Nonneutral Electron Plasma Research Articles

Vortex splitting in two-dimensional fluids and non-neutral electron plasmas with smooth vorticity profiles

Initially, elliptical, quasi-two-dimensional (2D) fluid vortices can split into multiple pieces if the aspect ratio is sufficiently large due to the growth and saturation of perturbations known as Love modes on the vortex edge. Presented here are experiments and numerical simulations, showing that the aspect ratio threshold for vortex splitting is significantly higher for vortices with realistic, smooth edges than that predicted by a simple “vortex patch” model, where the vorticity is treated as piecewise constant inside a deformable boundary. The experiments are conducted by exploiting the E × B drift dynamics of collisionless, pure electron plasmas in a Penning–Malmberg trap, which closely model 2D vortex dynamics due to an isomorphism between the Drift–Poisson equations describing the plasmas and the Euler equations describing ideal fluids. The simulations use a particle-in-cell method to model the evolution of a set of point vortices. The aspect ratio splitting threshold ranges up to about twice as large as the vortex patch prediction and depends on the edge vorticity gradient. This is thought to be due to spatial Landau damping, which decreases the vortex aspect ratio over time and, thus, stabilizes the Love modes. Near the threshold, asymmetric splitting events are observed in which one of the split products contains much less circulation than the other. These results are relevant to a wide range of quasi-2D fluid systems, including geophysical fluids, astrophysical disks, and drift-wave eddies in tokamak plasmas.

A buffer-gas trap for the NEPOMUC positron beam: optimization studies with electrons

Buffer-gas traps (BGTs) use inelastic interactions with nitrogen molecules to capture positrons from a continuous beam. These devices are invaluable for high-resolution studies of matter–antimatter interactions, antihydrogen research and positronium laser spectroscopy. We present a new project with the goal of producing a non-neutral plasma containing ${\sim }10^8$ low-energy positrons by installing a BGT on the NEPOMUC (NEutron induced POsitron source MUniCh) high-intensity positron beam. Details of the BGT are outlined and results are presented from experiments in which an electron beam, with a similar intensity and energy spread to the remoderated NEPOMUC beam, was used to create pulses of non-neutral electron plasma. The device is a vital component of the APEX (A Positron Electron eXperiment) project, which aims to create a low-temperature electron–positron pair plasma.

Non-neutral electron plasmas confined with a nested potential in a uniform magnetic field

Confinement properties of a non-neutral electron plasma are investigated with a nested potential in a uniform magnetic field. The main result is that the positive plug potentials can be maintained by applying an appropriate resonant RF field to the plug potentials. Since the nested potentials in a magnetic field can confine both positive and negative charged particles simultaneously, it is expected that the technique will be applied to study electron–positron plasmas experimentally.

Spectral analysis of forced turbulence in a non-neutral plasma

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

Autoresonances of m=2 diocotron oscillations in non-neutral electron plasmas.

The existence of autoresonances for m=2 diocotron oscillations of non-neutral electron plasmas in a uniform magnetic field was predicted by particle-in-cell simulations and it was confirmed in experiments. The obtained results show clear deviations from the standard threshold amplitude dependence on the sweep rate. The threshold amplitude approaches a constant at a lower sweep rate when there is a damping force. It was also found that the aspect ratio for the oval cross section of the confined plasma can be controlled by the frequency of the externally applied driving force.

Phase Space Volumes of Non-Neutral Electron Plasmas during Vortex Merging Processes

Phase Space Volumes of Non-Neutral Electron Plasmas during Vortex Merging Processes

Toward sub-Kelvin resistive cooling and non destructive detection of trapped non-neutral electron plasma

A resonant circuit tuned to a particular frequency of the motion of charged particles stored in a Penning trap and connected to a low noise amplifier allows, at the same time, cooling and non destructive detection of the particles. Its use is widely diffused when single or few particles are stored near the centre of a hyperbolic Penning trap. We present a consistent model that predicts the shape of the induced signal when the tuned circuit is used to detect and cool the axial motion of a cold non neutral plasma stored in an open-ended cylindrical Penning trap. The model correctly accounts for the not negligible axial plasma size. We show that the power spectrum of the signal measured across the tuned circuit provides information about the particle number and insights about the plasma temperature. We report on the design of a HEMT-based cryogenic amplifier working at 14.4 MHz and 4.2 K and the results of the noise measurements. We have measured a drain current noise in the range from 6 to 17 pA/√Hz, which corresponds to an increase of the tuned circuit equivalent temperature of at maximum 0.35 K. The cryogenic amplifier has a very low power consumption from few tens to few hundreds of μW corresponding to a drain current in the range 100–800 μ A. An additional contribution due to the gate noise has been identified when the drain current is below 300 μA; above that value an upper limit of the increase of the equivalent tuned circuit temperature due to this contribution of 0.02 K has been obtained. These features make the tuned circuit connected to this amplifier a promising device for detecting and cooling the axial motion of an electron plasma when the Penning trap is mounted inside a dilution refrigerator.

