Axially-Dependent Equilibrium of an Unneutralized Electron Beam in an Axial Magnetic Field,
Abstract
Axially-dependent Vlasov-Poisson equilibria are studied for monoenergetic unneutralized electron beams injected along magnetic field lines into a vacuum half-space and partially or totally reflected by the beam space charge. For simplicity, the entering beam electrons are assumed to be nonrelativistic and to have a rectangular distribution in momentum pitch angles with respect to the magnetic field. Electron density at any point along a field line is first expressed in terms of a potential for parallel motion (assuming conservation of magnetic moment), and this is then substituted into Poisson's equation to obtain a nonlinear partial differential equation for the space charge potential. The one-dimensional problem, in which only axial electric fields are considered, is reduced to quadrature and an exact solution is obtained in the singular case where the beam has no spread in pitch angles. The two-dimensional problem, in which radial electric fields transfer energy from the axial streaming motion to azimuthal ExB rotation to assist the axial reflection, has been reduced to a nonlinear partial differential suitable for computational solution. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1977
- Accession Number
- ADA070481
Entities
People
- J. Guillory
Organizations
- University of Maryland