Field Stability Issue for Normal Conducting Cavity under Beam Loading

Transcription

1 Field Stability Issue for Normal Conducting Cavity under Beam Loading Rihua Zeng, 3- - Introduction There is cavity field blip at the beginning of beam loading (~several ten micro-seconds) under PI control feedback for normal conducting cavities. It occurs even if cavity field amplitude and phase are set carefully to the same nominal values before beam coming. The solution to this problem is to adjust the beam injection time, having the beam injected before the cavity field gets constant and cancelling each other the voltages induced by beam and induced by generator current. In the case of beam injection time unable to adjust, feedforward compensation for corresponding beam mode helps solve the problem. Simulation background and parameters Under the matching condition of a beam-loaded cavity operation, the reflection power in the steady state is zero, and the coupling factor can be calculated from the generator power and the power transferred to the beam []:!!"# =!!!! =!!!!!!!. Therefore, some parameters used in the simulation of normal conducting cavity is calculated as follows given some known values (for DTL tank, energy gain: 9.MeV, required power:. MW, Q : ): The coupling factor!!"# and the shunt impedance R under matching condition can be calculated as well from the following equations[]:!!"# = +!"!!!"#!!!!"#!! =!!"#!!"#!

2 where,!! is the synchronous phase,!!"# is the cavity voltage, and!!! is the average DC beam current. In the simulation in this note, the cavity field in the case without beam is always kept constant by feeding a proper feedforward signal and frequency tracking in the filling stage to keep filling on resonance. Cavity field blip at beam loading If the cavity field is kept constant at first and then beam comes causing perturbation to cavity field, the cavity field blip at the beginning of beam loading (~several ten microseconds) is inevitable under PI control feedback for normal conducting cavities due to the following factors[3]: There is an unavoidable loop delay, in the order of µs. Relatively much low Ql for normal conducting cavity, around a factor of 3 lower than superconducting cavity. Beam loading perturbations is much larger than superconducting cavity in the first couple of micro-seconds (loop delay and feedback loop bandwidth limit). In PI controller for normal conducting cavity, the gain of proportional controller is very low (<) and the performance of integral controller degrades in the high frequency perturbations. Figure and Figure 3 show the remained blip under PI feedback. The blip is quite large, ~% error in amplitude, and. in phase. Figure shows further information of occurrence of beam loading perturbations, which reveals that the perturbation occurs despite that the phase and amplitude are set to the target values before beam coming. When the perturbation is too large, adding another adaptive feedforward loop (by nature a pulse-to-pulse feedback loop) might not totally eliminate the beam loading perturbation, which might be one of reason at SNS where the blip is still there after applying the learning feedforward. 3 Figure Cavity field stability issue under PI feedback control

3 Figure IQ signals of set points and real cavity field output under PI feedback control in simulation (yellow & pink: I&Q signal of set points, green & red: I&Q signals of cavity field) Possible solution One possible solution is to adjust the beam injection time, cancelling each other the voltages induced by beam and induced by generator current, like the proposed solution in superconducting cavities in other accelerators. The cavity field will maintain constant as soon as the beam is injected at proper injection time!!"# []:!!"# =! ln ( +!!"#!!!!!!!"#!! ), where,!! =.(!/!)!!,! =!!!!! is the cavity time constant. It should be noted that the pre-detuning for synchronous phase and frequency tracking at filling stage are already applied. Figure shows that there is significant improvement after adjusting beam injection time. When beam injection time cannot be adjusted in some cases such as in beam commission, where a variety of beam modes expect to pass through the cavity with different pulse lengths, peak currents, and arrival times, the way to improve field stability is to apply individual feedforward compensation for each beam mode. Figure and Figure show respectively the cavity fields and consumed powers for the cases without/with individual feedforward for each beam mode. More results not shown here indicate that even if there are errors in feedforward signal such as beam current fluctuation and droop, and beam arrival time jitters, the cavity field can be kept well. However, better performance is achieved when arrival time jitter is less than ns.

4 . forward power reflected power Figure 3 Cavity field and generator power consumed under PI feedback control for nominal beam operation (beam injected us after constant cavity field is built). forward power reflected power Figure Cavity field improvement by adjusting properly beam injection time for nominal beam operation (PI feedback has been applied) st,.ma, us nd, ma, us 3rd, ma, us st,.ma, us nd, ma, us 3rd, ma, us.. st, forward nd, forward 3rd, forward st, reflected nd, reflected 3rd, reflected Figure Cavity field and power consumed under PI feedback for different beam modes loading st,.ma, us nd, ma, us 3rd, ma, us 3 st,.ma, us nd, ma, us 3rd, ma, us.. st, forward nd, forward 3rd, forward st, reflected nd, reflected 3rd, reflected Figure Cavity field improvement by individual feedforward compensation for each beam mode in different beam loading (PI feedback has been applied)

5 Reference [] H. Padamsee, RF Superconductivity: Science, Technology, and Applications, Wiley, New York, 9. [] T. Schilcher. Vector Sum Control of Pulsed Accelerating Fields in Lorentz Force Detuned Superconducting Cavities. Ph. D. Thesis of DESY, 998 [3] R. Zeng, Power Overhead Reduction Considerations for RF Field Control in Beam Commissioning, ESS technotes, ESS-doc-3-v. [] R. Zeng, S. Molloy, Some Considerations on Predetuning for Superconducting Cavity, ESS technotes, ESS/AD/3.