Multifluid equations of a plasma with various species of positive ions and the Bohm criterion

Abstract

An explicit formula is found for the determinant of the system of multifluid equations of a quasi-neutral plasma. A close relation is revealed between this determinant and the Bohm criterion. A one-dimensional multifluid theory of a quasi-neutral plasma with M species of positive ions results in a (M + 1)-point boundary-value problem, one boundary condition referring to the sheath edge, M to the plasma-side boundary, and 2M − 2 to M − 1 free internal boundaries. The Bohm criterion is marginally satisfied not only at the sheath edge, but also at each internal boundary, and the sheath edge is distiguished by some additional conditions (the mean velocity of every ion species entering the sheath should exceed the velocity of sound of this species).

Floating Potentials in Two‐Electron Temperature Plasma with Two Species of Positive Ions: Kinetic Model and PIC Simulation

“…This means that each ion species fulfills its own Bohm criterion at the collector sheath entrance. Similar result was obtained in kinetic model by Franklin [3] and also fluid model by Benilov [2].…”

Formulation of Boundary Conditions for the Unmagnetized Multi-Ion-Component Plasma Sheath

“…which is identical with the definition of the SE introduced in [6] and [7]. In order to obtain the term ∂ z n e /∂ z n i and close the boundary conditions (9), one can use the following iteration.…”

“…The author considered two extreme cases: (i) highly Coulomb-collisional plasma, where due to collisional coupling all ions have the same velocity, and (ii) the case with collisionless ions. A more general approach has been used in [5]- [7]. These authors generalized the definition of the sheath edge (SE) for the MIC plasma.…”

Magnetized plasma sheath with two positive ions where collision frequencies have a power law dependency on ions velocities

“…Many works have investigated the collisional and magnetized plasma sheath containing ion and electron. Besides the works studying two-component plasma sheath composed of ion and electron, the investigation of multi-component plasma sheath has recently drawn considerable attention [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. For example, experimental investigation of plasma sheath containing two positive ions can be found in Refs.…”