The phenomenon of electric double layers in plasmas as a generalization of ambipolar effects and as an essential time dependent and oscillating phenomenon in the plasma interior, has emerged from studies in laser produced plasmas as well as from similar problems in space plasmas and their laboratory simulation experiments. While these results have been published occasionally in various places including the most prestigious journals and in small topical conferences, there was still a need to enter a more comprehensive presentation and overview into a referred journal.

Current driven electrostatic-wave- and electromagnetic-wave-produced resistivities do not occur in extragalactic jets for estimated values of the carried currents. Strong plasma double layers, however, may exist within self-maintained density cavities. The relativistic double-layer-emitted electron and ion beams drive plasma-wave resistivities in the low- and high-potential plasma adjacent to the double layers. The double-layeremitted electron beams may also emit polarized radio waves via a collectivebremsstrahlung process mediated by electrostatic two-stream instabilities.

Double layers in plasmas can be created by different means. For example, a potential difference forms between two plasmas with different temperatures (Hultqvist 1971; Ishiguro et al. 1985), in a plasma jet flowing along a converging magnetic field (Serizawa & Sato 1984), in a quiescent plasma submitted to an external difference of potential or in a turbulent plasma carrying an electric current. The first three cases can be current-free, but not necessarily, although the numerical simulations have been made under such conditions for the first two points (Ishiguro et al. 1985; Serizawa & Sato 1984). Apart from the third case, which is mainly of interest for laboratory experiments, these double layers are good candidates for accelerating the auroral electrons to the few keV observed.

Double layers (i.e., electric fields parallel to B) form along auroral field lines in the Earth's magnetosphere. They form in order to maintain current continuity in the ionosphere in the presence of a magnetospheric electric field E with ∇. E ≠ 0. Features which govern the formation of the double layers are: 1) the divergence of E; 2) the conductivity of the ionosphere; and 3) the current-voltage characteristics of auroral magnetic field lines. Astrophysical situations where ∇. E ≠ 0 is applied to a conducting plasma similar to the Earth's ionosphere are potential candidates for the formation of double layers. The region with ∇. E ≠ 0 can be generated within, or along field lines connected to, the conducting plasma. In addition to ∇. E, shear neutral flow in the conducting plasma can also form double layers.

The formation of a double layer is proposed as the mechanism which produces the critical velocity phenomenon. We examine this hypothesis, qualitatively, and find that the double layer can be a very efficient mechanism for transferring the kinetic energy of the neutral gas into the kinetic energy of electrons which, in turn, will ionize the neutral gas if the critical velocity has been reached or exceeded.

The properties of ion phase-space vortices are reviewed with particular attention to their role in the formation of small amplitude double-layers in current-carrying plasmas. In a one-dimensional analysis, many such double-layers simply add up to produce a large voltage drop. A laboratory experiment is carried out in order to investigate the properties of ion phase-space vortices in three dimensions. Their lifetime is significantly reduced as compared with similar results from one-dimensional numerical simulations of the problem.

The evolution processes of double-layers have been studied in a series of laboratory experiments using a triple plasma device. It was found that the existence of virtual cathode type potential wells at the electron injection boundary was the dominant triggering mechanism. The rapid growth of the potential well led to collisionless ion trapping and the establishment of the necessary trapped ion population. For double layers with small potential drops, collisionless ion trapping actually induced ion–ion streaming instabilities and the formation of ion phase-space vortices. In this regime, the system often exhibited relaxation type oscillations which corresponded to the disruption and the recovery of the double layers.

Various mechanisms for driving double layers in plasmas are briefly described, including applied potential drops, currents, contact potentials, and plasma expansions. Some dynamic features of the double layers are discussed. These features, as seen in simulations, laboratory experiments and theory, indicate that double layers and the currents through them undergo slow oscillations, which are determined by the ion transit time across an effective length of the system in which the double layers form. It is shown that a localized potential dip forms at the low potential end of a double layer, which interrupts the electron current through it according to the Langmuir criterion, whenever the ion flux into the double is disrupted. The generation of electric fields perpendicular to the ambient magnetic field by contact potentials is also discussed. Two different situations have been considered; in one, a low-density hot plasma is sandwiched between high-density cold plasmas, while in the other a high-density current sheet permeates a low-density background plasma. Perpendicular electric fields develop near the contact surfaces. In the case of the current sheet, the creation of parallel electric fields and the formation of double layers are also discussed when the current sheet thickness is varied. Finally, the generation of electric fields (parallel to an ambient magnetic field) and double layers in an expanding plasma are discussed.

