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  • 1.
    Dieckmann, Mark E
    et al.
    Ruhr-University Bochum.
    Bret, Antoine
    ETSI-Industriales University of Castilla-La Mancha.
    Shukla, Padma Kant
    Institut fuer Theoretische Physik IV Ruhr-University Bochum.
    Comparing electrostatic instabilities driven by mildly and highly relativistic proton beams2007In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 49, no December, p. 1989-2004Article in journal (Refereed)
    Abstract [en]

    An electrostatic instability driven by counter-propagating tenuous proton beams that traverse a bulk plasma consisting of electrons and protons is considered. The system is spatially homogeneous and is evolved in time with a one-dimensional particle-in-cell simulation, which allows for a good statistical plasma representation. Mildly and highly relativistic beam speeds are modeled. The proton beams with a speed of 0.9c result in waves that saturate by the trapping of electrons. The collapse of the phase space holes in the electron distribution scatters these to a flat-top momentum distribution. The final electric fields are weak and the proton beams are weakly modulated. No secondary instabilities are likely to form that could thermalize the proton beams. The proton beams moving with 0.99c initially heat the bulk plasma through a three-wave interaction. Coalescing phase space holes in the bulk proton distribution arising from the saturation of ion acoustic waves transport wave energy to low wavenumbers. Highly relativistic phase space holes form in the electron distribution, which are not spatially homogeneous. The spatial envelope of these electron phase space holes interacts with the fluctuations driven by the phase space holes in the bulk protons, triggering a modulational instability. A Langmuir wave condensate forms that gives rise to strong and long electrostatic wave packets, as well as to a substantial modulation of the proton beams. The final state of the system with the highly relativistic proton beams is thus more unstable to further secondary instabilities that may transfer a larger beam energy fraction to the electrons and thermalize the proton beams more rapidly

  • 2.
    Dieckmann, Mark E
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Doria, D.
    Queens University of Belfast, North Ireland.
    Sarri, G.
    Queens University of Belfast, North Ireland.
    Romagnani, L.
    Ecole Polytech, France.
    Ahmed, H.
    Queens University of Belfast, North Ireland.
    Folini, D.
    University of Lyon, France.
    Walder, R.
    University of Lyon, France.
    Bret, A.
    University of Castilla La Mancha, Spain; Institute Invest Energet and Aplicac Ind, Spain.
    Borghesi, M.
    Queens University of Belfast, North Ireland.
    Electrostatic shock waves in the laboratory and astrophysics: similarities and differences2018In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 60, no 1, article id 014014Article in journal (Refereed)
    Abstract [en]

    Contemporary lasers allow us to create shocks in the laboratory that propagate at a speed that matches that of energetic astrophysical shocks like those that ensheath supernova blast shells. The rapid growth time of the shocks and the spatio-temporal resolution, with which they can be sampled, allow us to identify the processes that are involved in their formation and evolution. Some laser-generated unmagnetized shocks are mediated by collective electrostatic forces and effects caused by binary collisions between particles can be neglected. Hydrodynamic models, which are valid for many large-scale astrophysical shocks, assume that collisions enforce a local thermodynamic equilibrium in the medium; laser-generated shocks are thus not always representative for astrophysical shocks. Laboratory studies of shocks can improve the understanding of their astrophysical counterparts if we can identify processes that affect electrostatic shocks and hydrodynamic shocks alike. An example is the nonlinear thin-shell instability (NTSI). We show that the NTSI destabilises collisionless and collisional shocks by the same physical mechanism.

