Non-neutral Plasma Research Articles

Amplitude scaling of asymmetry-induced transport in a non-neutral plasma trap

Initial experiments on asymmetry-induced transport in the Occidental non-neutral plasma trap found the radial particle flux at small radii to be proportional to φa2, where φa is the applied asymmetry amplitude. Other researchers, however, using the global expansion rate as a measure of the transport, have observed a φa1 scaling when the rigidity (the ratio of the axial bounce frequency to the azimuthal rotation frequency) is in the range of 1–10. In an effort to resolve this discrepancy, measurements have been extended to different radii and asymmetry frequencies. Although the results to date are generally in agreement with those previously reported (φa2 scaling at low asymmetry amplitudes falling off to a weaker scaling at higher amplitudes), some cases have been observed where the low amplitude scaling is closer to φa1. Both the φa2 and φa1 cases, however, have rigidities less than 10. Instead, the φa1 cases are characterized by an induced flux that is comparable in magnitude but opposite in sign to the background flux. This suggests that the mixing of applied and background asymmetries plays an important role in determining the amplitude scaling of this transport.

Injection of electron beam into a toroidal trap using chaotic orbits near magnetic null.

Injection of charged particle beam into a toroidal magnetic trap enables a variety of interesting experiments on non-neutral plasmas. Stationary radial electric field has been produced in a toroidal geometry by injecting electrons continuously. When an electron gun is placed near an X point of magnetic separatrix, the electron beam spreads efficiently through chaotic orbits, and electrons distribute densely in the torus. The current returning back to the gun can be minimized less than 1% of the total emission.

KANDINSKY: a PIC code for fluid simulations of Penning traps

We present simulations of the nonlinear dynamics of a nonneutral plasma in a Penning trap. We use KANDINSKY, an advanced cylindrical particle-in-cell (PIC) code based on a new method that avoids the traditional problems of cylindrical PIC codes. The principal novelty resides in defining a particle volume in addition to the usual particle charge. Results from the two-dimensional drift-Poisson model and a recently developed model with compression effects are presented.

Equilibrium of a non-neutral plasma in a toroidal magnetic shear configuration

The conventional rigid rotation model of thermal equilibrium does not apply to a toroidal non-neutral plasma trap; the nonuniformity of the magnetic field produces an inhomogeneous flow. For sufficiently large ωc/ωp (ωc: cyclotron frequency; ωp: plasma frequency), the flow can be approximated by the E×B drift velocity. The toroidal equilibrium of an electron plasma has been analyzed for a rather complex geometry of magnetic shear configuration.

Three designs for a magnetic trap that will simultaneously confine neutral atoms and a non-neutral plasma

Three trap designs are proposed for the simultaneous confinement of neutral atoms and a non-neutral plasma in close proximity. One design uses axially symmetric static magnetic fields with a magnetic minimum in a ring around the trap axis. Axial symmetry is required for confinement of the rotating non-neutral plasma, and the magnetic minimum traps the neutral atoms. The second design uses a rotating axially asymmetric magnetic field superimposed on a cusp field to create a time-averaged magnetic minimum (a “TOP” trap). The rotating asymmetry acts as a magnetic “rotating wall” to help confine the non-neutral plasma. In the third design, a cylindrically symmetric high-order multipole field traps the neutral atoms, which are made to rotate about the trap axis in order to avoid the magnetic null at the trap center. These designs may be useful for the production and confinement of cold antihydrogen.

Generation of Vorticity Hole Surrounding a Point Vortex in a Nonneutral Plasma

Depleted regions (holes) in the vorticity distribution of a nonneutral plasma often play a controlling role in the evolution of two-dimensional turbulence. We report experimental investigations of the generation process of ring holes surrounding strongly-peaked clumps of vorticity (point vortex) immersed in the background of a spatially extended vorticity distribution, and determine the empirical scaling for the generation time of the ring holes.

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.

Stabilization effect of magnetic shear on the diocotron instability

The diocotron instability in a magnetized non-neutral plasma is a close cousin of the Kelvin–Helmholtz instability. A sheared magnetic field brings about coupling between the diocotron modes and the Langmuir waves that propagate along the magnetic field. The motion of electrons parallel to the magnetic field cancels the electric charge produced by the diocotron modes, resulting in stabilization of the diocotron instability.

