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  • 1.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Axnas, I.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, D.
    Helmerson, U.
    A bulk plasma model for dc and HiPIMS magnetrons2008In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 17, no 4Article in journal (Refereed)
    Abstract [en]

    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 (HiPIMS) and conventional dc sputtering magnetrons. Demonstration calculations are made for the parameters of the HiPIMS sputtering magnetron at Link "oping University, and also benchmarked against results in the literature on dc magnetrons. New insight is obtained regarding the structure and time development of the currents, the electric fields and the potential profiles. The transverse resistivity eta(perpendicular to) has been identified as having fundamental importance both for the potential profiles and for the motion of ionized target material through the bulk plasma. New findings are that in the HiPIMS mode, as a consequence of a high value of eta(perpendicular to), (1) there can be an electric field reversal that in our case extends 0.01-0.04m from the target, (2) the electric field in the bulk plasma is typically an order of magnitude weaker than in dc magnetrons, (3) in the region of electric field reversal the azimuthal current is diamagnetic in nature, i.e. mainly driven by the electron pressure gradient, and actually somewhat reduced by the electron Hall current which here has a reversed direction and (4) the azimuthal current above the racetrack can, through resistive friction, significantly influence the motion of the ionized fraction of the sputtered material and deflect it sideways, away from the target and towards the walls of the magnetron.

  • 2.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Axnas, I.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Tennfors, E.
    Koepke, M.
    Radiation from an electron beam in a magnetized plasma: Whistler mode wave packets2006In: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 111, no A11Article in journal (Refereed)
    Abstract [en]

    Experimental studies are reported of oscillations and radiation that is spontaneously excited by an electron beam which is shot along a diverging magnetic field into a plasma from a hot cathode. In the present study we focus on oscillations below the electron gyrofrequency, where we find that whistler mode radiation appears in the form of bursts, or wave packets, each with typically 0.1-1 mu s time duration, and which together cover typically a few percent of the full time. Wave packets are found in a broad frequency range of 7-40 MHz, while each individual wave packet is dominated by a single frequency. There is propagation along two routes: at the group velocity resonance cone angle, away from the central channel where the waves are excited, and in a channel along the magnetic field. Features of the whistler mode wave packets that are studied include (1) the statistics of amplitudes, frequencies, and time durations; (2) the propagation and decay of wave packets with different frequencies; (3) the group and phase velocities; and (4) how the wave packet production varies with the energy, and the current density, in the electron beam.

  • 3.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Axnäs, Ingvar
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Koepke, Mark
    KTH.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Tennfors, Einar
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Radiation from an electron beam in magnetized plasma: excitation of a whistler mode wave packet by interacting, higher-frequency, electrostatic-wave eigenmodes2017In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 59, no 12, article id 124006Article in journal (Refereed)
    Abstract [en]

    Infrequent, bursty, electromagnetic, whistler-mode wave packets, excited spontaneously in the laboratory by an electron beam from a hot cathode, appear transiently, each with a time duration tau around similar to 1 mu s. The wave packets have a center frequency f(W) that is broadly distributed in the range 7 MHz < f(W) < 40 MHz. They are excited in a region with separate electrostatic (es) plasma oscillations at values of f(hf), 200 MHz < f(hf) < 500 MHz, that are hypothesized to match eigenmode frequencies of an axially localized hf es field in a well-defined region attached to the cathode. Features of these es-eigenmodes that are studied include: the mode competition at times of transitions from one dominating es-eigenmode to another, the amplitude and spectral distribution of simultaneously occurring es-eigenmodes that do not lead to a transition, and the correlation of these features with the excitation of whistler mode waves. It is concluded that transient coupling of es-eigenmode pairs at f(hf) such that vertical bar f(1, hf) - f(2, hf)vertical bar = f(W) < f(ge) can explain both the transient lifetime and the frequency spectra of the whistler-mode wave packets (f(W)) as observed in lab. The generalization of the results to bursty whistler-mode excitation in space from electron beams, created on the high potential side of double layers, is discussed.

  • 4.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Linköping University, Sweden; Université Paris-Sud, France.
    Gudmundsson, Jon Tomas
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, D.
    Minea, T.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Université Paris-Sud, France.
    Helmersson, U.
    The role of Ohmic heating in dc magnetron sputtering2016In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 25, no 6, article id 065024Article in journal (Refereed)
    Abstract [en]

    Sustaining a plasma in a magnetron discharge requires energization of the plasma electrons. In this work, Ohmic heating of electrons outside the cathode sheath is demonstrated to be typically of the same order as sheath energization, and a simple physical explanation is given. We propose a generalized Thornton equation that includes both sheath energization and Ohmic heating of electrons. The secondary electron emission yield gamma(SE) is identified as the key parameter determining the relative importance of the two processes. For a conventional 5 cm diameter planar dc magnetron, Ohmic heating is found to be more important than sheath energization for secondary electron emission yields below around 0.1.

