VALUES OF THE TRANSPORT COEFFICIENTS IN A PLASMA FOR ANY DEGREE OF IONIZATION BASED ON A MAXWELLIAN DISTRIBUTION

1961 ◽  
Vol 39 (11) ◽  
pp. 1619-1703 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Power Law ◽  
Collision Frequency ◽  
Transport Coefficients ◽  
Temperature Gradients ◽  
Electron Collision ◽  
Density Gradients ◽  
Ionized Gas ◽  
Degree Of Ionization ◽  
Coulomb Collisions ◽  
Neutral Particles

Values are presented for the electronic conductivity for any degree of ionization, radio frequency, and d-c. magnetic field strength, and various electron speed power law variations of the electron collision frequency with neutral particles. Also, the other transport coefficients, such as electron current due to electron density gradients and temperature gradients, and energy flow due to an electric field and due to density gradients and temperature gradients, are tabulated.The analysis is based on substitution of the usual series expansion of Laguerre polynomials into the Fokker–Planck equation for Coulomb collisions and into the Boltzmann equation for electron collisions with neutral particles. For Coulomb effects, the expressions are the same as those derived by Landshoff. Collisions of electrons with neutral particles are included in addition to ions, and a-c. electric fields are treated as well as d-c. magnetic fields. In the limit of a completely ionized gas, the results also agree with those of Spitzer and Harm and of Kaufman. For a slightly ionized gas, the results are compared with Allis' treatment and with calculations using the Dingle integrals. It is found that the Laguerre convergence is inadequate for large angular frequencies when the power law is less than −2 and for small angular frequencies when the power law is greater than 1.The final results can be put in a form which yields two factors, multiplying, respectively, the average collision frequency and radian frequency, to give correct results from simple equations. These factors are usually of order one, and are functions of three parameters, proportional to angular frequency, ratio of electron–neutral to ion averaged collision frequency, and ion charge number.

Effects of temperature and electron collision frequency on the elastic electron–ion collisions in a collisional plasma

2013 ◽  
Vol 79 (5) ◽  
pp. 553-558 ◽  
Author(s):  
YOUNG-DAE JUNG ◽  
WOO-PYO HONG
Keyword(s):  
Phase Shift ◽  
Temperature Effect ◽  
Cross Section ◽  
Collision Frequency ◽  
Electron Collision ◽  
Elastic Electron ◽  
Dynamic Temperature ◽  
Electron Collision Frequency ◽  
Dynamic Screening ◽  
Ion Collision

AbstractThe effects of dynamic temperature and electron–electron collisions on the elastic electron–ion collision are investigated in a collisional plasma. The second-order eikonal analysis and the velocity-dependent screening length are employed to derive the eikonal phase shift and eikonal cross section as functions of collision energy, electron collision frequency, Debye length, impact parameter, and thermal energy. It is interesting to find out that the electron–electron collision effect would be vanished; however, the dynamic temperature effect is included in the first-order approximation. We have found that the dynamic temperature effect strongly enhances the eikonal phase shift as well as the eikonal cross section for electron–ion collision since the dynamic screening increases the effective shielding distance. In addition, the detailed characteristic behavior of the dynamic screening function is also discussed.

Electronic transport coefficients in plasmas using an effective energy-dependent electron-ion collision-frequency

2017 ◽  
Vol 24 (10) ◽  
pp. 102701
Author(s):  
G. Faussurier ◽  
C. Blancard ◽  
P. Combis ◽  
A. Decoster ◽  
L. Videau
Keyword(s):  
Electronic Transport ◽  
Collision Frequency ◽  
Transport Coefficients ◽  
Effective Energy ◽  
Energy Dependent ◽  
Ion Collision

The Effects of Hall and Ion Slip on the Electrical Conductivity of Partially Ionized Gases for Magnetohydrodynamic Re-Entry Vehicle Application

1962 ◽  
Vol 84 (2) ◽  
pp. 177-184 ◽  
Author(s):  
M. J. Brunner
Keyword(s):  
Electrical Conductivity ◽  
Cross Sections ◽  
Effective Conductivity ◽  
Ionized Gas ◽  
Equilibrium Conditions ◽  
Degree Of Ionization ◽  
Slip Effects ◽  
Wide Range ◽  
Ion Slip ◽  
Partially Ionized

The presence of a partially ionized gas around a hypersonic vehicle permits the application of magnetohydrodynamic (MHD) devices during re-entry. The operation of such MHD devices on a re-entry vehicle will largely depend on the magnitude of the electrical conductivity of the gas between the electrodes. In some cases it may be necessary to seed the air in order to insure high conductivity. The operation of the re-entry vehicle at relatively low gas densities and high magnetic fields will produce Hall and ion slip effects which may materially reduce the effective conductivity between the electrodes. The electrical conductivity including Hall and ion slip effects for air is presented for a wide range of pressures and temperatures and for a typical re-entry vehicle, with and without seeding. The electrical conductivity is evaluated for equilibrium conditions considering the number density and collision cross sections for electrons, neutrals, and ions. The Hall and ion slip effects are evaluated from the degree of ionization, the cyclotron frequency, and the time between collisions for electrons, neutrals, and ions.

