Showing papers in "Physics of Plasmas in 1994"

Ignition and high gain with ultrapowerful lasers

Abstract: Ultrahigh intensity lasers can potentially be used in conjunction with conventional fusion lasers to ignite inertial confinement fusion (ICF) capsules with a total energy of a few tens of kilojoules of laser light, and can possibly lead to high gain with as little as 100 kJ. A scheme is proposed with three phases. First, a capsule is imploded as in the conventional approach to inertial fusion to assemble a high‐density fuel configuration. Second, a hole is bored through the capsule corona composed of ablated material, as the critical density is pushed close to the high‐density core of the capsule by the ponderomotive force associated with high‐intensity laser light. Finally, the fuel is ignited by suprathermal electrons, produced in the high‐intensity laser–plasma interactions, which then propagate from critical density to this high‐density core. This new scheme also drastically reduces the difficulty of the implosion, and thereby allows lower quality fabrication and less stringent beam quality and symmet...

Toroidal gyro‐Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes

Abstract: The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyrokinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro‐Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel three‐dimensional (3‐D) nonlinear ballooning mode representation. The representation is a Fourier transform of a field line following basis (ky’,kx’,z’) with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky’ = 0, kx’ ≠ 0) ‘‘radial modes’’ in s...

Interaction of an ultrashort, relativistically strong laser pulse with an overdense plasma

Abstract: The results of an analytical description and of a particle‐in‐cell simulation of the interaction of an ultrashort, relativistically intense laser pulse, obliquely incident on a nonuniform overdense plasma, are presented and several novel features are identified. The absorption and reflection of the ultraintense electromagnetic laser radiation from a sharp‐boundary plasma, high harmonic generation, and the transformation into low‐frequency radiation are discussed. In the case of weak plasma nonuniformity the excitation of nonlinear Langmuir oscillations in the plasma resonance region and the resulting electron acceleration are investigated. The vacuum heating of the electrons and the self‐intersection of the electron trajectories are also studied. In the case of a sharp‐boundary plasma, part of the energy of the laser pulse is found to be converted into a localized, relativistically strong, nonlinear electromagnetic pulse propagating into the plasma. The expansion of the hot electron cloud into the vacuum region and the action of the ponderomotive force of the laser pulse in the localized longitudinal electric field of the Langmuir oscillations lead to ion acceleration. The energy increase of a minority population of multicharged ions is found to be much greater than that of the ambient ions.

First results from Alcator‐C‐MOD*

Abstract: Early operation of the Alcator‐C‐MOD tokamak [I.H. Hutchinson, Proceedings of IEEE 13th Symposium on Fusion Engineering, Knoxville, TN, edited by M. Lubell, M. Nestor, and S. Vaughan (Institute of Electrical and Electronic Engineers, New York, 1990), Vol. 1, p. 13] is surveyed. Reliable operation, with plasma current up to 1 MA, has been obtained, despite the massive conducting superstructure and the associated error fields. However, vertical disruptions are not slowed by the long vessel time constant. With pellet fueling, peak densities up to 9×1020 m−3 have been attained and ‘‘snakes’’ are often seen. Initial characterization of divertor and scrape‐off layer is presented and indicates approximately Bohm diffusion. The edge plasma shows a wealth of marfe‐like phenomena, including a transition to detachment from the divertor plates with accompanying radiative divertor regions. Energy confinement generally appears to exceed the expectations of neo‐Alcator scaling. A transition to Ohmic H mode has been observed. Ion cyclotron heating experiments have demonstrated good power coupling, in agreement with theory.