  • 5.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Laboratoire de Physique des Gaz et Plasmas—LPGP, UMR 8578 CNRS, Université Paris-Saclay, France; Plasma and Coatings Physics Division, IFM-Materials Physics, Linköping University, Sweden.
    Gudmundsson, Jon Tomas
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Laboratoire de Physique des Gaz et Plasmas—LPGP, UMR 8578 CNRS, Université Paris-Sud, Université Paris-Saclay, France; Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Petty, T. J.
    Universite Paris Sud.
    Minea, Tiberiu
    Unicersite Paris Sud.
    Lundin, Daniel
    Universite Paris Sud.
    A unified treatment of self-sputtering, process gas recycling, and runaway for high power impulse sputtering magnetrons2017In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 26, no 12, article id 125003Article in journal (Refereed)
    Abstract [en]

    The combined processes of self-sputter (SS)-recycling and process gas recycling in high power impulse magnetron sputtering (HiPIMS) discharges are analyzed using the generalized recycling model (GRM). The study uses experimental data from discharges with current densities from the direct current magnetron sputtering range to the HiPIMS range, and using targets with self-sputter yields Y-SS from approximate to 0.1 to 2.6. The GRM analysis reveals that, above a critical current density of the order of J(crit) approximate to 0.2 A cm(-2), a combination of self-sputter recycling and gas-recycling is generally the case. The relative contributions of these recycling mechanisms, in turn, influence both the electron energy distribution and the stability of the discharges. For high self-sputter yields, above Y-SS approximate to 1, the discharges become dominated by SS-recycling, contain few hot secondary electrons from sheath energization, and have a relatively low electron temperature T-e. Here, stable plateau values of the discharge current develop during long pulses, and these values increase monotonically with the applied voltage. For low self-sputter yields, below Y-SS approximate to 0.2, the discharges above J(crit) are dominated by process gas recycling, have a significant sheath energization of secondary electrons and a higher T-e, and the current evolution is generally less stable. For intermediate values of YSS the discharge character gradually shifts between these two types. All of these discharges can, at sufficiently high discharge voltage, give currents that increase rapidly in time. For such cases we propose that a distinction should be made between 'unlimited' runaway and 'limited' runaway: in unlimited runaway the current can, in principle, increase without a limit for a fixed discharge voltage, while in limited runaway it can only grow towards finite, albeit very high, levels. For unlimited runway Y-SS > 1 is found to be a necessary criterion, independent of the amount of gas-recycling in the discharge.

  • 6.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Huo, Chunqing
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, Daniel
    Plasma and Coatings Physics Division, Linköping, Sweden.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Vitelaru, Catalin
    Stancu, Gabriel
    Minea, Tiberiu
    Helmersson, Ulf
    Understanding deposition rate loss in high power impulse magnetron sputtering: I. Ionization-driven electric fields2012In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 21, no 2, p. 025005-Article in journal (Refereed)
    Abstract [en]

    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 E-z 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 E-z 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 Pi(Townsend) is proposed. A parametric analysis of Pi(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.

  • 7.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Hurtig, T.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Conditions for plasmoid penetration across abrupt magnetic barriers2005In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 12, no 1Article in journal (Refereed)
    Abstract [en]

    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 plasi-noid 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 n(e), upsilon(o), B-perpendicular to, m(i), T-i, 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.

  • 8.
    Brenning, Nils
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Merlino, R. L.
    Lundin, D.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Helmersson, U.
    Faster-than-Bohm Cross-B Electron Transport in Strongly Pulsed Plasmas2009In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 103, no 22Article in journal (Refereed)
    Abstract [en]

    We report the empirical discovery of an exceptionally high cross-B electron transport rate in magnetized plasmas, in which transverse currents are driven with abruptly applied high power. Experiments in three different magnetic geometries are analyzed, covering several orders of magnitude in plasma density, magnetic field strength, and ion mass. It is demonstrated that a suitable normalization parameter is the dimensionless product of the electron (angular) gyrofrequency and the effective electron-ion momentum transfer time, omega(ge)tau(EFF), by which all of diffusion, cross-resistivity, cross-B current conduction, and magnetic field diffusion can be expressed. The experiments show a remarkable consistency and yield close to a factor of 5 greater than the Bohm-equivalent values of diffusion coefficient D-perpendicular to, magnetic-diffusion coefficient D-B, Pedersen conductivity sigma(P), and transverse resistivity eta(perpendicular to).

  • 9.
    Gudmundsson, Jon Tomas
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, D.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Huo, Chunqing
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Minea, T. M.
    An ionization region model of the reactive Ar/O-2 high power impulse magnetron sputtering discharge2016In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 25, no 6, article id 065004Article in journal (Refereed)
    Abstract [en]

    A new reactive ionization region model (R-IRM) is developed to describe the reactive Ar/O-2 high power impulse magnetron sputtering (HiPIMS) discharge with a titanium target. It is then applied to study the temporal behavior of the discharge plasma parameters such as electron density, the neutral and ion composition, the ionization fraction of the sputtered vapor, the oxygen dissociation fraction, and the composition of the discharge current. We study and compare the discharge properties when the discharge is operated in the two well established operating modes, the metal mode and the poisoned mode. Experimentally, it is found that in the metal mode the discharge current waveform displays a typical non-reactive evolution, while in the poisoned mode the discharge current waveform becomes distinctly triangular and the current increases significantly. Using the R-IRM we explore the current increase and find that when the discharge is operated in the metal mode Ar+ and Ti+ -ions contribute most significantly (roughly equal amounts) to the discharge current while in the poisoned mode the Ar+ -ions contribute most significantly to the discharge current and the contribution of O+ -ions, Ti+ -ions, and secondary electron emission is much smaller. Furthermore, we find that recycling of atoms coming from the target, that are subsequently ionized, is required for the current generation in both modes of operation. From the R-IRM results it is found that in the metal mode self-sputter recycling dominates and in the poisoned mode working gas recycling dominates. We also show that working gas recycling can lead to very high discharge currents but never to a runaway. It is concluded that the dominating type of recycling determines the discharge current waveform.

