rf considerations for the dedm ring
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RF considerations for the dEDM ring. Require coherent longitudinal oscillations with synchrotron tune around 0.2 Superconducting RF needed to produce such a tune. Cannot modulate RF phase at 0.2*frev so need another cavity with frequency offset from a revolution line by 0.2*frev

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Presentation Transcript
rf considerations for the dedm ring
RF considerations for the dEDM ring

Require coherent longitudinal oscillations with synchrotron

tune around 0.2

Superconducting RF needed to produce such a tune.

Cannot modulate RF phase at 0.2*frev so need another cavity

with frequency offset from a revolution line by 0.2*frev

With superconducting RF all amplitudes and phases vary

slowly compared to synchrotron oscillations and an adiabatic

excitation is required

longitudinal dynamics
Longitudinal dynamics

Thin lens equations of motion for energy deviation on turn n just before

entering the cavity at time

Initially, consider only two voltage terms

The approximation is only for analytic work

analytic considerations
Analytic considerations

Set so that

Where

Next set the momentum variable to

Dynamics are described by the hamiltonian

Where

analytic considerations 2
Analytic considerations 2

Now go over to action (J) angle () variables that rotate at

The new hamiltonian is

where small or fast terms have been dropped. Going back to Cartesian

Final hamiltonian

analytic considerations 3
Analytic considerations 3

Final hamiltonian

Fixed points where , and stable when

Plot of as

is raised with fixed drive .

The stable fixed point

migrates to larger x.

This is fully adiabatic.

analytic considerations 4
Analytic considerations 4

Intuitive picture of raising tune

simulations
Simulations

Applied voltage.

360 MHz for main harmonic

drive at 176.3 MHz

2nd harmonic 720 MHz

Final bunches

Expect slight changes

with extended field

region.

scaling laws for other rf frequencies
Scaling laws for other RF frequencies

Synchrotron tune is fixed by

Maximum velocity excursion

Inexpensive RF power in FM radio band and above 350 MHz

Cavities get larger as frequencies drop

conclusions
Conclusions
  • Principle appears to be sound
  • Need to decide on frequencies and drive phases (90 .vs. 180)
  • Power and RF control considerations remain
  • Full system cost of 3 to 5 million dollars (fully loaded with, design, over head, etc. and assuming no surprises)
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