C. F. Driscoll

Inviscid damping of asymmetries on a two-dimensional vortex

The inviscid damping of an asymmetric perturbation on a two-dimensional circular vortex is examined theoretically, and with an electron plasma experiment. In the experiment, an elliptical perturbation is created by an external impulse. After the impulse, the ellipticity (quadrupole moment) of the vortex exhibits an early stage of exponential decay. The measured decay rate is in good agreement with theory, in which the perturbation is governed by the linearized Euler equations. Often, the exponential decay of ellipticity is slow compared to a vortex rotation period, due to the excitation of a quasimode. A quasimode is a vorticity perturbation that behaves like a single azimuthally propagating wave, which is weakly damped by a resonant interaction with corotating fluid. Analytically, the quasimode appears as a wave packet of undamped continuum modes, with a sharply peaked frequency spectrum, and it decays through interference as the modes disperse. When the exponential decay rate of ellipticity is comparabl...

Vortex crystals from 2D Euler flow: Experiment and simulation

Vortex-in-cell simulations that numerically integrate the 2D Euler equations are compared directly to experiments on magnetized electron columns [K. S. Fine, A. C. Cass, W. G. Flynn, and C. F. Driscoll, “Relaxation of 2D turbulence to vortex crystals,” Phys. Rev. Lett. 75, 3277 (1995)], where turbulent flows relax to metastable vortex crystals. A vortex crystal is a lattice of intense small diameter vortices that rotates rigidly in a lower vorticity background. The simulations and experiments relax at the same rates to vortex crystals with similar vorticity distributions. The relaxation is caused by mixing of the background by the intense vortices: the relaxation rate is peaked when the background circulation is 0.2–0.4 times the total circulation. Close quantitative agreement between experiment and simulation provides strong evidence that vortex crystals can be explained without incorporating physics beyond 2D Euler theory, despite small differences between a magnetized electron column and an ideal 2D fluid.

Electron acoustic waves in pure ion plasmas

Standing electron acoustic waves (EAWs) are observed in a pure ion plasma. EAWs are slow nonlinear plasma waves; at small amplitude their phase velocities (vph≃1.4v¯ for small kλD) and their frequencies are in agreement with theory. At moderate amplitude, EAW-type plasma waves can be excited over a broad range of frequencies. This frequency variability comes from the plasma adjusting its velocity distribution so as to make the plasma mode resonant with the drive frequency. Wave-coherent laser-induced fluorescence shows the intimate nature of the wave-particle interaction, and how the particle distribution function is modified by the wave driver until the plasma mode is resonant with the driver.

Trapped particles and asymmetry-induced transport

Trapped particle modes and the associated asymmetry-induced transport are characterized experimentally in cylindrical electron plasmas. Axial variations in the electric or magnetic confinement fields cause the particle trapping, and enable the E×B drift trapped-particle modes. Collisional diffusion across the trapping separatrix causes the modes to damp, and causes bulk radial transport when the confinement fields also have θ asymmetries. The measured asymmetry-induced transport rates are directly proportional to the measured mode damping rates, with simple scalings for all other plasma parameters. Significant transport is observed for even weak trapping fields (δB/B∼10−3), possibly explaining the “anomalous” background transport observed so ubiquitously in single species plasmas.

The finite length diocotron mode

A simple model is presented of a finite length electron plasma column supporting a small amplitude diocotron wave with mode number m=1. The electrons are contained inside conducting cylinders in an axial magnetic field, with negative voltages on end cylinders providing axial containment. The m=1 diocotron mode is the E×B drift orbit of an offset electron column around the cylinder axis, due to radial electric fields from image charges on the wall. The model predicts that the mode frequency will be higher than that of an infinitely long column due to θ-drifts from the radial containment fields at the plasma ends. The predicted dependencies on plasma length, radius, and temperature agree well with experiments, where frequency increases up to 2.5× are observed. For very short plasmas, these containment fields predominate over the image charge fields, and the plasma orbit is called the “magnetron” mode. The shift in the magnetron frequency due to image charges is also calculated.