  • 10.
    Gudmundsson, Jon Tomas
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, D.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Minea, T.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    The current waveform in reactive high power impulse magnetron sputtering2016In: 2016 IEEE International Conference on Plasma Science (ICOPS), Institute of Electrical and Electronics Engineers (IEEE), 2016Conference paper (Refereed)
    Abstract [en]

    Summary form only given. The understanding of the current waveform for the non-reactive HiPIMS discharge is now rather well established [1,2]. It is described by a rise in the current to an initial peak and then a drop followed by a stable plateau. The drop is a result of a strong gas compression due to the sudden large flux of atoms from the target. For the reactive HiPIMS discharge striking differences are observed and those seem to depend on the mode of operation, the reactive gas and the target material. The discharge current waveform changes in shape as well as in the peak value when the target surface enters the poisoned mode. For Ar/O2 discharge with Ti target the discharge current waveform varies with oxygen partial pressure and pulse repetition frequency [3]. For the higher repetition frequencies the familiar nonreactive current waveform is observed. As the repetition frequency is lowered there is an increase in the current which transits into a different waveform as the repetition frequency is decreased further. The waveform observed at low repetition frequency is similar to the one observed at high reactive gas flow rate. Similarly, the current waveform in the reactive Ar/N2 HiPIMS discharge with Ti target is highly dependent on the pulse repetition frequency and the current is found to increase significantly as the frequency is lowered [4]. However, the discharge current keeps its shape and it remains as for the non-reactive case as the current increases. These findings will be compared with results for various combinations of gas mixtures and targets found in the literature [5]. Furthermore, we explore the current waveform in reactive HiPIMS using the ionization region model (IRM) [6] of the reactive Ar/O2 discharge with a Ti target. We discuss the current waveform development and how the discharge composition varies between metal and poisoned mode.

  • 11.
    Huo, Chunqing
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Hainan University, People ’ s Republic of China.
    Lundin, Daniel
    Universite Paris Sud.
    Gudmundsson, Jon Tomas
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Université Paris, France; University of Iceland, Iceland.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Bradley, James W.
    University of Liverpool.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Linköping University, Sweden.
    Particle-balance models for pulsed sputtering magnetrons2017In: Journal of Physics D: Applied Physics, ISSN 0022-3727, E-ISSN 1361-6463, Vol. 50, no 35, article id 354003Article in journal (Refereed)
    Abstract [en]

    The time-dependent plasma discharge ionization region model (IRM) has been under continuous development during the past decade and used in several studies of the ionization region of high-power impulse magnetron sputtering (HiPIMS) discharges. In the present work, a complete description of the most recent version of the IRM is given, which includes improvements, such as allowing for returning of the working gas atoms from the target, a separate treatment of hot secondary electrons, addition of doubly charged metal ions, etc. To show the general applicability of the IRM, two different HiPIMS discharges are investigated. The first set concerns 400 μs long discharge pulses applied to an Al target in an Ar atmosphere at 1.8 Pa. The second set focuses on 100 μs long discharge pulses applied to a Ti target in an Ar atmosphere at 0.54 Pa, and explores the effects of varying the magnetic field strength. The model results show that -ions contribute negligibly to the production of secondary electrons, while -ions effectively contribute to the production of secondary electrons. Similarly, the model results show that for an argon discharge with Al target the contribution of Al+-ions to the discharge current at the target surface is over 90% at 800 V. However, at 400 V the Al+-ions and Ar+-ions contribute roughly equally to the discharge current in the initial peak, while in the plateau region Ar+-ions contribute to roughly of the current. For high currents the discharge with Al target develops almost pure self-sputter recycling, while the discharge with Ti target exhibits close to a 50/50 combination of self-sputter recycling and working gas-recycling. For a Ti target, a self-sputter yield significantly below unity makes working gas-recycling necessary at high currents. For the discharge with Ti target, a decrease in the B-field strength, resulted in a corresponding stepwise increase in the discharge resistivity.

  • 12.
    Huo, Chunqing
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, Daniel
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Plasma and Coatings Physics Division.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Anders, André
    Gudmundsson, Jon Tomas
    KTH, School of Electrical Engineering (EES).
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    On sheath energization and Ohmic heating in sputtering magnetrons2013In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 22, no 4, p. 045005-Article in journal (Refereed)
    Abstract [en]

    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 100-150V. 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.

