Space-charge effects in warm ion sheet beams in the Vlasov–Maxwell approximation

Abraham-Shrauner, B.; Anderson, O. A.
September 1990
Physics of Fluids B: Plasma Physics;Sep90, Vol. 2 Issue 9, p2217
Academic Journal
A warm, intense, externally focused ion sheet beam is analyzed: a bounded one-component plasma that not only has practical interest but is well-suited for illustrating the use of some powerful new tools based on the use of Liouville invariants and Lie point group symmetries. The two-dimensional, time-independent Vlasov–Maxwell equations are shown to reduce to a set of one-dimensional, time-dependent, nonlinear Vlasov–Maxwell equations. Special examples of analytic solutions are given for two cases: (1) a uniform, but axially varying, warm ion beam and (2) a nonuniform, axially stationary, warm ion beam.With the spatial dependence of the ion beam density chosen, analytic expressions for the ion distribution function, electric fields, transverse bulk flow velocity, rms beam size, and rms emittance are derived. Some of these results corroborate previous work while others are new. In this derivation the usual Vlasov–Poisson equations for the ion beam are replaced by the self-consistent Vlasov–Maxwell equations; this generalization will be important for extensions of this treatment to asymmetric problems. A careful discussion of boundary conditions and of the simplifications used in the derivation is included.


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