The orbits of electrons and ions in a rotating magnetic field

1983 ◽  
Vol 29 (1) ◽  
pp. 155-171 ◽  
Author(s):  
Waheed N. Hugrass ◽  
Ieuan R. Jones
Keyword(s):  
Magnetic Field ◽  
Rotating Magnetic Field ◽  
Plasma Equilibrium ◽  
Complex Situation ◽  
Axis Of Rotation ◽  
Equivalent Potential ◽  
Realistic Situation ◽  
Electrons And Ions ◽  
Self Consistent ◽  
The Stability

The motion of electrons and ions in a system which consists of a uniform rotating magnetic field and a steady uniform magnetic field which is aligned with the axis of rotation is re-examined. Stable orbits are identified and explicit expressions for these orbits are provided. The more realistic situation of motion in the non-uniform self-consistent fields appropriate to a cylindrical plasma equilibrium maintained by the rotating field is investigated. Again, stable orbits are found. The stability of orbits in this more complex situation is examined using an equivalent potential concept.

The orbits of electrons and ions in the fields of the rotamak

1987 ◽  
Vol 37 (1) ◽  
pp. 1-13 ◽  
Author(s):  
W. N. Hugrass ◽  
M. Turley
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Charged Particles ◽  
The Self ◽  
Rotating Magnetic Field ◽  
Plasma Equilibrium ◽  
Rotating Magnetic Fields ◽  
Cylindrical Plasma ◽  
Electrons And Ions ◽  
Self Consistent

The motion of electrons and ions in the self-consistent fields of a compact toroidal equilibrium maintained by means of a rotating magnetic field is studied. It is found that the particles are confined although the lines of the instantaneous magnetic field are open. The results are compared with those obtained in an earlier study of the motion of charged particles in the self-consistent fields appropriate to cylindrical plasma equilibrium maintained by means of rotating magnetic fields.

The instability of a pinched fluid with a longitudinal magnetic field

1958 ◽  
Vol 245 (1241) ◽  
pp. 222-237 ◽  
Keyword(s):  
Magnetic Field ◽  
Longitudinal Magnetic Field ◽  
Short Wave ◽  
Longitudinal Field ◽  
Plasma Equilibrium ◽  
Azimuthal Magnetic Field ◽  
Long Wave ◽  
Pinched Plasma ◽  
Pinch Current ◽  
The Stability

The stability of a pinched plasma equilibrium with a longitudinal magnetic field superimposed on the characteristic azimuthal magnetic field of the pinch current is studied theoretically. The linearized solutions are developed as helical perturbations of the plasma surface, and the behaviour of these is given for the different cases of uniform longitudinal, longitudinal field zero inside the plasma, and for helices of the same and opposite sense to the helix which describes the total magnetic field. Approximately, the conclusions are: that the longitudinal field has the effect of stabilizing short-wave perturbations, but that some long-wave perturbations remain unstable no matter how large the externally imposed longitudinal magnetic field.

scholarly journals Boundary-layer Acceleration and Particle Mirroring in Pulsar Magnetospheres

1981 ◽  
Vol 34 (3) ◽  
pp. 317 ◽  
Author(s):  
RR Burman
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Crab Pulsar ◽  
Number Density ◽  
Southern Boundary ◽  
Axis Of Rotation ◽  
Electron Positron ◽  
Electrons And Ions ◽  
Field Lines

