Non-neutral Plasma Research Articles

Numerical study of azimuthally symmetric Dubin mode excited in non-neutral plasma trapped in a harmonic potential

The characteristic of the electrostatic mode excited in non-neutral plasma in the equilibrium state is closely related to the internal state of plasma. This relationship has been used for non-destructive diagnosis of non-neutral plasma. Under the present conditions, this diagnosis is only supported by simplified theory. We employ numerical simulation reflecting actual experimental conditions and examine the characteristic of this electrostatic mode.

Dynamics of two-sign point vortices in positive and negative temperature states

The characteristic features of a two-sign point vortex system in positive and negative temperature states are examined by massive numerical simulations using MDGRAPE-2. The temperature is determined by a density of states for a microcanonical ensemble consisting of randomly generated 10 7 states. Since the density of states lias a single peak. the system has negative temperature states. The distributions of vortices in time-asymptotic equilibrium states in positive and negative temperature are obtained by time-development simulations. In positive temperature, both-sign vortices mix with each other and neutralize. In negative temperature, part of the vortices condense and form clumps exclusively consisting of the same-sign vortices, while the other part of the vortices distribute uniformly outside the clumps. It is found that the vortices inside the clumps gain energy and the vortices outside the clumps lose energy to keep the total energy constant. This suggests the common and essential role of the background vortices in the energy-conserving system that assists the formation of the clumps as well as the crystallization and generation of the symmetric configuration observed in the non-neutral plasma experiments.

Construction and Initial Operation of the Columbia Nonneutral Torus

We report on the results from initial testing and operation of the Columbia Nonneutral Torus, a new stellarator experiment constructed at Columbia University to study the confinement of nonneutral plasmas, electron-positron plasmas, and stellarator confinement in the presence of strong electrostatic fields. A new algorithm for automatic identification of good magnetic surfaces, island chains, and stochastic regions in Poincaré maps is also described. We present some of the details of the design of the interlocked in-vessel coils and the vacuum system and report on initial vacuum performance. Magnetic surface mapping and visualization results are also presented, confirming the existence of ultralow aspect ratio magnetic surfaces with excellent quality and good agreement with numerical calculations.

Non-neutral plasma equilibria with weak axisymmetric magnetic perturbations

The effect of weak axisymmetric magnetic and/or electrostatic perturbations on the equilibrium of a non-neutral plasma in a Malmberg-Penning trap is analyzed. Analytical and semianalytical solutions for the potential variations inside the trap are found in a paraxial limit of the perturbations for various radial density profiles of the plasma, including the case of global thermal equilibrium. It is shown that a magnetic perturbation produces a potential variation with a sign which is changing along the plasma radius. The fraction of magnetically and electrostatically trapped particles thus created is calculated explicitly for the case of a Maxwellian distribution function, and it is shown to be independent from the sign of the magnetic field perturbation. The analysis of the potential perturbation is extended to the case of an anisotropic distribution function, with an arbitrary ratio between the parallel and the perpendicular plasma temperature. Two-dimensional thermal equilibrium simulations for parameters relevant to the CamV device [A. A. Kabantsev, J. H. Yu, R. B. Lynch, and C. F. Driscoll, Phys. Plasmas 10, 1628 (2003)] confirm the predictions of the analytical theory for smooth and weak perturbations of the magnetic field.

Rankine-Hugoniot relations of an axial shock in cylindrical non-neutral plasma

The Rankine-Hugoniot relations of an axial shock in cylindrical non-neutral plasma with current, electric and magnetic field are presented. These relations are all dependent on the radius of cylindrical plasma, and markedly different from the one-dimensional (i.e., nonradially dependent) case. These two-dimensional Rankine-Hugoniot relations cause at least two important new results. First, the radial profiles of the shock downstream parameters are always different from the upstream profiles due to the magnetic effects. Second, the critical Mach number for the shock existence will depend on the shock carried current (i.e., magnetic field). As an example, a set of shock downstream profiles is provided numerically when the upstream profiles are taken as a kind of typical equilibrium profiles of a Z-pinch-Bennett profiles. By comparing the downstream profiles to the corresponding upstream profiles, the dependents of both the amplitudes and profiles of the downstream parameters on the shock carried current are shown.

Magnetic insulation at finite temperatures

A finite-temperature non-neutral plasma (FTNNP) theory of magnetically insulated (MI) electron flows in crossed-field vacuum devices is developed and applied in planar geometry. It is shown that, in contrast to the single type of MI flow predicted by traditional cold-plasma treatments, the nonlinear FTNNP equations admit five types of steady flow, of which three types are MI flows, including flows in which the electric field and/or the tangential velocity at the cathode may be zero or nonzero. It is also shown that finite-temperature Vlasov-Poisson treatments yield solutions for electron number densities and electrostatic potentials that are a subset of the FTNNP solutions. The algorithms that are used to solve the FTNNP equations numerically are discussed, and the numerical results are presented for several examples of the three types of MI flow. Results include prediction of the existence, boundaries, number density profiles, and other properties of sheaths of electrons in the anode-cathode gap.