  • 3.
    Dieckmann, Mark E
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Eliasson, Bengt
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Shukla, Padma K
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Sircombe, Nathan J
    Space and Astrophysics Group University of Warwick.
    Dendy, Richard O
    Space and Astrophysics Group University of Warwick.
    Two-stream instability in collisionless shocks and foreshock2006In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no 12 B, p. B303-B311Article in journal (Other academic)
    Abstract [en]

    Shocks play a key role in plasma thermalization and particle acceleration in the near Earth space plasma, in astrophysical plasma and in laser plasma interactions. An accurate understanding of the physics of plasma shocks is thus of immense importance. We give an overview over some recent developments in particle-in-cell simulations of plasma shocks and foreshock dynamics. We focus on ion reflection by shocks and on the two-stream instabilities these beams can drive, and these are placed in the context of experimental observations, e.g. by the Cluster mission. We discuss how we may expand the insight gained from the observation of proton beam driven instabilities at near Earth plasma shocks to better understand their astrophysical counterparts, such as ion beam instabilities triggered by internal and external shocks in the relativistic jets of gamma ray bursts, shocks in the accretion discs of micro-quasars and supernova remnant shocks. It is discussed how and why the peak energy that can be reached by particles that are accelerated by two-stream instabilities increases from keV energies to GeV energies and beyond, as we increase the streaming speed to relativistic values, and why the particle energy spectrum sometimes resembles power law distributions.

  • 4.
    Dieckmann, Mark E
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
    Folini, Doris
    École Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, F-69622 Lyon, France.
    Bret, Antoine
    Universidad de Castilla La Mancha, ETSI Ind, E-13071 Ciudad Real, Spain.
    Walder, Rolf
    École Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, F-69622 Lyon, France.
    Simulation studies of temperature anisotropy driven pair-Alfvén and aperiodic instabilities in magnetized pair plasma2019In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 61, no 8, article id 085027Article in journal (Refereed)
    Abstract [en]

    We compare with one-dimensional particle-in-cell simulations the aperiodically growing instabilities driven by a bi-Maxwellian velocity distribution in unmagnetized electron plasma (Weibel instability) and in pair plasma. The simulation box is aligned with the cool direction. The waves in both simulations evolve towards a circularly polarized non-propagating magnetic structure. Its current and magnetic field are aligned and the structure is in a force-free state. We examine how a background magnetic field B 0, which is parallel to the simulation direction, affects the waves in the pair plasma. A weak B 0 cannot inhibit the growth of the aperiodically growing instability but it prevents it from reaching the force-free stable state. The mode collapses and seeds a pair Alfvén waves. An intermediate B 0 couples the thermal anisotropy to the pair Alfvén mode and propagating magnetowaves grow. The phase speed of the pair of Alfvén waves is increased by the thermal anisotropy. Its growth is suppressed when B 0 is set to the value that stabilizes the mirror mode.

  • 5.
    Dieckmann, Mark E
    et al.
    Ruhr-Universität Bochum.
    Meli, Athina
    Department of Physics National University of Athens, Greece.
    Shukla, Padma Kant
    Institut für Theoretische Physik IV Ruhr-Universität Bochum, D-44780 Bochum, Germany.
    Drury, Luke OC
    Cosmic Rays Section Dublin Institute for Advanced Studies, Dublin, Ireland.
    Mastichiadis, Apostolos
    Department of Physics, National University of Athens National University of Athens.
    Two-dimensional PIC simulations of ion beam instabilities in Supernova-driven plasma flows2008In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 50, p. 065020-1-14Article in journal (Refereed)
    Abstract [en]

    Supernova remnant blast shells can reach the flow speed vs = 0.1c and shocks form at its front. Instabilities driven by shock-reflected ion beams heat the plasma in the foreshock, which may inject particles into diffusive acceleration. The ion beams can have the speed vb vs. For vb vs the Buneman or upper-hybrid instabilities dominate, while for vb vs the filamentation and mixed modes grow faster. Here the relevant waves for vb vs are examined and how they interact nonlinearly with the particles. The collision of two plasma clouds at the speed vs is modelled with particle-in-cell simulations, which convect with them magnetic fields oriented perpendicular to their flow velocity vector. One simulation models equally dense clouds and the other one uses a density ratio of 2. Both simulations show upper-hybrid waves that are planar over large spatial intervals and that accelerate electrons to ~10 keV. The symmetric collision yields only short oscillatory wave pulses, while the asymmetric collision also produces large-scale electric fields, probably through a magnetic pressure gradient. The large-scale fields destroy the electron phase space holes and they accelerate the ions, which facilitates the formation of a precursor shock. 

