Phase Stability

1
Phase Stability

• Neil Marks,
• DLS/CCLRC,
• Daresbury Laboratory,
• Warrington WA4 4AD,
• U.K.
• Tel (44) (0)1925 603191
• Fax (44) (0)1925 603192

2
Phase stability in the longitudinal plane

• Diagram shows the r.f. accelerating voltage and
  the stable phase positions for non-relativistic
  and relativistic beams

relativistic (ie constant velocity) stable phase
particles with too high momentum take larger
radius longer path length per revolution
arrive late and see lower voltage.
non-relativistic (ie variable velocity) stable
phase particles with too high momentum travel
faster arrive early and see lower voltage.

• Consequences
• providing there is adequate peak volts, the beam
  momentum will follow any slow change in
  integrated magnetic bending field
• if the r.f. frequency is changed, the beam
  circumference will follow, to keep the beam in
  synchronism with the r.f.
• This will be covered properly in the course on
  longitudinal dynamics.