Pure Electron Plasma Research Articles

Hot electron plasmas trapped in helical magnetic surfaces

Experimental studies on nonneutrai (pure electron) plasmas of finite temperature, trapped in helical closed magnetic surfaces have been conducted. The helical electron plasmas are produced with thermal electrons launched from the outside of the last closed flux surface (LCFS). About 150 μs after the electron injection, the plasmas reach equilibrium state. Around the LCFS, a steep gradient of plasma space potential ϕs is formed. The corresponding radial electric field is about 2.5 kV/m. On the other hand, around the magnetic axis of helical magnetic surfaces, ϕs is almost constant, indicating that there are little electrons there. The volume-averaged electron density is on the order of 1013 m−3, smaller than the Brillouin density limit. The confinement time seems to be limited by a disruptive instability, and is so far about 1.5 ms.

Long-Lived Pure Electron Plasma in Ring Trap-1

The Ring Trap-1 (RT-1) experiment succeeded in producing a long-lived (of the order 10 2 s), stable, nonneutral (pure electron) plasma. Electrons are confined by a magnetospheric dipole field. To eliminate a loss channel of the plasmas caused by support structures, a superconducting coil was magnetically levitated. This coil levitationdrastically improvedthe confinement properties of the electron plasmacompared to previous PrototypeRing Trap (Proto-RT) experiments. c

A retractable electron emitter for the creation of unperturbed pure electron plasmas

A retractable electron emitter has been constructed for the creation of unperturbed pure electron plasmas on magnetic surfaces in the Columbia Non-neutral Torus stellarator. The previous method of electron emission using emitters mounted on stationary rods limited the confinement time to 20 ms. A pneumatically driven system that can retract from the magnetic axis to the last closed flux surface in less than 20 ms while filling the surfaces with electrons was designed. The motion of the retractable emitter was modeled with a system of dynamical equations. The measured position versus time of the emitter agrees well with the model and the fastest axis-to-edge retraction was measured to be 20 ms with 40 psig helium gas driving the pneumatic piston.

Formation of a symmetric vortex configuration in a pure electron plasma trapped with a penning trap

In the formation of vortical crystal structures of electrons, the distribution of background electrons works as a “cooler” of randomly moving, intense vortices. We examine the supporting effect of background electrons to forming crystal structures from the perspective of a reduction of the vortices’ random motion.

Large density variation predicted along the magnetic axis for cold electron plasmas in the Columbia Nonneutral Torus (CNT)

Cold pure electron plasmas confined in Penning-Malmberg traps with mirror fields are known to exhibit density variations along field lines, such that the density is roughly proportional to the magnetic field strength, n∼B. The Columbia Nonneutral Torus (CNT) is the first stellarator designed to study pure electron plasmas, and exhibits substantial mirroring, with Bmax≈1.8Bmin. However, results of a three-dimensional equilibrium solver, presented in this Letter, predict a factor of 5.3 increase in density from the minimum-field cross section to the maximum-field cross section along the magnetic axis, for a 1.5cm Debye length plasma (a≈15cm for CNT). In this Letter, it is shown that the density variation of electron plasmas in mirror traps can be significantly enhanced in a device that has a cross section that varies from cylinder-like to slab-like, such as the CNT. A simple analytic expression is derived that describes the axial density variation in such a device, and it is found to agree well with the computational predictions for CNT.

Determination of equilibrium density distribution and temperature of a pure electron plasma confined in a Penning trap

A fast scheme is proposed for determining the three-dimensional density distribution of a pure electron plasma under the thermal relaxation in a Penning trap on the basis of the observation of the axially integrated density distribution. The analysis that includes the contribution of the conducting wall reveals the appearance of a halo distribution surrounding the core distribution around the midplane. The core is confirmed to approach the Penning-type equilibrium distribution. Also proposed is a new scheme of the temperature determination of the electrons by analyzing a radial profile of the particles extracted with energy selection. This method is available on the basis of the self-consistent potential distribution associated with the equilibrium density distribution. The application of the two schemes of data analysis shows that the electron temperature decreases well below 0.1eV with a 1∕e folding time of ≈4× cyclotron-cooling time in the trap kept at room temperature.

Relaxation of Azimuthal Flow Pattern from Ring to Bell Shape through Two-Dimensional Turbulence Triggered by Diocotron Instability

Experimentally observed dynamics of vortex patches, as generated by the diocotron instability in a magnetized pure electron plasma, is examined in terms of the power spectra of the distributions of...

Experimental Confirmation of Stable, Small-Debye-Length, Pure-Electron-Plasma Equilibria in a Stellarator

The creation of the first small-Debye length, low temperature pure electron plasmas in a stellarator is reported. A confinement time of 20 ms has been measured. The long confinement time implies the existence of macroscopically stable equilibria and that the single particle orbits are well confined despite the lack of quasisymmetry in the device, the Columbia non-neutral torus. This confirms the beneficial confinement effects of strong electric fields and the resulting rapid E x B rotation of the electrons. The particle confinement time is presently limited by the presence of bulk insulating materials in the plasma, rather than any intrinsic plasma transport processes. A nearly flat temperature profile is seen in the inner part of the plasma.

