R. W. Gould

Space Charge Waves in Cylindrical Plasma Columns

When a plasma is of finite transverse cross section, space-charge waves may propagate even in the absence of a drift motion or thermal velocities of the plasma. Some of the properties of these space charge waves have been investigated by regarding the plasma as a dielectric and solving the resulting field equations. The effect of a steady axial magnetic field is considered, but motion of heavy ions and electron temperature effects are neglected. Waves are found to exist at frequencies low compared with the plasma frequency as well as waves with oppositely directed phase and group velocities (backward waves).Many of the features of these waves have been verified experimentally by measuring phase velocity and attenuation of waves along the positive column of a low pressure mercury arc in an axial magnetic field. Measurements of electron density have been made using these waves and the results are compared with those obtained by other methods. An interesting feature of these measurements, of value in plasma diagnostics, is that they can be made with frequencies which are small compared with the plasma frequency.

LONGITUDINAL ION OSCILLATIONS IN A HOT PLASMA

Linearized, longitudinal waves in a hot plasma include, besides the familiar electron plasma oscillations, in which the frequency ω is of order ωp = (4πne2/m)½, also ion plasma oscillations with ω ≈ ωp(m/M)½. The properties of the latter are explored using a Vlasov equation description of the plasma. For equal ion and electron temperatures, Te = Ti, there exists a discrete sequence of ion oscillations, but all are strongly damped, i.e., have ‐Im ω/Re ω ⪞ 0.5, and hence are not likely to be observable. The ratio Im ω/Re ω can be made to approach zero (facilitating detection of the waves) by either increasing Te/Ti or by producing a current flow in the plasma. In the latter case, Im ω can even be made positive (corresponding to growing waves), the current required for this being smaller the larger the value of Te/Ti. This growing wave is just the familiar two‐stream instability which is thus seen to be an unstable ion oscillation. It is also noteworthy that the ion oscillations, which for small k have the p...

Resonance Cones in the Field Pattern of a Radio Frequency Probe in a Warm Anisotropic Plasma

An experimental investigation of the angular field pattern of a small radio frequency probe in a plasma in a magnetic field is described. The field is observed to become very large along a resonance cone whose axis is parallel to the static magnetic field and whose opening angle is observed to vary with incident probe frequency, electron cyclotron frequency, and electron plasma frequency in agreement with simple cold plasma dielectric theory. The use of the resonance cone angle as a diagnostic tool to measure the plasma density in a plasma in a magnetic field is discussed. It is noted that similar cones might be expected near the ion cyclotron frequency. The relationship of these cones to the limiting phase- and group-velocity cones which appear in the theory of plane wave propagation is discussed. The necessity for examining the allowed directions of the group velocity rather than the allowed directions of the phase velocity and customary phase velocity plots when determining whether propagation between two remote points in a plasma is possible, is emphasized. The addition of electron thermal velocities to the theory is examined in the limit of a large static magnetic field. The resonance cone angle is shifted to a slightly smaller angle than that predicted by cold plasma theory, and a fine structure appears inside the cones and is shown to result from an interference between a fast electromagnetic wave and a slow plasma wave. The interference structure is observed experimentally, and measurements of the angular interference spacing are shown to agree with the warm plasma theory.

RESONANCE OSCILLATIONS IN A HOT NONUNIFORM PLASMA

A quantitative theory of resonance oscillations, such as observed by Dattner and others, is given. The first two moments of the collisionless Boltzmann equation assuming a scalar pressure are used in conjunction with a physically reasonable radial electron density profile to describe the oscillations of a hot nonuniform plasma cylinder. These equations coupled with Maxwells equations assuming a scalar potential are solved numerically to yield the frequency spectrum of the plasma wave resonances. It is found that the frequency spectrum depends on the parameter r/w2/ where rw is the radius of the plasma column and is the mean square Debye length of the electron plasma. New experimental observations of dipole and quadrupole spectra for two plasma columns of differing radii are reported and the results of these observations are in good agreement with the theory. The physical mechanism of the resonances is described.