Comparison of non-neutral electron plasma confinement in harmonic and rectangular potentials in a very dense regime

Confinement of high density electron plasmas in a strong uniform magnetic field was experimentally studied in a multi-ring trap (MRT). The trap was housed inside a bore tube and surrounded by a superconducting solenoid. A 5 T magnetic field was used to provide radial confinement while an electrostatic harmonic or rectangular potential well was used for axial confinement. For trapped electrons of N = 1.2 × 1010 in a harmonic potential well (HPW) with the trap length of LT = 320 mm, the plasma lifetime was about 104 s and it became much longer at lower N = 4.5 × 109. Such long holding times were achieved without application of rotating electric fields. Contrastingly, in a rectangular potential well (RPW), the plasma of N = 1.2 × 1010 under the same trap length expanded to cover the whole Faraday Cup within 200 s, where its radial expansion rate was η = 3.2 × 10−2 mm/s, which was 20 times faster than HPW. The lifetime for RPW became shorter with increasing LT and scaled as 1/[LT]2. This scaling found for high density plasmas is similar to the obtained one with different Penning–Malmberg traps at UC San Diego (USCD).

Density and potential profiles of non-neutral electron plasmas in a magnetic mirror field

Low-energy non-neutral electron plasmas were confined with an electrostatic potential and a magnetic mirror field of the mirror ratio up to 5. Using a conventional phosphor screen and the unique multiring trap, both radial and axial density profiles of plasmas were measured. With the present experimental parameters, it was confirmed that a plasma density increased at higher field with an electrostatic confinement and that it decreased at higher field with a magnetic mirror confinement. The electrostatic potentials along the magnetic field were estimated with computer simulations.

Electrostatic Oscillations Observed in Non-Neutral Electron Plasmas Confined in a Magnetic Field Gradient

Electrostatic Oscillations Observed in Non-Neutral Electron Plasmas Confined in a Magnetic Field Gradient

Successful production of non-neutral electron plasma of high density in the multi-ring trap

Accumulation of electrons to form dense electron plasma in a modified Malmberg–Penning trap, a multi-ring trap (MRT), is investigated. Under ultra-high vacuum conditions, the electron plasma is confined radially using a 5 T magnetic field and axially by using a harmonic potential well of depth 1000 V. Electron plasma of density higher than 1×1011 cm−3 was confined in the MRT, and the number of trapped electrons can be controlled by changing the trap depth and the trap length. A longitudinal plasma temperature of 0.1 eV was measured, and the cyclotron cooling time was found to scale as 4.5/B 2 (T).

Screening of the resistive-wall impedance by a cylindrical electron plasma

The effect of an electron cloud on the longitudinal coupling impedance is studied by idealizing it as a cold and uniformly distributed non-neutral plasma of electrons. The beam pipe is assumed to be of circular cross section with a thick resistive wall and the beam charge is idealized as a uniform disk. The electron contribution to the charge and current densities is obtained from the collective electron response to the beam passage through the pipe. In the presence of the electron background, a general closed formula for the longitudinal coupling impedance is obtained. The screening of the coupling impedance with the density of the electron plasma is studied and discussed for typical parameters in an accelerator beam pipe for the under-dense and the over-dense plasma regions.

Properties of non-neutral electron plasmas confined with a magnetic mirror field

A low energy non-neutral electron plasma was confined with a magnetic mirror field and an electrostatic potential to investigate the basic confinement properties of a simple magnetic mirror trap. The mirror ratio of the magnetic field was increased up to 5. As expected the confinement time became longer as a function of the mirror ratio. The axially integrated radial density profiles in equilibrium were measured and compared with a theoretical model. The axial electrostatic oscillations of a confined electron plasma were also observed.

