Non-neutral Plasma Research Articles

Confinement of Nonneutral Spheroidal Plasmas in Multi-Ring Electrode Traps

A nonneutral spheroidal plasma can be settled in a rigid rotor equilibrium inside a closed conducting cell independently of induced image charges on the cell wall if the electrostatic potential distribution on the wall surface is set equal to the sum of the external hyperbolic potential (r2 - 2z2) and the self-potential produced by the plasma. A confinement system equipped with a train of properly biased ring electrodes can approximately generate any axisymmetric potential, including the above field. Experiments on confinement of electron spheroids in such a system showed that the confinement time became the longest when the condition to diminish the image charge effects was satisfied. The observed frequency of the centre-of-mass harmonic oscillation of the plasma in this configuration was in good agreement with the estimated one.

Thermal equilibrium of warm clouds of charge with small aspect ratio

Global thermal equilibrium computations are presented for non-neutral plasmas whose radial size is much larger than their axial thickness. Axial and radial density profiles are computed for both ideal and nonideal Penning trap fields. Simple results are obtained in the limits of both low and high central density. Comparison is made to the grid calculations of Mason et al. [Phys. Plasmas 3 (5), 1502 (1996)].

Phase-Locked Rotation of Crystallized Non-neutral Plasmas by Rotating Electric Fields

Large numbers of particles with a single sign ofcharge can be trapped and cooled in Penning traps [1,2],which use a combination of static electric and magneticfields for particle confinement. The global rotation ofthese non-neutral plasmas about the magnetic field axisis necessary for the radial confinement [3]. Activecontrol of this rotation prevents plasmas from spinningdown under the ambient drag from static field errorsand background neutrals, and is important for a numberof experiments including Coulomb crystal studies [4,5],precision spectroscopy [6–8], measurements of particleand energy transport [9], trapping of antimatter plasmas[10,11], and storage of highly stripped ions [12]. As anexample, the second-order Doppler (time dilation) shiftdue to rotational velocity in a Penning trap atomic clockcan be minimized by stabilizing the rotation at a particularfrequency [7]. Radiation pressure from laser beams hasbeen used to vary the plasma rotation frequency [13,14].However, this method is limited to the few ion specieswhose atomic transitions are accessible by a laser, and isnot precise due to laser power, frequency, and pointingfluctuations. Recently, rotating azimuthally asymmetric(“rotating wall”) electric fields have been used to applya torque on Mg

Nonneutral Plasma Science Issues for Heavy Ion Drivers

A review of nonneutral plasma science issues for heavy ion drivers is presented. The requirements on transverse and longitudinal focusing at the target lead to constraints on the 6D phase space. Mechanisms which act to prevent focusability, including emittance growth, space charge and instabilities are discussed. Experiments which have explored and validated our understanding of beam transport and focusability of space-charge dominated heavy ion beams are described.

The decay instability of Langmuir waves in the non-neutral electron plasma column

The behaviour of large amplitude Langmuir waves is experimentally observed in a non-neutral electron plasma column with a cylindrical boundary. It is found that a Langmuir wave whose amplitude is above a threshold decays into lower frequency Langmuir waves. Since the dispersion relation is different from that of the unbounded neutral plasma, which is theoretically considered, the three-wave decay process of Langmuir waves becomes possible. In these processes, sidebands due to a large amplitude Langmuir wave satisfy the energy and momentum conservation relation. The threshold of this decay instability depends on the plasma temperature and becomes lower as the temperature becomes higher.

Electron Penning trap for the generation of high density non-neutral plasmas

We describe an experiment to produce high density pure electron plasmas in a cryogenic Penning trap. The apparatus and its operation are described in detail. A brief summary of data acquired to date and its interpretation are given. Possible uses and future work are mentioned.

Wall and Temperature Effects on Electrostatic Oscillations of Spheroidal Non-neutral Electron Plasmas in the Multi-Ring Electrode Trap

Electrostatic oscillations of spheroidal non-neutral electron plasmas are experimentally investigated with the multiring electrode trap which provides an electrostatic quadrupole potential with a long axial extent and enables confinement of plasmas with large aspect ratios. The frequencies of axial modes l = 2 and 3 of trapped plasmoids shifts upwards from those predicted by Dubin's cold plasma theory for the free boundary case, mainly due to the image charges induced on the conducting electrodes. These frequencies continue to increase as the plasma temperature is increased from 0.03 eV to 1.5 eV by rf heating. This temperature dependence can be interpreted as a change in the dielectric tensor caused by the temperature increase.

Neoclassical transport in an annular penning trap

A modified Penning trap is described with an annular confinement region and a toroidal magnetic field. A non-neutral electron plasma is confined axially by an electrostatic field and, in the radial direction, particles are constrained to lie within a small drift distance of a cylindrical flux surface. Drift orbits of all particles are banana-shaped and collisions cause neoclassical transport.