Electron collision frequency in plasmas

1982 ◽  
Vol 25 (3) ◽  
pp. 1623-1631 ◽  
Author(s):  
D. B. Boercker ◽  
F. J. Rogers ◽  
H. E. DeWitt
Keyword(s):  
Collision Frequency ◽  
Electron Collision ◽  
Electron Collision Frequency

scholarly journals Proton temperature-anisotropy-driven instabilities in weakly collisional plasmas: Hybrid simulations

2014 ◽  
Vol 81 (1) ◽  
Author(s):  
Petr Hellinger ◽  
Pavel M. Trávníček
Keyword(s):  
Magnetic Field ◽  
Langevin Equation ◽  
Transport Coefficients ◽  
Two Dimensional ◽  
Temperature Anisotropy ◽  
Coulomb Collisions ◽  
Proton Temperature ◽  
Collisionless Plasmas ◽  
High Beta ◽  
Kinetic Instabilities

Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the case of the parallel temperature anisotropy the dominant oblique fire hose instability efficiently reduces the anisotropy in a quasilinear manner. In the case of the perpendicular temperature anisotropy the dominant mirror instability generates coherent compressive structures which scatter protons and reduce the temperature anisotropy. For both the cases the instabilities generate temporarily enough wave energy so that the corresponding (anomalous) transport coefficients dominate over the collisional ones and their properties are similar to those in collisionless plasmas.

scholarly journals Expansion of HII Regions in Density Gradients

1989 ◽  
Vol 120 ◽  
pp. 96-103
Author(s):  
José Franco ◽  
Guillermo Tenorio-Tagle ◽  
Peter Bodenheimer
Keyword(s):  
Power Law ◽  
Azimuthal Angle ◽  
Weak Shock ◽  
Hii Regions ◽  
Ionization Front ◽  
Neutral Medium ◽  
Density Gradients ◽  
Hii Region ◽  
Cylindrically Symmetric ◽  
Oriented Parallel

AbstractThe main features of HII regions expanding in spherical and disk-like clouds with density gradients are reviewed. The spherical cases assume power-law density stratifications, r~w, and the disk-like cases include exponential, gaussian, and sech2 distributions. For power-law profiles, there is a critical exponent, wcrit = 3/2, above which the ionization front cannot be “trapped” and the cloud becomes fully ionized. For clouds with w < 3/2, the radius of the ionized region grows as t4/(7-2w) and drives a shock front into the ambient neutral medium. For w = wcrit = 3/2 the shock wave cannot detach from the ionization front and the two move together with a constant speed equal to about 2ci, where ci is the sound speed in the ionized gas. For w > 3/2 the expansion corresponds to the “champagne phase”, and two regimes, fast and slow, are apparent: between 3/2 < w ≤ 3, the slow regime, the inner region drives a weak shock moving with almost constant velocity through the cloud, and for w > 3, the fast regime, the shock becomes strong and accelerates with time.For the case of disk-like clouds, which are assumed cylindrically symmetric, the dimensions of the initial HII regions along each azimuthal angle, θ, are described in terms of the Strömgren radius for the midplane density, Ro, and the disk scale height, H. For yo = Rosin(θ)/H ≤ α (where α is a constant dependent on the assumed density distribution) the whole HII region is contained within the disk, and for yo > α a conical section of the disk becomes totally ionized. The critical azimuthal angle above which the HII region becomes unbounded is defined by θcrit =sin-1(αH/Ro). The expansion of initially unbounded HII regions (i.e. with yo > α) proceeds along the z-axis and, if the disk column density remains constant during the evolution, the ionization front eventually recedes from infinity to become trapped within the expanding disk. For clouds threaded by a B-field oriented parallel to the symmetry axis, as expected in magnetically dominated clouds, this effect can be very prominent. The expanding gas overtaken by the receding ionization front maintains its linear momentum after recombination and is transformed into a high-velocity neutral outflow. In the absence of magnetic fields, the trapping has only a short duration.

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