Drift in toroidal plasma

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(F. F. ~ Chen 2.19) A plasma is created in a toroidal chamber with average radius \(R=10\) cm and square cross section of size \(a=1\) cm. The magnetic fiel is generated by an electrical current $I$ along the symmetry axis. The plasma is Maxwellian with temperature \(kT=100\) eV and density \(n_0=10^{19}\) m\(^{-3}\).There is no applied electric field.

(a) Sketch the typical drift orbits in the non-uniform \(\vec{B}\) field, for both positive ions and electrons with \(v_\parallel=0\).

(b) Calculate the rate of charge accumulation (Coulomb per second) due to the curvature and gradient drifts on the upper part of the chamber. The magnetic field in the center of the chamber is 1 T and you can use the approximation \(R \gg a\) if necessary.