  • 13.
    Huo, Chunqing
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, Daniel
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. Plasma and Coatings Physics Division.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Anders, André
    Gudmundsson, Jon Tomas
    KTH, School of Electrical Engineering (EES). University of Iceland.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    On the road to self-sputtering in high power impulse magnetron sputtering: particle balance and discharge characteristics2014In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 23, no 2, p. 025017-Article in journal (Refereed)
    Abstract [en]

    The onset and development of self-sputtering (SS) in a high power impulse magnetron sputtering (HiPIMS) discharge have been studied using a plasma chemical model and a set of experimental data, taken with an aluminum target and argon gas. The model is tailored to duplicate the discharge in which the data are taken. The pulses are long enough to include both an initial transient and a following steady state. The model is used to unravel how the internal discharge physics evolves with pulse power and time, and how it is related to features in the discharge current-voltage-time characteristics such as current densities, maxima, kinks and slopes. The connection between the self-sputter process and the discharge characteristics is quantified and discussed in terms of three parameters: a critical target current density J(crit) based on the maximum refill rate of process (argon) gas above the target, an SS recycling factor Pi(SS-recycle), and an approximation alpha a of the probabilities of ionization of species that come from the target (both sputtered metal and embedded argon atoms). For low power pulses, discharge voltages UD <= 380V with peak current densities below approximate to 0.2A cm(-2), the discharge is found to be dominated by process gas sputtering. In these pulses there is an initial current peak in time, associated with partial gas rarefaction, which is followed by a steady-state-like plateau in all parameters similar to direct current magnetron sputtering. In contrast, high power pulses, with U-D >= 500V and peak current densities above J(D) approximate to 1.6Acm(-2), make a transition to a discharge mode where SS dominates. The transition is found not to be driven by process gas rarefaction which is only about 10% at this time. Maximum gas rarefaction is found later in time and always after the initial peak in the discharge current. With increasing voltage, and pulse power, the discharge can be described as following a route where the role of SS increases in four steps: process gas sputtering, gas-sustained SS, self-sustained SS and SS runaway. At the highest voltage, 1000V, the discharge is very close to, but does not go into, the SS runaway mode. This absence of runaway is proposed to be connected to an unexpected finding: that twice ionized ions of the target species play almost no role in this discharge, not even at the highest powers. This reduces ionization by secondary-emitted energetic electrons almost to zero in the highest power range of the discharge.

  • 14.
    Huo, Chunqing
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lundin, Daniel
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Gudmundsson, Jon Tomas
    Anders, André
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Gas rarefaction and the time evolution of long high-power impulse magnetron sputtering pulses2012In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 21, no 4, p. 045004-Article in journal (Refereed)
    Abstract [en]

    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. Data are taken from an experiment using square voltage pulses applied to an Al target in an Ar atmosphere at 1.8 Pa. The study is limited to low power densities, < 0.5 kW cm(-2), in which the discharge is far away from the runaway self-sputtering mode. The model used is the ionization region model, a time-dependent plasma chemistry discharge model developed for the ionization region in magnetron sputtering discharges. It gives a close fit to the discharge current during the whole pulse, both an initial high-current transient and a later plateau value of constant lower current. The discharge current peak is found to precede a maximum in gas rarefaction of the order of Delta n(Ar)/n(Ar),(0) approximate to 50%. The time durations of the high-current transient, and of the rarefaction maximum, are determined by the time it takes to establish a steady-state diffusional refill of process gas from the surrounding volume. The dominating mechanism for gas rarefaction is ionization losses, with only about 30% due to the sputter wind kick-out process. During the high-current transient, the degree of sputtered metal ionization reaches 65-75%, and then drops to 30-35% in the plateau phase. The degree of self-sputtering (defined here as the metal ion fraction of the total ion current to the target) also varies during the pulse. It grows from zero at pulse start to a maximum of 65-70% coinciding in time with the maximum gas rarefaction, and then stabilizes in the range 40-45% during the plateau phase. The loss in deposition rate that can be attributed to the back-attraction of the ionized sputtered species is also estimated from the model. It is low during the initial 10-20 mu s, peaks around 60% during the high-current transient, and finally stabilizes around 30% during the plateau phase.

  • 15. Hurtig, T.
    et al.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    The role of high frequency oscillations in the penetration of plasma clouds across magnetic boundaries2005In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 12, no 1Article in journal (Refereed)
    Abstract [en]

    Experiments are reported where a collissionfree plasma cloud penetrates a magnetic barrier by self-polarization. Three closely related effects, all fundamental for the penetration mechanism, are studied quantitatively: (1) anomalous fast magnetic field penetration (two orders of magnitude faster than classical), (2) anomalous fast electron transport (three orders of magnitude faster than classical and two orders of magnitude faster than Bohm diffusion), and (3) the ion energy budget as ions enter the potential structure set up by the self-polarized plasma cloud. It is concluded that all three phenomena are closely related and that they are mediated by highly nonlinear oscillations in the lower hybrid range, driven by a strong diamagnetic current loop which is set up in the plasma in the penetration process. The fast magnetic field penetration occurs as a consequence of the anomalous resistivity caused by the wave field and the fast electron transport across magnetic field lines is caused by the correlation between electric field and density oscillations in the wave field. It is also found that ions do not lose energy in proportion to the potential hill they have to climb, rather they are transported against the dc potential structure by the same correlation that is responsible for the electron transport. The results obtained through direct measurements are compared to particle in cell simulations that reproduce most aspects of the high frequency wave field.

