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.