Structure of Bernstein Modes in a Nonneutral Plasma Column

An analytical description of Bernstein modes in a nonneutral plasma column is presented and validated using the results of a particle-in-cell simulation. A new collisionless damping mechanism experienced by these modes is demonstrated.

Cross-Magnetic-Field Heat Conduction in Non-neutral Plasmas

This Letter discusses cross-magnetic-field collisional heat transport for a non-neutral plasma in the typical operating regime ${\ensuremath{\lambda}}_{D}\ensuremath{\gg}{r}_{c}$, where ${\ensuremath{\lambda}}_{D}$ is the Debye length and ${r}_{c}$ is the cyclotron radius. The dominant transport mechanism is the exchange of energy associated with velocity components parallel to the magnetic field. For a thermal gradient scale length ${L}_{T}\ensuremath{\gtrsim}100{\ensuremath{\lambda}}_{D}$, the energy exchange is dominated by interactions between particles separated by $O({\ensuremath{\lambda}}_{D})$ and yields a thermal diffusivity $\ensuremath{\chi}\ensuremath{\sim}{\ensuremath{\nu}}_{c}{\ensuremath{\lambda}}_{D}^{2}$, where ${\ensuremath{\nu}}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n\overline{v}{b}^{2}$ is the collision frequency. The diffusivity is even larger for larger ${L}_{T}$, where the energy exchange is dominated by the emission and absorption of plasma waves.

Confinement of test particles in a Malmberg–Penning trap with a biased axial wire

A non-neutral plasma trap has been constructed in which the radial electric field of a non-neutral plasma column is simulated by a biased wire stretched along the axis of the device. The confinement time of test electrons in this device is found to be comparable in magnitude and scaling with that found in pure electron plasma experiments, in spite of the fact that the test electron density is 102 times smaller than in a typical pure electron plasma. The confinement time is only weakly dependent on the central wire bias. These results may provide useful input to theoretical efforts to explain transport in these traps.

Beyond the Brillouin limit with the Penning Fusion Experiment

Several years ago, it was proposed that a dense non-neutral plasma could be produced in a Penning trap. Nonneutral plasmas have excellent confinement, and such a dense plasma might produce simultaneously high density and good confinement. Recently, this theoretical conjecture has been demonstrated in a small (3 mm radius) electron experiment, PFX (Penning Fusion Experiment). Densities up to 35 times the Brillouin density (limiting number density in a static trap) have been inferred from the observed strong (100:1) spherical focusing. Electrons are injected at low energy from a single pole of the sphere. A surprising observation is the self-organization of the system into a spherical state, which occurs precisely when the trap parameters are adjusted to produce a spherical well. This organization is caused by a bootstrapping mechanism which produces a hysteresis. Observations of energy-scattered electrons confirm the existence of a dense spherical focus.

Orbital resonances and chaos in a combined rf trap

The rf combined trap for confining a non-neutral plasma by a combination of rf fields and a uniform magnetic field is introduced. The particle motion is studied in such a trap in which the rf fields are given by the TM011 mode. The aim is to determine limits on a focus at the center for low angular momentum particles. Such a focus allows densities in excess of the local Brillouin limit. The motion is described in terms of an effective potential consisting of the ponderomotive potential Vpon(r,z) plus a radial potential mΩc2r2/8 due to the magnetic field Bz plus a centrifugal potential pθ2/2mr2. Near the origin r=0, z=0, the equations reduce to a pair of Mathieu equations for the r and z motions. For certain parameters the system is quasispherically symmetric, i.e. the effective ponderomotive frequencies Ωr, Ωz in r and z are equal. In this case the Brillouin limit for a uniform density plasma is shown to equal the usual cylindrical limit. Numerical integration of the ponderomotive equations is shown for parameters near those giving quasispherical symmetry. There is resonance for Ωr/Ωz=1, giving m=2, n=2 islands. The islands limit the size of the focus at the origin, even for pθ=0. For particles with large effective energy Eeff, there can also be chaos, depending on the elongation L/a of the rf cavity. It is found that the deleterious effect of islands and chaos on the focus is minimized by having the elongation L/a close to unity and having particles trapped deeply in the ponderomotive well.

Continuous spectrum of a non-neutral plasma column

The linearized dynamics about the cylindrical equilibrium of a non-neutral plasma in a uniform axial magnetic field is discussed. A spectral analysis shows the existence of two continua, both of which are shown to be stable. The possibility of Suydam-like rapidly oscillating solutions is also demonstrated. The Suydam solutions may imply the existence of an infinite sequence of unstable modes that belong to the discrete spectrum.