  • 16. Hurtig, T.
    et al.
    Brenning, Nils
    KTH, Superseded Departments, Alfvén Laboratory.
    Raadu, Michael A.
    KTH, Superseded Departments, Alfvén Laboratory.
    Three-dimensional electrostatic particle-in-cell simulation with open boundaries applied to a plasma beam entering a curved magnetic field2003In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 10, no 11, p. 4291-4305Article in journal (Refereed)
    Abstract [en]

    Three-dimensional electrostatic particle-in-cell simulations of a laboratory experiment with an elongated plasma cloud entering a curved magnetic field are presented. A moving grid is used to follow the plasma motion from a region with longitudinal magnetic field, through a transition region where the field curves, and into a region where the magnetic field has a constant angle of 45degrees to the flow direction. In order to isolate the physics from disturbing boundary effects a method to create open boundary conditions has been implemented. As a result the boundaries are essentially moved to infinity. The simulation reproduces and gives physical insight into several experimental results concerning the plasma's macroscopic behavior in the transition region, which have earlier been only partly understood. First, the deformation of the plasma from a cylinder to a slab; second, the formation of strong currents along the sides of the plasma cloud in the transition region, which continue into field-aligned currents in the (upstream) flow-parallel field region, and close across the magnetic field both in the front and in the back of the penetrating cloud; and, third, the formation of a potential structure including (in the transition region) magnetic-field-aligned electric fields, and (both in, and downstream of, the transition region) a potential trough structure in the plasma's rest frame. It is found that all these macroscopic phenomena are intimately linked and can be understood within one consistent physical picture. The basic driving mechanism is the azimuthal electric field that is induced when, in the plasma's rest frame, the transverse magnetic field grows in time. The plasma's response is complicated by the fact that penetrating plasma clouds are in a parameter range where currents are not related to electric fields by a local conductivity: the ion motion is instead determined by the macroscopic potential structure.

  • 17.
    Hurtig, Tomas
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Brenning, Nils
    KTH, Superseded Departments, Alfvén Laboratory.
    Raadu, Michael A.
    KTH, Superseded Departments, Alfvén Laboratory.
    The penetration of plasma clouds across magnetic boundaries: The role of high frequency oscillations2004In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 11, no 7, p. L33-L36Article in journal (Refereed)
    Abstract [en]

    Experiments are reported where a collision-free plasma cloud penetrates a magnetic barrier by self-polarization. Two closely related effects, both fundamental for the penetration mechanism, are studied quantitatively: anomalous fast magnetic field penetration (two orders of magnitude faster than classical), and anomalous fast electron transport (three orders of magnitude faster than classical and two orders of magnitude faster than Bohm diffusion). It is concluded that they are both mediated by highly nonlinear oscillations in the lower hybrid range, driven by a strong diamagnetic current loop which is set up in the plasma in the penetration process.

  • 18. Lundin, Daniel
    et al.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Jadernas, Daniel
    Larsson, Petter
    Wallin, Erik
    Lattemann, Martina
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Helmersson, Ulf
    Transition between the discharge regimes of high power impulse magnetron sputtering and conventional direct current magnetron sputtering2009In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 18, no 4Article in journal (Refereed)
    Abstract [en]

    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 distinguished during the pulses: (1) a high-current transient followed by (2) a plateau at lower currents. These results provide a link between the HiPIMS and the direct current magnetron sputtering (DCMS) discharge regimes. At high applied negative voltages the high-current transient had the characteristics of HiPIMS pulses, while at lower voltages the plateau values agreed with currents in DCMS using the same applied voltage. The current behavior was found to be strongly correlated with the chamber gas pressure, where increasing gas pressure resulted in increasing peak current and plateau current. Based on these experiments it is suggested here that the high-current transients cause a depletion of the working gas in the area in front of the target, and thereby a transition to a DCMS-like high-voltage, lower current regime.

  • 19. Lundin, Daniel
    et al.
    Gudmundsson, Jon Tomas
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Minea, Tiberu
    A study of the oxygen dynamics in a reactive Ar/O high power impulse magnetron sputtering discharge using an ionization region model2017In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 121, no 17, article id 171917Article in journal (Refereed)
    Abstract [en]

    The oxygen dynamics in a reactive Ar/O2high power impulse magnetron sputtering discharge hasbeen studied using a new reactive ionization region model. The aim has been to identify thedominating physical and chemical reactions in the plasma and on the surfaces of the reactoraffecting the oxygen plasma chemistry. We explore the temporal evolution of the density of theground state oxygen molecule O2ðX1RgÞ, the singlet metastable oxygen molecules O2ða1DgÞandO2ðb1RgÞ, the oxygen atom in the ground state O(3P), the metastable oxygen atom O(1D), thepositive ions Oþ2and Oþ, and the negative ion O. We furthermore investigate the reaction ratesfor the gain and loss of these species. The density of atomic oxygen increases significantly as wemove from the metal mode to the transition mode, and finally into the compound (poisoned) mode.The main gain rate responsible for the increase is sputtering of atomic oxygen from the oxidizedtarget. Both in the poisoned mode and in the transition mode, sputtering makes up more than 80%of the total gain rate for atomic oxygen. We also investigate the possibility of depositingstoichiometric TiO2in the transition mode.

