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.

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.

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.

Electromagnetic fluctuations from energetic particles in plasmas

1988 ◽  
Vol 40 (3) ◽  
pp. 407-417 ◽  
Author(s):  
Cheng Chu ◽  
J. L. Sperling
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Charged Particles ◽  
Velocity Distribution Function ◽  
Black Body ◽  
Black Body Radiation ◽  
Specific Model ◽  
Magnetized Plasma ◽  
Plasma Power ◽  
Correlation Techniques

Electromagnetic fluctuations, induced by energetic charged particles, are calculated using correlation techniques for a uniform magnetized plasma. Power emission in the ion-cyclotron range of frequencies (ICRF) is calculated for a specific model of velocity distribution function. The emissive spectra are distinct from that of the black-body radiation and have features that are consistent with experimental observation.

Semi-analytical inspection of the quasi-linear absorption of lower hybrid wave in presence of -particles in tokamak reactor

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
A. Cardinali ◽  
C. Castaldo ◽  
R. Ricci
Keyword(s):  
Distribution Function ◽  
Planck Equation ◽  
Current Drive ◽  
Dielectric Tensor ◽  
Lower Hybrid ◽  
Linear Diffusion ◽  
Tokamak Reactor ◽  
Slowing Down ◽  
Fokker Planck Equation ◽  
Fokker Planck

In a reactor plasma like demonstration power station (DEMO), when using the radio frequency (RF) for heating or current drive in the lower hybrid (LH) frequency range (Frankeet al.,Fusion Engng Des., vol. 96–97, 2015, p. 46; Cardinaliet al.,Plasma Phys. Control. Fusion, vol. 59, 2017, 074002), a large fraction of the ion population (the continuously born$\unicode[STIX]{x1D6FC}$-particle, and/or the neutral beam injection (NBI) injected ions) is characterized by a non-thermal distribution function. The interaction (propagation and absorption) of the LH wave must be reformulated by considering the quasi-linear approach for each species separately. The collisional slowing down of such an ion population in a background of an electron and ion plasma is balanced by a quasi-linear diffusion in velocity space due to the propagating electromagnetic wave. In this paper, both propagations are considered by including the ion distribution function, solution of the Fokker–Planck equation, which describes the collisional dynamics of the$\unicode[STIX]{x1D6FC}$-particles including the effects of frictional slowing down, energy diffusion and pitch-angle scattering. Analytical solutions of the Fokker–Planck equation for the distribution function of$\unicode[STIX]{x1D6FC}$-particles with a background of ions and electrons at steady state are included in the calculation of the dielectric tensor. In the LH frequency domain, ray tracing (including quasi-linear damping), can be analytically solved by iterating with the Fokker–Planck solution, and the interaction of the LH wave with$\unicode[STIX]{x1D6FC}$-particles, thermal ions and electrons can be accounted self-consistently and the current drive efficiency can be evaluated in this more general scenario.

scholarly journals Energetic ions scattered into the loss cone with observations of the Cluster satellite

2016 ◽  
Vol 34 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Ying Xiong ◽  
Zhigang Yuan ◽  
Jingfang Wang
Keyword(s):  
Field Line ◽  
Plasma Sheet ◽  
Outer Boundary ◽  
Scattering Mechanism ◽  
Loss Cone ◽  
Energetic Ions ◽  
Left Hand ◽  
Central Plasma ◽  
Emic Waves

Abstract. In this paper, we report in situ observations by the Cluster spacecraft of energetic ions scattered into the loss cone during the inbound pass from the plasma sheet into the plasmasphere. During the inbound pass of the plasma sheet, Cluster observed the isotropy ratio of energetic ions to gradually decrease from unity and the isotropic boundary extended to lower L value for higher-energy ions, implying that the field line curvature scattering mechanism is responsible for the scattered ions into the loss cone from the plasma sheet. In the outer boundary of a plasmasphere plume, Cluster 3 observed the increase of the isotropy ratio of energetic ions accompanied by enhancements of Pc2 waves with frequencies between the He+ ion gyrofrequency and O+ ion gyrofrequency estimated in the equatorial plane. Those Pc2 waves were left-hand circularly polarized and identified as electromagnetic ion cyclotron (EMIC) waves. Using the observed parameters, the calculations of the pitch angle diffusion coefficients for ring current protons demonstrate that EMIC waves could be responsible for the ions scattering and loss-cone filling. Our observations provide in situ evidence of energetic ion loss in the plasma sheet and the plasmasphere plume. Our results suggest that energetic ions scattering into the loss cone in the central plasma sheet and the outer boundary of the plasmaspheric plume are attributed to the field line curvature scattering mechanism and EMIC wave scattering mechanism, respectively.

Solitary Alfvén waveguide structures in a magnetized plasma

1980 ◽  
Vol 24 (1) ◽  
pp. 157-162 ◽  
Author(s):  
J. P. Sheerin ◽  
R. S. B. Ong
Keyword(s):  
Magnetic Field ◽  
Solitary Wave ◽  
Field Line ◽  
Magnetic Field Line ◽  
Axial Symmetry ◽  
Wave Structure ◽  
Magnetized Plasma ◽  
Alfven Wave ◽  
Wave Forms ◽  
The Magnetic Field

A nonlinear Alfvén wave structure with axial symmetry about the line of force of an ambient magnetic field is presented. The solitary wave forms a ‘ring’ shaped waveguide along the magnetic field line.

Magnetosonic solitons in space plasmas: dark or bright solitons?

2007 ◽  
Vol 73 (6) ◽  
pp. 981-992 ◽  
Author(s):  
O. A. POKHOTELOV ◽  
O.G. ONISHCHENKO ◽  
M. A. BALIKHIN ◽  
L. STENFLO ◽  
P. K. SHUKLA
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Velocity Distribution Function ◽  
Mhd Equations ◽  
Space Plasmas ◽  
Ion Distribution ◽  
Loss Cone ◽  
Solitary Solution ◽  
Background Magnetic Field ◽  
The Magnetic Field

AbstractThe nonlinear theory of large-amplitude magnetosonic (MS) waves in highβ space plasmas is revisited. It is shown that solitary waves can exist in the form of ‘bright’ or ‘dark’ solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory–Guest–Harris (DGH) or Kennel–Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by κdistributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a ‘bright’ soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall–MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined.

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