Analytical Models of Conductivity-Channel Tracking,
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A new analytical model for the tracking force on an ultrarelativistic electron beam in a conductivity channel is derived from the complete Frozen Field Equations. The model assumes the beam to be entirely within a sharp-edged constant conductivity channel. Axial return currents are ignored except at the channel boundary, and the drift tube wall is assumed to be at large radius. It is shown, however, that these latter restrictions are not serious, although a small drift tube radius may complicate measurement of the tracking force. This Frozen Field Tracking Model reduces to the Electrostatic Tracking Model in the appropriate limit, but in other cases predicts slightly larger, sometimes oscillatory forces. The analysis also indicates that magnetic fields can play a positive role in tracking. For completeness, channel tracking forces for the New Field Equations with and without an axial displacement current are derived. With the displacement current the New Field Equations exhibit tracking qualitatively similar to that of the full Frozen Field Equations, while without it they exhibit tracking as described by the Electrostatic Tracking Model.
- Particle Accelerators
- Electricity and Magnetism