Collisions
Collisions between charged particles in a plasma differ fundamentally from
those between molecules in a neutral gas because of the long range of the
Coulomb force. In fact, the discussion in Section 1.6 implies that
binary collision processes can only be defined for weakly coupled
plasmas. However, binary collisions in weakly coupled plasmas
are still modified by collective effects, because the manyparticle
process of Debye shielding enters in a crucial manner. (See Chapter 3.) Nevertheless, for
large
we can speak of binary collisions, and therefore of
a collision frequency, denoted by . Here,
measures the rate at which particles of species are scattered
by those of species . When specifying only a single subscript, one is
generally referring to the total collision rate for that species,
including impacts with all other species. Very roughly,

(1.21) 
The species designations are generally important. For instance,
the relatively small electron mass implies that, for unit ionic charge and
comparable species temperatures [see Equation (1.27)],

(1.22) 
The collision frequency, , measures the frequency with which a
particle trajectory undergoes a major angular change due to
Coulomb interactions with other particles. Coulomb collisions are, in fact,
predominately small angle scattering events, so the collision frequency
is not the inverse of the typical time between collisions. (See Chapter 3.) Instead, it is
the inverse of the typical time needed for enough collisions to occur that the particle trajectory is deviated through .
For this reason, the collision frequency is sometimes termed the scattering
rate.
It is conventional to define the meanfreepath,

(1.23) 
Clearly, the meanfreepath measures the typical distance a particle
travels between “collisions” (i.e.,
scattering events). A collisiondominated, or collisional,
plasma is simply one in which

(1.24) 
where is the observation lengthscale. The opposite limit of
long meanfreepath is said to correspond to a collisionless plasma.
Collisions greatly simplify plasma behavior by driving the system toward
statistical equilibrium, characterized by Maxwellian distribution
functions. (See Section 3.11.) Furthermore, short meanfreepaths generally ensure that plasma
transport is local (i.e., diffusive) in nature, which is a considerable
simplification.
The typical magnitude of the collision frequency is (see Section 3.14)

(1.25) 
Note that
in a weakly coupled plasma. It follows that
collisions do not seriously interfere with plasma oscillations in such systems.
On the other hand, Equation (1.25) implies that
in a strongly
coupled plasma, suggesting that collisions effectively prevent plasma
oscillations in such systems. This accords well with our basic picture of a strongly
coupled plasma as a system,
dominated by Coulomb interactions, that does not exhibit conventional
plasma dynamics.
Equations (1.7), (1.23), and (1.25) imply that the ratio of the meanfreepath
to the Debye length can be written

(1.26) 
It follows that the meanfreepath is much larger than the Debye length in a weakly coupled plasma.
This is a significant result because the effective range of the interparticle force (i.e., the Coulomb force) in a plasma is of approximately the
same magnitude as
the Debye length. We conclude that the meanfreepath is much larger than the effective range of the interparticle force in a
weakly coupled plasma.
Equations (1.5) and (1.20) yield

(1.27) 
Thus, diffuse, high temperature plasmas tend to be collisionless, whereas dense,
low temperature plasmas are more likely to be collisional.
While collisions are crucial to the confinement and dynamics of neutral gases, they play a far less important role in plasmas.
In fact, in many plasmas the magnetic field effectively plays the role that
collisions play in a neutral gas. In such plasmas, charged particles are
constrained from moving perpendicular to the field by their small Larmor
orbits, rather than by collisions. Confinement along the fieldlines is
more difficult to achieve, unless the fieldlines form closed loops
(or closed surfaces). Thus, it makes sense to talk about a
“collisionless plasma,” whereas it makes little sense to talk about
a “collisionless neutral gas.” Many plasmas are collisionless to
a very good approximation, especially those encountered in astrophysics and space plasma
physics contexts.