible "oscillators" together with some form of non-linearity.
Plasma Wave Echoes [34, 36, 37, 38, 40, 49, 50] (O'Neil, Malmberg, Wharton, Nishikawa). The echo criteria developed in the cyclotron echo work is fulfilled by Landau-damped plasma oscillations (Case-Van Kampen modes are the "oscillators") and a ballistic theory of the plasma wave echo was first worked out. A proposal was then made to Malmberg and Wharton to do the plasma wave echo experiment using the facility which had been used for the Landau damping experiment. After O'Neil and Gould worked out the self-consistent theory, the experiment was planned. It was performed in one week. It dramatically demonstrated the microscopic reversibility of the Vlasov equation, a fact never doubted by the theorists. Echoes were soon confirmed by other groups. Degradation of echoes due to collisions was subsequently studied.
Resonance Cones [46, 47, 51, 53, 54, 58, 59, 64] (Fisher, Singh, Burrell, Levine). Tne resonance cone experiment, motivated by a controversy in the antenna community about the radiation from an idealized dipole in an idealized anisotropic plasma, was the first experimental demonstration that cones really existed and that the cone angle varied with plasma parameters in a relatively simple way. It was found that warm plasma effects gave rise to a fine structure of the cones and this effect was used to determine electron temperature. Resonance cones at lower frequencies were also predicted and later extensively studied by others. Resonance Cones have turned out to be very important for lower hybrid heating and current drive in tokamaks.
Ion Cyclotron Waves in Tokamaks [62, 65, 76] (Hwang, Greene). Following Bob Taylor's pioneering demonstration of the utility of the small tokamak, a decision to build one at Caltech was made. Ion cyclotron waves in tokamaks were the first subject of study because they were important and there was little interest in studying them on the big fusion devices. Toroidal fast wave eigemnodes were found and studied and the input impedance of a loop (strap) antenna was measured. Additionally, ICRF wave packets were observed to propagate around the tokamak and their group velocity was determined. Subsequently ICRF research began on the big devices and it is now considered extremely important for fusion.
Plasma Turbulence [61, 66, 67, 68, 69, 71, 72, 73] (Kubena, Hedemann, McChesney, Zweben, Liewer). As big devices turned to ICRF, fluctuation phenomena in tokamaks appeared interesting and as yet little studied. In the first experiment, edge density fluctuations were found to be very large (20-40%) and they appeared to be due to drift waves. The Rechester-Rosenbluth theory of transport due to magnetic fluctuations was gaining credence so attention was turned to magnetic fluctuation measurements. The first measurements showed very small magnetic fluctuation levels (-.01%), too small to explain the observed transport. Imaging Langmuir probe arrays were developed and used to determine spatial and temporal spectra and correlation lengths, as well as to visualize the plasma turbulence. The spectra of both density and magnetic fluctuations in the edge plasma first measured in the Caltech Tokamak are in general agreement with what is found in big fusion devices today, where fluctuations and transport are now widely studied.
Cyclotron Resonance and Bernstein Modes in Non-neutral Plasmas [78, 79] (LaPointe). As meaningful tokamak research became increasingly difficult to pursue in University scale devices, non-neutral plasmas looked attractive. Despite the beautiful work already done in this field, there had been little work on high frequency waves. Initial observation of the m = 1 cyclotron resonance mode showed that the resonant frequency was downshifted from eB/m by the diocotron frequency and an elementary explanation was given. Bernstein modes with m=2,3,4... were found. These modes were Doppler shifted upward due to plasma rotation and were trapped in the interior of the plasma. They were used to estimate the electron temperature. The m = 1 and m = 2 modes are also seen in spontaneous emission (and absorption) and the measured radiation temperature is consistent with other electron temperature estimates, suggesting that the radiation is thermal in origin.
Mixing, Collisionless Damping, and Echoes in Rotating Fluids [80,82,83] (Pillai, Bachman). Nonneutral plasmas rotate about their axis and behave like inviscid fluids. A small initial density (vorticity) disturbance in the plasma is convected with the fluid and when there is differential rotation, this disturbance becomes increasingly sheared into fine thin filaments (mixing), to the point where the initial disturbance is hardly observable. This gives rise to collisionless damping (similar to Landau damping) which has be observed and studied experimentally. This mixing is reversible, and the application of a second disturbance can give rise to an echo.
Thermal Fluctuations in Non-neutral Plasmas [85,86,87,88,89,90] (Shiga, Anderegg, Driscoll, Danielson, Dubin). Pure electron plasmas in a Penning-Malmberg trap are at (or near) thermal equilibrium. Electrostatic modes of the plasma are thermally excited. By measuring the spectra of the thermal fluctuations which are induced on a nearby electrode, one can determine the plasma temperature.