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Title: Non-thermal electron acceleration in low Mach number collisionless shocks. II. Firehose-mediated Fermi acceleration and its dependence on pre-shock conditions

Abstract

Electron acceleration to non-thermal energies is known to occur in low Mach number (M{sub s} ≲ 5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M{sub s} = 3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is provided by oblique magnetic waves that are self-generated by the electrons escaping ahead of the shock. In the present work, we employ additional 2D PIC simulations to address the nature of the upstream oblique waves. We find that the waves are generated by the shock-reflected electrons via the firehose instability, which is driven by an anisotropy in the electron velocity distribution. We systematically explore how the efficiency of wave generation and of electron acceleration depend on the magnetic field obliquity, the flow magnetization (or equivalently, the plasma beta), and the upstream electron temperature. We find that the mechanism works for shocks with high plasma beta (≳ 20) atmore » nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. Our findings offer a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.« less

Authors:
;  [1];  [2]
  1. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
  2. NASA Einstein Postdoctoral Fellow. (United States)
Publication Date:
OSTI Identifier:
22370051
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 797; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; ANISOTROPY; DISTRIBUTION; EFFICIENCY; ELECTRON TEMPERATURE; EMISSION; GALAXY CLUSTERS; HOSE INSTABILITY; MACH NUMBER; MAGNETIC FIELDS; MAGNETIZATION; PLASMA; PLASMA SIMULATION; SCATTERING; SHOCK WAVES; SOLAR FLARES; SYNCHROTRON RADIATION; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Guo, Xinyi, Narayan, Ramesh, and Sironi, Lorenzo. Non-thermal electron acceleration in low Mach number collisionless shocks. II. Firehose-mediated Fermi acceleration and its dependence on pre-shock conditions. United States: N. p., 2014. Web. doi:10.1088/0004-637X/797/1/47.
Guo, Xinyi, Narayan, Ramesh, & Sironi, Lorenzo. Non-thermal electron acceleration in low Mach number collisionless shocks. II. Firehose-mediated Fermi acceleration and its dependence on pre-shock conditions. United States. doi:10.1088/0004-637X/797/1/47.
Guo, Xinyi, Narayan, Ramesh, and Sironi, Lorenzo. Wed . "Non-thermal electron acceleration in low Mach number collisionless shocks. II. Firehose-mediated Fermi acceleration and its dependence on pre-shock conditions". United States. doi:10.1088/0004-637X/797/1/47.
@article{osti_22370051,
title = {Non-thermal electron acceleration in low Mach number collisionless shocks. II. Firehose-mediated Fermi acceleration and its dependence on pre-shock conditions},
author = {Guo, Xinyi and Narayan, Ramesh and Sironi, Lorenzo},
abstractNote = {Electron acceleration to non-thermal energies is known to occur in low Mach number (M{sub s} ≲ 5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M{sub s} = 3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is provided by oblique magnetic waves that are self-generated by the electrons escaping ahead of the shock. In the present work, we employ additional 2D PIC simulations to address the nature of the upstream oblique waves. We find that the waves are generated by the shock-reflected electrons via the firehose instability, which is driven by an anisotropy in the electron velocity distribution. We systematically explore how the efficiency of wave generation and of electron acceleration depend on the magnetic field obliquity, the flow magnetization (or equivalently, the plasma beta), and the upstream electron temperature. We find that the mechanism works for shocks with high plasma beta (≳ 20) at nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. Our findings offer a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.},
doi = {10.1088/0004-637X/797/1/47},
journal = {Astrophysical Journal},
number = 1,
volume = 797,
place = {United States},
year = {Wed Dec 10 00:00:00 EST 2014},
month = {Wed Dec 10 00:00:00 EST 2014}
}
  • Electron acceleration to non-thermal energies in low Mach number (M{sub s} ≲ 5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-cell plasma simulations to study electron acceleration in low Mach number shocks. We focusmore » on the particle energy spectra and the acceleration mechanism in a reference run with M{sub s} = 3 and a quasi-perpendicular pre-shock magnetic field. We find that about 15% of the electrons can be efficiently accelerated, forming a non-thermal power-law tail in the energy spectrum with a slope of p ≅ 2.4. Initially, thermal electrons are energized at the shock front via shock drift acceleration (SDA). The accelerated electrons are then reflected back upstream where their interaction with the incoming flow generates magnetic waves. In turn, the waves scatter the electrons propagating upstream back toward the shock for further energization via SDA. In summary, the self-generated waves allow for repeated cycles of SDA, similarly to a sustained Fermi-like process. This mechanism offers a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.« less
  • Nonlinear evolution of the Buneman instability and its application to electron acceleration in collisionless shocks are discussed. Two-dimensional particle-in-cell simulations show that the saturation level of the instability is reduced from one-dimensional simulation results. It is demonstrated that the reduced saturation level is due to the resonant wave-particle interactions with large amplitude obliquely propagating waves. A new estimate for the saturation level is given by considering the interactions with oblique modes. The effects of the large amplitude oblique modes on electron shock surfing acceleration that is mainly controlled by the Buneman instability are also investigated. Two-dimensional particle-in-cell simulations of themore » shock transition region are performed by adopting a local model with the periodic boundary condition. The results indicate that the presence of oblique modes introduces a stochastic behavior to the trajectories of energetic electrons. The maximum energy is limited by the finite lifetime of the instability in the present periodic model. However, this will not be the case in the realistic shock transition region. The application to realistic shocks with Mach numbers typical of supernova remnants is also discussed.« less
  • An extreme case of electron shock drift acceleration (SDA) in low Mach number collisionless shocks is investigated as a plausible mechanism for the initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters, where the upstream plasma temperature is of the order of 10 keV and the degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even when a shock is rather moderate, a part of the thermal incoming electrons are accelerated and reflected through relativistic SDA and form a local non-thermal population just upstream of the shock. The accelerated electrons can self-generate localmore » coherent waves and further be back-scattered toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters, such as CIZA J2242.8+5301, which have well-defined radio relics.« less
  • A full particle simulation study is carried out on the electron acceleration at a collisionless, relatively low Alfven Mach number (M{sub A} = 5), perpendicular shock. Recent self-consistent hybrid shock simulations have demonstrated that the shock front of perpendicular shocks has a dynamic rippled character along the shock surface of low Mach number perpendicular shocks. In this paper, the effect of the rippling of perpendicular shocks on the electron acceleration is examined by means of large-scale (ion-scale) two-dimensional full particle simulations. It has been shown that a large-amplitude electric field is excited at the shock front in association with themore » ion-scale rippling, and that reflected ions are accelerated upstream at a localized region where the shock-normal electric field of the rippled structure is polarized upstream. The current-driven instability caused by the highly accelerated reflected ions has a high growth rate of up to large-amplitude electrostatic waves. Energetic electrons are then generated by the large-amplitude electrostatic waves via electron surfing acceleration at the leading edge of the shock-transition region. The present result suggests that the electron surfing acceleration is also a common feature at low Mach number perpendicular collisionless shocks.« less
  • The existence and properties of low Mach-number (M >~ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. By using this semi-analytical model, we also study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock propertiesmore » significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.« less