scholarly journals Tokamak equilibria with incompressible flow parallel to the magnetic field and pressure anisotropy

AIP Advances ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 065231
Author(s):  
G. Poulipoulis ◽  
G. N. Throumoulopoulos
Keyword(s):  
Magnetic Field ◽  
Incompressible Flow ◽  
Pressure Anisotropy ◽  
The Magnetic Field

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.

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.

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.

A formulation for computation of a class of collision-free plasmas in two dimensions

1982 ◽  
Vol 28 (1) ◽  
pp. 141-147 ◽  
Author(s):  
J. W. Dungey
Keyword(s):  
Magnetic Field ◽  
Dispersion Equation ◽  
Two Dimensions ◽  
Higher Moments ◽  
Time Step ◽  
Pressure Anisotropy ◽  
The Magnetic Field

The restrictions imposed are that the magnetic field is everywhere in the x direction, and that no quantity varies with x, but several interesting instabilities can still occur. After some discussion of objectives, a fluid-like formulation is pursued, in which the pressure anisotropy is retained, but higher moments neglected. It shows a resonance at twice the gyrofrequency, and for electrons the constraint on the time step would be unacceptable, so they should be treated more crudely. Then the dispersion equation shows only two modes, which appear sufficiently harmless for us to proceed to computations.

Ganymede’s magnetic footprint mapping: Modeling and HST observations

2020 ◽  
Author(s):  
Tatphicha Promfu ◽  
Suwicha Wannawichian ◽  
Jonathan Nichols ◽  
John Clarke
Keyword(s):  
Magnetic Field ◽  
Hubble Space Telescope ◽  
Volcanic Eruptions ◽  
Plasma Pressure ◽  
Magnetic Field Mapping ◽  
Hot Plasma ◽  
Pressure Anisotropy ◽  
Magnetic Field Model ◽  
Field Lines ◽  
The Magnetic Field

&lt;p&gt;In this work, the locations of observed Ganymede&amp;#8217;s magnetic footprint were compared with the locations predicted by the magnetic field model under different plasma conditions. The shifts of Ganymede's magnetic footprint locations from average footpath given by Grodent et al. (2008) were analyzed. The average path is created from about 1000 images taken by instruments onboarded Hubble Space Telescope (HST). The position shifts indicate the variation of magnetic field line mapping from Ganymede to Jupiter&amp;#8217;s ionosphere. The two sets of data from HST were analyzed to obtain the locations of Ganymede&amp;#8217;s magnetic footprint in 2007 and 2016. For both sets of data, at longitude ranging approximately from 170&amp;#176; to 180&amp;#176;, we found that the locations were significantly shifted in poleward direction between 0.5&amp;#176; to 2&amp;#176; from the average footpath. Different from data in May 2007, the Ganymede&amp;#8217;s magnetic footprint locations in May 2016 at longitude about 160&amp;#176; could possibly locate in equatorward direction. At orbital distance of Ganymede about 15 R&lt;sub&gt;J&lt;/sub&gt;, in Jupiter&amp;#8217;s middle magnetosphere, there is strong influence of plasma, whose major source is Io&amp;#8217;s volcanic eruptions. Thus, the variations of plasma resulting in the stretching of magnetic field lines affect the magnetic field mapping from Ganymede to ionosphere. Furthermore, based on the magnetodisc model, the hot plasma pressure anisotropy&amp;#160;strongly influences the stretching of the field lines and the mapped locations of Ganymede&amp;#8217;s footprint in ionosphere to be shifted in either poleward or equatorward directions. In this study, we detected both poleward and equatorward shifts in different observations, whose connection with the plasma environment in the middle magnetosphere awaits for further study.&lt;/p&gt;

scholarly journals The fast transit-time limit of magnetic pumping with trapped electrons

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
J. Egedal ◽  
E. Lichko
Keyword(s):  
Magnetic Field ◽  
Transit Time ◽  
Kinetic Equations ◽  
Nonlinear Effects ◽  
Time Limit ◽  
Superthermal Electrons ◽  
Pressure Anisotropy ◽  
Magnetic Perturbations ◽  
Field Lines ◽  
The Magnetic Field

Recently, the energization of superthermal electrons at the Earth's bow shock was found to be consistent with a new magnetic pumping model derived in the limit where the electron transit time is much shorter than any time scale governing the evolution of the magnetic fields. The new model breaks with the common approach of integrating the kinetic equations along unperturbed orbits. Rather, the fast transit-time limit allows the electron dynamics to be characterized by adiabatic invariants (action variables) accurately capturing the nonlinear effects of electrons becoming trapped in magnetic perturbations. Without trapping, fast parallel streaming along magnetic field lines causes the electron pressure to be isotropized and homogeneous along the magnetic field lines. In contrast, trapping permits spatially varying pressure anisotropy to form along the magnetic field lines, and through a Fermi process this pressure anisotropy in turn becomes the main ingredient that renders magnetic pumping efficient for energizing superthermal electrons. We here present a detailed mathematical derivation of the model.

