Asymptotic approximation for the dispersion relation of a hot magnetized plasma

1987 ◽  
Vol 38 (2) ◽  
pp. 275-286 ◽  
Author(s):  
A. Bravo-Ortega ◽  
D. G. Swanson ◽  
A. H. Glasser
Keyword(s):  
Dispersion Relation ◽  
Integral Representation ◽  
Asymptotic Approximation ◽  
Asymptotic Expression ◽  
Typical Case ◽  
Relative Accuracy ◽  
Magnetized Plasma ◽  
Dielectric Tensor

An asymptotic expression for the dielectric tensor e of a hot magnetized plasma is obtained employing the steepest descents method, via the transformation of the components of ε into their integral representation. The electrostatic Bernstein dispersion relation for oblique and perpendicular propagation is discussed under this treatment. It is shown that with this procedure the computation of the dispersion relation is up to 20 times faster when it is compared with the original expression, and the relative accuracy is usually as good as O·l% for a typical case.

Weakly relativistic dielectric tensor and dispersion functions of a Maxwellian plasma

1983 ◽  
Vol 30 (1) ◽  
pp. 125-131 ◽  
Author(s):  
V. Krivenski ◽  
A. Orefice
Keyword(s):  
Magnetic Field ◽  
Wave Vector ◽  
Magnetized Plasma ◽  
Harmonic Number ◽  
Dielectric Tensor ◽  
Absorption And Emission ◽  
Emission Properties ◽  
Maxwellian Plasma ◽  
Plasma Dispersion ◽  
The Magnetic Field

In order to study the absorption and emission properties of a magnetized plasma in the electron cyclotron range of frequencies, the weakly relativistic (Shkarofsky) plasma dispersion functions are simply and exactly expressed in terms of the Z function. This gives a useful working form to the dielectric tensor, for any wave vector and harmonic number, covering also the case of electron Maxwellian distributions drifting along the magnetic field.

Filamentation instability of electron/ion beams in magnetized plasma waveguide

2013 ◽  
Vol 80 (1) ◽  
pp. 81-87 ◽  
Author(s):  
A. Hasanbeigi ◽  
S. Moghani ◽  
S. Azimi ◽  
H. Mehdian
Keyword(s):  
Dispersion Relation ◽  
Relativistic Electron ◽  
Ion Beams ◽  
Magnetized Plasma ◽  
Plasma Waveguide ◽  
Velocity Difference ◽  
System Parameters ◽  
Wide Range ◽  
Difference Factor ◽  
Filamentation Instability

AbstractThe filamentation instability due to the interaction of two relativistic electron and ion beams with magnetized plasma in a waveguide is studied within the framework of a macroscopic cold fluid description. It is assumed that the background plasma provides charge and current neutralization of the injected beams. The dispersion relation is obtained by solving wave eigenvalue equation. The resulting dispersion equation is analyzed numerically over a wide range of system parameters. It is found that the velocity difference factor can strongly affect the filamentation instability.

Finite-frequency surface waves on current sheets

1991 ◽  
Vol 45 (3) ◽  
pp. 389-406 ◽  
Author(s):  
K. P. Wessen ◽  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Cyclotron Frequency ◽  
Low Frequency ◽  
Dielectric Tensor ◽  
Magnetic Field Direction ◽  
Field Reversal ◽  
Ion Cyclotron ◽  
The Magnetic Field

The dispersion relation for low-frequency surface waves at a current sheet between two magnetized plasmas is derived using the cold-plasma dielectric tensor with finite ion-cyclotron frequency. The magnetic field direction is allowed to change discontinuously across the sheet, but the plasma density remains constant. The cyclotron frequency causes a splitting of the dispersion relation into a number of mode branches with frequencies both less than and greater than the ion-cyclotron frequency. The existence of these modes depends in particular upon the degree of magnetic field discontinuity and the direction of wave propagation in the sheet relative to the magnetic field directions. Sometimes two modes can exist for the same direction of propagation. The existence of modes undamped by Alfvén resonance absorption is predicted. Analytical solutions are obtained in the low-frequency and magnetic-field-reversal limits. The solutions are obtained numerically in the general case.

Loss-cone index in distribution function in a hot magnetized plasma

2007 ◽  
Vol 73 (2) ◽  
pp. 207-214 ◽  
Author(s):  
R. P. SINGHAL ◽  
A. K. TRIPATHI
Keyword(s):  
Distribution Function ◽  
Growth Rates ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Magnetized Plasma ◽  
Dielectric Tensor ◽  
Loss Cone ◽  
Bernstein Waves ◽  
Cone Index

Abstract.The components of the dielectric tensor for the distribution function given by Leubner and Schupfer have been obtained. The effect of the loss-cone index appearing in the particle distribution function in a hot magnetized plasma has been studied. A case study has been performed to calculate temporal growth rates of Bernstein waves using the distribution function given by Summers and Thorne and Leubner and Schupfer. The effect of the loss-cone index on growth rates is found to be quite different for the two distribution functions.