  • 20.
    Lundin, Daniel
    et al.
    Plasma and Coatings Physics Division.
    Huo, Chunqing
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Helmersson, Ulf
    Deposition rate loss in high power impulse magnetron sputtering: understanding through computational modeling2011In: 54th Annual Technical Conference Proceedings, Chicago, IL April 16-21,2011, Society of Vacuum Coaters , 2011, p. 172-177Conference paper (Refereed)
    Abstract [en]

    A lower deposition rate for high power impulse magnetron sputtering (HiPIMS) compared to DC magnetron sputtering (DCMS) for the same average power is often reported. The invoked reason is in many cases back-attraction of ionized sputteredmaterial to the target, but other effects are also likely to appear. In this work experimental results on the plasma and discharge conditions from several different HiPIMS experiments have been analyzed using a global discharge model to get an overall understanding of the HiPIMS discharge. The objective has been to quantify mechanisms reducing the deposition rate by studying the ionization of sputtered material and the possibility of back-attraction of ionized species, as well as heating of the neutral process gas leading to gas rarefaction.

  • 21.
    Marklund, Göran
    et al.
    KTH, Superseded Departments, Alfvén Laboratory. KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, Superseded Departments, Alfvén Laboratory. KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lindqvist, Per-Arne
    KTH, Superseded Departments, Alfvén Laboratory. KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Effects of Birkeland Current Limitation on High-Latitude Convection Patterns1984Report (Other academic)
  • 22.
    Raadu, Michael A.
    KTH, Superseded Departments, Alfvén Laboratory.
    Effective distribution functions for electrostatic waves in dusty plasmas with a dust-size distribution2001In: IEEE Transactions on Plasma Science, ISSN 0093-3813, E-ISSN 1939-9375, Vol. 29, no 2, p. 182-185Article in journal (Refereed)
    Abstract [en]

    The kinetic theory for the electrostatic modes of dusty plasmas with a distribution of grain sizes is examined. It is assumed that the size distribution predominantly decreases exponentially with the mass for large sizes, and that a power law prevails for small sizes. Thermodynamic equilibrium leads to Maxwellian distributions over velocity with a fixed temperature and continuously varying mass. Smaller particles have higher thermal velocity and dominate the tail of the velocity distribution. The contribution of the dust component to the dispersion function is found to be non-Maxwellian and is equivalent to that for a kappa (generalized Lorentzian) distribution of monosized particles, Known results for kappa distributions may be exploited, However, the nonlinear response of the charge density of the dust to an electrostatic potential is quite different to that of a monosized kappa distribution. In general, the definition of an effective dust distribution function for linearized electrostatic modes leads to a useful straightforward procedure to find the dispersion function. It is important to realize that the combined effects of velocity and size distribution can, in general, strongly modify the kinetic behavior of the plasma dust component.

  • 23.
    Raadu, Michael A.
    KTH, Superseded Departments, Alfvén Laboratory.
    Generalised Sagdeev potentials for dusty plasmas with varying grain charges2003In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 68, no 4, p. 266-270Article in journal (Refereed)
    Abstract [en]

    Grain charges in a dusty plasma are deter-mined by the random currents from the ambient plasma and vary with the local conditions. The charge on a slowly moving grain will be close to the locally determined equilibrium. given for zero net current to the grain. For a steady electrostatic structure (e.g., solitary wave, double layer) integrals of motion for grains with varying charge can then be found. (These integrals reduce to the total energy if the charge is constant. but in general the electrostatic term becomes an integral of the grain charge with respect to the potential.) Steady state solutions of Vlasov's equation are piecewise given by arbitrary functions of these integrals of motion. A generalised Sagdeev (Classical) potential can be found, which is. to within an added constant. equal to minus the sum of the total particle pressures (including that of the grains). This extends the well known equivalence found for conventional plasmas and dusty plasmas with constant grain charges. The analysis of dust acoustic solitary waves is modified by additional terms proportional to potential derivatives of the charge. A grain size distribution may be incorporated. The second derivative of the Sagdeev potential (leading to the generalised Bohm condition) is then Riven in terms of the same effective distribution function as found for linear electrostatic modes. Comparisons are made with several analyses of nonlinear electrostatic structures including dynamical charging.

  • 24.
    Raadu, Michael A.
    KTH, Superseded Departments, Alfvén Laboratory.
    Particle acceleration mechanisms in space plasmas2001In: Physics and Chemistry of the Earth, Part C: Solar, Terrestial & Planetary Science, ISSN 1464-1917, E-ISSN 1873-4685, Vol. 26, no 03-jan, p. 55-59Article in journal (Refereed)
    Abstract [en]

    There are many possible mechanisms for particle acceleration in space plasmas. Among these are two broadly defined types that may be characterised on the one hand by large scale electric field structures and on the other hand by stochastic mechanisms and enhanced wave activity. Double layers (DLs) are an example of the first type. They sustain a net potential difference, across which particles are accelerated. Crucial questions concern the generator maintaining the potential, the rate of energy transfer, equilibrium and matching conditions. Magnetic reconnection at an X-type neutral line is another example and shares many characteristics with DLs, such as the cutting of field lines and constraints set by external MHD motions. Particle acceleration by the growth of the modified two- stream instability (MTSI) is an example of the second type. The MTSI is driven by cross magnetic field ion motion and rapidly accelerates electrons. It has been seen as a link in the critical ionisation velocity (CIV) mechanism, which has been extensively studied both in experiments and theory. Crucial questions concern the evolution of the particle energy distribution, the wave source and the saturation of the driving instability.