Theory of magnetohydrodynamic instabilities excited by energetic particles in tokamaks

Abstract: The resonant excitations of high‐n magnetohydrodynamic instabilities by the energetic ions/alpha particles in tokamaks are theoretically analyzed. Here, n is the toroidal mode number. The magnetohydrodynamic eigenmodes, typically, consist of two‐scale structures; one corresponds to the singular (‘‘inertial’’) region and the other the regular (ideal) region. Due to the finite‐size orbits, the energetic particle contributions in the singular region are suppressed. Analytical dispersion relations can be derived via the asymptotic matching analysis. The dispersion relations have the generic form of the ‘‘fishbone’’ dispersion relation [Phys. Rev. Lett. 52, 1122 (1984)] and demonstrate, in particular, the existence of two types of modes; that is, the discrete gap mode and the energetic‐particle continuum mode. Specific expressions are given for both the kinetic ballooning modes and the toroidal Alfven modes.

Magnetohydrodynamic processes in the solar corona: Flares, coronal mass ejections, and magnetic helicity*

Abstract: The magnetized, million‐degree solar corona evolves in cycles of about 11 years, in dynamical response to newly generated magnetic fluxes emerging from below to eventually reverse the global magnetic polarity. Over the larger scales, the corona does not erupt violently all the time. Violent events like the flares and episodic ejections of material into interplanetary space occur frequently, several times a day, but they often originate in long‐lived magnetic structures that form continually throughout the solar cycle. In this paper, the creation, stability, and eventual eruption of these structures are discussed from basic principles, drawing on recent advances in observation and theory. A global view is offered in which different pieces of observation relate physically, with distinct roles for the conservation of magnetic helicity and the release of magnetic energy in dissipated and ordered forms.

Creation and uses of positron plasmas

Abstract: Advances in positron trapping techniques have led to room‐temperature plasmas of 107 positrons with lifetimes of 103 s. Improvements in plasma manipulation and diagnostic methods make possible a variety of new experiments, including studies just being initiated of electron–positron plasmas. The large numbers of confined positrons have also opened up a new area of positron annihilation research, in which the annihilation cross sections for positrons with a variety of molecules have been measured, as well as the energy spread of the resulting gamma rays. Such measurements are of interest for fundamental physics and for the modeling of astrophysical plasmas.

Theory of the collisional presheath in an oblique magnetic field

Abstract: In the limit of a small Debye length (λD→0), the plasma boundary layer in front of a negative absorbing wall is split up into a collision‐free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to ion sound speed (Bohm criterion) Usually the presheath mechanism depends decisively on collisional friction of the ions, on ionization, or on geometric ion current concentration If the ion dynamics in the presheath is dominated by a magnetic field (nearly) parallel to the wall, an additional effect must be considered to provide an ion transport to the wall The special cases (a) of an ion transport by field lines intersecting the wall at a finite angle and (b) of an ion transport by collisions result in somewhat contradictory conclusions To get a coherent picture, a hydrodynamic model of the presheath is investigated accounting for an oblique magnetic field and for collisions The limiting cases (a) and (b) are discussed, and it is shown that (in plane geometry) the presheath ion acceleration depends always on elementary processes The main effect of a strong magnetic field is to ‘‘compress’’ the collisional presheath into a thin layer with a characteristic extension of the ion gyroradius ρi

A review of the ablative stabilization of the Rayleigh--Taylor instability in regimes relevant to inertial confinement fusion

Abstract: It has been recognized for many years that the most significant limitation of inertial confinement fusion (ICF) is the Rayleigh–Taylor (RT) instability. It limits the distance an ablatively driven shell can be moved to several times its initial thickness. Fortunately material flow through the unstable region at velocity vA reduces the growth rate to √kg/1+kL−βkvA with β from 2–3. In recent years experiments using both x‐ray drive and smoothed laser drive to accelerate foils have confirmed the community’s understanding of the ablative RT instability in planar geometry. The growth of small initial modulations on the foils is measured for growth factors up to 60 for direct drive and 80 for indirect drive. For x‐ray drive large stabilization is evident. After some growth, the instability enters the nonlinear phase when mode coupling and saturation are also seen and compare well with modeling. Normalized growth rates for direct drive are measured to be higher, but strategies for reduction by raising the isentrope are being investigated. For direct drive, high spatial frequencies are imprinted from the laser beam and amplified by the RT instability. Modeling shows an understanding of this ‘‘laser imprinting.’’

