Interplay of the Turbulence and Strong Coulomb’s Coupling in the Formation of the Anomalous Plasma Resistance Yurii V. Dumin Institute of Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow reg., Russia

The starting point of our investigation were the so- called “active space plasma experiments”, i.e. the experiments on artificial plasma ejection from rockets and satellites into the Earth’s ionosphere and magnetosphere. A quite typical phenomenon observed in such experiments is the anomalous electrical resistance of the ejected plasma. It is usually attributed to various kinds of the plasma turbulence, but the observed level of the turbulent noise is sometimes insufficient to explain the measured resistance. The aim of the present report is to show that there may be yet another mechanism of the electron quasi-capture in plasma, namely, transition of an expanding plasma cloud to the state with extremely high value of the Coulomb’s coupling parameter (on the order of unity). This can take place in a certain time interval, when equilibrium with respect to inelastic (ionization- recombination) processes is violated due to the sharp plasma expansion. But equilibrium with respect to elastic collisions still exists, which makes the notion of the electric conductivity coefficients sensible.

For example, in the case of two-electron channel of recombination, which is the most typical for planetary ionospheres and magnetospheres, supplemented by: (a) the equations of thermal balance, specifying the temperatures of light particles (electrons) and heavy particles (ions and neutrals), and (b) the equations (or model) of motion, specifying the velocity fields of the ionized and neutral components. Formation of strongly- coupled plasmas by sharp expansion of a plasma cloud in space To determine the temporal behavior of the Coulomb’s coupling parameter we need to solve the equation of continuity for charged particles,

Complete analytical classification of the various types of temporal behavior of the Coulomb’s coupling parameter can be performed under the following assumptions: (1) the velocity fields are given by the model of uniform plasma cloud at the inertial stage of expansion, … Physical interpretation: free expansion of an unmagnetized plasma cloud, expansion of magnetized charged particles along the external mag- netic field, driven by free expansion of the neutral gas, radial expansion of a specified plasma segment moving along a stationary jet. (continued on the next slide)

(1) …, where the outer boundary of the cloud moves by the linear law: (2) temperatures of the electrons and heavy particles (ions and neutrals) follow the adiabatic laws: (continuation from the previous slide), which corresponds to the inertial stage of expansion, when the most part of the initial thermal energy of the gas was transformed into kinetic energy of its macroscopic motion;. Complete analytical classification of the various types of temporal behavior of the Coulomb’s coupling parameter can be performed under the following assumptions:

Classification of the various types of temporal behavior of the Coulomb’s coupling parameter, In particular, the asymptotic behavior takes place for the expansion of unmagnetized plasma cloud whose concentration is governed by the two-electron channel of recombination.

The model of quasi-trapped particles is based on the two main assumptions: where is the average angular momentum of the electron with respect to the nearest ion. To a first approximation, it can be considered as adiabatic invariant and equal to its value at the instant of plasma transition to the strongly-coupled state (which is marked by asterisk). (1) Effective potential for the motion of a quasi- trapped electron in the field of a nearby ion is (2) Influence by the distant particles is treated as an effect of thermal environ- ment with an effective virial temperature.

Determination of the effective (“virial”) temperature for the strongly-coupled Coulomb’s system (1)(the exact result, which can be obtained by averaging the multiparticle distribution function); (2) (from the virial theorem for Coulomb’s field and the assumption of ergodicity); (3) (from geometric considerations). As a result, where is the effective temperature, which can be determined by the Multiparticle distribution function of the most general form is following 3 steps:,

Finally, the effective one-particle distribution function for the electrons takes the form Let us mention the interesting similarity between the strongly-coupled classical plasma and a degenerate Fermi gas, namely: (a) the electron distribution function does not depend on the temperature but is determined, to a first approximation, only by the concentration; (b) the most part of electrons have velocities considerably greater than their “classical” thermal velocity; and (c) only a small part of electrons, at the tail of the distribution function, parti- cipate in the transport processes (e.g. the electric conductivity). where.,

Concentration of the free charge carriers The probability of quasi-bound state of an electron is given by the integral of bability of quasi-free state, over the regi- on over the region;. In the limiting case when the plasma cloud expanded well beyond the scale of its transition to the strongly-coupled state), the relative con- centration of free charge carriers is,, (i.e. where. and the pro-

Conclusion: Exponential suppression of the relative concentration of free charge carriers in the course of plasma expansion represents a new mechanism of the anomalous electric resistance, which is supplementary to the commonly considered plasma turbulence. It should be taken into account in the analysis of experimental data.

A P P E N D I C E S

Development of the electron - ion correlations and relaxation of the electron velocities in strongly-coupled plasmas We performed a molecular-dyna- mic simulation with accurate taking into account the long-range Coulomb’s interactions between all the particles. This was done by using the concept of “mirror” cells and implementing a special mathematical technique for calcu- lation of Madelung sums.