Analyzing a Cylindrically Symmetric Plasma Column

[FunkyDwarf]

Homework Statement

A cylindrically symmetric plasma column in a uniform B field (= B0 in z direction) has
n(r) = n0 exp[-(r/r0)^2] and ni = ne = n0exp[e phi/kb Te] where phi is the potential and Te is the temp of the electrons.

(a) Show that Ve and VDe are equal and opposite

Homework Equations

We were told not to use poissons equation unless it is unavoidable (not sure if this is) but i get an answer that works using that, however i am looking for an alternate method.

The Attempt at a Solution

See attached pdf, shows my work for Ve, VDe worked out fine where VDe = -2kb T r/((r0)^2 e B) in the theta direction.

Cheers!
-Graeme

 

[FunkyDwarf]

nobody? =(