Equilibrium and Stability of the Solenoidal Lens Betatron,
Abstract
The solenoidal lens betatron uses a series of solenoidal lenses arranged around a race-track shaped drift-tube to provide strong transverse focusing for a high-currently electron ring. Equilibrium behavior of the circulating beam is examined. The tolerance of the beam to mismatches in the toroidal and vertical fields is evaluated analytically and using a particle simulation code. The linear and nonlinear development of the negative-mass instability in the device is also studied. A new linearized, rigid-disk model of negative mass instabilities in high current betatrons. Taking the beam and accelerator cavity cross sections to be rectangular permits the electromagnetic fields to be evaluated exactly in toroidal geometry. Growth rates from the model agree well with results of three-dimensional numerical simulation for beams and cavities with rectangular or cylindrical cross sections. Generally, negative mass instability growth rates are greatest for beam energies within a factor of two of the so-called transition energy and in that energy regime scale inversely with the square root of the toroidal magnetic field strength.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1985
- Accession Number
- ADA157225
Entities
People
- B. B. Godfrey
- T. P. Hughes