Trapped-Particle-Mediated Collisional Damping of Nonaxisymmetric Plasma Waves

Weak axial variations in magnetic or electric confinement fields in pure electron plasmas cause slow electrons to be trapped locally, and collisional diffusion across the trapping separatrix then causes surprisingly large trapped-particle-mediated (TPM) damping and transport effects. Here we characterize TPM damping of m theta not equal to 0, m(z) = +/-1 Trivelpiece-Gould plasma modes in large-amplitude long-lived Bernstein-Greene-Kruskal states. The TPM damping gives gammaBGK/omega approximately 10(-4) and seems to dominate in regimes of weak interparticle collisions.

A nonextensive statistics approach for Langmuir waves in relativistic plasmas

Abstract. The nonextensive statistics formalism proposed by Tsallis has found many applications in systems with memory effects, long range spatial correlations, and in general whenever the phase space has fractal or multi-fractal structure. These features may appear naturally in turbulent or non-neutral plasmas. In fact, the equilibrium distribution functions which maximize the nonextensive entropy strongly resemble the non-Maxwellian particle distribution functions observed in space and laboratory and turbulent pure electron plasmas. In this article we apply the Tsallis entropy formalism to the problem of longitudinal oscillations in a proton-electron plasma. In particular, we study the equilibrium distribution function and the dispersion relation of longitudinal oscillations in a relativistic plasma, finding interesting differences with the nonrelativistic treatment.

Quasi-stationary States of Two-Dimensional Electron Plasma Trapped in Magnetic Field

We have performed numerical simulations on a pure electron plasma system under a strong magnetic field, in order to examine quasi-stationary states that the system eventually evolves into. We use ring states as the initial states, changing the width, and find that the system evolves into a vortex crystal state from a thinner-ring state while a state with a single-peaked density distribution is obtained from a thicker-ring initial state. For those quasi-stationary states, density distribution and macroscopic observables are defined on the basis of a coarse-grained density field. We compare our results with experiments and some statistical theories, which include the Gibbs-Boltzmann statistics, Tsallis statistics, the fluid entropy theory, and the minimum enstrophy state. From some of those initial states, we obtain the quasi-stationary states which are close to the minimum enstrophy state, but we also find that the quasi-stationary states depend upon initial states, even if the initial states have the same energy and angular momentum, which means the ergodicity does not hold.

Transport processes of a non-neutral plasma coupled to an external rotating wave

Experimental investigations are carried out on radial transport phenomena of a pure electron plasma under the application of an external rotating wave that belongs to Trivelpiece-Gould (T-G) modes. Substantial radial compression of the density distribution is achieved by application of a properly controlled rotating electric field to one side of the plasma. Analyses of the observed plasma wave indicate that the efficient increase of the on-axis density entails the substantial damping of the T-G wave propagating in the plasma. The radial particle flux observed during the density compression is consistent with that of the theoretical model based on the drift-kinetic Vlasov equation [Y. Kiwamoto et al., Phys. Plasmas 12, 094501 (2005)]. This result implies that the radial compression of the plasma density distribution consists of the transverse E×B drift of particles subject to resonant wave-particle interaction in the axial dynamics.

Covariant Kinetic Theory with an Application to the Coma Cluster

In this paper, we introduce a novel solution to the covariant Landau equation for a pure electron plasma. The method conserves energy and particle number, and reduces smoothly to the Rosenbluth potentials of non-relativistic theory. In addition, we find that a fully relativistic plasma equilibrates in only 1/100th of a Spitzer time--much faster than in the non-relativistic limit--a factor of significant import to situations in which distortions to a Maxwellian distribution are produced by anomalous methods of acceleration. To demonstrate the power of our solution in dealing with hot, astrophysical plasmas, we use this technique to show that one of the currently considered models--continuous stochastic acceleration--for the hard X-ray emission in the Coma cluster actually cannot work because the energy gained by the particles is distributed to the {\it whole} plasma on a time scale much shorter than that of the acceleration process itself.

Thermally excited fluctuations as a pure electron plasma temperature diagnostic

Thermally excited charge fluctuations in pure electron plasma columns provide a diagnostic for the plasma temperature over a range of 0.05<kBT<10eV. Three different nonperturbative methods have been developed to determine the plasma temperature. The first method fits the near-Lorentzian spectrum of thermal fluctuations near a single weakly damped mode. This method works well where the modes are weakly damped, i.e., when λD∕Rp<0.3. The second method utilizes the emission spectrum over a broad frequency range encompassing several modes and the nonresonant fluctuations between modes. This method works for long columns with λD∕Rp>0.2, so that Landau damping is dominant and well modeled by theory. The third method compares the total (frequency-integrated) number δN of fluctuating image charges on the wall antenna to a simple thermodynamic calculation. This method works when λD∕Rp>0.2.

