Determination of the stationary solutions of the Vlasov equation for an axially symmetric beam of charged particles in a longitudinal magnetic field

1987 ◽  
Vol 27 (2) ◽  
pp. 62-70 ◽  
Author(s):  
O.I. Drivotin ◽  
D.A. Ovsyannikov
Keyword(s):  
Magnetic Field ◽  
Vlasov Equation ◽  
Longitudinal Magnetic Field ◽  
Charged Particles ◽  
Stationary Solutions ◽  
Axially Symmetric

scholarly journals Two-fluid simulations of the magnetic field evolution in neutron star cores in the weak-coupling regime

2020 ◽  
Vol 498 (2) ◽  
pp. 3000-3012 ◽  
Author(s):  
F Castillo ◽  
A Reisenegger ◽  
J A Valdivia
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Charged Particles ◽  
Stable Stratification ◽  
Composition Gradient ◽  
Axially Symmetric ◽  
Drag Forces ◽  
Degeneracy Pressure ◽  
The Magnetic Field ◽  
Two Fluid

ABSTRACT In a previous paper, we reported simulations of the evolution of the magnetic field in neutron star (NS) cores through ambipolar diffusion, taking the neutrons as a motionless uniform background. However, in real NSs, neutrons are free to move, and a strong composition gradient leads to stable stratification (stability against convective motions) both of which might impact on the time-scales of evolution. Here, we address these issues by providing the first long-term two-fluid simulations of the evolution of an axially symmetric magnetic field in a neutron star core composed of neutrons, protons, and electrons with density and composition gradients. Again, we find that the magnetic field evolves towards barotropic ‘Grad–Shafranov equillibria’, in which the magnetic force is balanced by the degeneracy pressure gradient and gravitational force of the charged particles. However, the evolution is found to be faster than in the case of motionless neutrons, as the movement of charged particles (which are coupled to the magnetic field, but are also limited by the collisional drag forces exerted by neutrons) is less constrained, since neutrons are now allowed to move. The possible impact of non-axisymmetric instabilities on these equilibria, as well as beta decays, proton superconductivity, and neutron superfluidity, are left for future work.

Threshold speed for two-dimensional confinement of charged particles in certain axisymmetric magnetic fields

2018 ◽  
Vol 96 (5) ◽  
pp. 519-523 ◽  
Author(s):  
K. Kabin ◽  
G. Kalugin ◽  
E. Spanswick ◽  
E. Donovan
Keyword(s):  
Magnetic Field ◽  
Power Law ◽  
Critical Speed ◽  
Longitudinal Magnetic Field ◽  
Strong Dependence ◽  
Charged Particles ◽  
Transcendental Equation ◽  
Power Exponent ◽  
Magnetic Field Magnitude ◽  
The Magnetic Field

In this paper we discuss conditions under which charged particles are confined by an axisymmetric longitudinal magnetic field with power law dependence on the radius. We derive a transcendental equation for the critical speed corresponding to the threshold between bounded and unbounded trajectories of the particles. This threshold speed shows strong dependence on the direction, and this dependence becomes more prominent as the exponent of the power law increases. The equation for threshold speed can be solved exactly for several specific values of the power exponent, but in general it requires a numerical treatment. Remarkably, if the magnetic field magnitude decreases more slowly than the inverse of the radius, charged particles remain confined no matter how large their energies may be.

On stationary solutions for free quasi-parallel mixing layers with a longitudinal magnetic field

2002 ◽  
Vol 452 ◽  
pp. 337-359 ◽  
Author(s):  
I. G. SHUKHMAN
Keyword(s):  
Magnetic Field ◽  
Longitudinal Magnetic Field ◽  
Critical Role ◽  
Infinite Plate ◽  
Stationary Solutions ◽  
Mixing Layers ◽  
Stationary Flows ◽  
Inviscid Fluids ◽  
Relative Differences ◽  
The Magnetic Field