  • 6.
    Dieckmann, Mark E
    et al.
    Ruhr-Universität Bochum.
    Shukla, Padma K
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Electron surfing acceleration by the electron two-stream instability in a weak magnetic field2006In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no October, p. 1515-1530Article in journal (Refereed)
    Abstract [en]

    The thermalization of relativistically flowing colliding plasmas is not well understood. The transition layer, in which both plasmas interact and thermalize, is wide and highly structured and the instabilities in this layer may yield non-thermal particle distributions and shock-less energy dissipation. The objective in this work is to explore the ability of an electron two-stream instability for thermalizing a plasma beam that moves at the mildly relativistic speed 0.3c through weakly magnetized plasma and to identify the resulting particle distributions. It is demonstrated here with particle-in-cell simulations that the electron two-stream instability leads to waves that propagate within a wide angular range relative to the flow velocity. The waves are thus not planar, as required for efficient electron surfing acceleration (ESA). The short lifetime of the waves implies, however, only weak modifications of the ESA by the oblique modes, since the waves are sufficiently homogeneous. The ion (proton) beams are not modulated, which would be required to extract some of their energy. The instability can thus heat the electrons significantly, but it fails to accelerate them to relativistic energies and it cannot form a shock layer by thermalizing the protons, at least not for the system and the resolved timescales considered here.

  • 7.
    Dieckmann, Mark E
    et al.
    Ruhr-Universität Bochum.
    Sircombe, Nathan J
    Space and Astrophysics Group University of Warwick, UK.
    Parviainen, Madelene
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Shukla, Padma K
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Dendy, Richard O
    Space and Astrophysics Group University of Warwick.
    Phase speed of electrostatic waves: the critical parameter for efficient electron surfing acceleration2006In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no 4, p. 489-508Article in journal (Refereed)
    Abstract [en]

    Particle acceleration by means of nonlinear plasma wave interactions is of great topical interest. Accordingly, in this paper we focus on the electron surfing process. Self-consistent kinetic simulations, using both relativistic Vlasov and particle-in-cell (PIC) approaches, show here that electrons can be accelerated to highly relativistic energies (up to 100mec2) if the phase speed of the electrostatic wave is mildly relativistic (0.6c to 0.9c for the magnetic field strengths considered). The acceleration is strong because of relativistic stabilization of the nonlinearly saturated electrostatic wave, seen in both relativistic Vlasov and PIC simulations. An inverse power law momentum distribution can arise for the most strongly accelerated electrons. These results are of relevance to observed rapid changes in the radio synchrotron emission intensities from microquasars, gamma ray bursts and other astrophysical objects that require rapid acceleration mechanisms for electrons.

  • 8.
    Dieckmann, Mark Eric
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    The filamentation instability driven by warm electron beams: statistics and electric field generation2009In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 51, no 12, p. 124042-Article in journal (Refereed)
    Abstract [en]

    The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size of the flow aligned and the perpendicular currents are thus equal. It is confirmed that the electrostatic and the magnetic forces are equally important, when the filamentation instability saturates in 1D. Their balance is apparently the saturation mechanism of the filamentation instability for our initial conditions. The electric force is relatively weaker but not negligible in the 2D simulation, where the electron temperature is set higher to reduce the computational cost. The magnetic pressure gradient is the principal source of the electrostatic field, when and after the instability saturates in the 1D simulation and in the 2D simulation.

