Existence conditions for collisionless hydromagnetic shock waves along the magnetic field

1971 ◽  
Vol 6 (3) ◽  
pp. 467-493 ◽  
Author(s):  
Yusuke Kato† ◽  
Masayoshi Tajiri ◽  
Tosiya Taniuti
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Flow Velocity ◽  
Maxwell Equations ◽  
Collisionless Plasma ◽  
Electrostatic Waves ◽  
Pressure Anisotropy ◽  
Existence Conditions ◽  
Upstream Flow ◽  
The Magnetic Field

This paper is concerned with existence conditions for steady hydromagnetic shock waves propagating in a collisionless plasma along an applied magnetic field. The electrostatic waves are excluded. The conditions are based on the requirement that solutions of the Vlasov-Maxwell equations deviate from a uniform state ahead of a wave. They are given as the conditions on the upstream flow velocity in the wave frame (i.e. in the form of inequalities among the upstream flow velocity and some critical velocities). The conditions crucially depend on the pressure anisotropy, and demonstrate possibilities of exacting collisionless shock waves for high β plasmas.

Evolutionary conditions for shock waves in collisionless plasma and stability of the associated flow

1968 ◽  
Vol 2 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Shigeki Morioka ◽  
John R. Spreiter
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Heat Flux ◽  
Mach Number ◽  
Shock Waves ◽  
Strong Magnetic Field ◽  
Collisionless Plasma ◽  
Shock Stability ◽  
The Magnetic Field ◽  
Evolutionary Condition

The evolutionary condition for transverse and normal shock waves, and the fire- hose and mirror instability conditions for the associated flow, in a collisionless, anisotropic plasma having a strong magnetic field are determined using the theoretical representation of Chew, Goldberger & Low (1956) for such a medium. The results are expressed in terms of the Mach number, Alfvén Mach number, and the ratio of the temperatures parallel and perpendicular to the magnetic field in the flow approaching the shock wave, and applied to ascertain in what range of these parameters various types of instabilities may occur. The effect of the heat flux, which does not vanish generally in a collisionless plasma, on the shock stability is discussed.

The Research of a New Method for Manipulating Magnetic Beads through Multi-Layered Flat Micro-Coils Coupled with Permanent Magnet

2013 ◽  
Vol 753-755 ◽  
pp. 1571-1575
Author(s):  
Zhi Hua Liu ◽  
Yu Feng Huang ◽  
Jian Peng Li ◽  
Xin Wei Xu
Keyword(s):  
Magnetic Field ◽  
Permanent Magnet ◽  
Flow Velocity ◽  
Magnetic Beads ◽  
Magnetic Bead ◽  
New Method ◽  
Viscous Resistance ◽  
Main Factors ◽  
The Magnetic Field

Magnetic bead droplet's non-contacted manipulation can be realized in Electromagnetic MEMS, but how to achieve magnetic beads manipulation is the major problem. A new method of multi-layered flat coils coupled with permanent magnet was proposed. Firstly, the theory of magnetic bead manipulation was analyzed and the main factors affected the magnetic beads manipulation was identified; then the magnetic field of multi-layered flat coils and Stokes viscous resistance of magnetic beads were analyzed and simulated quantificationally; finally the magnetic bead capture area was got under different flow velocity. Consequently the feasibility and correctness of this method was verified.

scholarly journals On annihilation of the relativistic electron vortex pair in collisionless plasmas

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
K. V. Lezhnin ◽  
F. F. Kamenets ◽  
T. Zh. Esirkepov ◽  
S. V. Bulanov
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Vortex Formation ◽  
Vortex Pair ◽  
Skin Depth ◽  
Secondary Vortex ◽  
Vortex System ◽  
Collisionless Plasmas ◽  
Secondary Vortices ◽  
The Magnetic Field

