Re: What is non-equilibrium cold plasma?

Your question is remarkably vague: are you simply asking for one-sentence
definitions of "equilibrium" or "cold" plasmas?  Or are you asking for a
far more detailed answer?  I recommend that you read a little bit, perhaps
from one of the basic plasma physics textbooks that are available.  Two
textbooks that come to mind are:

"Introduction to Plasma Physics" by R.J.Goldston and P.H.Rutherford, and
"Introduction to Plasma Physics and Controlled Fusion, Volume 1: Plasma
Physics" by F.F.Chen.

In any introductory plasma physics textbook, there will be discussions of
various basic plasma modelling ideas, including "equilibrium" versus
"non-equilibrium" and "hot" versus "cold" plasmas.  Typically, one can find
whole chapters devoted to these topics.  Maybe after you've cracked a book,
your questions (or answers) will become more clear.

But, assuming for the moment that you just want some quick answers to your
assigned homework problems without reading a lot of text, here are some
quick working definitions for the concepts you've asked about (your mileage
may vary, so it's probably prudent to also ask your instructor):

"Equilibrium" plasmas are simply those plasmas that are modelled in a
steady state, with no time dependence.  This means that all the various
d/dt terms drop out of the equations, leaving a set of "equilibrium"
equations that can be further manipulated (e.g., the magnetohydrodynamic
equilibrium equations manipulated to produce the Grad-Shafranov Equation).
 "Non-equilibrium" simply means any modelled plasma which is not in
equilibrium.  Which is, unfortunately, nearly all the cases of interest,
including reconnection, waves, instabilities and other dynamic processes.

"Cold plasma" is an approximation, where one or more "ion" species is
assumed to have no thermal energy, and no kinetic energy aside from bulk
flow.  Most invocations of the "cold plasma" approximation are trying to
keep the heavy ions out of the dynamics, but there are cases where both
ions and electrons are assumed to be "cold". "Cold plasma" is an appealing
simplification, and it may be a valid assumption in certain settings, but
it can definitely lead you astray when solving problems in thermonuclear
fusion, the solar corona, or even (if I recall correctly) plasma processing
here on Earth.

Good luck on your studies!
Aaron