  • 25.
    Raadu, Michael A.
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Shafiq, M.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Wake potential of a test charge using the stationary phase method2005Conference paper (Refereed)
    Abstract [en]

    The linear response of a dusty (complex) plasma to a moving test charge can be determined using an appropriate plasma dielectric function and a three dimensional Fourier analysis. Many analytical results have been found for a slowly moving test charge. For intermediate and large velocities numerical methods of integration are commonly used. However general asymptotic results valid at large distances can be found, using a combination of the residue calculus applied to the zeroes of the dielectric function and the method of stationary phase for integration over a wave vector component. The method can be expressed in terms of conditions on the group and phase velocity of waves in the reference frame of the moving test charge. In particular for a given radial direction the asymptotic response is determined by wave vectors for which the group velocity is directed radially outwards. The analysis is close to that due to Kelvin for ship waves in deep water. An essential difference is that in the present case three spatial dimensions are involved instead of only two, and also that the dispersion relation for plasma waves is more complicated.

  • 26.
    Raadu, Michael A.
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Shafiq, Muhammad
    KTH, Superseded Departments, Alfvén Laboratory.
    Shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging2003In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 10, no 9, p. 3484-3491Article in journal (Refereed)
    Abstract [en]

    The dynamical charging of grains in a dusty plasma enhances the shielding of test charges. Time scales for charging are determined by the ambient plasma parameters and the grain dimensions. They can be very short, approaching the ion plasma period for grain sizes of the order of an electron Debye length. For a slowly moving test charge the response potential is found as a power series in the test charge velocity. Collisional effects are included. Analytical expressions for the response potential, valid for all radial distances, are found up to second order in the test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. The remaining first-order terms are given by analytical expressions that yield the well known asymptotic power law forms for large distances.

  • 27.
    Raadu, Michael A.
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Shafiq, Muhammad
    KTH, Superseded Departments, Alfvén Laboratory.
    Test charge response of a dusty plasma with a grain size distribution2002In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 305, p. 79-86Article in journal (Refereed)
    Abstract [en]

    The form of the grain size distribution strongly influences the linear dielectric response of a dusty plasma. For a class of size distributions there is an equivalence to a Lorentzian distribution of mono-sized particles. The electrostatic response to a slowly moving test charge, using a second order approximation, is found. The effects of collisions are investigated.

  • 28.
    Raadu, Michael
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Axnäs, Ingvar
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Gudmundsson, Jon Tomas
    Shanghai Jiao Tong University; University of Iceland.
    Huo, Chunqing
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Brenning, Nils
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    An ionization region model for high-power impulse magnetron sputtering discharges2011In: Plasma sources science & technology (Print), ISSN 0963-0252, E-ISSN 1361-6595, Vol. 20, no 6, p. 065007-Article in journal (Refereed)
    Abstract [en]

    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, e. g., the temporal variations of the ionized fractions of the working gas and the sputtered vapor, the electron density and temperature, and the gas rarefaction and refill processes. A separation is made between aspects that can be followed with a certain precision, based on known data, such as excitation rates, sputtering and secondary emission yield, and aspects that need to be treated as uncertain and defined by assumptions. The input parameters in the model can be changed to fit different specific applications. Examples of such changes are the gas and target material, the electric pulse forms of current and voltage, and the device geometry. A basic version, ionization region model I, using a thermal electron population, singly charged ions, and ion losses by isotropic diffusion is described here. It is fitted to the experimental data from a HiPIMS discharge in argon operated with 100 mu s long pulses and a 15 cm diameter aluminum target. Already this basic version gives a close fit to the experimentally observed current waveform, and values of electron density n(e), the electron temperature T(e), the degree of gas rarefaction, and the degree of ionization of the sputtered metal that are consistent with experimental data. We take some selected examples to illustrate how the model can be used to throw light on the internal workings of these discharges: the effect of varying power efficiency, the gas rarefaction and refill during a HiPIMS pulse, and the mechanisms determining the electron temperature.

  • 29.
    Raadu, Michael
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Shafiq, Mohammad
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Charge fluctuation effects on solitary waves in dusty plasmas2005In: New Vistas in Dusty Plasmas, 2005, Vol. 799, p. 486-489Conference paper (Refereed)
    Abstract [en]

    In a dusty plasma the charge on a moving dust grain changes in response to the variations in the local plasma conditions. The charge on a slowly moving grain should be close to a locally determined equilibrium. For a time independent electrostatic structure an integral of motion for a grain with varying charge can then be found. Solutions of Vlasov's equation are given by arbitrary functions of these integrals of motion, so that, using the Poisson equation, a generalised Sagdeev (Classical) potential can be found (Raadu, 2003, Phys. Scripta vol.68, 266). Solitary wave solutions may be investigated making use of this generalised Sagdeev potential. The influence of charge fluctuations on the range of parameters for the existence of solitary waves is considered here. A modified form of the relation between the amplitude and the wave velocity is found.