Where the number density of a species becomes very small, inertial development of vorticity occurs; so a magnetospheric zone in which a species is contained must be enclosed by a vortical boundary layer. Where zones of corotating electrons and ions abut, there exists a large local non-corotational electric field, directed so as to force a merging of the electron and ion boundary layers. The poloidalaccelerations and azimuthal drift velocities generated in these layers are estimated here. Ions are accelerated to nonrelativistic or mildly relativistic poloidal speeds, then penetrate into the electron corotation zones where they are centrifugally decelerated as they travel approximately along magnetic field lines. They mirror between points above the stellar surface and the boundary layer, resumably moving to lower magnetic field lines until they reach the star. Electrons are accelerated to poloidal speeds that are relativistic for istances from the axis of rotation exceeding about 1/30 of the radius of the light cylinder. They enter the ion corotation zone where they are further accelerated as they travel approximately along outgoing portions of the closed magnetic field lines, and are then decelerated on ingoing portions. They mirror between the northern and southern boundary layers, presumably moving to lower magnetic field lines until they reach the star. The electrons in the outer parts of the ion.zone are very highly relativistic and emit gamma radiation which, in the case of the Crab pulsar, might create electron-positron pairs.

scholarly journals Prominence Oscillations and the Influence of the Distant Photosphere

1998 ◽  
Vol 167 ◽  
pp. 147-150
Author(s):  
N.A.J. Schutgens ◽  
M. Kuperus ◽  
G.H.J. van den Oord
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
The Other ◽  
Forced Oscillations ◽  
Crossing Time ◽  
Self Consistent ◽  
Normal Polarity ◽  
The Stability ◽  
The Magnetic Field ◽  
Flux Conservation

AbstractWe model vertical prominence dynamics, describing the evolution of the magnetic field in a self-consistent way. Since the photosphere imposes a boundary condition on the field (flux conservation), the Alfvén crossing time τ0/2 between prominence and photosphere has to be taken into account. Using an electrodynamical description of the prominence we are able to compare two basic prominence models: Normal Polarity (NP) and Inverse Polarity (IP).The results indicate that for IP prominences, the stability properties are sensitive to ωτ0 (ω: oscillation frequency of prominence). For ωτ0 ≳ 1 instability results. Forced oscillations of five minutes are efficiently excited in IP prominences that meet certain criteria only. NP prominences on the other hand, are insensitive to the Alfvén crossing time. Forced oscillations of five minutes are difficult to excite in NP prominences.

Stability of a positive column in the presence of an axial magnetic field

1982 ◽  
Vol 28 (1) ◽  
pp. 113-124 ◽  
Author(s):  
Mahinder S. Uberoi ◽  
Chuen-Yen Chow
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electron Density ◽  
Electric Fields ◽  
Positive Column ◽  
Axial Magnetic Field ◽  
Previous Analysis ◽  
Self Consistent ◽  
The Stability ◽  
Axisymmetric Perturbations

Self-consistent infinitesimal perturbations of electron density and electric field are used to analyse the stability of the plasma. The axisymmetric perturbations are stable for any magnetic and electric field strengths. The non-axisymmetric perturbations with azimuthal modes m ≥ 1 and less than a certain integer are unstable for certain ranges of magnetic and electric fields. The mode m = 2 can be more unstable than the mode m = 1. Previous analysis by other authors was confined to the case m = 1 and the perturbations were not self-consistent. Our results differ significantly from the earlier results.

On the stability of self-consistent large-amplitude waves in a cold plasma. Part 3. Transverse circularly polarized waves in the presence of a large-scale magnetic field

1979 ◽  
Vol 21 (1) ◽  
pp. 43-50 ◽  
Author(s):  
M. A. Lee ◽  
I. Lerche
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Cold Plasma ◽  
Large Scale ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Large Scale Magnetic Field ◽  
Self Consistent ◽  
Instability Rate ◽  
The Stability

We demonstrate that a self-consistent large-amplitude circularly polarized wave, propagating in a cold plasma in the presence of a large-scale magnetic field, is unstable if the constant bulk streaming speed of the plasma is zero in the frame in which the wave depends oniy on time. The growth rate is of the order of the plasma frequency or the gyrofrequency at short perturbation wavelengths, and is proportional to the perturbation wave vector at long wavelengths. For nonzero but small streaming the instability rate increases for one streaming direction and decreases for the other. We conclude that instability is the rule rather than the exception for large-amplitude waves in a cold plasma.

