When the mean free path length of a plasma is much less than the system length, the analytical solution of the confinement time of plasma has been obtained, in the solenoid of the tandem mirror having spatially varying magnetic field and ambipolar electrostatic potential.
The solution is related to the previous works of $Pastukhow^{[1],[2]}$, $Rognlien^{[3]}$, and Kuni-hiro $Sato^{[4]}$.