Role of the radial electric field in the transition from L (low) mode to H (high) mode to VH (very high) mode in the DIII‐D tokamak*

Abstract: The hypothesis of stabilization of turbulence by shear in the E×B drift speed successfully predicts the observed turbulence reduction and confinement improvement seen at the L (low)–H (high) transition; in addition, the observed levels of E×B shear significantly exceed the value theoretically required to stabilize turbulence. Furthermore, this same hypothesis is the best explanation to date for the further confinement improvement seen in the plasma core when the plasma goes from the H mode to the VH (very high) mode. Consequently, the most fundamental question for H‐mode studies now is: How is the electric field Er formed? The radial force balance equation relates Er to the main ion pressure gradient ∇Pi, poloidal rotation vθi, and toroidal rotation vφi. In the plasma edge, observations show ∇Pi and vθi are the important terms at the L–H transition, with ∇Pi being the dominant, negative term throughout most of the H mode. In the plasma core, Er is primarily related to vφi. There is a clear temporal and spatial correlation between the change in E×B shear and the region of local confinement improvement when the plasma goes from the H mode to the VH mode. Direct manipulation of the vφi and E×B shear using the drag produced by a nonaxisymmetric magnetic perturbation has produced clear changes in local transport, consistent with the E×B shear stabilization hypothesis. The implications of these results for theories of the L–H and H–VH transitions will be discussed.

Generalized two-fluid theory of nonlinear magnetic structures

Abstract: A system of equations is introduced and discussed that describe the nonlinear dynamics of magnetic perturbations in a magnetized, high‐temperature plasma. Diamagnetism, ion gyroradii effects, and finite electron mass are taken into account. These equations govern Alfven as well as electrostatic waves and vortices and describe the nonlinear evolution of reconnecting modes. Electrons are treated in a fluid model. The equation for the ion response is new and is a nonlinear generalization to all orders in the thermal ion gyroradius of the nonlinear fluid model. This system of equations conserves two fluxes that are different from, but related to, the magnetic flux. Two‐dimensional equilibrium solutions in the form of stationary propagating magnetic structures are obtained with the methods introduced in the theory of vector nonlinearities in electrostatic drift vortices. In the noncollisional regimes of interest the inertia of the electrons resolves the singularity in the current density that tends to develop at magnetic separatrices. The positions of the X points of the conserved fluxes are mirror symmetric and at a distance of the order of the electron skin depth from the resonant surface. The set of equations admits an energy integral and can be cast in noncanonical Hamiltonian form. The role of the Casimir invariants, that are functions of the conserved fluxes, is investigated and the connection with ‘‘reduced magnetohydrodynamics’’ is emphasized.

Investigation of magnetic reconnection during a sawtooth crash in a high‐temperature tokamak plasma

Abstract: In this paper a laboratory investigation is made on magnetic reconnection in high‐temperature Tokamak Fusion Test Reactor (TFTR) plasmas [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 51]. The motional Stark effect (MSE) diagnostic is employed to measure the pitch angle profile of magnetic field lines, and hence the q profile. An analytical expression that relates pitch angle to q profile is presented for a toroidal plasma with circular cross section. During the crash phase of sawtooth oscillations in plasma discharges, the ECE (electron cyclotron emission) diagnostic measures a fast flattening of the two‐dimensional (2‐D) electron temperature profile in a poloidal plane, an observation consistent with the Kadomtsev reconnection theory. On the other hand, the MSE measurements indicate that central q values do not relax to unity after the crash, but increase only by 5%–15%, typically from 0.7 to 0.8. The latter result is in contrad...

