Plasma density distribution

(F. F.Chen 3.6) An isothermal plasma is confined between the planes $x=\pm a$ in a magnetic field $\vec{B}=B_0\vec{u}_z$. The density distribution is $n(x)=n_0\left(1-x^2/a^2\right)$.

(a) Derive an expression for the electron diamagnetic drift velocity, as a function of $x$.

(b) Draw a diagram showing the density profile and the direction of the electron diamagnetic drift on both sides of the midplane, if $\vec{B}$ points out of the paper.

(c)Evaluate $v_D$ at $x=a/2$, if \(B=0.2$ T, $kT_e=2$ eV and \(a=4$ cm.