Temperature fluctuations and heat transport in the edge regions of a tokamak

Electron temperature fluctuations have been investigated in the edge region of the Caltech research tokamak [S. J. Zweben and R. W. Gould, Nucl. Fusion 25, 171 (1985)], and an upper limit to this fluctuation level was found at Te/Te <~ 15%. This measurement, together with previous measurements of density and electric and magnetic field fluctuations, allows a unique comparison of the heat transport resulting from three basic turbulent mechanisms: (1) heat flux from the particle flux resulting from microscopic density and electric field fluctuations; (2) thermal conduction resulting from microscopic temperature and electric field fluctuations; and (3) thermal conduction resulting from microscopic magnetic field fluctuations. The measurements indicate that, in the edge regions, the electron heat transport caused by the measured turbulence-induced particle flux is comparable to or greater than that caused by the thermal conduction associated with the electron temperature and electric field fluctuations, and is significantly greater than that resulting from the measured magnetic fluctuations. This electron heat loss caused by the plasma turbulence is found to be an important electron energy loss mechanism in the edge regions.

Temporal and Spatial Plasma Wave Echoes

It is shown that, if a longitudinal wave is excited in a collision‐free plasma and Landau‐damps away, and later a second wave is excited and also damps away, then a third wave will spontaneously appear in the plasma. This wave appears long after the first two waves have damped away at a time proportional to the interval between the first two waves, and is in that sense an echo. It is also shown that, if a wave is continuously excited at one point in a plasma and a second wave is continuously excited many Landau damping lengths from the first point, then a third wave will spontaneously appear many Landau damping lengths from the second point. Fundamentally, plasma wave echoes are possible because of the reversible nature of Landau damping. However, small‐angle Coulomb collisions are very effective in destroying the echo.

Edge plasma transport experiments in the Caltech Tokamak

Abstract This paper describes two experiments on edge plasma transport in the Caltech Research Tokamak ( B T = 4 kG , R = 45 cm , a = 15 cm , T( edge ) ≅25 eV , n( edge )~2 × 10 12 cm −3 ). The first aims to understand the mechanism of edge plasma cross-field transport by attempting to measure with Langmuir probes the local E and n and their correlation in order to compute the fluctuation-induced particle flux Λ rad = c · 〈 E pol · n 〉/B T . The second experiment aims at demonstrating control of the plasma-limiter interaction through use of a local divertor coil mounted inside the limiter itself.

Scaling of edge-plasma turbulence in the Caltech tokamak

Edge-plasma turbulence was investigated over a wide range of plasma and field parameters in the Caltech research tokamak. Fluctuation levels and spectra were measured using Langmuir probes in the region r/a = 0.75–1.0. Under almost all conditions the edge plasma was turbulently unstable, with a broadband fluctuation spectrum in the drift-wave range of frequencies f = 10–1000 kHz. A stable state was observed only in the very cold, low-current discharges formed at unusually high neutral filling pressure. Otherwise, the relative fluctuation level as monitored by the ion saturation current J+ was very high, in the range J+/J+ 0.2–0.8, while the fluctuation power spectra were roughly invariant in shape. The relative fluctuation level was always highest near the wall and decreased monotonically toward the plasma centre. The same edge turbulence was observed with or without an outer limiter present. The relative fluctuation level was observed to be independent of the local collisionality over a range of nearly 100. The radial variation of J+/J+ can be related to the radial density scale length Ln by J+/J+ (3–5)ρs/Ln.

Observation of Plasma Wave Echoes

Experimental observation of a new nonlinear plasma phenomenon, the plasma wave echo, is reported. A recent theory predicts that if a longitudinal electron plasma wave is excited at one position in a collisionless plasma and Landau damps away, and a second wave is excited at another position and also damps away, then a third wave (i.e., the echo) will spontaneously appear at a third position. The existence of various echoes, associated with various orders of the perturbation theory, is demonstrated experimentally. The echoes appear at the predicted position in the plasma. The frequency of the echo wave and the dependence of its amplitude on the amplitude of the initial wave are also in agreement with the theory. Experimental data on the saturation of echo amplitude with increasing initial wave amplitude and increasing distance are given. Data are also presented on another new, but related, phenomenon “the sheath echo.”

Optical imaging of edge turbulence in the caltech tokamak

A linear photodiode array is used to image visible-light emission from the edge plasma of the Caltech Tokamak. The patterns of light fluctuation show small-scale broadband structure similar to that previously measured for plasma edge density turbulence. A high correlation is found between these light fluctuations and the fluctuations measured by a nearby Langmuir probe.