Simulations of diocotron instability using a special-purpose computer, MDGRAPE-2

The diocotron instability in a low-density non-neutral electron plasma is examined via numerical simulations. For the simulations, a current-vortex filament model and a special-purpose computer, MDGRAPE-2 are used. In the previous work, a simulation method based on the current-vortex filament model, which is called “current-vortex method,” is developed. It is assumed that electric current and vorticity have discontinuous filamentary distributions, and both point electric current and point vortex are confined in a filament, which is called “current-vortex filament.” In this paper, the current-vortex method with no electric current is applied to simulations of the non-neutral electron plasma. This is equivalent to the traditional point-vortex method. MDGRAPE-2 was originally designed for molecular dynamics simulations. It accelerates calculations of the Coulomb interactions, the van der Waals interactions and so on. It can also be used to accelerate calculations of the Biot–Savart integral. The diocotron modes reproduced by the simulations agree with the result predicted by linear theory. This indicates that the current-vortex method is applicable to problems of the non-neutral plasma. The linear growth rates of the diocotron instability in the simulations also agree with the theoretical ones. This implies that MDGRAPE-2 gives the sufficiently accurate results for the calculations of the current-vortex method. A mechanism of merging of electron clumps is demonstrated by the simulations. It is concluded that the electric field induced by the conducting wall makes the nonlinear stage unstable and causes the clumps to merge.

Electron diffusion in the annular Penning trap

Transport by cross-field diffusion has been studied in the annular Penning trap in which a nonneutral plasma of electrons is contained between concentric cylinders. At densities sufficiently low (<105 cm−3) to suppress mobility transport arising from the space charge electric field, the dominant sources of transport are diffusion from collisions of electrons with added helium gas and asymmetry transport from stray fields. The collisional diffusivity is shown to scale linearly with collision frequency and inversely with the square of the axial magnetic field. The measured mean energy is initially 0.3 eV and the least energetic electrons are lost more slowly as a consequence of the energy dependence of the diffusivity. Decay constants are about a factor of four higher than calculated from the electron–helium momentum transfer collision frequency. Both the asymmetry transport and the collisional transport are shown to depend upon the cleanliness of the trap surfaces.

Diocotron instability in an annular sheath of a gas-discharge nonneutral electron plasma

The diocotron instability influence on the value of average electron density in a discharge with crossed electric and magnetic fields has been studied in magnetron and inverted magnetron geometries. The obtained results is in agreement with experimental data. It is found that in magnetron with a thin cathode the mode l=1 is unstable in a narrow interval of electron densities. The width of this interval vanishes when the cathode radius tends to zero.

Hysteresis and Bifurcation for the Axisymmetric Waves in a Nonneutral Electron Plasma

The hysteresis phenomena of the axisymmetric waves in a nonneutral electron plasma were observed by sweeping frequencies of the externally applied sinusoidal oscillations. The nonlinear response for the fundamental mode showed distinct hysteresis phenomenon with positive frequency shift. The response profile was obtained in the three-dimensional control space and compared with the theoretical stationary one. The bifurcation was also observed for the mode. The frequency shift changed its sign from positive to negative when the waves increased in the axial wavenumber. The observed responses for higher modes exhibited hysteresises with negative frequency shifts accompanied by sawtooth-like behavior due to the mode transitions. The mechanism was examined based on the ponderomotive force including the finite effect of the plasma column length.

Expansion rate measurements at moderate pressure of non-neutral electron plasmas in the Electron Diffusion Gauge (EDG) experiment

Measurements of the expansion rate of pure-electron plasmas have been performed on the Electron Diffusion Gauge (EDG) device at background helium gas pressures in the 5×10−8 Torr to 2×10−5 Torr range, where plasma expansion due to electron-neutral collisions dominates over plasma expansion due to trap asymmetries. It is found that the expansion rate, defined as the time rate of change of the particles’ mean-square radius, scales approximately linearly with pressure and inversely as the square of the magnetic field strength in this regime, in agreement with classical predictions.

Experimental observation of the trapped particle pinch effect.

The trapped particle pinch effect (Ware's drift) has been observed in a non-neutral plasma of electrons in a modified Malmberg-Penning trap in which electrons are contained in the annular volume between concentric cylinders. A pulsed azimuthal electric field is applied by increasing the flux within a solenoid on the axis. Radial displacements of the electrons are observed which show that they remain on a surface enclosing constant axial flux. These displacements are independent of the azimuthal field and thus are consistent with Ware's drift and inconsistent with the guiding center drift alone.

Numerical model for collisions in the drift approximation that reproduces classical and neoclassical transport

A numerical method is described for including collisions in the drift approximation in a way that reproduces diffusion of the guiding center and of the drift orbit center. For untrapped particles, the method gives transport that agrees with classical values for mobility and diffusivity both parallel and perpendicular to the magnetic field. For trapped particles, the method correctly reproduces the neoclassical mobility and diffusivity. The model has been applied to the annular Penning trap in which a non-neutral plasma of electrons in a helical magnetic field makes collisions with neutral gas. The model shows that the transport makes a transition from neoclassical to classical values as the collision frequency goes from less than to greater than the axial bounce frequency.