  • 9.
    Dieckmann, Mark Eric
    et al.
    Centre for Plasma Physics, Queen's University Belfast, UK .
    Bret, Antoine
    Harvard-Smithsonian Center for Astrophysics, Cambridge, MA , USA .
    Sarri, Gianluca
    Centre for Plasma Physics, Queen's University Belfast, UK .
    Perez Alvaro, Erica
    ETSI Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain .
    Kourakis, Ioannis
    Centre for Plasma Physics, Queen's University Belfast, UK .
    Borghesi, Marco
    Centre for Plasma Physics, Queen's University Belfast, UK .
    Particle simulation study of electron heating by counter-streaming ion beams ahead of supernova remnant shocks2012In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 54, no 8, p. 085015-Article in journal (Refereed)
    Abstract [en]

    The growth and saturation of Buneman-type instabilities is examined with a particle-in-cell (PIC) simulation for parameters that are representative for the foreshock region of fast supernova remnant shocks. A dense ion beam and the electrons correspond to the upstream plasma and a fast ion beam to the shock-reflected ions. The purpose of the 2D simulation is to identify the nonlinear saturation mechanisms, the electron heating and potential secondary instabilities that arise from anisotropic electron heating and result in the growth of magnetic fields. We confirm that the instabilities between both ion beams and the electrons saturate by the formation of phase space holes by the beam-aligned modes. The slower oblique modes accelerate some electrons, but they cannot heat up the electrons significantly before they are trapped by the faster beam-aligned modes. Two circular electron velocity distributions develop, which are centred around the velocity of each ion beam. They develop due to the scattering of the electrons by the electrostatic wave potentials. The growth of magnetic fields is observed, but their amplitude remains low.

  • 10.
    Dieckmann, Mark Eric
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Sarri, Gianluca
    Centre for Plasma Physics, Queen's University Belfast, Belfast BT7 1NN, UK.
    Romagnani, Lorenzo
    Centre for Plasma Physics, Queen's University Belfast, Belfast BT7 1NN, UK.
    Kourakis, Ioannis
    Centre for Plasma Physics, Queen's University Belfast, Belfast BT7 1NN, UK.
    Borghesi, Marco
    Centre for Plasma Physics, Queen's University Belfast, Belfast BT7 1NN, UK.
    Simulation of a collisionless planar electrostatic shock in a proton–electron plasma with a strong initial thermal pressure change2010In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 52, no 2, p. 025001-Article in journal (Refereed)
    Abstract [en]

    The localized deposition of the energy of a laser pulse, as it ablates a solid target, introduces high thermal pressure gradients in the plasma. The thermal expansion of this laser-heated plasma into the ambient medium (ionized residual gas) triggers the formation of non-linear structures in the collisionless plasma. Here an electron–proton plasma is modelled with a particle-in-cell simulation to reproduce aspects of this plasma expansion. A jump is introduced in the thermal pressure of the plasma, across which the otherwise spatially uniform temperature and density change by a factor of 100. The electrons from the hot plasma expand into the cold one and the charge imbalance drags a beam of cold electrons into the hot plasma. This double layer reduces the electron temperature gradient. The presence of the low-pressure plasma modifies the proton dynamics compared with the plasma expansion into a vacuum. The jump in the thermal pressure develops into a primary shock. The fast protons, which move from the hot into the cold plasma in the form of a beam, give rise to the formation of phase space holes in the electron and proton distributions. The proton phase space holes develop into a secondary shock that thermalizes the beam.

  • 11.
    Eliasson, Bengt
    et al.
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Shukla, Padma K
    Institute of Theoretical Physics IV Institute of Theoretical Physics IV.
    Dieckmann, Mark E
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Theory and simulations of nonlinear kinetic structures in plasmas2006In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no 12 B, p. B257-B265Article in journal (Other academic)
    Abstract [en]

    We present analytical and numerical studies of the dynamics of relativistic electron and ion holes in a collisionless plasma. Electromagnetic radiation can be trapped in relativistic electron phase-space holes mainly due to the relativistic mass increase of the electrons that are accelerated by the potential of the phase-space hole and by the quivering component of the electromagnetic field. Relativistic ion holes may exist in plasmas where the electrons are thermalized to extremely ultra-relativistic energies. They may be responsible for the acceleration of particles to GeV energies in active galactic nuclei and supernova remnant shocks. The analytic solutions are employed as initial conditions for numerical simulations in which the dynamics and stability of the phase-space holes are investigated. The results have relevance for intense laser-plasma experiments and for astrophysical plasmas.