Exact dielectric tensor for relativistic magnetized plasma with loss-cone and field-aligned drift

1989 ◽  
Vol 42 (2) ◽  
pp. 193-204 ◽  
Author(s):  
Peter H. Yoon ◽  
Tom Chang
Keyword(s):  
Distribution Function ◽  
External Field ◽  
Field Line ◽  
Maxwell Equations ◽  
Exact Result ◽  
Magnetized Plasma ◽  
Dielectric Tensor ◽  
Exact Form ◽  
Loss Cone ◽  
Equilibrium Function

An exact form of the dielectric tensor for a wide variety of relativistic magnetized plasmas is derived from the fully relativistic linearized Vlasov-Maxwell equations. The equilibrium function chosen incorporates a loss-cone in perpendicular momentum space, and a net drift along the external field-line. This choice of distribution function is fully relativistic, and the resulting form of the dielectric tensor is valid for arbitrary value of temperature, arbitrary degrees of loss-cone, and arbitrary drift velocity along the field-line. The exact result is simplified in several limiting cases relevant to various physical applications.

scholarly journals Dielectric Tensor of Weakly Relativistic Electron Distributions Separable in Momentum and Pitch Angle

1986 ◽  
Vol 39 (1) ◽  
pp. 57 ◽  
Author(s):  
PA Robinson
Keyword(s):  
Pitch Angle ◽  
Analytical Investigation ◽  
Current Drive ◽  
Magnetized Plasma ◽  
Larmor Radius ◽  
Dispersion Function ◽  
Dielectric Tensor ◽  
Angle Distribution ◽  
Action Current ◽  
Loss Cone

The dielectric tensor of a weakly relativistic, magnetized plasma is derived for distributions separable in momentum and pitch angle by using an expansion in powers of the Larmor radius. The results are initially expressed in terms of an integral over the electron pitch angle distribution which is itself unrestricted apart from a single symmetry condition. These results include relativistic and finite Larmor radius effects contributed by harmonics s with - 2 .;;; s .;;; 2 for all propagation angles and thus provide a useful framework for both numerical and analytical investigation of electron cyclotron phenomena (propagation and absorption of waves, maser action, current drive etc.) in a wide variety of isotropic and anisotropic plasmas. Explicit results are presented for the dielectric properties of isotropic, loss cone, anti-loss cone and hollow beam distributions, and for wave propagation perpendicular to the magnetic field. In these cases the pitch angle integrals are performed in terms of functions related to the standard plasma dispersion function.

Homogenization theory for the effective permittivity of a turbulent tokamak plasma in the scrape-off layer

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
F. Bairaktaris ◽  
K. Hizanidis ◽  
A. K. Ram ◽  
P. Papagiannis ◽  
C. Tsironis ◽  
...  
Keyword(s):  
Radio Frequency ◽  
Turbulent Plasma ◽  
Magnetized Plasma ◽  
Homogenization Theory ◽  
Tokamak Plasma ◽  
Dielectric Tensor ◽  
Homogenization Technique ◽  
Spatially Inhomogeneous ◽  
Radio Frequency Waves ◽  
Micro Structures

There has been a growing interest, over the past few years, on understanding the effect on radio frequency waves due to turbulence in the scrape-off layer of tokamak plasmas. While the far scrape-off layer density width is of the order of centimetres in contemporary tokamaks, in ITER (International Thermonuclear Experimental Reactor), and in future fusion reactors, the corresponding width will be of the order of tens of centimetres. As such, this could impact the spectral properties of the waves and, consequently, the transport of wave energy and momentum to the core plasma. The turbulence in the scrape-off layer spans a broad range of spatial scales and includes blobs and filaments that are elongated along the magnetic field lines. The propagation of radio frequency waves through this tenuous plasma is given by Maxwell’s equations. The characteristic properties of the plasma appear as a permittivity tensor in the expression for the current in Ampere’s equation. This paper develops a formalism for expressing the permittivity of a turbulent plasma using the homogenization technique. This technique has been extensively used to express the dielectric properties of composite materials that are spatially inhomogeneous, for example, due to the presence of micro-structures. In a similar vein, the turbulent plasma in the scrape-off layer is spatially inhomogeneous and can be considered as a composite material in which the micro-structures are filaments and blobs. The classical homogenization technique is not appropriate for the magnetized plasma in the scrape-off layer, as the radio frequency waves span a broad range of wavelengths and frequencies – from tens of megahertz to hundreds of gigahertz. The formalism in this paper makes use of the Fourier space components of the electric and magnetic fields of the radio frequency waves for the scattered fields and fields inside the filaments and blobs. These are the eigenvectors of the dispersion matrix which, using the Green’s function approach, lead to a homogenized dielectric tensor.

scholarly journals Electron Bernstein waves in a collisionless magnetoplasma with Cairns distribution function

2018 ◽  
Vol 96 (4) ◽  
pp. 406-410
Author(s):  
M. Usman Malik ◽  
W. Masood ◽  
Aman-ur Rehman ◽  
Arshad M. Mirza ◽  
Anisa Qamar
Keyword(s):  
Dielectric Constant ◽  
Distribution Function ◽  
Dispersion Relation ◽  
Dispersion Curves ◽  
Magnetized Plasma ◽  
Modified Dispersion Relation ◽  
Bernstein Waves

In this paper, we have investigated the electrostatic electron Bernstein waves in a collisionless magnetized plasma using the Cairns distribution function. In this regard, we have derived a generalized dielectric constant for the Bernstein waves and derived the modified dispersion relation in the presence of Cairns distribution function. We have found that the dispersion curves for the electron Bernstein waves using the Cairns distribution function show a very significant deviation from the Maxwellian results. It has been found that the behavior of the Bernstein waves across the entire band between the adjacent harmonics shows a departure from the Maxwellian result for the different values of the non-thermality parameter for the Cairns distribution function.

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