Fundamentals of Plasma Physics

1.11 Simple transport phenomena 17

section isσneut ∼ 3 × 10 −^20 m^2 .When a particle hits a neutral it can simply scatter with
no change in the internal energy of the neutral;this is calledelastic scattering.It can also
transfer energy to the structure of the neutral and so cause an internal change in the neutral;
this is calledinelastic scattering. Inelastic scattering includes ionization and excitation of
atomic level transitions (with accompanying optical radiation).
Another process can occur when ions collide with neutrals — the incident ion can cap-
ture an electron from the neutral and become neutralized while simultaneously ionizing the
original neutral. This process, calledcharge exchangeis used for producing energetic neu-
tral beams. In this process a high energy beam of ions is injected into a gas of neutrals,
captures electrons, and exits as a high energy beam of neutrals.
Because ions have approximately the same mass as neutrals, ions rapidly exchange
energy with neutrals and tend to be in thermal equilibrium with the neutrals if the plasma
is weakly ionized. As a consequence, ions are typically cold in weakly ionizedplasmas,
because the neutrals are in thermal equilibrium with the walls of the container.

1.11 Simple transport phenomena

1. Electrical resistivity- When a uniform electric fieldEexists in a plasma, the electrons
   and ions are accelerated in opposite directions creating a relative momentum between
   the two species. At the same time electron-ion collisions dissipate this relative mo-
   mentum so it is possible to achieve a steady state where relative momentum creation
   (i.e., acceleration due to theEfield) is balanced by relative momentum dissipation due
   to interspecies collisions (this dissipation of relative momentum is knownas ‘drag’).
   The balance of forces on the electrons gives

0 =−

e

me

E−υeiurel (1.21)

since the drag is proportional to therelativevelocityurelbetween electrons and ions.

However, the electric current is justJ=−neeurelso that Eq.(1.21) can be re-written

as

E=ηJ (1.22)

where

η=

meυei

nee^2

(1.23)

is the plasma electrical resistivity. Substitutingυei=σ∗nivTeand noting from quasi-

neutrality thatZni=nethe plasma electrical resistivity is

η=

Ze^2

2 πmeε^20 v^3 Te

ln

(

λD

bπ/ 2

)

(1.24)

from which we see that resistivity is independent of density, proportional toTe−^3 /^2 ,

and also proportional to the ion chargeZ.This expression for the resistivity is only

approximate since we did not properly average over the electron velocity distribution

(a more accurate expression, differing by a factor of order unity, will bederived in

Chapter 13). Resistivity resulting from grazing collisions between electrons and ions

as given by Eq.(1.24) is known as Spitzer resistivity (Spitzer and Harm 1953). It