In contrast to hydrodynamic vortices, vortices in a plasma contain an electric current circulating around the centre of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices and plasma waves. Two major contributors to the energy damping of a double vortex system, namely, magnetic field annihilation and secondary vortex formation, are regulated by the size of the vortex with respect to the electron skin depth, which scales with the electron$\unicode[STIX]{x1D6FE}$factor,$\unicode[STIX]{x1D6FE}_{e}$, as$R/d_{e}\propto \unicode[STIX]{x1D6FE}_{e}^{1/2}$. Magnetic field annihilation appears to be dominant in mildly relativistic vortices, while for the ultrarelativistic case, secondary vortex formation is the main channel for damping of the initial double vortex system.

scholarly journals Relativistic Particle Acceleration in Plerions

1994 ◽  
Vol 142 ◽  
pp. 797-806
Author(s):  
Jonathan Arons ◽  
Marco Tavani
Keyword(s):  
Magnetic Field ◽  
Particle Acceleration ◽  
Shock Waves ◽  
Shock Front ◽  
Heavy Ions ◽  
Surface Brightness ◽  
Crab Nebula ◽  
Electrons And Positrons ◽  
The Crab Nebula ◽  
The Magnetic Field

AbstractWe discuss recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is either pure electrons and positrons or primarily electrons and positrons with an admixture of heavy ions. Particle-in-cell simulation techniques as well as analytic theory have been used to show that such shocks in pure pair plasmas are fully thermalized—the downstream particle spectra are relativistic Maxwellians at the temperature expected from the jump conditions. On the other hand, shocks containing heavy ions which are a minority constituent by number but which carry most of the energy density in the upstream medium do put ~20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) ∝ E−2, where N(E)dE is the number of particles with energy between E and E + dE.The mechanism of thermalization and particle acceleration is found to be synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front. The synchrotron maser modes radiated by the heavy ions are absorbed by the pairs at their (relativistic) cyclotron frequencies, allowing the maximum energy achievable by the pairs to be γ±m±c2 = mic2γ1/Zi, where γ1 is the Lorentz factor of the upstream flow and Zi, is the atomic number of the ions. The shock’s spatial structure is shown to contain a series of “overshoots” in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value.This shock model is applied to an interpretation of the structure of the inner regions of the Crab Nebula, in particular to the “wisps,” surface brightness enhancements near the pulsar. We argue that these surface brightness enhancements are the regions of magnetic overshoot, which appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar’s wind in the Crab Nebula is spatially resolved, and allows one to measure γ1, and a number of other properties of the pulsar’s wind. We also discuss applications of the shock theory to the termination shocks of the winds from rotation-powered pulsars embedded in compact binaries. We show that this model adequately accounts for (and indeed predicted) the recently discovered X-ray flux from PSR 1957+20, and we discuss several other applications to other examples of these systems.Subject headings: acceleration of particles — ISM: individual (Crab Nebula) — relativity — shock waves

scholarly journals Rapidly Evolving Structures in the Photosphere of the Mira Variable TX Cam

2001 ◽  
Vol 205 ◽  
pp. 252-255 ◽  
Author(s):  
P. J. Diamond ◽  
A. J. Kemball
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Shock Waves ◽  
Circumstellar Envelope ◽  
Structural Variations ◽  
Mira Variable ◽  
The Magnetic Field ◽  
Dynamical Mode

44 VLBA observations of the 43 GHz SiO masers in the circumstellar envelope surrounding the Mira variable TX Cam reveal dramatic structural variations over the 80 week stellar cycle. The dominant dynamical mode is one of expansion although other complex motions are visible. The gravitational field of the star does not have a significant effect on the dynamics observed, these are probably governed more by the magnetic field and the effects of the shock waves resulting from the pulsation of the Mira itself.

scholarly journals Jump conditions for pressure anisotropy and comparison with the Earth's bow shock

2001 ◽  
Vol 8 (3) ◽  
pp. 167-174 ◽  
Author(s):  
D. F. Vogl ◽  
H. K. Biernat ◽  
N. V. Erkaev ◽  
C. J. Farrugia ◽  
S. Mühlbachler
Keyword(s):  
Magnetic Field ◽  
Tangential Component ◽  
Bow Shock ◽  
Jump Conditions ◽  
Plasma Parameters ◽  
Pressure Anisotropy ◽  
Threshold Conditions ◽  
Wind Spacecraft ◽  
Earth’S Bow Shock ◽  
The Magnetic Field

