mode - CERN Accelerator School
mode - CERN Accelerator School
mode - CERN Accelerator School
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Bunch<br />
position at<br />
max E(t)<br />
Transverse dynamics - RF<br />
defocusing<br />
→ RF defocusing experienced by particles crossing a gap<br />
on a longitudinally stable phase phase.<br />
→ In the rest frame of the particle, only electrostatic<br />
forces → no stable points (maximum or minimum) →<br />
radial defocusing<br />
defocusing.<br />
→ Lorentz transformation and calculation of radial<br />
momentum impulse per period (from electric and<br />
magnetic g field contribution in the laboratory y frame): )<br />
Δ<br />
p r<br />
π e E0<br />
T L r sinϕ<br />
= −<br />
2 2<br />
c β γ λ<br />
→ Transverse defocusing ~ 1/γ 2 disappears at relativistic velocity (transverse<br />
magnetic force cancels the transverse RF electric force).<br />
→ Important p consequence: q in an electron linac, , transverse and longitudinal g<br />
dynamics are decoupled !<br />
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