Localized explosion in a material with a magnetic field and the consequences of finite conductivity in a magnetohydrodynamic model

1991 ◽  
Vol 32 (3) ◽  
pp. 316-321
Author(s):  
A. M. Bergel'son ◽  
Yu. P. Raizer ◽  
S. T. Surzhikov
Keyword(s):  
Magnetic Field ◽  
Finite Conductivity ◽  
Magnetohydrodynamic Model

Zur Energieabgabe eines modulierten Ionenstrahls im Plasma mit Magnetfeld

1960 ◽  
Vol 15 (5-6) ◽  
pp. 506-512 ◽  
Author(s):  
R. Kippenhahn ◽  
H. L. de Vries
Keyword(s):  
Magnetic Field ◽  
Energy Loss ◽  
Ion Source ◽  
Finite Conductivity ◽  
Great Loss ◽  
Normal Case ◽  
Straight Beam ◽  
Field Lines ◽  
Parallel Case ◽  
Alfven Velocity

A beam of ions penetrating a plasma perpendicular to a homogeneous magnetic field is investigated. The particle density of the beam may be modulated by varying the intensity of the ion source with the frequency ω. For simplicity, the ions are assumed to move with equal velocity w. The modulation of the beam produces oscillations of the plasma and the ions of the beam will loose energy; therefore it should be possible to trap the injected particles in the plasma. Furthermore the kinetic energy of the trapped particles will be transformed into thermal energy of the plasma 2.The ion source is assumed to deliver a linear beam (of sufficiently small diameter). Upon being shot into a plasma with a magnetic field the ions will travel along a curved line. In order to treat the problem exactly one would have to solve simultaneously the equations of motion for the plasma coupled with those for the individual ions of the beam. We simplify the problem in that we do not solve the equation of motion of the ions in the beam. Instead we imagine that they are forced to travel in a straight beam.The problem becomes especially simple if we assume the ion source to be a slit instead of a point source. Then the ions do not all travel along the same straight line, but in parallel straight lines in the plasma. The direction of motion is always perpendicular to the magnetic field. Then we may distinguish two cases of the relation of the field direction to the direction of the plane:1) the field lines are parallel to the plane of the beam (parallel case, Fig. 1),2) the field lines are normal to the plane (normal case, Fig. 3).If the modulating frequency of the beam is small compared to the gyrofrequency of the electrons and compared to the plasma frequency, if the conductivity is infinite, and if the gas pressure in the plasma may be neglected, one obtains for the mean relative energy loss of an ion per cm of path, in the parallel case(N1 number of particles per cm2 of beam surface of the unmodulated part of the beam, N2 the number of ions per cm2 of the modulated part, ri the classical ion radius, P the square of the ratio of ion velocity to ALFVÉN velocity, Q the square of the ratio of the modulating frequency to the ion gyro-frequency.) In case of P equal to one the energy loss of the beam is infinite. For P < 1 the energy loss will vanish identically. In the normal case the energy loss of each particle is in general of the same order of magnitude, and vanishes identically when P < 1 and ω is greater than the gyrofrequency of the ions. If the ions move with the ALFVÉN velocity, one has a resonance with an infinitely great loss of energy by radiation. In reality of course there will be damping because of the finite conductivity. Assuming N1=N2=107 particles (per cm2 of the beam), the formula mentioned above in case of Q+P—1\P(P—l)½ ≈ 1 will give a relative loss of energy per cm path of about 10-8, which means that a particle has to travel about 6 miles in order to suffer an energy loss of about 1%. This disappointingly small loss leads us to te conclusion that only in cases of resonance measurable effects can be expected. It is certain that the energy loss in the case of the resonance P=1 will exceed the value estimated above by several powers of ten. A detailed discussion of this resonance has to take into account finite conductivity of the plasma.

Kinematic dynamo problem in a linear velocity field

1984 ◽  
Vol 144 ◽  
pp. 1-11 ◽  
Author(s):  
Ya. B. Zel'Dovich ◽  
A. A. Ruzmaikin ◽  
S. A. Molchanov ◽  
D. D. Sokoloff
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Velocity Field ◽  
Random Matrix ◽  
Magnetic Energy ◽  
Linear Velocity ◽  
Finite Conductivity ◽  
Kinematic Dynamo ◽  
Linear Velocity Field ◽  
The Magnetic Field

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

On resistive instabilities

1972 ◽  
Vol 272 (1223) ◽  
pp. 303-330 ◽  
Keyword(s):  
Magnetic Field ◽  
Mathematical Method ◽  
Electrical Resistance ◽  
Asymptotic Properties ◽  
Critical Layer ◽  
Finite Conductivity ◽  
Mathematical Approach ◽  
Novel Variant ◽  
Laplace Integral Representation ◽  
Significant Class

