Download N-Body Dynamics of Strongly- Coupled (Nonideal) Plasmas

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,
142190 Troitsk, Moscow reg., Russia
E-mail: [email protected]
The starting point of our investigation were the socalled “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 (ionizationrecombination) 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.
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
For
example, in
the case of two-electron channel of recombination
supplemented
by:
(a) the equations of, thermal balance, specifying the temperatures of light
particles
(electrons)
and heavy
particlesionospheres
(ions and neutrals),
and
which is the
most typical
for planetary
and magnetospheres,
(b) the equations (or model) of motion, specifying the velocity fields of the
ionized and neutral components.
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 magnetic 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)
Complete analytical classification of the various types of temporal behavior of the
Coulomb’s coupling parameter can be performed under the following assumptions:
(continuation from the previous slide)
(1) …, where the outer boundary of the cloud moves by the linear law:
,
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;
(2) temperatures of the electrons and heavy particles (ions and neutrals) follow the
adiabatic laws:
.
Classification of the various types of temporal behavior
of the Coulomb’s coupling parameter
,
In particular, the asymptotic behavior
takes place for
whose concentration
the expansion of unmagnetized plasma cloud
is governed by the two-electron channel of recombination
.
The model of quasi-trapped particles
is based on the two main assumptions:
(1) Effective potential for the motion of a quasitrapped electron in the field of a nearby ion is
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).
(2) Influence by the distant particles is treated as an effect of thermal environment with an effective virial temperature.
Determination of the effective (“virial”) temperature
for the strongly-coupled Coulomb’s system
Multiparticle distribution function of the most general form is
,
where
is the effective temperature, which can be determined by the
following 3 steps:
(1)
(2)
(3)
As a result,
(the exact result, which can be obtained by averaging
the multiparticle distribution function);
(from the virial theorem for Coulomb’s field and
the assumption of ergodicity);
(from geometric considerations).
Finally, the effective one-particle distribution function for the electrons takes the
form
,
where
.
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, participate in the transport processes (e.g. the electric conductivity).
Concentration of the free charge carriers
The probability of quasi-bound state of
an electron is given by the integral of
over the region ; and the probability of quasi-free state, over the region
.
In the limiting case
(i.e.
when the plasma cloud expanded well
beyond the scale of its transition to the
strongly-coupled state), the relative concentration of free charge carriers is
,
where
,
.
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.
APPENDICE S
Development of the electron -ion correlations and relaxation of
the electron velocities in strongly-coupled plasmas
We performed a molecular-dynamic 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 calculation of Madelung sums.