Noncollisional kinetic model for non-neutral plasmas in a Penning trap: general properties and stationary solutions

This work deals with a noncollisional kinetic model for non-neutral plasmas in a Penning trap. Using the spatial coordinates r, theta, z and the axial velocity v(z) as phase-space variables, a kinetic model is developed starting from the kinetic equation for the distribution function f(r,theta,z,v(z),t). In order to reduce the complexity of the model, the kinetic equations are integrated along the axial direction by assuming an ergodic distribution in the phase space (z,v(z)) for particles of the same axial energy epsilon and the same planar position. In this way, a kinetic equation for the z-integrated electron distribution F(r,theta,epsilon,t) is obtained taking into account implicitly the three-dimensionality of the problem. The general properties of the model are discussed, in particular the conservation laws. The model is also related to the fluid model that was introduced by Finn et al. [Phys. Plasmas 6, 3744 (1999); Phys. Rev. Lett. 84, 2401 (2000)] and developed by Coppa et al. [Phys. Plasmas 8, 1133 (2001)]. Finally, numerical investigations are presented regarding the stationary solutions of the model.