Minority-ion distribution function of a plasma under fundamental and second-harmonic ion-cyclotron heating

1995 ◽  
Vol 53 (1) ◽  
pp. 3-23 ◽  
Author(s):  
B. Weyssow
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Second Harmonic ◽  
Hermite Polynomials ◽  
Collision Term ◽  
Algebraic Equations ◽  
Ion Temperature ◽  
Ion Distribution ◽  
Ion Cyclotron ◽  
Analytical Result

The distribution function of the minority ions during ion-cyclotron heating is calculated from a kinetic equation composed of a Landau collision term and a surface-averaged quasi-linear heating term. The kinetic equation is solved by a moment method in which the minority-ion distribution function is expanded in irreducible tensorial Hermite polynomials. The coefficients of the expansion are shown to be solutions of a system of coupled algebraic equations, and the effective minority-ion temperature is deduced from a compatibility constraint. The latter equation is in general too complicated to be solved analytically. The distribution function obtained here is therefore a semi-analytical result.

Quasilinear dynamics of ion cyclotron instability in an anisotropic plasma

1970 ◽  
Vol 4 (1) ◽  
pp. 175-186 ◽  
Author(s):  
J. Preinhaelter ◽  
J. Václavík
Keyword(s):  
Distribution Function ◽  
Magnetoactive Plasma ◽  
Ion Distribution ◽  
Magnetostatic Field ◽  
Ion Cyclotron Waves ◽  
Anisotropic Temperature ◽  
Electrons And Ions ◽  
Ion Cyclotron ◽  
Cold Electrons ◽  
Maximum Increment

It is shown that in a dense magnetoactive plasma c/cA ≫ 1 with cold electrons and ions with an anisotropic temperature the ion cyclotron waves propagating along the magnetostatic field are excited with a maximum increment. The dynamics of the quasilinear stage of this instability is investigated. It turns out that, at any moment, the ion distribution function is of the form of a step with the steep front. The speed of the front in the velocity space and the characteristic time of the relaxation process are found. It is ascertained that the distribution function arising in the course of the relaxation is stable with respect to the ion cyclotron waves propagating obliquely to the magnetostatic field.

scholarly journals Enhanced ion acoustic lines due to strong ion cyclotron wave fields

2008 ◽  
Vol 26 (8) ◽  
pp. 2081-2095 ◽  
Author(s):  
H. Bahcivan ◽  
R. Cosgrove
Keyword(s):  
Distribution Function ◽  
Electric Fields ◽  
Near Field ◽  
Electron Distribution Function ◽  
Ion Distribution ◽  
Incoherent Scatter Radars ◽  
Ion Acoustic ◽  
Ion Cyclotron ◽  
Observational Fact ◽  
Step Mechanism

Abstract. The Fast Auroral Snapshot Explorer (FAST) satellite detected intense and coherent 5–20 m electric field structures in the high-latitude topside auroral ionosphere between the altitudes of 350 km and 650 km. These electric fields appear to belong to electrostatic ion cyclotron (EIC) waves in terms of their frequency and wavelengths. Numerical simulations of the response of an electron plasma to the parallel components of these fields show that the waves are likely to excite a wave-driven parallel ion acoustic (IA) instability, through the creation of a highly non-Maxwellian electron distribution function, which when combined with the (assumed) Maxwellian ion distribution function provides inverse Landau damping. Because the counter-streaming threshold for excitation of EIC waves is well below that for excitation of IA waves (assuming Maxwellian statistics) our results suggest a possible two step mechanism for destabilization of IA waves. Combining this simulation result with the observational fact that these EIC waves share a common phenomenology with the naturally enhanced IA lines (NEIALS) observed by incoherent scatter radars, especially that they both occur near field-aligned currents, leads to the proposition that this two-step mechanism is an alternative path to NEIALS.

scholarly journals Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Alessandro Geraldini
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Electrostatic Potential ◽  
Grazing Angle ◽  
Debye Length ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Ion Temperature ◽  
Ion Distribution ◽  
Orbit Model

A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

scholarly journals Sterile Neutrinos as Dark Matter: Alternative Production Mechanisms in the Early Universe

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 264
Author(s):  
Daniel Boyanovsky
Keyword(s):  
Dark Matter ◽  
Distribution Function ◽  
Kinetic Equation ◽  
Standard Model ◽  
Early Universe ◽  
Quantum Kinetic Equation ◽  
Sterile Neutrinos ◽  
The Standard Model ◽  
Production Mechanisms ◽  
Freeze Out

We study various production mechanisms of sterile neutrinos in the early universe beyond and within the standard model. We obtain the quantum kinetic equations for production and the distribution function of sterile-like neutrinos at freeze-out, from which we obtain free streaming lengths, equations of state and coarse grained phase space densities. In a simple extension beyond the standard model, in which neutrinos are Yukawa coupled to a Higgs-like scalar, we derive and solve the quantum kinetic equation for sterile production and analyze the freeze-out conditions and clustering properties of this dark matter constituent. We argue that in the mass basis, standard model processes that produce active neutrinos also yield sterile-like neutrinos, leading to various possible production channels. Hence, the final distribution function of sterile-like neutrinos is a result of the various kinematically allowed production processes in the early universe. As an explicit example, we consider production of light sterile neutrinos from pion decay after the QCD phase transition, obtaining the quantum kinetic equation and the distribution function at freeze-out. A sterile-like neutrino with a mass in the keV range produced by this process is a suitable warm dark matter candidate with a free-streaming length of the order of few kpc consistent with cores in dwarf galaxies.

scholarly journals A construction of the general relativistic Boltzmann equation

1984 ◽  
Vol 7 (3) ◽  
pp. 591-597 ◽  
Author(s):  
P. Dolan ◽  
A. C. Zenios
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Simple Model ◽  
State Space ◽  
Differential Forms ◽  
Relativistic Boltzmann Equation ◽  
Dimensional State Space ◽  
General Relativistic ◽  
Invariant Differential

Our work depends essentially on the notion of a one-particle seven-dimensional state-space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state-space.

scholarly journals On the macroscopic–mesoscopic mixture of a magnetorheological fluid

2006 ◽  
Vol 462 (2068) ◽  
pp. 1123-1144 ◽  
Author(s):  
Kuo-Ching Chen
Keyword(s):  
Distribution Function ◽  
Chemical Reaction ◽  
Constitutive Relations ◽  
Position Vector ◽  
Collision Term ◽  
Mr Fluid ◽  
Production Term ◽  
Macroscopic Equation ◽  
Mesoscopic Theory ◽  
Time Discontinuity

This paper is concerned with the modelling of a magnetorheological (MR) fluid in the presence of an applied magnetic field as a twofolded mixture—a macroscopic fluid continuum and mesoscopic multi-solid continua. By assigning to each solid particle a vectorial mesoscopic variable, which is defined as the nearest relative position vector with respect to other particles, the solid medium of the MR fluid is further treated as a mixture consisting of different components, specified by these mesoscopic variables. The treatment of multi-solid continua is similar to that in the mesoscopic theory of liquid crystals. However, the key difference lies in the fact that the time-discontinuity of the defined vectorial mesoscopic variable will give rise to a ‘pseudo’ chemical reaction in the solid continuum. The equation of the phenomenological mesoscopic distribution function of the solid continuum then has an additional production term from the pseudo chemical reaction, analogous to the collision term appearing in the Boltzmann equation. The mesoscopic and macroscopic balance equations are then derived and by assuming the special constitutive relations the macroscopic equation for the second moment of the distribution function can be obtained.

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