scholarly journals An Equation of the Quasilinear Theory with Wide Resonance Region

2018 ◽  
Vol 63 (3) ◽  
pp. 232
Author(s):  
Ya. I. Kolesnichenko ◽  
V. V. Lutsenko ◽  
T. S. Rudenko
Keyword(s):  
Distribution Function ◽  
Particle Distribution ◽  
Resonance Region ◽  
Particle Energy ◽  
Ion Acceleration ◽  
Quasilinear Theory ◽  
Ion Energy ◽  
Wide Resonance ◽  
Quasilinear Diffusion ◽  
Resonant Heating

An equation of the quasilinear theory is derived. It is based on the same assumptions as the well-known equation in [1]. However, it has another form of the quasilinear operator, which does not contain the longitudinal wavenumber. Due to this, characteristics of the derived equation determine the routes of a quasilinear evolution of the particle distribution function, even when the resonance region determined by the spectrum of longitudinal wavenumbers is wide. It is demonstrated that during the ion acceleration by the ion cyclotron resonant heating, (i) the change of the longitudinal ion energy can be considerable and (ii) the increase of the particle energy may well exceed the increase described by characteristics of the Kennel–Engelmann equation (which are shown, in particular, in [10]), because these characteristics represent the ways of the quasilinear diffusion only when the resonance region is narrow.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

Informational Measures of the Shape of the Amoroso Distributions for the Research of Dispersed Materials

2021 ◽  
Vol 1031 ◽  
pp. 58-66
Author(s):  
Vitaly Polosin
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Applied Research ◽  
Particle Distribution ◽  
Size Distribution Function ◽  
Distribution Model ◽  
Information Uncertainty ◽  
Particle Size Distribution Function

For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. The article proposes a uniform model for setting the interval of information uncertainty of non-symmetric particle size distributions. Based on the analysis of statistical and information uncertainty intervals, new shape coefficients of distribution models are constructed, these are the entropy coefficients for shifted and non shifted distributions of the Amoroso family. Graphics of dependence of entropy coefficients of non-symmetrical distributions show that distributions well-known are distinguish at small of the shapes parameters. Also it is illustrated for parameters of the form more than 2 that it is preferable to use the entropy coefficients for the unshifted distributions.The material contains also information measures for the well-known logarithmic normal distribution which is a limiting case of distribution Amorozo.

scholarly journals Investigations on low temperature laser-generated plasmas

2008 ◽  
Vol 26 (2) ◽  
pp. 265-271 ◽  
Author(s):  
F. Caridi ◽  
L. Torrisi ◽  
D. Margarone ◽  
A. Borrielli
Keyword(s):  
Target Surface ◽  
Ion Acceleration ◽  
Ion Temperature ◽  
Free Electron Density ◽  
Ion Energy ◽  
Equilibrium Plasma ◽  
Ablation Yield ◽  
Ion Energy Distributions ◽  
Acceleration Voltage ◽  
Non Equilibrium

AbstractA nanosecond pulsed Nd-Yag laser, operating at an intensity of about 109 W/cm2, was employed to irradiate different metallic solid targets (Al, Cu, Ta, W, and Au) in vacuum. The measured ablation yield increases with the direct current (dc) electrical conductivity of the irradiated target. The produced plasma was characterized in terms of thermal and Coulomb interaction evaluating the ion temperature and the ion acceleration voltage developed in the non-equilibrium plasma core. The particles emission produced along the normal to the target surface was investigated measuring the neutral and the ion energy distributions and fitting the experimental data with the “Coulomb-Boltzmann-shifted” function. Results indicate that the mean energy of the distributions and the equivalent ion acceleration voltage of the non-equilibrium plasma increase with the free electron density of the irradiated element.

Quasi-linear theory of the loss-cone instability

1967 ◽  
Vol 1 (1) ◽  
pp. 105-112 ◽  
Author(s):  
A. A. Galeev
Keyword(s):  
Linear Equation ◽  
Free Path ◽  
Linear Theory ◽  
Particle Distribution ◽  
Mean Free Path ◽  
Ion Distribution ◽  
Quasilinear Theory ◽  
Loss Cone ◽  
Small Loss ◽  
The Mean

The loss-cone instability of plasma confined in a mirror-type trap is considered. Relaxation of the particle distribution in the trap with a length larger than the mean free path between ‘turbulent’ collisions is described by conventional quasilinear theory. A quasi-linear equation for the ion distribution is solved analytically for the case of a small loss-cone volume of particles in velocity space (it takes place, for instance, in the case of a trap with a larger mirror ratio).

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