Rarefaction waves, solitons, and holes in a pure electron plasma

The propagation of holes, solitons, and rarefaction waves along the axis of a magnetized pure electron plasma column is described. The time dependence of the radially averaged density perturbation produced by the nonlinear waves is measured at several locations along the plasma column for a wide range of plasma parameters. The rarefaction waves are studied by measuring the free expansion of the plasma into a vacuum. A new hydrodynamic theory is described that quantitatively predicts the free expansion measurements. The rarefaction is initially characterized by a self‐similar plasma flow, resulting in a perturbed density and velocity without a characteristic length scale. The electron solitons show a small increase in propagation speed with increasing amplitude and exhibit electron bursts. The holes show a decrease in propagation speed with increasing amplitude. Collisions between holes and solitons show that these objects pass through each other undisturbed, except for a small offset.

Cyclotron resonance phenomena in a non-neutral multispecies ion plasma

Cyclotron modes of a non‐neutral Mg ion plasma were studied in a long cylindrical Penning–Malmberg trap. Several modes with angular dependence exp(ilθ), l≥1, are observed near the cyclotron frequencies of the various Mg ions. The l=1 modes for the majority species are downshifted from the cyclotron frequencies, with downshifts as large as four times the diocotron frequency. These large shifts are quantitatively explained by a multispecies cold‐plasma theory, including the dependence on the plasma size and composition. These dependencies allow the plasma size and composition to be obtained from the measured mode frequencies. In contrast, the l=1 downshifts for minority species are generally close to twice the diocotron frequency, and remain unexplained. Cyclotron heating of the plasma ions was also observed with a surprising effect of improving the plasma confinement.

Experiments with pure electron plasmas

A series of experiments at UCSD on pure electron plasmas is described. The apparatus and methods of measurements are discussed. Results are given on various wave experiments including the dispersion of electron plasma waves, feedback growth and damping of the l=1 diocotron wave, and the unstable growth of diocotron waves on plasmas with hollow radial profiles. The nonlinear saturation of diocotron waves, subsequent vortex merging and the decay of the resulting two‐dimensional turbulence are observed. Transport processes resulting from both the single particle and collective response of the plasma to externally imposed field asymmetries have been studied. Evolution of the confined plasma to thermal equilibrium has been observed and scaling of the rate of this evolution with magnetic field has been measured. The relaxation rate of an anisotropic velocity distribution has been measured in both the usual parameter regime and the cryogenic regime where the rate is greatly reduced due to the existence of a many...

A NEW PURE ION PLASMA DEVICE WITH LASER INDUCED FLUORESCENCE DIAGNOSTIC

We describe a new apparatus for magnetic confinement of a pure ion plasma, with laser diagnostics to measure test particle transport across the magnetic field. In addition to the axisymmetric trapping potential, rotating electrostatic wall perturbation is used to counteract the plasma loss processes, giving steady-state ion confinement for weeks. Electronic spin polarization of the ion ground states is used to label the test particles; this spin orientation is controlled by direct optical pumping. The laser-induced fluorescence (LIF) technique is used to nondestructively measure the ion velocity distribution; and an absolute calibration of the charge density is obtained from the LIF measurement of the plasma rotation velocity. Two new technological improvements compatible with ultrahigh vacuum systems have been used: a semirigid Teflon insulated coaxial cable has low microphonic noise, and an antireflective coating is used to reduce reflection of ultraviolet light inside the vacuum chamber.

Measurements of the Weak Warm Beam Instability

Experiments are described on the interaction of a weak warm beam with a broad spectrum of unstable waves on a traveling wave tube. The wave–particle interactions are similar to those in beam–plasma systems, and are traditionally described by quasilinear theory. The precise wave evolution is obtained by launching a specified waveform, allowing it to interact with the beam, and analyzing the received waveform. Significant mode coupling is observed, resulting in saturated waves correlated less than 0.5 with their launch values. Experimentally, each wave is separated into a component proportional to the launch amplitude and a component due solely to mode coupling. The measured properties of these separate components agree quantitatively with a four‐wave coupling model. Strongest coupling is observed between waves whose wave numbers match within about an inverse turbulent trapping length. In the linear growth regime, the measured ensemble‐averaged wave growth rates and beam velocity diffusion rates agree reaso...