Finding the radial parallel temperature profile in a non-neutral plasma using equilibrium calculations on experimental data

In 1992, Eggleston et al. [D. L. Eggleston et al., Phys. Fluids B 4, 3432 (1992)] reported on a technique for measuring the radial temperature profile in a pure-electron plasma confined in a Malmberg-Penning trap by partially dumping the plasma onto a charge collector at the end of the trap. For short plasmas and short confining rings, the assumptions in their paper are violated and a more general calculation is needed. This paper presents a variation of the standard equilibrium calculation to find the temperature profile of a pure-electron plasma. Eggleston’s shortcut “evaporation” temperature method is found to require a correction factor that can be calculated using methods described in this paper. For typical conditions, the evaporation method overstates the actual temperature by a factor ranging from 1.1 to 1.5 or more, depending on the plasma’s total charge and temperature and the geometry of the trap.

Simulation of Stationary States of the Two Dimensional Electron Plasma Trapped in Magnetic Field

We have performed numerical simulations on the pure electron plasma system under strong magnetic field, and examined stationary states that the system eventually evolves into from various initial configurations. We compare our results with experiments and some statistical theories, which include the Gibbs-Boltzmann statistics, Tsallis statistics, the fluid entropy theory, and the minimum enstrophy state. We find that the final stationary states depend upon initial states, even if the initial states have the same energy and angular momentum; this means this system is not ergodic. From some of those initial states we obtain the final states which are close to the minimum enstrophy state. However, we find that from some other initial states, the system evolves not into stationary state but into the vortex crystal state, which strongly depends upon microscopic structure of the initial states due to the chaotic dynamics of transient vortex clumps.

Deformation of Weakly Unstable Density Distribution of Non-Neutral Plasma Stimulated by Resonant Clumps

Accelerated deformations are observed in the density distribution of a pure electron plasma that is weakly diocotron-unstable when l clumps are introduced along a circle where the rotation frequency advected by the target plasma is close to the phase-rotation frequency of an unstable wave with the mode number of l. When the advection frequency is not close to the phase frequency, the clumps are modified in their orbit by the most unstable wave of the target plasma and bunched azimuthally into the distribution modulated by the wave.

Stable confinement of toroidal electron plasma in an internal conductor device Prototype-Ring Trap

A pure electron plasma has been produced in an internal conductor device Prototype-Ring Trap (Proto-RT). The temporal evolution of the electron plasma was investigated by the measurement of electrostatic fluctuations. Stable confinement was realized when the potential profile adjusted to match the magnetic surfaces. The confinement time varies as a function of the magnetic field strength and the neutral gas pressure, and is comparable to the diffusion time of electrons determined by the classical collisions with neutral gas. Although the addition of a toroidal magnetic field stabilized the electrostatic fluctuation of the plasma, the effects of the magnetic shear shortened the stable confinement time, possibly because of the obstacles of coil support structures.

Electron plasma expansion rate studies on the Electron Diffusion Gauge experimental device

The expansion of pure electron plasmas due to collisions with background neutral gas atoms in the Electron Diffusion Gauge experimental device is observed to be in good agreement with the predictions of a macroscopic fluid model with uniform electron temperature. Measurements of the expansion with a two-dimensional (2-D), phosphor-screen density diagnostic suggest that expansion rates measured with the 1-D diagnostic were observed concurrently with substantial changes in the plasma that are not due to electron-neutral collisions. Measurements of the on-axis, parallel plasma temperature evolution support this conclusion and further indicate that the plasmas are continuously losing energy during the expansion, presumably through inelastic collisions with trace background gases.

Numerical studies of driven, chirped Bernstein, Greene, and Kruskal modes

Recent experiments showed the possibility of creating long-lived, nonlinear kinetic structures in a pure-electron plasma. These structures, responsible for large-amplitude periodic density fluctuations, were induced by driving the plasma with a weak oscillating drive, whose frequency was adiabatically decreased in time [W. Bertsche, J. Fajans, and L. Friedland, Phys. Rev. Lett. 91, 265003 (2003)]. A one-dimensional analytical model of the system was developed [L. Friedland, F. Peinetti, W. Bertsche, J. Fajans, and J. Wurtele, Phys. Plasmas 11, 4305 (2004)], which pointed out the phenomenon responsible for the modifications induced by the weak drive in the phase-space distribution of the plasma (initially Maxwellian). In order to validate the theory and to perform quantitative comparisons with the experiments, a more accurate description of the system is developed and presented here. The new detailed analysis of the geometry under consideration allows for more precise simulations of the excitation process, in which important physical and geometrical parameters (such as the length of the plasma column) are evaluated accurately. The numerical investigations probe properties and features of the modes not accessible to direct measurement. Due to the presence of two distinct time scales (because of the adiabatic chirp of the drive frequency), a fully two-dimensional numerical study of the system is expected to be rather time consuming. This becomes particularly important when, as here, a large number of comparisons (covering a wide range of drive parameters) are performed. For this reason, a coupled one-dimensional, radially averaged model is derived and implemented in a particle-in-cell code.