Stability of high beta tokamak plasmas

Abstract: Stability at high beta (the ratio of plasma pressure to magnetic fieldpressure) is an important requirement for a compact, economically attractive fusion reactor. It is also important in present large tokamak experiments, where the best performance is now often limited by instabilities rather than by energy transport. The past decade has seen major advances in our understanding of the stability of high beta tokamak plasmas, as well as in the achievement of high values of beta. Ideal magnetohydrodynamic(MHD) theory has been remarkably successful in predicting the stability limits, and the scaling of maximum stable beta with the normalized plasma current predicted by Troyon and others has been confirmed in many experiments, yielding a limit βmax≊3.5 (%‐m‐T/MA) I/aB (where I is the plasma current, a is the minor radius, and B is the toroidal field). The instabilities which are predicted to limit beta have been observed experimentally, in good agreement with theoretical predictions, including long‐wavelength kink modes and short‐wavelength ballooning instabilities. Advances in understanding of tokamak stability have opened several paths to higher values of beta. The use of strong discharge shaping, approaching the limits of axisymmetric stability, has allowed beta values as high as 12% to be reached in agreement with Troyon scaling. Recent experimental results and ideal MHD modeling have shown that the beta limit depends on the form of the pressure and current density profiles, and modification of the current density to create a centrally peaked profile has allowed beta values up to 6I/aB to be achieved experimentally. Recent experiments have also begun to explore both local and global access to the predicted second stable regime for ballooning modes, with the potential for very high values of β/(I/aB). Preliminary experimental investigations of wall stabilization and radio‐frequency (RF) current profile control hold the promise of further improvements in beta through passive and active control of instabilities. The developing understanding of high beta stability and the application of this understanding to present experiments and future fusion devices hold the potential for production of stable, steady state plasmas at high beta with good confinement.

A unified Monte Carlo interpretation of particle simulations and applications to non-neutral plasmas

Abstract: Using a ‘‘Monte Carlo interpretation’’ of particle simulations, a general description of low‐noise techniques, such as the δf method, is developed in terms well‐known Monte Carlo variance reduction methods. Some of these techniques then are applied to linear and nonlinear studies of pure electron plasmas in cylindrical geometry, with emphasis on the generation and nonlinear evolution of electron vortices. Long‐lived l=1 and l=2 vortices, and others produced by unstable diocotron modes in hollow profiles, are studied. It is shown that low‐noise techniques make it possible to follow the linear evolution and saturation of even the very weakly unstable resonant diocotron modes.

Particle simulation study of driven magnetic reconnection in a collisionless plasma

Abstract: Driven magnetic reconnection in a collisionless plasma, ‘‘collisionless driven reconnection,’’ is investigated by means of two‐and‐one‐half‐dimensional particle simulation. Magnetic reconnection develops in two steps, i.e., slow reconnection, which takes place in the early stage of the compression when the current layer is compressed as thin as the orbit amplitude of an ion meandering motion (ion current layer), and subsequent fast reconnection, which takes place in the late stage when the electron current is concentrated into the narrow region with a spatial scale comparable to the orbit amplitude of an electron meandering motion (electron current layer). The global dynamic evolution of magnetic reconnection is controlled by the physics of the ion current layer. The maximum reconnection rate is roughly in proportion to the driving electric field. It is also found that both ion heating and electron heating take place in accordance with the formation of two current layers and the ion temperature becomes two or more times as high as the electron temperature.

The biorthogonal decomposition as a tool for investigating fluctuations in plasmas

Abstract: The investigation of fluctuation phenomena in plasmas often necessitates the analysis of spatiotemporal signals. It is shown how such signals can be analyzed using the biorthogonal decomposition, which splits them into orthogonal spatial and temporal modes. The method, also referred to as the singular value decomposition, allows complex spatiotemporal patterns to be decomposed into a few coherent modes that are often easier to interpret. This is illustrated with two applications to fluctuating soft x‐ray and magnetic signals, as measured in a tokamak. Emphasis is given to the physical interpretation of the biorthogonal components and their link with known physical models is discussed. It is shown how new insight can be gained in the interpretation of spatiotemporal plasma dynamics.

