Langmuir probe theory and the problem of anisotropic collection

A more general understanding of Langmuir probe theory by going beyond particular coordinate systems as far as possible was studied. To delineate the role of initial velocities in the problem and to characterize the interaction between the velocity flow field and the electrostatic potential field both of which enter into the determination of particle trajectories are desired. The probe is supposed to be negatively charged throughout and the ensuing region of positive space charge about it differs fundamentally from the plasma region beyond in the sense that the former represents a region in which deterministic trajectories dominate while the lattice is a region dominated by statistical interactions largely controlled by the collisionless stationary Boltzmann equation. A general solution of this Boltzmann equation is given and its relationship to the problem of saturation current density in 3D is elucidated.