Fundamentals of Atmospheric, Ionospheric, and Magnetospheric Plasma Dynamics - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 43

Collisional case Collisionless case

lons

lons

B

E

Electrons

Electrons

e , i ø 1

e , i ¿ 1

(a) (b)

Intermediate case

lons i 5 1

(c)

Figure 2.4 Ion and electron trajectories for various values of κ for particles initially

at rest.

and thus collisions are still very important. But in the perpendicular direction,
the second term on the left-hand side of (2.34) dominates and the components
perpendicular to B become
V j

b j E −

+ D j / H j ˆ g × B

⊥ = κ − 1

D j ∇ n / n (2.36b)

j

or, equivalently, when κ j is evaluated we have

V j 1

B 2 E − k B T j /

q j ∇ + M j / q j g ×

⊥ =

/ n / n B (2.36c)

The individual terms on the right-hand side of (2.36c) are all perpendicular to
the forces that drive them. Furthermore, since the first term does not depend
on the charge, it is identical for ions and electrons. The ions and electrons move
together at the “ E

B ” velocity in a collisionless plasm, and no net current
flows in response to an applied electric field. Thus, Ohm's law in its usual form
is of little use in a collisionless magnetized plasma. There is another interesting
subtlety in (2.36c). Ignoring

×

∇ n and g , we express all the remaining variables in

earth-fixed coordinates:
V j −

U

B 2

⊥ =[ (

E + U × B ) × B ] /