Fundamentals of Plasma Physics

1.11 Simple transport phenomena 19

where
μe=−

e

meυe

(1.28)

is called the electron mobility. Similarly, the net ionflux is

Γi =niμiE−Di∇ni (1.29)

where
μi=

e

miυi

(1.30)

is the ion mobility. In order to maintain quasineutrality, the electricfield automatically
adjusts itself to giveΓe=Γi=Γambipolarandni=ne=n;this ambipolar electric
field is

Eambipolar =

(De−Di)

(μe−μi)

∇lnn

≃

De

μe

∇lnn

=

κTe

e

∇lnn (1.31)

Substitution forEgives the ambipolar diffusion to be

Γambipolar =−

(

μeDi−Deμi

μe−μi

)

∇n (1.32)

so the ambipolar diffusion coefficient is

Dambipolar =

μeDi−Deμi

μe−μi

=

Di

μi

−

De

μe

1

μi

−

1

μe

=

Di

miυi

e

+De

meυe

e

miυi

e

+

meυe

e

=

κ(Ti+Te)

miυi

(1.33)

where Eqs.(1.25) and (1.26) have been used as well as the relationυi ∼(me/mi)^1 /^2 υe.
If the electrons are much hotter than the ions, then for a given ion temperature, the
ambipolar diffusion scales asTe/mi. The situation is a little like that of a small child
tugging on his/her parent (the energy of the small child is like the electron temperature,
the parental mass is like the ion mass, and the tension in the arm which accelerates
the parent and decelerates the child is like the ambipolar electric field);the resulting
motion (parent and child move together faster than the parent would like and slower
than the child would like) is analogous to electrons being retarded and ions being ac-
celerated by the ambipolar electric field in such a way as to maintain quasineutrality.