1. SABER Longitudinal Tracking Studies P. Emma, K. Bane Mar. 1, 2006
Longitudinal jitter tolerances
2D & 6D tracking
CSR effects (none)
RW-wakefields in the arc (none)

2. Short Bunch Generation in the South Arc
6 mm
Damping Ring (ge  30 mm)
1.1 mm
0.36 mm
SLAC Linac
1 GeV
30 GeV
LCLS
RTL
25 mm
South Arc
North Arc
1.1%
14 kA
25 mm
rms
28.5 GeV
3.4 nC

3. SABER Accelerator Layout
Q = 3.4 nC
NDR
1.2 GeV
z  6 mm
  0.08 %
LBCC
L 14 m
R56-76 mm
LCLS
GUN
Sec. 2-9
L 810 m
rf  -23.3°
sectors 2-9
Sec
L 936 m
rf  0
sectors 10-20
bypass
RTL
LCLS
RTL
V  42 MV
R560.59 m
R5626 mm
1.2 GeV
z  1.1 mm
  1.0 %
9 GeV
z  0.36 mm
  2.0 %
28.5 GeV
z  0.36 mm
  1.1 %
28.5 GeV
z  mm
  1.1 %
SLAC linac tunnel
South Arc

4. szmin  18 mm Minimum bunch length achievable…
Damping ring energy (1.2 GeV)
Damping ring energy spread (0.08%)
Damping ring bunch length
(6 mm)
energy in arc (28 GeV)
max. energy spread in arc (1.1%)
preservation of longitudinal emittance
szmin  18 mm

5. Longitudinal Parameters
Value
Unit
Bunch charge
3.4 nC
DR electron energy
1.19
GeV
DR initial rms bunch length
6.0 mm
DR initial rms relative energy spread
0.08 %
RTL Voltage 42 MV
RTL R56
0.590* m
RTL T566
1.05*
Sec. 2-6 RF phase
-23.3*
deg
LBCC Chicane energy
9.0
Sec RF phase
Deg
Bypass-line R56
13.2*
S. Arc R56
13.0*
S. Arc + bypass T566
94*
Final electron energy
28.5
* sign convention is with head of bunch at z < 0 and j = 0 at RF crest

6. Particle tracking in 2D energy profile phase space temporal profile
0.08 %
6.0 mm
1.19 GeV
1.2 %
6.0 mm
1.19 GeV
1.0 %
1.19 GeV
1.1 mm
2.0 %
9.00 GeV
1.1 mm
2.0 %
0.32 mm
9.00 GeV
28.5 GeV
1.1 %
0.32 mm
25 mm
28.5 GeV
1.1 %

7. Final Energy and Peak Current Jitter vs
Final Energy and Peak Current Jitter vs. DR Extraction Timing and Charge Jitter
0.1% relative energy jitter
20% peak current jitter
200 fs timing jitter
DR ext. time 
charge 

8. Final Energy and Peak Current Jitter vs RTL Phase and Voltage Jitter
RTL voltage 

9. Final Energy and Peak Current Jitter vs 2-6 Phase and Voltage Jitter

10. Final Energy and Peak Current Jitter vs 10-20 Phase and Voltage Jitter

11. Tolerance Budget for RF and Beam Jitter
All tolerances are rms and when applicable they apply to the average phase or voltage variations of the multiple-klystron linac section.

12. Track in 2D 1000 times with jitter based on tolerance budget

13. Twiss Parameters from 20-5 Bypass-Start to S. Arc Inst. Section
Convert Yuri’s MAD file into Elegant for particle tracking with CSR

14. Bunch length (ss) and relative energy spread (sd) vs
Bunch length (ss) and relative energy spread (sd) vs. S-position (with CSR) ss sd
25 mm

15. Tracking With and Without CSR
sy = 4.33 mm
without CSR
sz = 25.1 mm
sx = 3.05 mm
sy = 4.36 mm
with CSR
sz = 24.9 mm
sx = 3.08 mm

16. Tracking With Incoh. Sync. Rad.
sy = 4.8 mm
with ISR (only)
sz = 25.2 mm
sx = 4.3 mm
E  28.6 GeV

17. 1st order (no CSR) 2nd order (no CSR)
Tracking in 1st & 2nd Order
sy = 4.33 mm
1st order
(no CSR)
sz = 25.1 mm
sx = 3.05 mm
sy = 5.59 mm
2nd order
(no CSR)
sz = 26.3 mm
sx = 3.53 mm
(Gaussian fits)

18. De/ex  6.7% (6% due to ISR) min. sz
CSR tracking through sec-10 chicane with SABER beam (1.15 mm  320 mm)
sz =
1.15 mm
1D calculation
De/ex  6.7%
(6% due to ISR)
over-compression
min. sz
sz =
340 mm B1 B2 B3 B4

19. plot-limits are chamber walls
Sector-10 chicane energy spread is larger in SABER than in SPPS (1.6  2%)
SPPS
(x-y at chicane center)
1.6% (11s)
SPPS
1.6 %
plot-limits are chamber walls
SABER 1%
2.0 %
Chicane dipole field quality tolerances may be strained

20. AC Resistive-Wall Wake for Aluminum Chamber in South Arc
(a = 5.5 mm)
no RW-wake
with RW-wake
Resistive-wall wake (AC) effect is small: Dz/sz  0.5%

21. SABER without a bypass (1-km more wake)
sE/E  1.5%
E  28.5 GeV
sz  28 mm

22. Damping Ring Energy Reduced to 0.9 GeV (from 1.2 GeV)
(damping time still sufficient at 30 Hz)
sE/E  1.1%
RTL R56 = 460 mm ?
sz  11 mm

23. Send LCLS Beam into South Arc (no by-pass)
sE/E  0.2%
E  13.6 GeV
gex,y  1 mm ?
No CSR, No RW-Wake, etc.
sz  2.6 mm
(8 fsec rms)
No possibility to do this in present design