  • 12.
    Sarri, Gianluca
    et al.
    Queen's University Belfast, UK.
    Schumaker, W
    University of Michigan, Ann Arbor, USA.
    Di Piazza, A
    Max-Planck-Institut für Kernphysik, Germany.
    Poder, K
    Imperial College, London, UK.
    Cole, JM
    Imperial College, London, UK.
    Vargas, M
    University of Michigan, Ann Arbor, USA.
    Doria, Domenico
    The Queen's University of Belfast, UK.
    Kushel, S
    Helmholtz Institute Jena, Germany.
    Dromey, Brendan
    The Queen's University of Belfast, UK.
    Grittani, G
    Consiglio Nazionale delle Ricerche, Italy.
    Gizzi, L
    Consiglio Nazionale delle Ricerche, Italy.
    Dieckmann, Mark Eric
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, The Institute of Technology.
    Green, A
    The Queen's University of Belfast, UK.
    Chvykov, V
    University of Michigan, Ann Arbor, USA.
    Maksimchuk, A
    University of Michigan, Ann Arbor, USA.
    Yanovsky, V
    University of Michigan, Ann Arbor, USA.
    He, ZH
    University of Michigan, Ann Arbor, USA.
    Hou, BX
    University of Michigan, Ann Arbor, USA.
    Nees, JA
    University of Michigan, Ann Arbor, USA.
    Kar, S
    The Queen's University of Belfast, UK.
    Najmudin, Z
    Helmholtz Institute Jena, Germany.
    Thomas, AGR
    University of Michigan, Ann Arbor, USA.
    Keitel, CH
    Max-Planck-Institut für Kernphysik, Germany.
    Krushelnick, K
    University of Michigan, Ann Arbor, USA.
    Zepf, Matt
    The Queen's University of Belfast, UK.
    Laser-driven generation of collimated ultra-relativistic positron beams2013In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 55, no 12Article in journal (Refereed)
    Abstract [en]

    We report on recent experimental results concerning the generation of collimated (divergence of the order of a few mrad) ultra-relativistic positron beams using a fully optical system. The positron beams are generated exploiting a quantum-electrodynamic cascade initiated by the propagation of a laser-accelerated, ultra-relativistic electron beam through high-Z solid targets. As long as the target thickness is comparable to or smaller than the radiation length of the material, the divergence of the escaping positron beam is of the order of the inverse of its Lorentz factor. For thicker solid targets the divergence is seen to gradually increase, due to the increased number of fundamental steps in the cascade, but it is still kept of the order of few tens of mrad, depending on the spectral components in the beam. This high degree of collimation will be fundamental for further injection into plasma-wakefield afterburners.

  • 13.
    Shukla, Padma K
    et al.
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Bingham, Robert
    CCLRC Rutherford-Appleton Labs, UK.
    Eliasson, Bengt
    Institute of Theoretical Physics IV Ruhr-University Bochum, Germany.
    Dieckmann, Mark E
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Stenflo, Lennart
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.
    Nonlinear aspects of the solar coronal heating2006In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no 12 B, p. B249-B255Article in journal (Other academic)
    Abstract [en]

    The heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron and ion heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the plasma particles. In this paper, we discuss two important nonlinear aspects of the electron and ion heating caused by finite amplitude obliquely propagating dispersive Alfvén (DA) waves and magnetic field-aligned circularly polarized electromagnetic ion-cyclotron Alfvén (EMICA) waves that may exist in the solar terrestrial environment. Specifically, DA waves may contribute to the solar coronal electron heating via Joule heating involving electron-wave interactions, and resonant ion EMICA wave interactions may contribute to differential ion heating in the solar corona.

