1. Cavity tuning options for synchronization
R. Rimmer, J. Guo
H. Wang, S. Wang,

2. Synchronization options
E-ring RF frequency fe0=1497MHz*7/22= MHz, harmonic Number=3416.
Three basic synchronization schemes were put on the table:
1). Change e-ring path length to sync with β variation in i-ring, have to change RF frequency of both rings accordingly:
The PEP-II RF cavities need to tune down by MHz in addition to detuning for beam
The SRF cavities needs to double this due to they are MHz, which is MHz
Maximum e-ring path length change is cm.
2). Change e-ring path, change I-ring harmonic number from 3416 to 3424 for the ion energies of 100 to 12 GeV/u to reduce range of e-ring path.
The maximum tuning of PEP-II cavity and SRF cavity is only 139 and 279KHz respectively
maximum E-ring path length is 63cm only. No need to change the I-ring path length.
If two fold symmetry is required, harmonic number must be even, max e-ring path length change is 126cm, RF frequency range will be 280kHz for e-ring, 560kHz for iring
However, collision of electron bunch with different ion bunch in each turn.
3). Change the I-ring path length only
No need to change both ring's harmonic numbers=3416
No need to tune both NCRF/SRF cavities
No need to change E-ring's path length, but I-ring's.
Maximum I-ring path length change is -227cm.
With harmonic change, reduce range of path length change to 63cm or 126cm, same as in 2).

3. PEP-II cavity tuning range
PEP-II cavities have one fixed and one movable tuner
Each tuner has ~ kHz range
Adequate for retuning to MHz plus beam loading
May be OK to tune over whole energy range.
Moving plunger tuner
Fixed tuner
Moving tuner

4. JLab SRF cavity tuners Original CEBAF tuner Mechanism in LHe.
Fairly large hysteresis.
Warm motor (external).
Rotary feedthroughs
10+ years service in CEBAF/FEL
Upgrade Scissor-type tuner
Very Low hysteresis.
Warm motor (external).
Linear feedthrough (Bellows)
In service in CEBAF/FEL
Upgrade zero length tuner
Low hysteresis.
Cold motor.
Tested but not yet installed
SNS-type tuner
End mount
Low hysteresis.
Cold motor.
In service in SNS

5. SRF cavity tuning range
Typical JLab SRF cavity tuner kHz at 1497 MHz, limited by switches. Could be kHz? (Tom Powers).
Where is the warm/cold elastic limit?
Analysis needed.
Scales to ~ kHz at MHz.
±140kHz required for harmonic change of 1, ±280kHz for even harmonics
Probably OK for tuning over even harmonics.
Not sufficient for full energy range.
Need to change the design to allow larger tuning range
Decrease stiffness of cavity (in a controlled way)
Longer stroke tuners
Use plungers or external reactive tuners?
Have some ideas…

6. Parameters: change harmonic by 1, change e-ring path and i-ring harmonic number, change frequency for both rings
Energy(GeV/u)
max dfe (kHz)
139.42
max dfi (kHz)
278.83
max(dLe) (cm)
62.93
ions γ β Ne Np
fe (MHz)
dfe (kHz)
fp (MHz)
dfp (kHz)
Le (m)
dLe (cm)
100
3416
69.719 90
64.943 80
58.289 70
48.628
97.255 60
33.827
67.654 50
9.475
18.949
-4.277
0.000 40
15.728
31.465
3417 32
36.381
72.763 28
9.384
31.447
3418
31.428
3419
31.410
3420
31.392
3421
31.373
3422
31.355
3423
31.336
3424
31.318

7. Parameters: change harmonic by 1, change e-ring path and i-ring harmonic number, change frequency for both rings
e-ring harmonic number:
3416
iring circumference
optimized ion Energy:
47.252
GeV
E-ring center circumference
e-ring circumference(m)
min
Max
Δ=0.63
i-ring Harmonic number
i-ring Energy(GeV/u) γ β
max
35.266
38.586
3417
25.531
35.268
28.211
38.588
3418
20.931
25.534
23.308
28.214
3419
18.117
20.933
20.309
23.310
3420
16.170
18.119
18.233
20.311
3421
14.720
16.172
16.688
18.236
3422
13.586
14.722
15.480
16.690
3423
12.669
13.588
14.502
15.482
3424
11.906
12.671
13.690
14.504
E-ring Frequency(MHz)
Δf(kHz) e-ring
Δf(kHz) i-ring
min
max
df min
df max
476.25
476.39
-69.71
69.73
139.46

8. Parameters: change harmonic by 2, change e-ring path and i-ring harmonic number, change frequency for both rings
Energy(GeV/u)
max dfe (kHz)
278.79
max dfi (kHz)
557.59
max(dLe) (cm)
125.84
ions γ β Ne Np
fe (MHz)
dfe (kHz)
fp (MHz)
dfp (kHz)
Le (m)
dLe (cm)
100.00
107.58
3416
62.921
90.00
95.92
60.525
80.00
85.26
57.420
70.00
74.61
52.891
60.00
63.95
45.914
50.00
53.29
76.080
34.341
40.00
43.63
34.821
69.642
15.717
35.27
38.59
0.000
30.00
32.97
25.53
28.21
3418
23.00
25.51
72.592
32.767
20.93
23.31
0.040
0.080
0.018
20.00
22.32
18.12
20.31
3420
16.17
18.24
0.122
0.243
0.055
14.72
16.69
3422
13.59
15.48
0.203
0.406
0.092
12.67
14.50
3424
11.91
13.69
0.284
0.568
0.128
11.26
13.00

9. Parameters: change harmonic by 2, change e-ring path and i-ring harmonic number, change frequency for both rings
e-ring harmonic number:
3416
iring Circumference
optimized ion Energy:
GeV
center circumference
e-ring Circumference(m)
min
Max
Δ=1.26
i-ring Harmonic number
Energy(GeV/u) γ β
max
25.532
28.212
3418
18.116
25.536
20.307
28.216
3420
14.719
18.120
16.687
20.312
3422
12.667
14.722
14.501
16.691
3424
11.258
12.671
12.999
14.505
E-ring Frequency(MHz)
Δf(kHz) e-ring
Ion ring
min
max
df min
df max
476.18
476.46
139.48
278.96