  • 30. Samuelsson, Mattias
    et al.
    Lundin, Daniel
    Jensen, Jens
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Gudmundsson, Jon Tomas
    KTH, School of Electrical Engineering (EES).
    Helmersson, Ulf
    On the film density using high power impulse magnetron sputtering2010In: Surface & Coatings Technology, ISSN 0257-8972, E-ISSN 1879-3347, Vol. 205, no 2, p. 591-596Article in journal (Refereed)
    Abstract [en]

    The influence on thin film density using high power impulse magnetron sputtering (HIPIMS) has been investigated for eight different target materials (Al, Ti, Cr. Cu, Zr, Ag, Ta, and Pt). The density values as well as deposition rates have been compared to results obtained from thin films grown by direct current magnetron sputtering (DCMS) under the same experimental conditions. Overall, it was found that the HIPIMS deposited coatings were approximately 5-15% denser compared to the DCMS deposited coatings This could be attributed to the increased metal ion bombardment commonly seen in HIPIMS discharges, which also was verified using a global plasma model to assess the degree of ionization of sputtered metal One key feature is that the momentum transfer between the growing film and the incoming metal ions is very efficient due to the equal mass of film and bombarding species, leading to a less pronounced columnar microstructure As expected the deposition rates were found to be lower for HiPIMS compared to DCMS For several materials this decrease is not as pronounced as previously reported in the literature, which is shown in the case of Ta. Pt, and Ag with rate(HIPIMS)/rate(DCMS)-70-85%. while still achieving denser coatings.

  • 31.
    Shafiq, Mohammad
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Effect of grain charging dynamics on the wake potential of a moving test charge in a dusty plasma2007In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 14, no 1, p. 012102-Article in journal (Refereed)
    Abstract [en]

    The response potential of a dusty (complex) plasma to a moving test charge strongly depends on its velocity. For a test charge moving with a velocity exceeding the dust-acoustic speed, a distinctive wake-field is produced trailing behind the test charge. Here the response to a fast moving test charge, when dispersion effects are small and the dust behaves as a cold plasma component, is considered. The effects of dynamical grain charging are included, and the cases with and without these effects are analyzed and compared. The plasma dielectric function is chosen assuming that all grains are of the same size and includes a response term for charging dynamics. The wake field potential is found either explicitly in terms of known functions or by using numerical methods for the integral expression. Maximum response is found on the wake cone with apex angle determined by the ratio between the dust acoustic velocity and the test charge velocity. The structure of the wake field stretches in the direction of the test charge velocity when this increases. The functional form of the field is given by separately changing the length scales parallel and perpendicular to the velocity. The potential on the axis gives an electric field close behind the test charge that can attract charges with the same sign. The grain charging dynamics leads to a spatial damping and a phase shift in the potential response.

  • 32.
    Shafiq, Mohammad
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Raadu, Michael. A.
    KTH, Superseded Departments, Alfvén Laboratory.
    Delayed shielding of a test charge due to dynamical grain charging in a dusty plasma2004In: IEEE Transactions on Plasma Science, ISSN 0093-3813, E-ISSN 1939-9375, Vol. 32, p. 627-631Article in journal (Refereed)
    Abstract [en]

    The dynamical charging of grains in a dusty plasma modifies the plasma dielectric response function and the nature of the electrostatic wave modes. The grain charging leads to an additional shielding effect that acts in the same way as Debye shielding. Both the additional shielding and the charging rate are important in determining the response of a dusty plasma to a moving test charge. The dynamics of the charging can be approximated by using a time delay. An alternative analysis of the potential of a slowly moving test charge is performed introducing a delay operator for the grain charge response. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. This gives a physical interpretation of earlier results which are identical to first order in the test charge velocity.

  • 33.
    Shafiq, Mohammad
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Energy loss of test charges in a dusty plasma in the presence of dynamical grain charging, in New Vistas in Dusty Plasmas2005In: New Vistas in Dusty Plasmas / [ed] Boufendi, L; Mikikian, M; Shukla, PK, 2005, Vol. 799, p. 490-493Conference paper (Refereed)
    Abstract [en]

    Thedynamical charging of dust grains is an important process andis found to enhance the shielding of a test chargepassing through a multi-component dusty plasma. In the present work,the energy loss of a test charge projectile passing througha dusty plasma in the presence of dynamical grain chargingis studied. The electric forces can be written in termsof the Maxwell stress tensor for a sphere around thetest charge. For sphere with radius tending to zero theforce is just that on the test charge. For afinite radius, forces on the plasma are also included whichmakes it possible to see how the force on thetest charge is balanced by the force on the plasma.The method fails for the zero radius but the dragforce can be found from a simple physical model. Thegeneral analytical results are presented and are compared with theprevious results.

  • 34.
    Shafiq, Mohammad
    et al.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Raadu, Michael A.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Test charge response for a dusty plasma with both grain size distribution and dynamical charging2007In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 14, no 1, p. 012105-Article in journal (Refereed)
    Abstract [en]

    The form of the grain size distribution strongly influences the linear dielectric response of a dusty plasma. For a class of size distributions and a thermal velocity distribution, there is an equivalence to a Lorentzian distribution of monosized particles. The electrostatic response to a slowly moving test charge can then be found. Dynamical charging of grains in a dusty plasma leads to an enhanced time-dependent shielding of a test charge. Here the combined effect of both grain size distribution and dynamical grain charging on the response to a slowly moving test charge is analyzed. The dynamical charging contribution to the plasma dielectric has a complicated dependence on the parameters for the size distribution and on the charging rate. However, this dependence can be expressed in terms of known functions. Series expansions are used to derive the potential response to a slowly moving test charge. Previously known results may be recovered as special limiting cases of this investigation. The analytical expression for the plasma dielectric may be used for more general cases and is applicable to the study of electrostatic waves.

1 - 34 of 34
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