Solution for jump conditions at fast shocks in an anisotropic magnetized plasma

2000 ◽  
Vol 64 (5) ◽  
pp. 561-578 ◽  
Author(s):  
N. V. ERKAEV ◽  
D. F. VOGL ◽  
H. K. BIERNAT
Keyword(s):  
Magnetic Field ◽  
Mach Number ◽  
Tangential Component ◽  
Magnetized Plasma ◽  
Normal Velocity ◽  
Jump Conditions ◽  
Plasma Parameters ◽  
Closure Relation ◽  
Pressure Anisotropy ◽  
The Magnetic Field

We study the magnetic field and plasma parameters downstream of a fast shock as functions of normalized upstream parameters and the rate of pressure anisotropy (defined as the ratio of perpendicular to parallel pressure). We analyse two cases: with the shock (i) perpendicular and (ii) inclined with respect to the magnetic field. The relations on the fast shock in a magnetized anisotropic plasma are solved taking into account the criteria for the mirror instability and firehose instability bounding the pressure anisotropy downstream of the shock. Our analysis shows that the parallel pressure and the parallel temperature as well as the tangential component of the velocity are the parameters that are most sensitive to the rate of pressure anisotropy. The variations of the other parameters, namely density, normal velocity, tangential component of the magnetic field, perpendicular pressure, and perpendicular temperature are much less pronounced, in particular when the perpendicular pressure exceeds the parallel pressure. The variations of all parameters increase substantially for a very low rate of anisotropy, which is bounded by the firehose instability in the case of inclined shocks. Using the criterion for mirror instability as a closure relation for the jump conditions at the fast shock, we obtain the plasma parameters and the magnetic field downstream of the shock as functions of the Alfvén Mach number. For each Alfvén Mach number, the criterion for mirror instability determines the minimum jumps in such parameters as density, tangential magnetic field component, parallel pressure, and temperature, and determines the maximum values of the velocity components and the perpendicular temperature. Ideal anisotropic magnetohydrodynamics (MHD) has wide applications for space plasma physics. Observations of the field and plasma behaviour in the solar wind as well as in the Earth's magnetosheath have highlighted the need for an MHD model where the plasma pressure is treated as a tensor.

scholarly journals Fluctuation dynamo in a weakly collisional plasma

2020 ◽  
Vol 86 (5) ◽  
Author(s):  
D. A. St-Onge ◽  
M. W. Kunz ◽  
J. Squire ◽  
A. A. Schekochihin
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Numerical Study ◽  
Collisional Plasma ◽  
Mhd Equations ◽  
Saturated State ◽  
Mhd Dynamo ◽  
Pressure Anisotropy ◽  
Field Lines ◽  
The Magnetic Field

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

On the formation of a plasma pressure anisotropy in the dayside magnetosheath

1995 ◽  
Vol 13 (3) ◽  
pp. 237-241
Author(s):  
B. V. Rezhenov ◽  
V. V. Safargaleev ◽  
W. B. Lyatsky
Keyword(s):  
Magnetic Field ◽  
Equatorial Plane ◽  
Momentum Equation ◽  
Plasma Pressure ◽  
Meridian Plane ◽  
Small Pitch ◽  
Pressure Anisotropy ◽  
Subsolar Point ◽  
Field Lines ◽  
The Magnetic Field

Abstract. We present a numerical solution for the momentum equation of the magnetosheath particles that describes the distribution of the pressure anisotropy of the magnetosheath plasma in the midday meridian plane. The pressure anisotropy is a maximum near the magnetopause subsolar point (p⊥/p\\Vert ≌ 10). The pressure anisotropy is caused by two factors: particles with small pitch angles (V\\Vert>V⊥) which travel along the magnetic field lines away from the equatorial plane of the magnetosheath; and particles, after crossing the bowshock, which reach the bulk velocity component directed along the magnetic field lines again, away from the magnetosheath equatorial plane. This velocity increases with increasing distance from the subsolar point of the bowshock, and does not permit particles with large pitch angles (V⊥>V\\Vert) to move toward the equatorial plane.

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