Paul trap experiment to simulate intense nonneutral beam propagation through a periodic focusing field configuration

This paper describes the design concept for a compact Paul trap experimental configuration that fully simulates the collective processes and nonlinear transverse dynamics of an intense charged particle beam that propagates over large distances through a periodic quadrupole magnetic field. To summarize, a long nonneutral plasma column ( L⪢ r p) is confined axially by applied DC voltages V ̂ = const. on end cylinders at z=± L, and transverse confinement is provided by segmented cylindrical electrodes (at radius r w) with applied oscillatory voltages ± V 0( t) over 90° segments. Because the transverse focusing force is similar in waveform to that produced by a discrete set of periodic quadrupole magnets in a frame moving with the beam, the Paul trap configuration offers the possibility of simulating intense beam propagation in a compact experimental facility. The nominal operating parameters in the experimental design are: barium ions ( A=137); plasma column length 2L=2 m ; wall radius r w =10 cm ; plasma radius r p =1 cm ; maximum wall voltage V ̂ 0=400 V ; end electrode voltage up to V ̂ =500 V ; and voltage oscillation frequency f 0=1/T=60 kHz .

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.

Field Analysis of Two-Dimensional Dynamics of Non-neutral Plasma by Imaging Diagnostics and Examination by Sector Probing

The linear response of the luminosity of the charge-coupled-device (CCD) camera image to the electron-flux distribution on the phosphor screen is demonstrated as the basis of two dimensional (2D) analyses of non-neutral plasma dynamics. We present a fast and sufficiently accurate procedure to construct the potential and the electric field distribution from the observed 2D images. Such field analyses are essential for deep and extensive studies of vortex dynamics or turbulence. Using this procedure, we quantitatively compare the image diagnostics by sector probing for the first time to show that core dynamics which is observed clearly by imaging is severely obscured by probing; thus, its application should be limited to simple dynamics of a small number of discrete distributions of particles.

Collective resonance model of energy exchange in 3D nonequipartitioned beams.

Energy exchange between the longitudinal and transverse degrees of freedom of nonequipartitioned bunched beams (non-neutral plasmas) is investigated by means of 3D simulation. It is found that collective instability may lead to energy transfer in the direction of equipartition, without full progression to it, in certain bounded regions of parameter space where internal resonance conditions are satisfied, in good agreement with stability charts from an earlier derived 2D Vlasov analysis. Nonequipartitioned stable equilibria, however, exist in relatively wide regimes of parameter space. This provides evidence that such regimes may be safely used in the design of future high-intensity linacs.

Finite length diocotron modes

Diocotron modes are discussed for a finite length nonneutral plasma column under the assumption of bounce averaged E×B drift dynamics and small Debye length. In this regime, which is common to experiments, Debye shielding forces the mode potential to be constant along field lines within the plasma (i.e., ∂δφ/∂z=0). One can think of the plasma as a collection of magnetic-field aligned rods that undergo E×B drift across the field and adjust their length so as to maintain the condition ∂δφ/∂z=0 inside the plasma. Using the Green function (for a region bounded by a conducting cylinder) to relate the perturbed charge density and the perturbed potential, imposing the constraint ∂δφ/∂z=0, and discretizing yields a matrix eigenvalue problem. The mode eigenvector δNl,ω(rj)≡∫dz δnl,ω(rj,z) is the lth azimuthal Fourier component of the z-integrated density perturbation, and the frequency ω is the eigenvalue. The solutions include the full continuum and discrete stable and unstable diocotron modes. Finite column length introduces a new set of discrete diocotron-like modes. Also, finite column length makes possible the exponential growth of l=1 diocotron modes, long observed in experiments. The paper focuses on these two problems. To approach quantitative agreement with experiment for the l=1 instabilities, the model is extended to include the dependence of a particle’s bounce averaged rotation frequency on its axial energy. For certain distributions of axial energies, this dependence can substantially affect the instability.

Evidence for highly charged ion Coulomb crystallization in multicomponent strongly coupled plasmas.

Multicomponent non-neutral ion plasmas in a Penning trap consisting of Be(+) and highly charged Xe ions, having different mass-to-charge ratios than Be(+), are cooled to form strongly coupled plasmas by applying a laser-based collisional cooling scheme. The temperature of the plasma was determined from a Doppler broadened transition in Be(+). For the Xe ions, which are centrifugally separated from the Be, the Coulomb coupling parameter was estimated to be approximately 1000. Molecular dynamics simulations of the ion mixture show ordered structures, indicating crystallization of the Xe.