Abstract. Taking into account the pressure anisotropy in the solar wind, we study the magnetic field and plasma parameters downstream of a fast shock, as functions of upstream parameters and downstream pressure anisotropy. In our theoretical approach, we model two cases: a) the perpendicular shock and b) the oblique shock. We use two threshold conditions of plasma instabilities as additional equations to bound the range of pressure anisotropy. The criterion of the mirror instability is used for pressure anisotropy p \\perp /p\\parrallel > 1. Analogously, the criterion of the fire-hose instability is taken into account for pressure anisotropy p \\perp /p\\parrallel < 1. We found that the variations of the parallel pressure, the parallel temperature, and the tangential component of the velocity are most sensitive to the pressure anisotropy downstream of the shock. Finally, we compare our theory with plasma and magnetic field parameters measured by the WIND spacecraft.

Magneto-gasdynamic flow over a wedge

1966 ◽  
Vol 25 (1) ◽  
pp. 165-178 ◽  
Author(s):  
D. C. Pack ◽  
G. W. Swan
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Shock Waves ◽  
Wave Pattern ◽  
Ionized Gas ◽  
Current Sheets ◽  
Gasdynamic Flow ◽  
The Stability ◽  
The Magnetic Field ◽  
Insight Into

The solution for the flow of a fully ionized gas over a wedge of finite angle is known for the case when the applied magnetic field is aligned with the incident stream. In this flow there are current sheets on the surfaces of the wedge. When the magnetic field is allowed to deviate slightly from the stream, the current sheets may move into the gas and become shock waves. The magnetic fields adjacent to the wedge above and below it have to be matched. A perturbation method is introduced by means of which expressions for the unknown quantities in the different regions may be determined when there are four shocks attached to the wedge. The results give insight into the manner in which the shock-wave pattern develops as the obliquity of the magnetic field to the stream increases. The question of the stability of the shock waves is also examined.

WAVE PROPAGATION IN A PLASMA WITH ANISOTROPIC PRESSURE

1967 ◽  
Vol 45 (10) ◽  
pp. 3189-3198 ◽  
Author(s):  
S. R. Sharma
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Resonant Frequency ◽  
Transverse Wave ◽  
Anisotropy Parameter ◽  
Anisotropic Pressure ◽  
Electrostatic Forces ◽  
Pressure Anisotropy ◽  
Component Plasma ◽  
The Magnetic Field

Wave propagation in an unbounded, magnetoactive, one-component plasma is considered with the help of modified Burgers equations. The pressure is assumed to be anisotropic and the effect of collisions on the wave propagation is examined. New modes of propagation have been reported in which the magnetic field and pressure anisotropy play an important role, while the electrostatic forces are comparatively less important. For the collisionless case, under certain conditions, new resonances appear in the transverse wave propagation, the resonant frequency being dependent upon the anisotropy parameter β. Cases have been pointed out where spatial instabilities may occur for certain values of β and the collision frequencies. It is further shown that the collisions may also offset the velocity–space instabilities which occur in a plasma with anisotropic pressure.

Whistler instability in plasmas with anisotropic and non-Maxwellian velocity distributions

1971 ◽  
Vol 6 (3) ◽  
pp. 449-456 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Transverse Velocity ◽  
Distribution Functions ◽  
Loss Cone ◽  
Circularly Polarized ◽  
Electron Plasmas ◽  
Thermal Spread ◽  
The Magnetic Field

The instability of right-handed, circularly polarized electromagnetic waves, propagating along an external magnetic field (whistler mode), is studied for electron plasmas with distribution functions peaked at some non-zero value of the transverse velocity. Based on the linearized Vlasov-Maxwell equations, the criteria for instability are given both for non-resonant instabilities arising from distribution functions with no thermal spread parallel to the magnetic field, and for resonant instabilities arising from distribution functions with Maxwellian dependence in the parallel velocities. It is found that, in general, the higher the average perpendicular energy, the more is the plasma susceptible to the whistler instability. These criteria are then applied to a sharply peaked ring distribution, and to loss-cone distributions of the Dory, Guest & Harris (1965) type.

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