The paper is devoted to the theoretical investigation of the possible existence of stationary mixing layers and of their structure in nearly perfectly conducting, nearly inviscid fluids with a longitudinal magnetic field. A system of two equations is used, which generalizes the well-known Blasius equation (for flow around a semi-infinite plate) to the case under consideration. The system depends on the magnetic Prandtl number, Pm=ν/νm, where ν and νm are the usual and the magnetic viscosities, respectively.For the existence of stationary flows the ratio between the flow velocity vx and the Alfvén velocity cA=Hx/(4πρ)1/2 (ρ being the fluid density) plays a critical role. Super-Alfvén (vx>cA) flows are possible at any value of Pm and for any values of vx and Hx on the layer boundaries. Sub-Alfvén (vx<cA) stationary flows are impossible at any value of Pm and for any values of the differences in vx and Hx across the layer, except for two cases: Pm=0 and Pm=1. When Pm=0, i.e. when the fluid is strictly inviscid, ν=0, flow is possible in both the super- and sub-Alfvén regimes; however, the magnetic field must be uniform, Hx=const, Hy=0 in this case. For Pm=1 both flow regimes are also possible; however, the sub-Alfvén flow is possible only for a definite relationship between the magnetic field and velocity differences: ΔHx=−δvx (in corresponding units). For the case where the relative differences in vx and Hx across the layer are small, Δvx[Lt ]vx, ΔHx[Lt ]Hx, solutions are obtained in explicit form for arbitrary Pm (here vx and Hx are averaged over the layer). For the specific case Pm=1, exact analytical solutions of basic system are found and studied in detail.

scholarly journals Determination of Plasma Electron Temperature from the Reversal of Radial Ambipolar Electric Field in a Longitudinal Magnetic Field

1972 ◽  
Vol 27 (10) ◽  
pp. 1439-1443 ◽  
Author(s):  
Günter Franck ◽  
R. Held ◽  
H. D. Pfeil
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Longitudinal Magnetic Field ◽  
Plasma Electron ◽  
Langmuir Probes ◽  
Field Reversal ◽  
Field Diffusion ◽  
The One ◽  
Good Agreement

Abstract When a longitudinal magnetic field is superimposed to a low pressure plasma, reversal of the radial ambipolar electric field takes place at a definite magnetic field Br. From the Br-values electron temperatures Te in the plasma can be found, when classical magnetic field diffusion exists. In the negative H2-and He-glow plasmas with superimposed longitudinal magnetic field, electron temperatures have been measured on the one hand by the method of electric field reversal and on the other hand with Langmuir probes. There is a fairly good agreement between the Te-values obtained by both methods.

scholarly journals Epicyclic oscillations of charged particles in stationary solutions immersed in a magnetic field with application to the Kerr–Newman black hole

2019 ◽  
Vol 28 (01) ◽  
pp. 1950013 ◽  
Author(s):  
Mustapha Azreg-Aïnou
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Circular Orbit ◽  
Uniform Magnetic Field ◽  
Charged Particles ◽  
Stationary Solutions ◽  
Stable Circular Orbit ◽  
Newman Black Hole ◽  
Innermost Stable Circular Orbit ◽  
Physical Consequences

We consider a stationary metric immersed in a uniform magnetic field and determine the general expressions for the epicyclic frequencies of charged particles. Applications to the Kerr–Newman black hole are reached of physical consequences and reveal some new effects among which are the existence of radially and vertically stable circular orbits in the region enclosed by the event horizon and the so-called “innermost” stable circular orbit (ISCO) in the plane of symmetry.

scholarly journals Quasiharmonic oscillations of charged particles in static axially symmetric space-times immersed in a uniform magnetic field

2020 ◽  
Vol 101 (12) ◽  
Author(s):  
Carlos A. Benavides-Gallego ◽  
Ahmadjon Abdujabbarov ◽  
Daniele Malafarina ◽  
Cosimo Bambi
Keyword(s):  
Magnetic Field ◽  
Symmetric Space ◽  
Uniform Magnetic Field ◽  
Charged Particles ◽  
Axially Symmetric
Sign in / Sign up

Export Citation Format

Share Document