Collisionless shock waves in plasmas

Biskamp, D.

doi:10.1088/0029-5515/13/5/010

Cited by 149 publications

(106 citation statements)

References 68 publications

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“…As a matter of fact, the measured Mach number at the transition M w = (1+B m )/2 ∼ 2 is exactly the critical Mach number obtained for a magnetosonic soliton with vanishing resistivity [2,41,42,45].…”

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confidence: 72%

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Role of Magnetosonic Solitons in Perpendicular Collisionless Shock Reformation

2017

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The nature of the magnetic structure arising from ion specular reflection in shock compression studies is examined by means of 1d particle in cell simulations. Propagation speed, field profiles and supporting currents for this magnetic structure are shown to be consistent with a magnetosonic soliton. Coincidentally, this structure and its evolution are typical of foot structures observed in perpendicular shock reformation. To reconcile these two observations, we propose, for the first time, that shock reformation can be explained as the result of the formation, growth and subsequent transition to a super-critical shock of a magnetosonic soliton. This argument is further supported by the remarkable agreement found between the period of the soliton evolution cycle and classical reformation results. This new result suggests that the unique properties of solitons can be used to shed new light on the long-standing issue of shock non-stationarity and its role on particle acceleration.Introduction.-Collisionless shocks have been intensively studied since the late 1950's by virtue of of the role they are believed to play in plasma heating and charged particle acceleration (see, e. g., Refs. [1][2][3][4][5][6][7] and references therein). One of the most important features in high Mach number shocks is the specular reflection of upstream ions, which serves as an energy dissipation mechanism [8] to satisfy to shock conservation equations: ion specular reflection is paramount to both ion acceleration and shock structure.Further to its role in ion acceleration, ion specular reflection is responsible for the non-stationarity of quasiperpendicular shocks. This temporal variability has been demonstrated through numerical simulations (see, e. g., Refs [9-13]), observations [14][15][16][17] and experiments [18]. Although four different non-stationarity mechanisms have been suggested in full generality [5], the most likely candidate for explaining shock reformation in a 1-d exactly perpendicular shock (θ = 90• , with θ the angle between the upstream magnetic field and the shock normal) is the so-called self-reformation mechanism (see, e. g., Ref. [7]). This self reformation cycle can be summarized as follows. First, ions reflected by the shock form a foot ahead of the ramp. Due to the gyro-motion, these reflected ions pile up upstream of the foot at a distance slightly smaller than an ion gyro-radius ahead of the shock ramp, and create local magnetic field and density maxima there. Through a feedback mechanism, this foot then grows until it becomes as large as the initial shock ramp, effectively becoming the new ramp. Finally, this new ramp reflects incoming ions and the process repeats, with the shock advancing in a step-wise fashion. Numerical simulations suggest that the onset of this non-stationary reformation process is conditioned

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confidence: 72%

“…[1][2][3][4][5][6][7] and references therein). One of the most important features in high Mach number shocks is the specular reflection of upstream ions, which serves as an energy dissipation mechanism [8] to satisfy to shock conservation equations: ion specular reflection is paramount to both ion acceleration and shock structure.…”

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confidence: 99%

Role of Magnetosonic Solitons in Perpendicular Collisionless Shock Reformation

2017

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“…Although not very significant for the present case, it can be seen in Figure lc that the incoming ions acquire negative y velocities in the foot region, which necessarily results in some x deceleration (equation (8) is less steady than in the case discussed here (see next section) without recovering their results, however. According to Biskamp [ 1973], the reflected ions in the foot region of the particle simulation pile up when they reach their turning point (vx = 0) and therefore produce a local increase of density, large enough to reflect other particles, and so on. The discrepancy between particle and hybrid simulations may be due to the fact that a larger number of ions are reflected in the dissipationless particle code than in the hybrid code.…”

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confidence: 99%

The structure of perpendicular bow shocks

Leroy¹,

Winske²,

Goodrich³

et al. 1982

J. Geophys. Res.

461

369

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A hybrid simulation model with kinetic ions, massless fluid electrons, and phenomenological resistivity is used to study the perpendicular configuration of the bow shocks of the earth and other planets. We investigate a wide range of parameters, including the upstream Mach number, electron and ion beta (ratios of thermal to magnetic pressure), and resistivity. Electron beta and resistivity are found to have little effect on the overall shock structure. Quasi-stationary structures are obtained at moderately high ion beta (/3i '• 1), whereas the shock becomes more dynamic in the low ion beta, large Mach number regime (/3i '• 0.1, MA > 8). The simulation results are shown to be in good agreement with a number of observational features of quasi-perpendicular bow shocks, including the morphology •'• of the reflected ion stream, the magnetic field profile throughout the shock, and the Mach number dependence of the magnetic field overshoot.