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.

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.

Drift resonance in high density non-neutral plasmas

Theoretical studies of the operation of crossed-field electron vacuum devices such as magnetrons and crossed-field amplifiers (CFA) have usually centered on their initial growth, taking this as an indication of their operating modes. In such an analysis one solves the equations for the density profile, the operating frequency, the growth rate, and other features of these devices. What one really obtains then are only the conditions for the device to turn on. The dominant interaction in this stage is a Rayleigh-type instability which initiates a quasilinear diffusion process whereby the electron density profile redistributes itself into a profile which will be in equilibrium with the ponderomotive-like forces produced by the growing rf fields. Eventually the rf fields will saturate and an operating device will settle into a stationary operating regime. This stage of a device’s operation is called the “saturation stage.” This latter stage involves a different set of physical interactions from the initiation stage. No longer is there a growth rate; rather the rf amplitudes have saturated and as a result, the ponderomotive-like forces have also vanished along with the quasilinear diffusion. In this saturation stage, we find that new rf modes appear. In fact, there are a total of five rf modes, two of which are the usual slow modes of the initiation stage, and three of which have fast oscillations in the vertical direction. One fast mode corresponds to a drift plasma oscillation while the other two fast modes are drift cyclotron modes. In this paper, we will describe how the drift plasma oscillation interacts and couples with the slow rf modes at the diocotron resonance.

Particle-in-cell method for parallel dynamics in magnetized electron plasmas: Study of high-amplitude BGK modes

The present paper describes the numerical technique that has been developed, in the framework of the particle-in-cell (PIC) method, to study the dynamics of a nonneutral plasma along the magnetic field lines. In particular, the technique has been employed to simulate the formation and long-term evolution of large-amplitude electrostatic waves experimentally observed in electron plasmas confined in a Penning trap [W. Bertsche, J. Fajans, L. Friedland, Phys. Rev. Lett. 91 (2003) 265003]. Due to the peculiar features of the physical system, namely the existence of different time scales and the presence of a perturbative oscillating potential, ad hoc numerical techniques have been developed. In particular, with a suitable radial decomposition all important two-dimensional phenomena are fully taken into account while keeping the computational effort to that of a standard one-dimensional PIC codes. Moreover, a novel particle loading technique (ergodic loading) has been developed, which ensures a significant reduction of numerical noise. The results obtained with the present technique are in excellent agreement with the experiments [F. Peinetti, W. Bertsche, J. Fajans, J. Wurtele, L. Friedland, Phys. Plasmas 12 (2005) 062112]. Moreover, results presented here furnish clear evidences of the close relationship between the observed nonlinear structures and the Bernstein–Greene–Kruskal modes.

Effect of axial magnetic field variations on asymmetry-induced transport in a non-neutral plasma trap

It has been suggested that magnetically trapped particles play a role in the asymmetry-induced radial transport observed in the Occidental non-neutral plasma trap. This magnetic trapping would occur due to a small increase (β≡δB∕B≈0.4%) in magnetic field at the center of our solenoid and would keep low velocity particles confined to the ends of the trap. To test this suggestion, three coils of additional windings have been added to the trap solenoid thus allowing adjustment of the axial field variation δB. The effect of these adjustments on typical radial flux resonances is investigated. Making B as uniform as possible reduces β by a factor of 5.9, but this produces little change in the transport. Varying β over the broader range from −8.5% to 9.5% gives variations of 20%–90% in the magnitude, peak frequency, and width of the flux resonances, but these variations do not match the predictions of a simple model of trapped particle transport based on isotropic particle distributions.

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.

Spiral galaxies as gravitational plasmas

This article reviews recent studies of dynamics of disk-shaped galaxies with special emphasis on their spiral structures. In a local version of kinetic stability theory, the very existence and the value of the critical wavelength of the spiral structure arising due to nonresonant Jeans-type instability of gravity perturbations is explained. A formal analogy between the collective oscillations in a rotating self-gravitating disk and the oscillations of a hot nonneutral plasma in a magnetic field is explored.

Dynamics of Two-Sign Point Vortices in Positive and Negative Temperature States

Dynamics of two-sign point vortices in positive and negative temperature states is examined by a special-purpose supercomputer (MDGRAPE-2). Temperature T is determined by random sampling of 10 7 states for microcanonical ensemble in which system energy and angular impulse are kept constant. Distributions of the vortices in time-asymptotic equilibrium state are obtained by time development simulations for various values of T. When T > 0, both-sign vortices mix with each other and neutralize. When T < 0, a part of the vortices condenses and forms the clumps exclusively consisting of the same-sign vortices, while the other part of the vortices distributes outside the clumps uniformly. It is found that the vortices inside the clumps gain energy and the ones outside the clumps lose energy to keep the total energy constant. It suggests the common and essential role of the background vortices in the energy-conserving system that assists the formation of the clumps as well as the crystallization and generation of symmetric configuration observed in the nonneutral plasma experiments.

