Quadrupole

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Booster Note 93-05
 
Longitudinal Quadrupole Damper Studies in the Booster
Dave McGinnis
June 9, 1993
 
Introduction
 
A prototype longitudinal quadrupole mode damper was installed in the Booster low level system during the week of May 25, 1993. Longitudinal bunch length oscillations are excited after transition in the Booster. These oscillations can be clearly seen by the horizontal ion profile monitor located at sector Long 4 in region of 2 meters of dispersion as shown in Fig. 1. These oscillations are also evident by peak detecting the beam signal from the resistive wall monitor as shown in Fig. 2.The intensity normalized AC oscillation of the peak detected signal is a measure of the strength of the bunch length oscillation. As shown in Fig. 3, the strength of this oscillation seems to be independent of intensity. Thus, the oscillation is not an instability and is probably caused by the beam to bucket mismatch which is a result of crossing transition with a high synchronous phase angle. The bunch length oscillates at twice the synchrotron frequency which is under 5 kHz after transition as shown in Fig. 4. Note that the synchrotron frequency decreases as the intensity of the beam increases. Also note that the bunch length before transition which is proportional to the intensity normalized DC value of the peak detector response also decreases as the intensity increases as shown in Fig. 5. The peak detected signal in Figures 2-5 were measured by using the Tektronix DSA 602 in Envelope mode and averaging over a number of Booster cycles.
 
Damper Configuration

 The system block diagram is shown in Fig. 6. The damper detects the mode 0 bunch length oscillation by peak detecting the third harmonic of the RF beam signal from the LONG 17 resistive wall monitor. The design and response of third harmonic filter with amplifier is shown in Figs. 7-8.
 
The transfer function of the filter, amplifier and peak detector is shown in Fig. 9. The peak detected signal which is under 5 kHz, is phase shifted by -90° by a 20 kHz band pass filter. The design of the 20 kHz filter is shown in Fig. 10. The response of the filter is shown in Fig. 11. Note that the gain of the filter is 17 dB at 5 kHz with a phase shift of -1000. Because the damper is only needed and designed for use after transition, the damper signal is multiplied with a variable length one shot which is triggered by a TCLOCK signal. The multiplier circuit is shown in Fig. 12. This signal is then summed with the anode curve into the anode program distribution network. The summing circuit is shown in Fig. 13 (The multiplier and summing circuit were developed by Jim Steimel for use in the PPOFF2 circuit.)
 
Results
The mountain range plots of the Booster bunches after transition is shown in Figs 14-19. The horizontal resolution is 1 ns/div. The first trace is triggered 70 us before transition and the number of traces is 30. In Figs. 14-16 there is a 100 turn delay between each trace. Thus the plot shows a time history of about 4.8 mS. Figure 14 shows the bunch profile with the damper off while Fig. 15-16 shows the bunches for the damper on with a one shot gate of 4 and 17 mS respectively. The bunch quality is improved with the damper on.The delay between traces for Figs. 17-19 is 375 turns corresponding to time history of 18 mS. Figure 17 is with the damper off while Figs. 18-19 show the bunches for the damper on with a one shot gate of 4 'and 17 mS respectively. One sees that while the longitudinal emittance is improved early, large dipole modes are strongly excited with the damper on.
 
 

Figure 14 
 
Figure 15 
 
Figure 16 
 
14. Mountain range plot triggered at 18700 mS with 30 sweeps, 100 turn delay between sweeps with damper off. The horizontal resolution is 1 ns/div. 15. Mountain range plot triggered at 18700 mS with 30 sweeps, 100 turn delay between sweeps with damper on and a 4 mS one shot gate. The horizontal resolution is 1 ns/div. 16. Mountain range plot triggered at 18700 mS with 30 sweeps, 100 turn delay between sweeps with damper on and a 17 mS one shot gate. The horizontal resolution is 1 ns/div. 
Figure 17 
 
Figure 18 
 
Figure 19
17. Mountain range plot triggered at 18700 mS with 30 sweeps, 375 turn delay between sweeps with damper off. The horizontal resolution is 1 ns/div. 18. Mountain range plot triggered at 18700 mS with 30 sweeps, 375 turn delay between sweeps with damper on and a 4 mS one shot gate. The horizontal resolution is I ns/div. 19. Mountain range plot triggered at 18700 mS with 30 sweeps, 375 turn delay between sweeps with damper on and a 17 mS one shot gate. The horizontal resolution is 1 ns/div. 
 
It is assumed that the reduced longitudinal emittance causes the growth rate of the coupled bunch dipole modes to increase. Figures 20 and 21 show the FFT of the resistive wall monitor signal at 35 mS into the cycle with the damper off and on, respectively. Figures 22 and 23 show the growth rate of mode 36 throughout the acceleration cycle with a 4 mS and a 17 mS one shot gate, respectively. (Note because of the frequency sweep this data is only valid after transition. The large spike at the beginning is the result of the crossover of the 2nd harmonic.) It is clear that mode 36 is excited by about 15 dB more with the damper on.
 
For added information, the scope traces of the input to the 20 kHz BPF (CHII), the output of the 20 kHz BPF (CH2), the anode curve (CH3), the intensity in the Booster and Main Ring was recorded (Fast Time Plot). Figures 24-36 (fig. 24-26) are the data with the damper off. Figures 27-29 are with the damper on and a 4 mS one shot gate. Figures 30-32 are with the dampers on and a 17 mS gate. Note that there is no beam loss in the Booster for any configuration while the Main Ring intensity is strongly affected by the coupled bunch mode strength of the Booster.
 
To increase the Landau damping by decreasing the RF bucket size in hopes of increasing the coupled bunch instability threshold, the total anode voltage was reduced by 5% as shown in Fig. 33. Figures 34-35 (below) are mountain range photos spanning transition to extraction with the damper off and on, respectively. Figure 36 is a growth plot of mode 36 as a function of time in the cycle. Figures 35 and 36 seem to indicate that reducing the anode voltage did not cure the coupled bunch mode instability. Figures 37 and 38 are the Booster and Main Ring intensity at reduced anode voltage with the damper off and on, respectively. Figure 37 shows a large beam loss after transition in the Booster with the damper off and the anode voltage reduced while no beam loss is recorded with the damper on. This seems to indicate that the reason why the Booster needs a large amount of RF voltage at transition is the result of the large bunch length oscillation. Thus the total RF voltage for the Booster can be reduced if the bunch length oscillation is controlled.
 
Figure 34
 
Figure 35 
 
34. Mountain range plot triggered at 18700 mS with 30 sweeps, 375 turn delay between sweeps with damper off and reduced anode voltage. The horizontal resolution is 1 ns/div. 35. Mountain range plot triggered at 18700 mS with 30 sweeps, 375 turn delay between sweeps with damper on, a 17 mS one shot gate, and reduced anode voltage. The horizontal resolution is 1 ns/div.

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