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)
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
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. 10-20 L 936 m rf 0 sectors 10-20 bypass RTL LCLS RTL V 42 MV R560.59 m R5626 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 0.025 mm 1.1 % SLAC linac tunnel South Arc
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
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. 10-20 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
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 %
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
Final Energy and Peak Current Jitter vs RTL Phase and Voltage Jitter RTL voltage
Final Energy and Peak Current Jitter vs 2-6 Phase and Voltage Jitter
Final Energy and Peak Current Jitter vs 10-20 Phase and Voltage Jitter
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.
Track in 2D 1000 times with jitter based on tolerance budget
Twiss Parameters from 20-5 Bypass-Start to S. Arc Inst. Section Convert Yuri’s MAD file into Elegant for particle tracking with CSR
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
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
Tracking With Incoh. Sync. Rad. sy = 4.8 mm with ISR (only) sz = 25.2 mm sx = 4.3 mm E 28.6 GeV
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)
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
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% (11s) SPPS 1.6 % plot-limits are chamber walls SABER 1% 2.0 % Chicane dipole field quality tolerances may be strained
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: Dz/sz 0.5%
SABER without a bypass (1-km more wake) sE/E 1.5% E 28.5 GeV sz 28 mm
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
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