  • 14.
    Stockem, Anne
    et al.
    Institut fuer Theoretische Physik IV Ruhr-University Bochum.
    Dieckmann, Mark E
    Ruhr-University Bochum.
    Schlickeiser, Reinhard
    Institut fuer Theoretische Physik IV Ruhr-University Bochum.
    Suppression of the filamentation instability by a flow-aligned magnetic field: testing the analytic threshold with PIC simulations2008In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 50, no 2, p. 025002-1-25002-18Article in journal (Refereed)
    Abstract [en]

    The impact of a flow-aligned and spatially homogeneous magnetic field on the filamentation instability (FI) is examined in a system of two equal counterstreaming non-relativistic cool electron beams. Particle-in-cell simulations that represent the plane perpendicular to the flow velocity vector confirm the reduction of the linear growth rate by the initial magnetic field. The FI is, however, not inhibited by a magnetic field with the critical strength, for which the solution of the linear dispersion relation predicts a full suppression. The saturation of the electromagnetic fields in the plasma involves a balance between the magnetic pressure gradient and the electric field resulting from the charge displacement. The simulations demonstrate that the magnetic energy gain and the field structure upon saturation do not depend on the initial magnetic field strength. This can be explained by the qualitative similarity of the spectrum of unstable wavenumbers, at least for subcritical strengths of the background magnetic field, and by the vanishing of the pressure gradient of a spatially homogeneous magnetic field. Magnetic trapping is apparently not the saturation mechanism for the considered plasma parameters. The spatial power spectrum of the saturated magnetic fields in the simulation plane can be approximated by a power-law function and the magnetic and electric spectra are similar at high wavenumbers. The final electron velocity distributions are comparable for all magnetic field strengths.

  • 15.
    Stockem, Anne
    et al.
    Theoretical Physics IV, Ruhr-University Bochum, Germany.
    Dieckmann, Mark Eric
    Ruhr-University Bochum.
    Schlickeiser, R
    Theoretical Physics IV, Ruhr-University Bochum, Germany.
    PIC simulations of the temperature anisotropy-driven Weibel instability: analysing the perpendicular mode2010In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 52, no 8Article in journal (Refereed)
    Abstract [en]

    An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe, in accordance with previous works, the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not accounted for by the linearized theory. A single-fluid-based theory is used to determine the source of this non-linear electric field. It is demonstrated that the magnetic stress tensor, which vanishes in a 1D geometry, is more important in this two-dimensional model used here. The electric field grows to an amplitude, which yields a force on the electrons that is comparable to the magnetic one. The peak energy density of each magnetic field component in the simulation plane agrees with previous estimates. Eddy currents develop, which let the amplitude of the third magnetic field component grow, which is not observed in a 1D simulation.

  • 16.
    Stockem, Anne
    et al.
    Theoretical Physics IV, Ruhr-University Bochum, Germany.
    Dieckmann, Mark Eric
    Ruhr-University Bochum.
    Schlickeiser, Reinhard
    Theoretical Physics IV, Ruhr-University Bochum, Germany.
    PIC simulations of the thermal anisotropy-driven Weibel instability: field growth and phase space evolution upon saturation2009In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 51, no 7, p. 075014-1-075014-13Article in journal (Refereed)
    Abstract [en]

    The Weibel instability is investigated with PIC simulations of an initially unmagnetized and spatially uniform electron plasma. This instability, which is driven by the thermally anisotropic electron distribution, generates electromagnetic waves with wave vectors perpendicular to the direction of the higher temperature. Two simulations are performed: a 2D simulation, with a simulation plane that includes the direction of higher temperature, demonstrates that the wave spectrum is initially confined to one dimension. The electric field components in the simulation plane generated by the instability equalize at the end of the simulation through a secondary instability. A 1D PIC simulation with a high resolution, where the simulation box is aligned with the wave vectors of the growing waves, reveals details of the electron phase space distribution and permits a comparison of the magnetic and electric fields when the instability saturates. It is shown that the electrostatic field is driven by the magnetic pressure gradient and that it and the magnetic field redistribute the electrons in space.

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