Self-consistent Vlasov equilibria for intense hollow relativistic electron beams
- 1 December 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Plasma Physics
- Vol. 12 (3), 353-364
- https://doi.org/10.1017/s0022377800025320
Abstract
This paper discusses the procedure for constructing intense hollow relativistic electron beam equilibria within the framework of the steady-state (∂/∂t = 0) Vlasov–Maxwell equations. It is assumed that the electron beam propagates parallel to a uniform axial guide field Bext0 = B0 êz inside a grounded cylindrical conductor, and that the positive ions provide a partially neutralizing background with density n0i(r) = fn0e(r), where f = const. = fractional neutralization. The equilibrium properties are calculated for the specific choice of electron distribution function , where H, Pθ, and Pz are the energy, canonical angular momentum, and axialcanonical momentum, respectively, for an electron moving in the equilibrium fields, and , and P0 are constants. For this choice of distribution function, the mean axial velocity of the electron beam is equal to , and the beam density profile is hollow with inner and outer radii, R0 and R1, determined self-consistently from nonlinear boundary conditions that involve the equilibrium parameters Po, γb, γ0, etc., and the equilibrium self fields. Closed expressions for Ro and B1 are obtained for the case where the collisionless skin depth c/ωpe is large in comparison with the characteristic radius of the electron beam, and the beam density is sufficiently low that . The two cases, Po>0 and Po<0, are considered.Keywords
This publication has 7 references indexed in Scilit:
- Plasma heating by an intense relativistic electron beamApplied Physics Letters, 1973
- Destructive Instabilities in Hollow Intense Relativistic Electron BeamsPhysical Review Letters, 1973
- STABILITY OF RELATIVISTIC ELECTRON BEAMS IN A PLASMA AND THE PROBLEM OF CRITICAL CURRENTSSoviet Physics Uspekhi, 1971
- Propagation of High Current Relativistic Electron BeamsPhysics of Fluids, 1970
- Vlasov Equilibria and Stability of an Electron GasPhysics of Fluids, 1970
- Self-Focusing StreamsPhysical Review B, 1955
- Magnetically Self-Focussing StreamsPhysical Review B, 1934