Nonextensive statistics and the sheath criterion in collisional plasmas
Abstract
The Bohm criterion in an electropositive plasma containing nonextensively distributed electrons and warm ions is investigated by using a steady state twofluid model. Taking into account the ionneutral collisions and finite temperature of ions, a modified Bohm criterion is derived which limits both maximum and minimum allowable velocity of ions at the sheath edge (u{sub 0i}). It is found that the degree of nonextensivity of electrons (q) and temperature of positive ions (T{sub i}) affect only the lower limit of the entrance velocity of ions into the sheath while the degree of ion collisionality (α) influences both lower and upper limits of the ion velocities at the sheath edge. In addition, depending on the value of q, it is shown that the minimum velocity of positive ions at the sheath edge can be greater or smaller than its Maxwellian counterpart. Moreover, it is shown that, depending on the values of α and T{sub i}, the positive ions with subsonic velocity may enter the sheath for either q > 1 or −1 < q < 1. Finally, as a practical application, the density distribution of charged particles in the sheath region is studied for different values of u{sub 0i}, and it is shown that monotonical reduction ofmore »
 Authors:
 Physics Department of K. N. Toosi University of Technology, 1541849611, Tehran (Iran, Islamic Republic of)
 Publication Date:
 OSTI Identifier:
 22408035
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOHM CRITERION; CATIONS; COLLISIONAL PLASMA; COLLISIONS; ELECTRONS; FLOW MODELS; ION DENSITY; ION TEMPERATURE; PLASMA SHEATH; STATISTICS; STEADYSTATE CONDITIONS; VELOCITY
Citation Formats
Hatami, M. M., Email: mhatami@kntu.ac.ir. Nonextensive statistics and the sheath criterion in collisional plasmas. United States: N. p., 2015.
Web. doi:10.1063/1.4906355.
Hatami, M. M., Email: mhatami@kntu.ac.ir. Nonextensive statistics and the sheath criterion in collisional plasmas. United States. doi:10.1063/1.4906355.
Hatami, M. M., Email: mhatami@kntu.ac.ir. 2015.
"Nonextensive statistics and the sheath criterion in collisional plasmas". United States.
doi:10.1063/1.4906355.
@article{osti_22408035,
title = {Nonextensive statistics and the sheath criterion in collisional plasmas},
author = {Hatami, M. M., Email: mhatami@kntu.ac.ir},
abstractNote = {The Bohm criterion in an electropositive plasma containing nonextensively distributed electrons and warm ions is investigated by using a steady state twofluid model. Taking into account the ionneutral collisions and finite temperature of ions, a modified Bohm criterion is derived which limits both maximum and minimum allowable velocity of ions at the sheath edge (u{sub 0i}). It is found that the degree of nonextensivity of electrons (q) and temperature of positive ions (T{sub i}) affect only the lower limit of the entrance velocity of ions into the sheath while the degree of ion collisionality (α) influences both lower and upper limits of the ion velocities at the sheath edge. In addition, depending on the value of q, it is shown that the minimum velocity of positive ions at the sheath edge can be greater or smaller than its Maxwellian counterpart. Moreover, it is shown that, depending on the values of α and T{sub i}, the positive ions with subsonic velocity may enter the sheath for either q > 1 or −1 < q < 1. Finally, as a practical application, the density distribution of charged particles in the sheath region is studied for different values of u{sub 0i}, and it is shown that monotonical reduction of the positive ion density distribution occurs only when the velocity of positive ions at the sheath edge lies between two above mentioned limits.},
doi = {10.1063/1.4906355},
journal = {Physics of Plasmas},
number = 1,
volume = 22,
place = {United States},
year = 2015,
month = 1
}

Recently, Valentini [Phys. Plasmas {bold 3}, 1459 (1996)] investigated the influence of collisions on the space charge formation and derived a modified Bohm criterion accounting for collisions in the sheath. It is shown that this derivation is wrong and is based on a misinterpretation of the plasma sheath concept. {copyright} {ital 1996 American Institute of Physics.}

Nonextensive statistics and skin depth of transverse wave in collisional plasma
Skin depth of transverse wave in a collisional plasma is studied taking into account the nonextensive electron distribution function. Considering the kinetic theory for charge particles and using the BhatnagarGrossKrook collision model, a generalized transverse dielectric permittivity is obtained. The transverse dispersion relation in different frequency ranges is investigated. Obtaining the imaginary part of the wave vector from the dispersion relation, the skin depth for these frequency ranges is also achieved. Profiles of the skin depth show that by increasing the q parameter, the penetration depth decreases. In addition, the skin depth increases by increasing the electron temperature. Finally, itmore » 
Bohm criterion for the collisional sheath
Using a twofluid model it is shown analytically that in collisional slightly ionized plasmas, i.e., for many typical low pressure discharges, at the sheath edge the drift velocity of the plasma can be smaller than the ambipolar sound speed of the ions. This basic result was known earlier by numerical calculations but it is demonstrated here using simple analytical expressions. Under these conditions the Bohm criterion, in its usual formulation, is a sufficient condition for the existence of a positive boundary sheath, but it is not a necessary condition. {copyright} {ital 1996 American Institute of Physics.} 
Comments on Structure of the plasma sheath in collisional to weakly collisional plasmas'' (Phys. Fluids B 2, 647 (1990))
Recently, Zawaideh {ital et} {ital al}. published a paper (Phys. Fluids B {bold 2}, 647 (1990)) asserting that they had obtained, from a more accurate set of fluid equations, physically reasonable plasma sheath solutions of an oscillating nature violating Bohm's criterion. In contrast to this statement, it is shown here that the violation of Bohm's criterion is based on an incorrect interpretation of the plasma sheath concept and that the oscillations are due to an incorrect initial condition in the calculations. 
Structure of the plasma sheath in collisional to weakly collisional plasmas
Recently, a set of two fluid equations has been derived that describes the transport of plasmas with anisotropic pressure along the lines of force and is valid for collisional to weakly collisional regimes (Phys. Fluids {bold 29}, 463 (1986); {bold 31}, 3280 (1988)). These transport equations coupled with Poisson's equation are used to study the structure of the nonquasineutral transition region between the plasma and the material wall. This transition region is defined as the electric sheath region. The Bohm sheath criteria has been derived by various authors by examining behavior of the solution to the plasmasheath equation. These investigationsmore »