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8Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2019
ON THE ION DRIFT IN COLD GAS S.A. Maiorov12
1Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow, Russia
Joint Institute for High Temperature of the Russian Academy of Sciences, Moscow, Russia
e-mail: mayorov_sa@mail.ru
The problem of ion drift in such a strong electric field that the ion drift velocity significantly exceeds the thermal velocity of atoms is considered. In the case where the ion massis identical to the gas particle mass, scattering is isotropic in the center-of-mass system and the ion scattering cross section is independent of the collision velocity (hard sphere model). In the known solution to this problem [1], the ion velocity distribution function was set as the shifted two-temperature Maxwellian distribution
/. (v )
f ™ V2 (
m
exp
m(u - W)2 m(v2 + w ) 2T 2T±
(1)
where Ti = (TT±2) , and T and T± - are the temperatures along and across the field, respectively. The parameters for the ion distribution function (1) were found from integral relations for average ion characteristics [1] and are written as W = 1.07 (eEA/ m)1/2, T = 0.555eEA , T± = 0.294eEA, where
A = 1/ an is the mean free path, a is the cross section of ion_atom collisions, and n is the numerical atomic density.
Table lists the results of Monte Carlo calculations of the drift velocity, longitudinal and transverse temperatures, the average ion energy, and diffusion coeffcients in longitudinal and transverse directions. We choose the quantitiesuA = (eEA/m)1/2 and sA = eEA as characteristic velocities and energies, respectively. As a characteristic value of the diffusion coeffcient, we choose Da =A(eEA/ m)12, then the Chapman-Enskog diffusion coefficient for hard spheres is written as
DC-E / Da= 3y[x /8 « 0.66466.
W / ux <£> / ^A T / T± / ^ A Dl{ / Da D± / Da
[1], approximate solutions 1.07 0.555 0.294
[1], exact solution 1.14 1.170 0.454 0.293
Monte Carlo [2] 1.1467 1.1723 0.4431 0.2933 0.324 0.477
The ion velocity distribution function is calculated by the Monte Carlo method, its characteristics and diffusion coeffient are determined. A comparison with known numerical and analytical solutions is performed. It is found that average characteristics (drift velocity, longitudinal and transverse temperatures) are in very good agreement with the values obtained from integral relations for the two-temperature Maxwellian distribution; however, the ion velocity distribution itself differs signiffcantly from the shifted two-temperature Maxwellian distribution. This work was supported by the RFBR grant No. 19-08-00611a.
References
[1] B. M. Smirnov. Physics of Weakly Ionized Gas in Problems with Solutions, Nauka, Moscow, 1988.
[2] S. A. Maiorov. 2019 Bulletin of the Lebedev Physics Institute 46 (1) 9.
