Comments on the paper ‘Self-similar state of a weakly turbulent plasma’

1982 ◽  
Vol 27 (1) ◽  
pp. 189-190 ◽  
Author(s):  
G. E. Vekstein ◽  
D. D. Ryutov ◽  
R. Z. Sagdeev
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Collisionless Plasma ◽  
Turbulent Plasma ◽  
The Self ◽  
Similar Solution ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One

In a recent paper, Balescu (1980) criticizes the self-similar solution in the problem of anomalous plasma resistivity (Vekstein, Ryutov & Sagdeev 1970) and comes to the conclusion that this solution is not correct. The aim of this comment is to show why Balescu's arguments are erroneous.We consider here the simplest case of the one-dimensional collisionless plasma in the presence of an external electric field.

A self-similar solution for expansion into a vacuum of a collisionless plasma bunch

1998 ◽  
Vol 59 (1) ◽  
pp. 83-90 ◽  
Author(s):  
A. V. BAITIN ◽  
K. M. KUZANYAN
Keyword(s):  
Electron Distribution Function ◽  
Collisionless Plasma ◽  
Electron Component ◽  
One Dimensional ◽  
Ultrarelativistic Electron ◽  
Plasma Bunch ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

The process of expansion into a vacuum of a collisionless plasma bunch with relativistic electron temperature is investigated for the one-dimensional case. Self-similar solutions for the evolution of the electron distribution function and ion acceleration are obtained, taking account of cooling of the electron component of plasma for the cases of non-relativistic and ultrarelativistic electron energies.

Self-similar and asymptotic solutions for a one-dimensional Vlasov beam

1983 ◽  
Vol 29 (1) ◽  
pp. 139-142 ◽  
Author(s):  
J. R. Burgan ◽  
M. R. Feix ◽  
E. Fijalkow ◽  
A. Munier
Keyword(s):  
Asymptotic Solution ◽  
Initial Conditions ◽  
The Self ◽  
Similar Solution ◽  
Asymptotic Solutions ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
New Equation

Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

On the stability of a class of self-similar solutions to the filtration-absorption equation

2002 ◽  
Vol 13 (2) ◽  
pp. 179-194 ◽  
Author(s):  
ALINA CHERTOCK
Keyword(s):  
The Self ◽  
Initial Condition ◽  
Cauchy Problems ◽  
One Dimensional ◽  
Self Similar ◽  
Analytical Result ◽  
Axisymmetric Solutions ◽  
The Stability ◽  
The One ◽  
Similar Solutions

We consider the one-dimensional and two-dimensional filtration-absorption equation ut = uΔu−(c−1)(∇u)2. The one-dimensional case was considered previously by Barenblatt et al. [4], where a special class of self-similar solutions was introduced. By the analogy with the 1D case we construct a family of axisymmetric solutions in 2D. We demonstrate numerically that the self-similar solutions obtained attract the solutions of non-self-similar Cauchy problems having the initial condition of compact support. The main analytical result we provide is the linear stability of the above self-similar solutions both in the 1D case and in the 2D case.

On the continuity equation for electrons in microwave-afterglow plasmas

1992 ◽  
Vol 47 (2) ◽  
pp. 193-195 ◽  
Author(s):  
H. I. Abdel-Gawad
Keyword(s):  
Continuity Equation ◽  
Spherical Geometry ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Self Similar

We construct a continuity equation for electrons in microwave-afterglow plasmas. The self-similar solution of the equation is obtained for a plasma with plane, cylindrical or spherical geometry.

scholarly journals Phase-space structure of cold dark matter haloes inside splashback: multistream flows and self-similar solution

2020 ◽  
Vol 493 (2) ◽  
pp. 2765-2781 ◽  
Author(s):  
Hiromu Sugiura ◽  
Takahiro Nishimichi ◽  
Yann Rasera ◽  
Atsushi Taruya
Keyword(s):  
Dark Matter ◽  
Phase Space ◽  
Cold Dark Matter ◽  
The Self ◽  
Similar Solution ◽  
Sharp Drop ◽  
Self Similar Solution ◽  
Self Similar ◽  
Fitting Parameters ◽  
Radial Phase

ABSTRACT Using the motion of accreting particles on to haloes in cosmological N-body simulations, we study the radial phase-space structures of cold dark matter (CDM) haloes. In CDM cosmology, formation of virialized haloes generically produces radial caustics, followed by multistream flows of accreted dark matter inside the haloes. In particular, the radius of the outermost caustic called the splashback radius exhibits a sharp drop in the slope of the density profile. Here, we focus on the multistream structure of CDM haloes inside the splashback radius. To analyse this, we use and extend the SPARTA algorithm developed by Diemer. By tracking the particle trajectories accreting on to the haloes, we count their number of apocentre passages, which is then used to reveal the multistream flows of the dark matter particles. The resultant multistream structure in radial phase space is compared with the prediction of the self-similar solution by Fillmore & Goldreich for each halo. We find that $\sim \!30{{\ \rm per\ cent}}$ of the simulated haloes satisfy our criteria to be regarded as being well fitted to the self-similar solution. The fitting parameters in the self-similar solution characterize physical properties of the haloes, including the mass accretion rate and the size of the outermost caustic (i.e. the splashback radius). We discuss in detail the correlation of these fitting parameters and other measures directly extracted from the N-body simulation.

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