In a scenario where the west cavities are driven by the klystron
and the east cavities are driven by the beam, we depend on the
beam to transfer energy from west to east. The power required to
maintain a particular accelerating voltage in the passive cavity
P = V_acc^2/(R/Q)/Q_ext and is independent of the beam current.
The electron(positron) energy that must be transferred from active
to passive cavity is E = P/I and results by displacing the bunch by
phase phi from the zero crossing
If Q_ext = 1e6, R/Q=89ohms, V_acc=2.5MV, and I=50mA the
- P_{pass} = 70.2kW
- E = 1.4MV
- phi = 0.6 radians
Consider the
effect of adding 1.4MV at the west cavities and then subtracting
1.4MV in the east.
Note that the energy loss due to synchrotron radiation is
negligible in comparison to energy shifts from the RF.
The results are shown in the plot. The pair on the left
show the closed orbits with phi=0, that is no energy gain at either cavity.
The pair on the right show closed orbits with phi=0.6radians for the west
cavities and phi=-0.6radians for the east. The upper pair show energy vs s
and the lower pair horizontal displacement vs s. Separators are off. Red
is positrons and green is electrons.
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Alternatively, if
Q_ext = 3e6, R/Q=89ohms, V_acc=2.5MV, and I=50mA then
- P_{pass} = 23.4kW
- E = 0.468MV
- phi = 0.19 radians
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