Solution of the drift‐kinetic equation for global plasma modes and finite particle orbit widths

Abstract: The response of a collisionless plasma to global electromagnetic perturbations of an axisymmetric toroidal equilibrium is derived. By adopting a variational formulation for guiding center motion, the perturbed distribution function is expressed in terms of the linearized guiding center Lagrangian. Finite orbit widths are retained. In particular, the high particle energy limit where mirror‐trapped banana orbits are distorted into ‘‘potato‐shaped’’ orbits is considered. In this limit, the time scales associated with the drift and bounce motions of a mirror‐trapped orbit become comparable, yielding important consequences on plasma stability. Quadratic forms are constructed in the context of kinetic‐magnetohydrodynamic (MHD) models of plasmas composed of a thermal component obeying fluid‐like equations and a high‐energy component described in terms of the collisionless drift‐kinetic equation. Relevant applications include improved modeling of energetic ion effects on toroidicity‐induced Alfven gap modes and i...

Generalized weighting scheme for δf particle‐simulation method

Abstract: An improved nonlinear weighting scheme for the δf method of kinetic particle simulation is derived. The method employs two weight functions to evolve δf in phase space. It is valid for quite general, non‐Hamiltonian dynamics with arbitrary sources. In the absence of sources, only one weight function is required and the scheme reduces to the nonlinear algorithm developed by Parker and Lee [Phys. Fluids B 5, 77 (1993)] for sourceless simulations. (It is shown that their original restriction to Hamiltonian dynamics is unnecessary.) One‐dimensional gyrokinetic simulations are performed to show the utility of this two‐weight scheme. A systematic kinetic theory is developed for the sampling noise due to a finite number of marker trajectories. The noise intensity is proportional to the square of an effective charge qeff=q(w/D), where w ∼δf/f is a typical weight and D is the dielectric response function.

Propagation of waves in dusty plasmas with variable charges on dust particles

Abstract: The propagation of electromagnetic and Langmuir waves in multicomponent unmagnetized plasmas with dust particles is investigated. The effect of capture of plasma electrons and ions by the dust particles is taken into account. The recent theory proposed by Tsytovich and Havnes [Comments Plasma Phys. Controlled Fusion 15, 267 (1993)] to describe the kinetics of the capture process, as well as its perturbations, is further developed. The new wave damping due to this effect is calculated.

Calculation of the dielectric tensor for a generalized Lorentzian (kappa) distribution function

Abstract: Expressions are derived for the elements of the dielectric tensor for linear waves propagating at an arbitrary angle to a uniform magnetic field in a fully hot plasma whose constituent particle species σ are modeled by generalized Lorentzian distribution functions. The expressions involve readily computable single integrals whose integrands involve only elementary functions, Bessel functions, and modified plasma dispersion functions, the latter being available in the form of finite algebraic series. Analytical forms for the integrals are derived in the limits λ→0 and λ→∞, where λ=(k⊥ρLσ)2/2, with k⊥ the component of wave vector perpendicular to the ambient magnetic field, and ρLσ the Larmor radius for the particle species σ. Consideration is given to the important limits of wave propagation parallel and perpendicular to the ambient magnetic field, and also to the cold plasma limit. Since most space plasmas are well modeled by generalized Lorentzian particle distribution functions, the results obtained in this paper provide a powerful tool for analyzing kinetic (micro‐) instabilities in space plasmas in a very general context, limited only by the assumptions of linear plasma theory.