Stability Of Rotating Gravitating Streams

2005 ◽  
Vol 60 (7) ◽  
pp. 484-488 ◽  
Author(s):  
P. K. Bhatia ◽  
R. P. Mathur
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Critical Wave Number ◽  
Horizontal Magnetic Field ◽  
Axis Of Rotation ◽  
Streaming Velocity ◽  
The Stability ◽  
The Magnetic Field

This paper treats the stability of two superposed gravitating streams rotating about the axis transverse to the horizontal magnetic field. The critical wave number for instability is found to be affected by rotation for propagation perpendicular to the axis about which the system rotates. The critical wave number for instability is not affected by rotation when waves propagate along the axis of rotation. The critical wave number is affected by both the magnetic field and the streaming velocity in both cases. Both the magnetic field and the rotation are stabilizing, while the streaming velocity is destabilizing.

On self-consistent waves and their stability in warm plasmas. Part 2. Instability of circularly polarized waves both in the presence and the absence of an ambient magnetic field

1980 ◽  
Vol 24 (1) ◽  
pp. 89-102 ◽  
Author(s):  
M. A. Lee ◽  
I. Lerche
Keyword(s):  
Magnetic Field ◽  
Nonlinear Wave ◽  
Large Scale ◽  
Wave Amplitude ◽  
Circularly Polarized ◽  
Polarized Waves ◽  
Large Scale Magnetic Field ◽  
Self Consistent ◽  
Warm Plasma ◽  
The Stability

The stability of a self-consistent, large-amplitude, circularly polarized wave in a warm plasma is investigated. For perturbations to the system propagating normal to the plane of circular polarization, a dispersion relation is derived employing an expansion in the nonlinear wave amplitude and the momentum of the plasma particles in the plane of polarization. Instability results both in the absence and presence of a large-scale magnetic field with a growth rate of the order of the nonlinear wave amplitude.

On fluid flow induced by a rotating magnetic field

1965 ◽  
Vol 22 (3) ◽  
pp. 521-528 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Transverse Magnetic ◽  
Rotating Magnetic Field ◽  
Cylindrical Container ◽  
General Shape ◽  
Electrically Conducting ◽  
Axis Parallel ◽  
Induced Currents ◽  
The Stability

The interior of an insulating cylindrical container is supposed filled with an incompressible, electrically conducting, viscous fluid. An externally applied magnetic field is caused to rotate uniformly about an axis parallel to the cylinder generators (by applying two alternating components out of phase at right angles). Induced currents in the fluid give rise to a Lorentz force which drives a velocity field, which in general may have a steady and a fluctuating component. The particular case of a circular cylindrical container in a transverse magnetic field is studied in detail. Under certain reasonable assumptions, the resulting flow is shown to have only the steady component, and the distribution of this component is determined. Some conjectures are offered about the stability of this flow and about the corresponding flows in cavities of general shape.

Stability of axially symmetric flow driven by a rotating magnetic field in a cylindrical cavity

2001 ◽  
Vol 431 ◽  
pp. 407-426 ◽  
Author(s):  
I. GRANTS ◽  
G. GERBETH
Keyword(s):  
Magnetic Field ◽  
Metal Flow ◽  
Finite Amplitude ◽  
Rotating Magnetic Field ◽  
Axially Symmetric ◽  
Stable Regime ◽  
Görtler Vortices ◽  
Gortler Vortices ◽  
Steady Solutions ◽  
The Stability

This paper deals with the stability analysis of an axially symmetric liquid metal flow driven by a rotating magnetic field in a cylinder of finite dimensions. The limit of linear stability with respect to axially symmetric perturbations is found for diameter-to-height ratios between 0.4 and 1. This oscillatory instability is shown to be different from the expected Taylor–Görtler vortices. Several linearly unstable steady solutions are found close to the stable basic state. It is shown that small finite-amplitude perturbations in the form of Taylor–Görtler vortices give rise to instability in the linearly stable regime.

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