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“…In the absence of an ambient magnetic field, the shock waves are electrostatic [7,8], and the dissipation is provided by the population of electrons trapped beyond the shock front [6,9] and, for stronger shocks, by the ion reflection from the shock front [10]. Whilst the properties of shocks induced by collision of identical plasma shells, or by compression of plasma clouds, have been extensively studied in the past [5,6,7,8,9,10,11,12,13,14], the properties of the electrostatic shock waves formed during the collision of diverse plasma slabs of arbitrary temperature and density are rather unexplored [15]. The theory for electrostatic shocks induced by impact of identical plasma shells predicts an absolute maximum Mach number M max ≃ 3 (or, when ion reflection and thermal effects are included, M * max ≃ 6).…”

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Very High Mach-Number Electrostatic Shocks in Collisionless Plasmas

Sorasio¹,

Marti²,

Fonseca³

et al. 2006

Phys. Rev. Lett.

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The kinetic theory of collisionless electrostatic shocks resulting from the collision of plasma slabs with different temperatures and densities is presented. The theoretical results are confirmed by selfconsistent particle-in-cell simulations, revealing the formation and stable propagation of electrostatic shocks with very high Mach numbers (M ≫ 10), well above the predictions of the classical theories for electrostatic shocks. The collision of clouds of plasma with different properties (temperature, density, composition etc.) is a scenario quite common in nature. For instance, during supernovae explosions, large quantities (10 solar masses) of high temperature plasma ( T ∼ 10 6−8 K) are ejected into the interstellar medium (n ∼ 1 cm −3 , T ∼ 10 2−4 K) [1,2], and plasma cloud collisions are at the core of the fireball model for gamma ray bursters [3]. Plasma cloud collisions also occur when the solar wind interacts with the Earth Magnetosphere, or when it encounters the interstellar medium in the heliosphere region [4]. In the laboratory, such scenarios appear during the laser induced compression of plasma foils in solid targets [5].The collision of plasma shells leads to the onset of plasma instabilities and to the development of nonlinear structures, such as solitons, shocks and double layers [6]. In the absence of an ambient magnetic field, the shock waves are electrostatic [7,8], and the dissipation is provided by the population of electrons trapped beyond the shock front [6,9] and, for stronger shocks, by the ion reflection from the shock front [10]. Whilst the properties of shocks induced by collision of identical plasma shells, or by compression of plasma clouds, have been extensively studied in the past [5,6,7,8,9,10,11,12,13,14], the properties of the electrostatic shock waves formed during the collision of diverse plasma slabs of arbitrary temperature and density are rather unexplored [15]. The theory for electrostatic shocks induced by impact of identical plasma shells predicts an absolute maximum Mach number M max ≃ 3 (or, when ion reflection and thermal effects are included, M * max ≃ 6). However, collisionless shock waves with Mach numbers ranging between 10 and 10 3 have been observed in many astrophysical scenarios [1], and very large Mach number cosmic shock waves are thought to play a crucial role in the evolution of the large scale structure of the Universe [16,17].In this Letter, we present a kinetic theory describing the properties of the very high Mach number (M ≫ 10) laminar shock waves arising from the collision of slabs of plasma with different properties (temperatures, densities), and in the absence of an ambient magnetic field. We demonstrate that the shock properties are strongly influenced by Θ, the ratio of the electron temperatures in the two slabs, and by Υ, the ratio of the electron densities in the two slabs. The analysis shows that when the electron temperature T e R of the downstream slab (R) is higher than the electron temperature T e L of the upstream slab (L), the shock wav...

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Collisionless shock waves in plasmas

Cited by 149 publications

References 68 publications

Role of Magnetosonic Solitons in Perpendicular Collisionless Shock Reformation

Role of Magnetosonic Solitons in Perpendicular Collisionless Shock Reformation

The structure of perpendicular bow shocks

Very High Mach-Number Electrostatic Shocks in Collisionless Plasmas

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