Effective parameters for Maxwellian and non-Maxwellian magnetoplasmas

1968 ◽  
Vol 46 (13) ◽  
pp. 1547-1562 ◽  
Author(s):  
P. M. Bakshi ◽  
R. E. Haskell ◽  
R. J. Papa
Keyword(s):  
Power Law ◽  
Collision Frequency ◽  
Electron Distribution Function ◽  
Distribution Functions ◽  
Electron Velocity ◽  
Effective Parameters ◽  
Plasma Parameters ◽  
Effective Collision Frequency ◽  
Weakly Ionized ◽  
The Relationship

The velocity dependence of the electron–neutral collision frequency may be taken into account by introducing an effective collision frequency and an effective plasma frequency. The properties of these effective parameters are examined for cold, weakly ionized magnetoplasmas. The relationship between these effective parameters and a new collisional response function R(y) is described for Maxwellian distribution functions. For this case of Maxwellian distributions, curves are presented of the effective parameters as a function of frequency for both a pure power-law dependence of collision frequency on electron velocity and for the case of a coupling between two power-law variations. When the a-c. electric field becomes sufficiently strong to alter the form of the isotropic part of the electron distribution function, the effective plasma parameters will become functions of the ellipticity and intensity of the a-c. field. Graphs are presented of the effective parameters as a function of normalized frequency, normalized field strength, and dependence of collision frequency on electron velocity for the case where only pure (unmixed) high-intensity modes are present in the weakly ionized magnetoplasma.

scholarly journals Coulomb collisions in strongly anisotropic plasmas II. Cyclotron cooling in laboratory pair plasmas

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
D. Kennedy ◽  
P. Helander
Keyword(s):  
Long Range ◽  
Collision Frequency ◽  
Electron Distribution Function ◽  
Collision Operator ◽  
Distribution Functions ◽  
Line Geometry ◽  
Plasma Parameters ◽  
Radiation Emission ◽  
Coulomb Collisions ◽  
Electron Positron

The behaviour of a strongly magnetised collisional electron–positron plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Indeed, these are the exact conditions likely to be attained in the first laboratory electron–positron plasma experiments currently being developed, which will typically have very low densities and be confined in very strong magnetic fields. The constraint of strong magnetisation adds an additional complication in that long-range Coulomb collisions, which are usually negligible, must now be considered. A rigorous collision operator for these long-range collisions has never been written down. Nevertheless, we show that the collisional scattering can be accounted for without knowing the explicit form of this collision operator. The rate of radiation emission is calculated and it is found that the loss of energy from the plasma is proportional to the parallel collision frequency multiplied by a factor that only depends logarithmically on plasma parameters. That is, this is a self-accelerating process, meaning that the bulk of the energy will be lost in a few collision times. We show that in a simple case, that of straight field-line geometry, there are no unstable drift waves in such plasmas, despite being far from Maxwellian.

scholarly journals Coulomb collisions in strongly anisotropic plasmas I. Cyclotron cooling in electron–ion plasmas

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
D. Kennedy ◽  
P. Helander
Keyword(s):  
Electron Distribution ◽  
Collision Frequency ◽  
Electron Distribution Function ◽  
Collision Operator ◽  
Distribution Functions ◽  
Collision Time ◽  
Plasma Parameters ◽  
Radiation Emission ◽  
Coulomb Collisions ◽  
Emission Time

The behaviour of a collisional plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various time scales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Unusually for plasma physics, the collision operator can nevertheless be calculated analytically although the plasma is far from Maxwellian. The rate of radiation emission is calculated and found to be governed by the collision frequency multiplied by a factor that only depends logarithmically on plasma parameters.

