RF Systems Design. Stephen Molloy RF Group ESS Accelerator Division. AD Seminarino 17 / 02/2012. Outline. Some basic concepts (Hopefully not *too* basic…) Steady-state analysis Optimising a cavity Optimising the linac Transient Filling a cavity Commissioning the machine
ESS Accelerator Division
Parallel LCR circuit, where L, C, & R, depend on geometry & material.
Resonant with a certain quality factor, Q0.
Generator current after transformation by the coupler
Transmission line impedance seen from “the other side” of the transformer.
Note it is in parallel with the cavity resistance, R.
Note that loaded R & Q both scale in the same way when shunted by the coupler.
Therefore R/Q is unchanged.
R/Q is a function of the geometry only, and so the circuit resistance, (R/Q)QL, is set by choosing the coupler loading.
Vcav= Vforward + Vreflected
Vg= Vcav - Vbeam
A non-zero synchronous phase angle will always lead to reflected power, unless…
Driving a resonator off-resonance leads to a drop in the amplitude and a rotation of the phase of the excited signal.
The higher power required to achieve the same cavity field could be easily compensated by the elimination of the reflected power
Forward voltage can be made equal to the cavity voltage no reflected power!
See ESS Tech Note: ESS/AD/0025
β=β0 may seem problematic as the cosine will go to zero, however the denominator also goes to zero. In this limit:
Velocity bandwidth may be approximated by the closest zeros of the cosine:
That the optimum β is greater than β0 is a well known phenomenon.
This curve agrees very well with simulation/measurement.
R/Q depends on square of V.
Note the large reflected power from the spoke cavities
In reality, LLRF would detect the incorrect cavity amplitude & phase, and the large reflected power, and act to prevent this.