It has been established by Furth, Killeen & Rosenbluth (1963), and by Johnson, Greene & Coppi (1963), that a hydromagnetic equilibrium which is stable on a theory in which electrical resistance is ignored, may yet be unstable through finite conductivity effects. These authors have isolated and categorized several types of such instabilities which, they show, originate from the critical layer in which the perturbation wavefront is perpendicular to the equilibrium magnetic field. In this paper, the asymptotic properties of the critical layer equations, for large values of the critical layer coordinate, are obtained in a number of cases of interest, using the sheet pinch model with uniform resistivity. The mathematical approach is a novel variant of the Laplace integral representation, which allows results of greater generality to be obtained than those given by previous authors. The technique is applied first to the slow interchange mode, and the restricted (but most significant) class of solutions found by Johnson et al . is recovered. It is also shown that modes entirely localized within the critical layer do not occur. Such modes do exist for the more rapid interchange modes, and a new discussion of these is presented. Finally, the oscillatory resistive modes, which arise when the perturbation wavefront is not perpendicular to the equilibrium magnetic field, are studied by a similar mathematical method, and a class of eigenvalues is obtained.

scholarly journals Modeling of Small DC Magnetic Field Response in Trilayer Magnetoelectric Laminate Composites

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
B. Zadov ◽  
A. Elmalem ◽  
E. Paperno ◽  
I. Gluzman ◽  
A. Nudelman ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Piezoelectric Layer ◽  
Permanent Magnets ◽  
Finite Size ◽  
Finite Conductivity ◽  
Electric Field Effect ◽  
Induced Voltage ◽  
The Finite Element Method ◽  
Laminate Composites ◽  
Analytical Result

We consider a magnetoelectric laminate which comprises two magnetostrictive (Ni) layers and an in-between piezoelectric layer (PZT). Using the finite-element method-based software COMSOL, we numerically calculate the induced voltage between the two faces of the PZT piezoelectric layer, by an external homogeneous small-signal magnetic field threading the three-layer Ni/PZT/Ni laminate structure. A bias magnetic field is simulated as being produced by two permanent magnets, as it is done in real experimental setups. For approaching the real materials’ properties, a measured magnetization curve of the Ni plate is used in the computations. The reported results take into account the finite-size effects of the structure, such as the fringing electric field effect and the demagnetization, as well as the effect of the finite conductivity of the Ni layers on the output voltage. The results of the simulations are compared with the experimental data and with a widely known analytical result for the induced magnetoelectric voltage.

scholarly journals Non-thermal line broadening due to braiding-induced turbulence in solar coronal loops

2020 ◽  
Vol 639 ◽  
pp. A21 ◽  
Author(s):  
D. I. Pontin ◽  
H. Peter ◽  
L. P. Chitta
Keyword(s):  
Magnetic Field ◽  
Extreme Ultraviolet ◽  
Plasma Heating ◽  
Heating Process ◽  
Coronal Loops ◽  
Line Broadening ◽  
Magnetohydrodynamic Model ◽  
Non Gaussian ◽  
Thermal Line ◽  
Solar Coronal

Aims. Emission line profiles from solar coronal loops exhibit properties that are unexplained by current models. We investigate the non-thermal broadening associated with plasma heating in coronal loops that is induced by magnetic field line braiding. Methods. We describe the coronal loop by a 3D magnetohydrodynamic model of the turbulent decay of an initially-braided magnetic field. From this, we synthesised the Fe XII line at 193 Å that forms around 1.5 MK. Results. The key features of current observations of extreme ultraviolet (UV) lines from the corona are reproduced in the synthesised spectra: (i) Typical non-thermal widths range from 15 to 20 km s−1. (ii) The widths are approximately independent of the size of the field of view. (iii) There is a correlation between the line intensity and non-thermal broadening. (iv) Spectra are found to be non-Gaussian, with enhanced power in the wings of the order of 10–20%. Conclusions. Our model provides an explanation that self-consistently connects the heating process to the observed non-thermal line broadening. The non-Gaussian nature of the spectra is a consequence of the non-Gaussian nature of the underlying velocity fluctuations, which is interpreted as a signature of intermittency in the turbulence.

Nonlinear dispersive waves in a Hall plasma with a finite conductivity

1981 ◽  
Vol 109 ◽  
pp. 301-309 ◽  
Author(s):  
A. T. Granik
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Nonlinear Equation ◽  
Hall Effect ◽  
Oscillatory Solution ◽  
Turbulent Plasma ◽  
Finite Conductivity ◽  
Dispersive Waves ◽  
Hall Plasma ◽  
Shock Profile

The study of nonlinear magnetosonic waves in a turbulent plasma is extended to include the effects of the Hall term. The turbulence and Hall effect are characterized by an effective electrical conductivity and an ion gyrofrequency respectively. It is shown that the magnetosonic waves are governed by a nonlinear equation which can be considered as the generalization of a Korteweg & de Vries (1895) equation with dispersion. For a stationary solution two cases are considered in detail: (a) an unperturbed magnetic field is almost parallel to a wave vector, and (b) they are almost perpendicular. In the case (a) it is shown that the presence of the Hall term can lead to an oscillatory solution which decays due to the finite conductivity. In the second case the Hall effect does not affect the monotonous character of a decaying Taylor-shock profile.

Sign in / Sign up

Export Citation Format

Share Document