The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox

Abstract: The role of dissipation in the theory and simulations of homogeneous plasma slices is analyzed with the goal of understanding the ‘‘entropy paradox,’’ which is that a certain positive‐definite functional of the perturbed distribution function increases without bound in some situations even though the potentials appear to have achieved a steady state. Confusion arises from an interchange of the limits t→∞ and η→0, where η is a measure of dissipation. It is argued that it is never strictly correct to neglect η; the averaged dissipation approaches a nonzero limit (proportional to the averaged flux) even as η→0. An exactly soluble model is worked out to illustrate the point. In collisionless particle simulations, the particle and heat fluxes may nevertheless saturate with their correct values. The relations of kinetic and fluid entropy balances are discussed with the aid of (1) the Terry–Horton model for collisionless drift waves, and (2) a simple model of the ion‐temperature‐gradient‐driven mode. The rationale for simulations of homogeneous slices of plasma is given, with particular emphasis being placed on the relationship of dissipation in such slices to dissipation in a complete physical domain.

Rotation shear induced fluctuation decorrelation in a toroidal plasma

Abstract: The enhanced decorrelation of fluctuations by the combined effects of the E×B flow (VE) shear, the parallel flow (V∥) shear, and the magnetic shear is studied in toroidal geometry. A two‐point nonlinear analysis previously utilized in a cylindrical model [Phys. Fluids B 2, 1 (1990)] shows that the reduction of the radial correlation length below its ambient turbulence value (Δr0) is characterized by the ratio between the shearing rate ωs and the ambient turbulence scattering rate ΔωT. The derived shearing rate is given by ω2s= (Δr0)2[(1/Δφ2){(∂/∂r)(qVE/r)}2 +(1/Δη2){(∂/∂r)(V∥/qR)}2], where Δφ and Δη are the correlation angles of the ambient turbulence along the toroidal and parallel directions. This result deviates significantly from the cylindrical result for high magnetic shear or for ballooning‐like fluctuations. For suppression of flute‐like fluctuations, only the radial shear of qVE/r contributes, and the radial shear of V∥/qR is irrelevant regardless of the plasma rotation direction.

Tabletop x-ray lasers

Abstract: Details of schemes for two tabletop size x‐ray lasers that require a high‐intensity short‐pulse driving laser are discussed. The first is based on rapid recombination following optical‐field ionization. Analytical and numerical calculations of the output properties are presented. Propagation in the confocal geometry is discussed and a solution for x‐ray lasing in Li‐like N at 247 A is described. Since the calculated gain coefficient depends strongly on the electron temperature, the methods of calculating electron heating following field ionization are discussed. Recent experiments aimed at demonstrating lasing in H‐like Li at 135 A are discussed along with modeling results. The second x‐ray laser scheme is based on the population inversion obtained during inner‐shell photoionization by hard x rays. This approach has significantly higher‐energy requirements, but lasing occurs at very short wavelengths (λ≤15 A). Experiments that are possible with existing lasers are discussed.

Applications of intense pulsed ion beam to materials science

Abstract: In addition to being initially developed as an energy driver for an inertial confinement fusion, an intense, pulsed, light‐ion beam (LIB) has been found to be applied to materials science. If a LIB is used to irradiate targets, a high‐density ‘‘ablation’’ plasma is produced near the surface since the range of the LIB in materials is very short. Since the first demonstration of quick preparation of thin films of ZnS by an intense, pulsed, ion‐beam evaporation (IBE) using the LIB‐produced ablation plasma, various thin films have been successfully prepared, such as of ZnS:Mn, YBaCuO, BaTiO3, cubic BN, SiC, ZrO2, ITO, B, C, and apatite. Some of these data will be presented in this paper, with its analytic solution derived from a one‐dimensional, hydrodynamic, adiabatic expansion model for the IBE. The temperature will be deduced using ion‐flux signals measured by a biased ion collector. Reasonable agreement is obtained between the experiment and the simulation. High‐energy LIB implantation to make chemical co...

Laser guiding in an axially nonuniform plasma channel

Abstract: A plasma channel produced by a short laser pulse is axially nonuniform due to self‐defocusing of the laser. When a delayed second laser pulse propagates through the channel, diffraction and refraction effects do not balance each other exactly, resulting in periodic beam radius variation with the distance of propagation.

