Michael A. Raadu

The physics of double layers and their role in astrophysics

Abstract Research on electrostatic double layers (DLs) is surveyed and astrophysical applications are reviewed. Strong highly relativistic DLs directly accelerate equal numbers of ions and electrons, whereas in the non-relativistic limit electron acceleration predominates. The existence criteria for DLs are discussed. There is a close relationship between the Bohm criteria, the plasma dispersion relation and the Penrose stability condition. Current-driven instabilities can lead to DL formation, and account for the fluctuations associated with strong DLs. A class of weak DLs may be described using the modified Korteweg-de Vries equation, and the conditions for the emergence of a DL from arbitrary initial conditions can be specified. Simulation studies of strong DL formation reveal important dynamical features. Weak DLs are found in simulations of ion-acoustic instabilities. Laboratory DLs have been studied in great detail. There is a strong coupling between a DL and the global current system. The results of theoretical, simulation and observational investigations of magnetospheric DLs are presented. High-energy observations of solar flares agree well with a DL model. DLs may be a feature of many high-energy astrophysical phenomena.

THE ROLE OF ELECTROSTATIC INSTABILITIES IN THE CRITICAL IONIZATION VELOCITY MECHANISM

The role of electrostatic instabilities in the critical ionization velocity mechanism is investigated. The analysis is based on the theory developed by Sherman, which interprets Alfvéns critical velocity in terms of a circular process. This process involves the acceleration of electrons by a two-stream instability modified by the presence of a magnetic field. A general expression for the energy and momentum of ions and electrons associated with an electrostatic mode is derived in terms of the plasma dielectric constant. This is used in the case of the modified two-stream instability to determine the distribution of energy between ions and electrons. An extrapolation from the linear phase then gives an estimate of the energy delivered to the electrons which is compared to that required to ionize the neutral gas.

Transition between the discharge regimes of high power impulse magnetron sputtering and conventional direct current magnetron sputtering

Current and voltage have been measured in a pulsed high power impulse magnetron sputtering (HiPIMS) system for discharge pulses longer than 100 mu s. Two different current regimes could clearly be ...

Gas rarefaction and the time evolution of long high-power impulse magnetron sputtering pulses

Model studies of 400 mu s long discharge pulses in high-power impulse magnetron sputtering have been made to study the gas dynamics and plasma chemistry in this type of pulsed processing plasma. Da ...

Dynamical Aspects of Electrostatic Double Layers

Electrostatic double layers have been proposed as an acceleration mechanism in solar flares and other astrophysical objects. They have been extensively studied in the laboratory and by means of computer simulations. The theory of steady-state double layers implies several existence criteria, in particular the Bohm criteria, restricting the conditions under which double layers may form. In the present paper several already published theoretical models of different types of double layers are discussed. It is shown that the existence conditions often imply current-driven instabilities in the ambient plasma, at least for strong double layers, and it is argued that such conditions must be used with care when applied to real plasmas. Laboratory double layers, and by implication those arising in astrophysical plasmas often produce instabilities in the surrounding plasma and are generally time-dependent structures. Naturally occuring double layers should, therefore, be far more common than the restrictions deduced from idealised time-independent models would imply. In particular it is necessary to understand more fully the time-dependent behaviour of double layers. In the present paper the dynamics of weak double layers is discussed. Also a model for a moving strong double layer, where an associated potential minimum plays a significant role, is presented.

Conditions for plasmoid penetration across abrupt magnetic barriers

The penetration of plasma clouds, or plasmoids, across abrupt magnetic barriers (of the scale less than a few ion gyro radii, using the plasmoid directed velocity) is studied. The insight gained earlier, from detailed experimental and computer simulation investigations of a case study, is generalized into other parameter regimes. It is concluded for what parameters a plasmoid should be expected to penetrate the magnetic barrier through self-polarization, penetrate through magnetic expulsion, or be rejected from the barrier. The scaling parameters are ne, v0, B⊥, mi, Ti, and the width w of the plasmoid. The scaling is based on a model for strongly driven, nonlinear magnetic field diffusion into a plasma which is a generalization of the earlier laboratory findings. The results are applied to experiments earlier reported in the literature, and also to the proposed application of impulsive penetration of plasmoids from the solar wind into the Earth’s magnetosphere.

An ionization region model for high-power impulse magnetron sputtering discharges

A time-dependent plasma discharge model has been developed for the ionization region in a high-power impulse magnetron sputtering (HiPIMS) discharge. It provides a flexible modeling tool to explore ...

Understanding deposition rate loss in high power impulse magnetron sputtering: I. Ionization-driven electric fields

The lower deposition rate for high power impulse magnetron sputtering (HiPIMS) compared with direct current magnetron sputtering for the same average power is often reported as a drawback. The often invoked reason is back-attraction of ionized sputtered material to the target due to a substantial negative potential profile, sometimes called an extended presheath, from the location of ionization toward the cathode. Recent studies in HiPIMS devices, using floating-emitting and swept-Langmuir probes, show that such extended potential profiles do exist, and that the electric fields Ez directed toward the target can be strong enough to seriously reduce ion transport to the substrate. However, they also show that the potential drops involved can vary by up to an order of magnitude from case to case. There is a clear need to understand the underlying mechanisms and identify the key discharge variables that can be used for minimizing the back-attraction. We here present a combined theoretical and experimental analysis of the problem of electric fields Ez in the ionization region part of HiPIMS discharges, and their effect on the transport of ionized sputtered material. In particular, we have investigated the possibility of a ?sweet spot? in parameter space in which the back-attraction of ionized sputtered material is low. It is concluded that a sweet spot might possibly exist for some carefully optimized discharges, but probably in a rather narrow window of parameters. As a measure of how far a discharge is from such a window, a Townsend product ?Townsend is proposed. A parametric analysis of ?Townsend shows that the search for a sweet spot is complicated by the fact that contradictory demands appear for several of the externally controllable parameters such as high/low working gas pressure, short/long pulse length, high/low pulse power and high/low magnetic field strength.

A bulk plasma model for dc and HiPIMS magnetrons

A plasma discharge model has been developed for the bulk plasma (also called the extended presheath) in sputtering magnetrons. It can be used both for high power impulse magnetron sputtering (HiPIM ...

On sheath energization and Ohmic heating in sputtering magnetrons

In most models of sputtering magnetrons, the mechanism for energizing the electrons in the discharge is assumed to be sheath energization. In this process, secondary emitted electrons from the cathode surface are accelerated across the cathode sheath into the plasma, where they either ionize directly or transfer energy to the local lower energy electron population that subsequently ionizes the gas. In this work, we present new modeling results in support of an alternative electron energization mechanism. A model is experimentally constrained, by a fitting procedure, to match a set of experimental data taken over a large range in discharge powers in a high-power impulse magnetron sputtering (HiPIMS) device. When the model is matched to real data in this way, one finding is that the discharge can run with high power and large gas rarefaction without involving the mechanism of secondary electron emission by twice-ionized sputtered metal. The reason for this is that direct Ohmic heating of the plasma electrons is found to dominate over sheath energization by typically an order of magnitude. This holds from low power densities, as typical for dc magnetrons, to so high powers that the discharge is close to self-sputtering, i.e. dominated by the ionized vapor of the sputtered gas. The location of Ohmic heating is identified as an extended presheath with a potential drop of typically 100–150 V. Such a feature, here indirectly derived from modeling, is in agreement with probe measurements of the potential profiles in other HiPIMS experiments, as well as in conventional dc magnetrons.