Collisions

(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

It is conventional to define the *mean-free-path*,

Clearly, the mean-free-path measures the typical distance a particle travels between ``collisions'' (i.e., scattering events). A collision-dominated, or

(1.24) |

where is the observation lengthscale. The opposite limit of long mean-free-path is said to correspond to a

The typical magnitude of the collision frequency is (see Section 3.12)

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 mean-free-path to the Debye length can be written

(1.26) |

It follows that the mean-free-path is much larger than the Debye length in a weakly coupled plasma. This is a significant result because the effective range of the inter-particle force (i.e., the Coulomb force) in a plasma is of approximately the same magnitude as the Debye length. We conclude that the mean-free-path is much larger than the effective range of the inter-particle force in a weakly coupled plasma.

Equations (1.5) and (1.20) yield

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 field-lines is more difficult to achieve, unless the field-lines 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.