Thomson scattering from Langmuir fluctuations in a parabolic layer of a collisional plasma

2018 ◽  
Vol 96 (9) ◽  
pp. 1053-1058 ◽  
Author(s):  
V.A. Puchkov
Keyword(s):  
Plasma Layer ◽  
Collision Frequency ◽  
Thomson Scattering ◽  
Distribution Functions ◽  
Electron Collision ◽  
Plasma Parameters ◽  
Probe Wave ◽  
Electron Collision Frequency ◽  
Collisional Damping ◽  
Plasma Line

Thomson scattering of a probe wave by the Langmuir fluctuations inside a plasma layer with a parabolic density profile is considered. The collisional damping of plasma fluctuations is taken into account. The plasma line part of the scattered spectrum is calculated depending on the layer thickness, electron collision frequency, and the form of the distribution functions for the electrons and ions. Simple analytic expressions for the plasma line shape and characteristic spectrum width are found. It is shown that this plasma line is asymmetric, and the asymmetry depends on the layer type (maximum or minimum). Some important plasma parameters, such as the electron collision frequency and the sign of the electron density deviation inside the layer can be obtained from the plasma line spectrum calculated in this paper.

Plasma immersion ion implantation characteristics with q-nonextensive electron velocity distribution

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
N. Navab Safa ◽  
H. Ghomi ◽  
A. R. Niknam
Keyword(s):  
Distribution Function ◽  
Ion Implantation ◽  
Fluid Model ◽  
Electron Distribution Function ◽  
Implantation Dose ◽  
Electron Velocity ◽  
Plasma Parameters ◽  
Electron Velocity Distribution ◽  
Implantation Process ◽  
Plasma Immersion Ion Implantation

The plasma immersion ion implantation process is investigated in the presence ofq–nonextensive electrons by using a one-dimensional fluid model. The effect of the nonextensivity parameter,q, on the plasma parameters and sheath dynamics during the implantation process is studied. The results show that the implantation dose can be enhanced in the presence of energetic electrons at the tail of the distribution function. Different parameters of plasma such as sheath thickness, ion velocity and ion density show more change at the larger values of theq–parameter. Furthermore, the results of simulation tend to what is predicted by the Maxwellian electron distribution function (q= 1).

scholarly journals Skew-kappa Distribution Functions and Whistler Heat Flux Instability in the Solar Wind: The Core-strahlo Model

2021 ◽  
Vol 923 (2) ◽  
pp. 180
Author(s):  
Bea Zenteno-Quinteros ◽  
Adolfo F. Viñas ◽  
Pablo S. Moya
Keyword(s):  
Heat Flux ◽  
Solar Wind ◽  
High Heat ◽  
Distribution Functions ◽  
Electron Velocity ◽  
High Heat Flux ◽  
Kappa Distribution ◽  
Plasma Parameters ◽  
Electron Heat ◽  
The Stability

Abstract Electron velocity distributions in the solar wind are known to have field-aligned skewness, which has been characterized by the presence of secondary populations such as the halo and strahl. Skewness may provide energy for the excitation of electromagnetic instabilities, such as the whistler heat flux instability (WHFI), which may play an important role in regulating the electron heat flux in the solar wind. Here we use kinetic theory to analyze the stability of the WHFI in a solar-wind-like plasma where solar wind core, halo, and strahl electrons are described as a superposition of two distributions: a Maxwellian core, and another population modeled by a Kappa distribution to which an asymmetry term has been added, representing the halo and also the strahl. Considering distributions with small skewness, we solve the dispersion relation for the parallel-propagating whistler mode and study its linear stability for different plasma parameters. Our results show that the WHFI can develop in this system and provide stability thresholds for this instability, as a function of the electron beta and the parallel electron heat flux, to be compared with observational data. However, since different plasma states, with different stability level to the WHFI, can have the same moment heat flux value, it is the skewness (i.e., the asymmetry of the distribution along the magnetic field), and not the heat flux, that is the best indicator of instabilities. Thus, systems with high heat flux can be stable enough to WHFI, so that it is not clear whether the instability can effectively regulate the heat flux values through wave–particle interactions.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

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