Control of Non-Neutral Plasmas and Generation of Ultra-Slow Antiproton Beam

The Antiproton Decelerator (AD) devoted primarily to atomic physics experiments has been stably operated since 2000. Until now, three proposals have been approved, two of which are on the production and spectroscopy of antihydrogen, and the third one is on atomic collisions and precision spectroscopy of antiprotonic atoms, ASACUSA collaboration. One of the unique features of the ASACUSA collaboration is to develop intense slow and ultra slow antiproton beams of high quality, which will open a new multidisciplinary field involving atomic physics, nuclear physics and elementary particle physics. The ultra slow antiprotons will be prepared by combining the AD (down to 5.3 MeV), the RFQD (Radio Frequency Quadrupole Decelerator) (down to several tens keV), and an electron cooling device which will be called “MUSASHI” (Monoenergetic Ultra Slow Antiproton Source for High-precision Investigations) (down to several eV). MUSASHI produces the eV antiproton beam through an electron cooling of trapped antiprotons and a radial compression followed by an extraction through a transport beam line. The transport beam line is specially designed so that the pressure at the trap region can be maintained more than six orders of magnitude better than the collision region and at the same time the transport efficiency is kept at almost 100%. The ultra slow antiproton beam allows for the first time to study collision dynamics such as antiprotonic atom formation and ionization processes under single collision conditions, and also to study spectroscopic nature of various metastable antiprotonic atoms such as $${\bar p}$$ p, $${\bar p}$$ He+, $${\bar p}$$ He++, etc. Metastable $${\bar p}$$ p are particularly interesting because they allow to make high precision spectroscopy of two body exotic atoms. Production and spectroscopy of antiprotonic atoms consisting of unstable exotic nuclei will also be discussed.

Molecular Dynamics Simulations of Collisional Cooling of Highly Charged Ions in a Penning Trap

Molecular dynamics simulations of the cooling of highly-charged ions captured into a Penning ion trap (RETRAP) along with Be+ ions are described. Experimentally, the Be+ ions were directly cooled continuously using a laser, and collisional coupling to these laser-cooled ions cooled the highly-charged ions. The simulation is described as a tool for experimental interpretation and refinement. Under conditions closely related to the experimental parameters, the highly charged ions were found to form ordered structures, and to exhibit characteristics of a magnetized non-neutral plasma.

The diocotron spectrum of a toroidal non-neutral plasma

The equilibrium and stability of a toroidal non-neutral plasma of low density has been studied numerically. The equilibrium is computed using the variational moment method, while linear stability is computed using a Fourier representation in the poloidal coordinate and a finite difference approximation in the radial coordinate. The computation has been carried out for various configurations to obtain frequencies of stable modes and the growth rate of instabilities.

Bifurcations in elliptical, asymmetric non-neutral plasmas

A pure electron plasma held in a Malmberg–Penning trap deforms into an ellipse when subjected to a stationary, l=2 voltage perturbation on the trap wall. At first, the plasma’s ellipticity is proportional to the strength of the perturbation, but once the perturbation increases beyond a critical value, the plasma equilibrium bifurcates into two stable off-axis equilibria and an unstable saddle. At the bifurcation point, the l=1 diocotron frequency dips to near zero. The diocotron orbits become very elliptical just below the bifurcation, and, after the bifurcation, split into three classes delimited by a separatrix: two classes surrounding the individual new equilibria, and one class surrounding both equilibria. The mode frequencies slow near the separatrix, and the trajectories themselves slow near the saddle at the origin. Interaction with the elliptical mode causes the diocotron mode to spontaneously and reversibly jump across the separatrix.

Two regimes of asymmetry-induced transport in non-neutral plasmas

Confinement of charged particles in cylindrical Penning-Malmberg traps depends strongly on cross-magnetic-field transport induced by electric and/or magnetic asymmetries. New measurements in pure-electron plasmas demonstrate two separate transport regimes depending on the particle bounce-to-rotation ratio, or rigidity, R identical with&fmacr;(b)/f(E). For R<10, the transport scales as V(a)R-2, where V(a) is the strength of an applied electrostatic asymmetry. For R greater, similar10-20, this " R-2 transport" ceases abruptly, leaving " B-independent" transport which scales as V(2)(a) and does not depend directly on the rigidity.