Nonmonotonic plasma potential structures are a common feature of many double layers and sheaths. Steady state plasma potential wells separating regions having different plasma potentials are often found in laboratory experiments. In order to exist, such structures all must find a solution to a common problem. Ions created by charge exchange or ionization in the region of the potential well are electrostatically confined and tend to accumulate and fill up the potential well. The increase in positive charge should eliminate the well. Nevertheless, steady state structures are found in which the wells do not fill up. This means that it is important to take into account processes which ‘pump’ ions from the well. As examples of ion pumping of plasma wells, we consider potential dips in front of a positively biased electron collecting anode in a relatively cold, low density multidipole plasma. Pumping is provided by ion leaks from the edges of the potential dip or by oscillating the applied potential. In the former case the two dimensional character of the problem is shown to be important.

A Genuine two-fluid model of plasmas with collisions permits the calculation of dynamic electric fields and double layers inside plasmas including oscillations and damping. For the first time a macroscopic model for coupling of electromagnetic and Langmuir waves was achieved with realistic damping. Starting points were laser produced plasmas showing very high dynamic electric fields in nonlinear force produced cavitons and inverted layers, in agreement with experiments. Applications for any inhomogeneous plasma as in laboratory or in astrophysical plasmas can then be followed up by a transparent hydrodynamic description. We find the rotation of plasmas in magnetic fields and a new second harmonic resonance. Explanation of inverted double layers, second harmonic emission from laser produced plasmas, and laser acceleration of charged particles by the very high fields of the double layers is given.

Analytical study of the linear stability of one-dimensional double layers in nonmagnetized plasmas based on the solution of the Vlasov–Poisson system is presented. Electromagnetic effects are not included. A self-consistent equilibrium electrostatic potential Φ0(z) that monotonically increases from a low level at z = − ∞ to a high level at z = + ∞ is assumed. We model this potential as a piecewise continuous function of z and we assume that Φ0(z) has constant values for − ∞ z ≤ 0 and L ≤ z < ∞, L being the thickness of the double layer. The BGK states for the Vlasov–Poisson system provide an explicit expression for the velocity distribution of the reflected electrons required for the particular double layer configuration. The stability of the double layers is studied via the linearized Vlasov and Poisson equations using the WKB approximation.

Previous work on the evolution of weak double layers in a hydrogen plasma has been extended to include H+ and O+ with relative drift. It has been shown (Bergmann & Lotko 1986) that the relative drift between hydrogen and oxygen ions due to a quasistatic parallel electric field gives rise to a strong linear fluid instability which dominates the ion acoustic mode at the bottom of the auroral acceleration region. This ion–ion instability can modify ion distributions at lower altitudes and the subsequent nonlinear evolution of weak double layers at higher altitudes in the ion acoustic regime. We have found that ion hole formation can occur for smaller relative electron-ion drifts than seen in previous simulations, due to the hydrogen-oxygen two-stream instability. This results in local modification of the ion distributions in phase space, and a partial filling of the valley between the hydrogen and oxygen peaks, which would be expected at higher altitudes on auroral field lines. It is shown that the observed velocity diffusion does not necessarily preclude ion hole and double layer formation in hydrogen in the ion acoustic regime. These simulation results are consistent with the experimentally measured persistence of separate hydrogen and oxygen peaks, and the observation of weak double layers above an altitude of 3000 km on auroral field lines.

The discussion of parallel electric fields in the earth's magnetosphere has undergone a notable shift of emphasis in recent years, away from wave-generated anomalous resistivity towards the more large-scale effects of magnetic confinement of current carrying plasmas. This shift has been inspired in large part by the more extensive data on auroral particle distribution functions that have been made available, data that may often seem consistent with a dissipation-free acceleration of auroral electrons over an extended altitude range.

