Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 2. Stationary solution and evolution of initial distributions

1991 ◽  
Vol 46 (2) ◽  
pp. 219-229 ◽  
Author(s):  
Victor S. Krivitsky ◽  
Sergey V. Vladimirov
Keyword(s):  
Distribution Function ◽  
Particle Acceleration ◽  
Nonlinear Interaction ◽  
Particle Distribution ◽  
Temporal Evolution ◽  
Linear Interaction ◽  
One Dimensional ◽  
The One ◽  
Initial Distributions ◽  
Stochastic Particle

The evolution of the distribution function due to the simultaneous nonlinear interaction of plasma particles with resonant and non-resonant waves is studied. A stationary particle distribution resulting from a balance of the quasi-linear interaction and the nonlinear one is found. The temporal evolution of an initial δ-function-shaped distribution (like a ‘beam’) is examined in the one-dimensional case. General formulae are obtained for stochastic particle acceleration (taking account of the nonlinear interaction studied here).

scholarly journals Exact Statistical Mechanics of a One-Dimensional Self-Gravitating System

1971 ◽  
Vol 10 ◽  
pp. 56-72
Author(s):  
George B. Rybicki
Keyword(s):  
Distribution Function ◽  
Statistical Mechanics ◽  
Vlasov Equation ◽  
Total Mass ◽  
Particle Distribution ◽  
Spatial Density ◽  
One Dimensional ◽  
Large Numbers ◽  
Order Of Magnitude ◽  
The One

AbstractThe statistical mechanics of an isolated self-gravitating system consisting of N uniform mass sheets is considered using both canonical and microcanonical ensembles. The one-particle distribution function is found in closed form. The limit for large numbers of sheets with fixed total mass and energy is taken and is shown to yield the isothermal solution of the Vlasov equation. The order of magnitude of the approach to Vlasov theory is found to be 0(1/N). Numerical results for spatial density and velocity distributions are given.

scholarly journals Correlation magnetodynamics equations taking into account the uniaxial quadratic correction in the approximation of the one-particle distribution function

2021 ◽  
pp. 1-16
Author(s):  
Anton Valerievich Ivanov
Keyword(s):  
Distribution Function ◽  
Particle Distribution ◽  
Nearest Neighbors ◽  
Particle Distribution Function ◽  
Phase Transition Region ◽  
Simulation Results ◽  
The One ◽  
Bogolyubov Chain ◽  
New System ◽  
Good Agreement

The system of equations for correlation magnetodynamics (CMD) is based on the Bogolyubov chain and approximation of the two-particle distribution function taking into account the correlations between the nearest neighbors. CMD provides good agreement with atom-for-atom simulation results (which are considered ab initio), but there is some discrepancy in the phase transition region. To solve this problem, a new system of CMD equations is constructed, which takes into account the quadratic correction in the approximation of the one-particle distribution function. The system can be simplified in a uniaxial case.

Exact damped sinusoidal electric field of nonlinear one-dimensional Vlasov-Maxwell equations

1984 ◽  
Vol 32 (2) ◽  
pp. 197-205 ◽  
Author(s):  
B. Abraham-Shrauner
Keyword(s):  
Distribution Function ◽  
Electric Field ◽  
Maxwell Equations ◽  
Angular Frequency ◽  
Wave Number ◽  
One Dimensional ◽  
Damping Decrement ◽  
Sinusoidal Electric Field ◽  
The One ◽  
Special Case

An exact solution for a temporally damped sinusoidal electric field which obeys the nonlinear, one-dimensional Vlasov-Maxwell equations is given. The electric field is a generalization of the O'Neil model electric field for Landau damping of plasma oscillations. The electric field is a special case of the form found from the invariance of the one-dimensional Vlasov equation under infinitesimal Lie group transformations. The time dependences of the damping decrement, of the wave-number and of the angular frequency are derived. Use of a time-dependent BGK one-particle distribution function is justified for weak damping where, in general, it is necessary to carry out a numerical calculation of the invariant of which the distribution function is a functional.

The Nature of Chaos in a Simple Dynamical System

1979 ◽  
Vol 34 (11) ◽  
pp. 1283-1289 ◽  
Author(s):  
Akira Shibata ◽  
Toshihiro Mayuyama ◽  
Masahiro Mizutani ◽  
Nobuhiko Saitô
Keyword(s):  
Dynamical System ◽  
Distribution Function ◽  
Probability Distribution ◽  
Correlation Functions ◽  
Probability Distribution Function ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
One Dimensional ◽  
Initial Distributions ◽  
Simple Dynamical System

A simple one-dimensional transformation xn = axn-1 + 2 - a (0 ≦ xn-1 ≦ 1 - 1 / a ) , xn = a( 1 - xn-1) (1 - 1 a ≦ xn-1 ≦ 1) (1 ≦ a ≦ 2) is investigated by introducing the probability distribution function Wn(x). Wn ( x ) converges when n → oo for a > V 2 , but oscillates for 1 < a ≦ V2. The final distribution of Wn(x) does not depend on the initial distributions for a > V2, but does for 1 < a ≦V2 Time-correlation functions are also calculated

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