Steady-State Confinement of Non-neutral Plasmas by Rotating Electric Fields

We apply ``rotating wall'' electric fields to spin up a non-neutral plasma in a Penning-Malmberg trap, resulting in steady-state confinement (weeks) of up to ${10}^{9}{\mathrm{Mg}}^{+}$ ions. The resulting ion columns can be near global thermal equilibrium, with near-uniform temperature and rotation frequency. The equilibrated plasma $\mathbf{E}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ rotation rate ${f}_{E}$ is observed to be somewhat less than the drive frequency ${f}_{w}$, with slip $\ensuremath{\Delta}f\ensuremath{\equiv}{f}_{w}{\ensuremath{-}f}_{E}$ depending on temperature as $\ensuremath{\Delta}f\ensuremath{\propto}{T}^{1/2}$ for $0.05\ensuremath{\lesssim}T\ensuremath{\lesssim}5\mathrm{eV}$. Dynamic measurements of applied torque versus slip frequency show plasma spin up and compression for $\ensuremath{\Delta}f>0$ and plasma slowing and expansion for $\ensuremath{\Delta}f<0$. By gradually increasing ${f}_{w}$, density compression up to 20% of the Brillouin density limit has been achieved. Heating resonances and hysteresis in plasma parameters are also observed.

Observation of Spherical Focus in an Electron Penning Trap

We produce simultaneously dense and well-confined nonneutral plasmas by spherical focusing. A small (3 mm radius) Penning trap has low-energy electrons injected at a single pole of the sphere. Precisely when the trap parameters are adjusted to produce a spherical well, the system self-organizes into a spherical state through a bootstrapping mechanism which produces a hysteresis. Additional confirmation of the dense spherical focus is provided by electrons scattered by the central core. Core densities up to 35 times the Brillouin density have been inferred from the data.

Damped diocotron quasi-modes of non-neutral plasmas and inviscid fluids

Computations of damped diocotron oscillations (quasi-modes) are described for non-neutral plasmas and inviscid fluids. The numerical method implements a suggestion made by Briggs, Daugherty, and Levy some 25 years ago [Phys. Fluids 13, 421 (1970)] to push the branch line that forms the continuum into the complex ω-plane by solving the mode equation in the complex r-plane. For the special case of power-law density profiles the calculation finds the same quasi-mode frequencies found recently by Corngold [Phys. Plasmas 2, 620 (1995)]. It is found that the feature of the continuum eigenfunctions which indicates the presence of a nearby quasi-mode is continuity of the derivative of the regular part of the eigenfunctions near the singularity. The evolution of Rayleigh modes, found in density profiles with steps, is also studied as the density steps are smoothed.

The non-neutral plasma: an introduction to physics with relevance to cyclotron resonance mass spectrometry

The non-neutral plasma has been used as a valuable experimental medium separately by a generation of physicists and chemists. This work provides an introduction to the field of non-neutral plasma physics and reviews those findings that apply to the practice of cyclotron resonance mass spectrometry. We begin with fundamental concepts and definitions and continue in the logical order with characterizations of the equilibrium state, transport to equilibrium, and lastly the modes and waves supported by an unneutralized charge cloud. Because the emphasis throughout is placed on an intuitive presentation of the physics with relevance specifically to mass spectrometry, numerous citations to more complete work are provided.

Toroidal magnetic confinement of non-neutral plasma

A concept of toroidal magnetic trap for a positron plasma has been examined. The key parameter studied in this paper is the connection length between a source (radio-isotope such as 22Na) and a sink (a material that intersects the orbit). A long connection length allows us to apply a slow deceleration mechanism such as a wave-particle interaction. The connection length is remarkably increased when the positron source is placed just on the separatrix. This is due to non-periodic (chaotic) motion of particles near the separatrix.

ℓ=1 electrostatic instability induced by electron-neutral collisions in a nonneutral electron plasma interacting with background neutral gas

This paper investigates theoretically the electrostatic stability properties of a nonneutral electron plasma interacting with background neutral gas through elastic collisions with constant collision frequency νen. The model treats the electrons as a strongly magnetized fluid (ωpe2/ωce2≪1) immersed in a uniform magnetic field B0êz, and assumes small-amplitude perturbations with azimuthal mode number ℓ=1 and negligible axial variation (∂/∂z=0). The analysis also assumes weak electron collisions with νen/ωce=ε≪1, and that the process of heat conduction is sufficiently fast that the electrons have relaxed through electron-electron collisions to a quasiequilibrium state with scalar pressure P(r,θ,t)=n(r,θ,t)T, and isothermal temperature T. Assuming that perturbed quantities vary with time according to exp(−iωt), the detailed stability analysis carried out to first order in νen/ωce≪1 shows that the real oscillation frequency and growth rate for the ℓ=1 diocotron mode are given, respectively, by the simple expressions Re ω=ω0 and Im ω=(νen/ωce)ω0. Here, ω0=Nec/r2wB0, where rw is the perfectly conducting wall radius, and N=∫d2x n is the number of electrons per unit axial length. This analysis suggests that a measurement of the oscillation frequency and growth rate for the ℓ=1 diocotron mode can be used to infer νen, and thereby serve as a sensor for the background neutral pressure.