Efforts to interpret these data have brought new vigor to the concept that a smooth and static electric field can be self-consistently generated by suitable pitch-angle anisotropies among the high-altitude particle populations, different for electrons and ions, and that such an electric field is both necessary and sufficient to maintain the plasma in a quasi-neutral steady state. This paper reviews and criticizes certain aspects of this concept, both from a general theoretical standpoint and from the standpoint of what we know about the magnetospheric environment. It is argued that this concept has flaws and that the actual physical problem is considerably more complicated, requiring a more complex electric field, possibly including double layer structures.

We present experimental results on three dynamic properties of very strong double layers observed in a triple plasma device. First, it is observed that when an inductance of sufficient size is inserted in series with the external bias supply used to produce the double layer, disruptions in the plasma current occur accompanied by disruptions in the double layer potential. Second, it is observed that with all external reactances reduced as much as possible, a sort of jitter-motion occurs in the position of the double layer around its equilibrium position. Third, when the external bias supply is pulsed, the initial potential distribution is observed to have an essentially uniform slope, as in the case of a vacuum capacitor. The disruption phenomenon may be explained in terms of the behavior of the potential structure as a function of the bias voltage and this explanation is discussed along with the experimental evidence for its validity. A comparable understanding of the other two phenomena has not been achieved, but in both cases there are qualitative differences between the behavior reported here and what has been observed in Q-machines and these differences are discussed.

In a triple plasma device, the injection of electron current from the source chamber to the target chamber causes the formation of a potential double layer. At a low current density, the space charge of the injected current produces a virtual cathode-type potential double layer. This double layer is stable and various wave instabilities are observed to associate with this double layer. As the current density is increased, the double layer becomes unstable and a moving double layer results. As the current density is increased further, the enhanced ionization causes the neutralization of the space charge of the electron beam and the ‘beam plasma discharge’ is ignited.

The earth's auroral zone contains dynamic processes occurring on scales from the length of an auroral zone field line (about 10RE) which characterizes Alfven wave propagation to the scale of microscopic processes which occur over a few Debye lengths (less than 1 km). These processes interact in a time-dependent fashion since the current carried by the Alfven waves can excite microscopic turbulence which can in turn provide dissipation of the Alfven wave energy. This review will first describe the dynamic aspects of auroral current structures with emphasis on consequences for models of microscopic turbulence. In the second part of the paper a number of models of microscopic turbulence will be introduced into a large scale model of Alfven wave propagation to determine the effect of various models on the overall structure of auroral currents. In particular, we will compare the effect of a double layer electric field which scales with the plasma temperature and Debye length with the effect of anomalous resistivity due to electrostatic ion cyclotron turbulence in which the electric field scales with the magnetic field strength. It is found that the double layer model is less diffusive than the resistive model leading to the possibility of narrow, intense current structures.

We report on our work to simulate auroral double layers (DL's) with ‘realistic’ particle-in-cell models. An early model simulated weak DL's formed in a self-consistent circuit but under conditions subject to the ion-acoustic instability. More recent work has focused on strong DL's formed when currentless jets are injected into a dipole magnetic field.

The evolution and long-time stability of a double layer in a discrete auroral arc requires that the parallel current in the arc, which may be considered uniform at the source, be diverted within the arc to charge the flanks of the U-shaped double-layer potential structure. A simple model is presented in which this current re-distribution is effected by anomalous transport based on electrosatic lower hybrid waves driven by the flank structure itself. This process provides the limiting constraint on the double-layer potential. The flank charging may be represented as that of a nonlinear transmission line. A simplified model circuit, in which the transmission line is represented by a nonlinear impedance in parallel with a variable resistor, is incorporated in a 1-d simulation model to give the current density at the DL boundaries. Results are presented for the scaling of the DL potential as a function of the width of the arc and the saturation efficiency of the lower hybrid instability mechanism.

The possibility of an X-ray laser by irradiation of muon beams on a thin rod of deuterium-tritium mixture is discussed. The excited state of dtμ-mesomolecules (J, v) = (1, 0) can be induced to make radiative chain transitions with photon energy of 90 eV to the ground state (0, 0), evacuated by fusion.

The work proposes a straightforward method for determining the nuclear reaction cross sections at extremely low energies (E ≃ 1–100 keV) on the basis of the measurements of the relative yield of fast particles which are products of the nuclear reactions in a target under laser compression. On the other hand, the proposed method makes it possible to find the averaged form of the ion velocity distribution function if the low-energy behaviour of the respective cross sections is known.