The excitation of obliquely propagating fast Alfvén waves at fusion ion cyclotron harmonics

Abstract: The theory of the magnetoacoustic cyclotron instability, which has been proposed as a mechanism for suprathermal ion cyclotron harmonic emission observed in large tokamaks, is generalized to include finite parallel wave number k∥. This extension introduces significant new physics: the obliquely propagating fast Alfven wave can undergo cyclotron resonant interactions with thermal and fusion ions, which affects the instability driving and damping mechanisms. The velocity–space distribution of the fusion ions is modeled by a drifting ring, which approximates the distribution calculated for the emitting region in tritium experiments on the Joint European Torus (JET) [Cottrell et al., Nucl. Fusion 33, 1365 (1993)]. Linear instability can occur simultaneously at the fusion ion cyclotron frequency and all its harmonics when the fusion ion concentration is extremely low, because the finite k∥ gives rise to a Doppler shift, which decouples cyclotron damping due to thermal ions from wave growth associated with fusi...

Non‐neutral ion plasmas and crystals, laser cooling, and atomic clocks*

Abstract: Experimental work which uses Penning and Paul traps to confine non‐neutral ion plasmas is discussed. Penning traps use a static uniform magnetic field and a static electric field to confine ions. The Paul trap uses the ponderomotive force from inhomogeneous radio‐frequency fields to confine ions to a region of minimum field strength. In many atomic physics experiments, these traps are designed to produce a harmonic restoring force for small numbers of stored ions (<104). Under these conditions and at low temperatures, both traps produce plasmas with simple shapes whose mode properties can be calculated exactly. Laser cooling has been used to reduce the temperature of trapped ions to less than 10 mK with ion spacings less than 20 μm. At such temperatures and interion spacings, the Coulomb potential energy between nearest neighbor ions is greater than the ion thermal energy and the ions exhibit spatial correlations characteristic of a liquid or crystal. Laser beams also apply a torque which, by changing the plasma angular momentum, changes the plasma density. Atomic clocks are an important application of ion trap plasmas. Better control of the plasma dynamics will reduce fluctuations in the relativistic time dilation, yielding better clocks.

Electron emission: From the Fowler–Nordheim relation to the Child–Langmuir law

Abstract: Universal voltage‐current characteristics are presented for a planar diode, showing the general transition from the Fowler–Nordheim relation to the Child–Langmuir law. These curves are normalized to the intrinsic scales that are constructed from the Fowler–Nordheim coefficients A, B. They provide an immediate assessment of the importance of the space charge effects, once the gap voltage, gap spacing, and the Fowler–Nordheim coefficients are specified. An example in the parameter regime of vacuum microelectronics is presented.

Shielding of a slowly moving test charge in dusty plasmas

Abstract: The far‐field potential of a slowly moving test charge in dusty plasmas is calculated accounting for the dust grain charge fluctuations. It is found that the latter cause a damping, which in turn gives rise to a dipole‐like far‐field potential. The presence of the dipole‐like potential is attributed to the dust grain charge perturbations caused by the oscillating electron and ion currents induced by the motion of a test charge.

Interpenetration and ion separation in colliding plasmas

Abstract: The interpenetration of colliding plasmas in the transition regime, where the ion–ion mean‐free path is of the same order as the gradient scale length, is studied by one‐dimensional simulations and dimensional analysis. Separate fluid equations for multiple species are solved, with coupling between the different species due to the electric field and Coulomb collisions. These simulations show initial interpenetration followed by a ‘‘soft’’ stagnation. For colliding plasmas characteristic of opposing laser heated disks, the stagnation time, the stagnation density and temperature, and the interpenetration distance are shown to depend primarily on a single parameter, defining the ratio of the scale length to the ion–ion mean‐free path. Simulations of colliding plasmas from exploding plastic foils with separate ion fluids for the carbon and hydrogen are presented, showing appreciable ion separation. These results may provide a guide for the design of interpenetrating plasma experiments.