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.

Centrifugal separation of ions and an oppositely charged non-neutral plasma

The motion of a single ion confined in a Penning-Malmberg trap together with a plasma column of electrons or positrons is described by means of a simple model. The model qualitatively reproduces the basic mechanism of the centrifugal separation for multispecies plasma composed of particles with the same sign of charge. The ion is pushed toward the plasma boundary also when its charge and the plasma charge have opposite signs. An estimation of the characteristic time scale for the separation is obtained and discussed.

Jump Conditions of a Shock with Current in CylindricalNon-Neutral Plasma

Jump conditions of the parameters (mass flow, momentum flow and energyflow) of a shock with current (thereby, electric and magnetic field) incylindrical non-neutral plasma are presented and derived from Maxwell'sequations and two fluid equations for electron and ion fluid. Thecritical Mach number for the shock existence is calculated, whichdepends on the shock carried current, the ion charge, and thecomposition of the magnetic and thermal pressure. The numerical resultsshow that both the strength and profiles of the downstream shockparameters will be affected obviously by the shock carried current,electric and magnetic field in the two-dimensional shock.

Theory of weak switching of arbitrary collector voltages in non-neutral plasma diodes

The response function concept is used to describe analytically the dynamics of electrons in a non-neutral diode in which the collector voltage is switched on at t = 0 from zero to a weak but otherwise arbitrary time-dependent voltage. It generalizes previous investigations of simple switching (Akimov et al 2003 J. Appl. Phys. 93 1246; Ender et al 2004 Phys. Plasmas 11 3212), where the final voltage is assumed to be constant. Use is made of the Laplace transformation technique and a remarkably simple expression is found for the Laplace-transformed emitter electric field from which analytic solutions for the time-dependent, highly transient response of the diode can be obtained. As an application, the switching to a final harmonic collector potential called cos-switching is investigated and the usefulness of an approximative response function approach is demonstrated by a comparison of the approximative with the exact results. For diodes with different charge non-neutrality parameter and branches with no electron reflection various scenarios for cos-switching are explored, revealing the exact time behaviour of the emitter electric field and of the net current density. The amplitude A∞(ω) of the asymptotically driven oscillation as a function of the driven frequency ω is also presented. Of upmost importance is a novel resonance phenomenon we found in that part of the second zone of generalized Pierce diodes for which the non-reflecting equilibria are linearly stable against aperiodic and oscillatory eigenmodes. In a narrow band region A∞(ω) amplifies by a factor 50. This driven internal oscillation takes place on a high current level raising high promises e.g. for microwave generators and/or circuit current amplifiers as well as for diagnostic purposes.

On steady flows in smooth-walled magnetrons: Fundamental modes and no-cutoff flows in planar geometry

The Maxwell equations coupled with the ideal fluid equations for a warm isothermal non-neutral plasma are applied without approximation to predict three modes of time-independent electron flow in smooth-walled planar magnetrons, at any temperature. For all three modes, the equations predict that the fluid flow velocity tangent to the cathode is the Brillouin velocity. One of the modes is the well-known magnetic insulation mode, in which the magnetic field is larger than the Hull cutoff field [Phys. Rev. 18, 31 (1921)], the anode current is essentially zero, and virtually all the electrons reside in a sheath near the cathode. The other two modes exhibit fairly large anode currents. One of these modes is the well-known Child-Langmuir flow [Phys. Rev. 32, 492 (1911); ibid. 21, 419 (1923)], in which the magnetic field is smaller than the Hull cutoff field. The other high-current mode, in which the magnetic field is larger than the Hull cutoff field, has not been discussed previously; in this paper, it is called the “no-cutoff” (NC) mode. Experiments using a thin smooth-walled magnetron were conducted, during which large anode currents were observed even for magnetic fields much larger than the Hull cutoff field. It is shown that NC mode parameters can be adjusted to produce a complete agreement with the experimental results, but that this requires the transverse flow velocity near the cathode to be superthermal and even mildly relativistic for the larger magnetic fields. Matching the experimental values also predicts a number density that is larger near the anode than near the cathode, but is small enough that space-charge effects are negligible in most cases.

Diocotron instability in non-neutral plasmas with a stationary point in the rotation frequency profile

A new analytical solution to the problem of the l=1 diocotron mode instability in a hollow density non-neutral plasma column with finite lenght is presented. The starting point of the analysis is the paper of Finn et al. [J. M. Finn, D. del-Castillo-Negrete, and D. C. Barnes, Phys. Plasmas 6, 3744 (1999)], where the instability mechanism involves compression of the plasma in the direction parallel to the magnetic field, with conservation of its line-integrated density. In the limit of small curvature of the plasma end-fronts, the method presented here provides both eigenvalue and eigenfunction for the unstable l=1 “extreme mode.”