1. SESAME – TAC 2012: M. Attal Maher Attal SESAME Booster Characterization

2. SESAME – TAC 2012: M. Attal The Booster Optics  The design optics with (Q x = 2.2, Q z = 2.13) is adopted.  The beam has the maximum sizes ±3  x  ±5 mm and ±3  z  ±12 mm. VC zz xx xx

3. SESAME – TAC 2012: M. Attal Sensitivity of Booster Lattice to Magnetic Misalignments Misalignment (3rms)Peak x-distortionx-amplification factorPeak z-distortionz-amplification factor Dipoles dx = 0.5 mm0000 dz = 0.2/ 0.5 mm00±3 mm / ±8 mm15 ds = 0.2/ 0.5 mm00±1.2 mm / ±3 mm6 d  s = 0.2/ 0.5 mrad 00±8 mm / ±20 mm40 d  x = 0.2/ 0.5 mrad 00±0.8 mm / ±2 mm4 d  z = 0.2/ 0.5 mrad ±0.6 mm / ±1.5 mm300 Quadrupoles dx = 0.2/ 0.5 mm±2.4 mm / ±6 mm1200 dz = 0.2/ 0.5 mm00±8 mm / ±20 mm40 ds = 0.2/ 0.5 mm0000 d  s, d  x, d  z 0000

4. SESAME – TAC 2012: M. Attal The Closed Orbit Distortion 0.5 mm/mrad 0.2 mm/mrad 0.1 mm/mrad  The 0.5 mm/mrad misalignment is not acceptable.  If the 0.1 mm/mrad misalignment is achieved, then we may not need to correct the orbit.

5. SESAME – TAC 2012: M. Attal Closed Orbit Correction in Case of 0.2 mm/mrad Misalignments  6 BPMs  6 original hor. correctors of L = 0.166 m installed in the 6 straight sections.  6 multi-wire cables rotated on the 6 defocusing quadrupoles as vertical correctors.

6. SESAME – TAC 2012: M. Attal  3 rms of x-corrector strengths = 0.36 mrad B = 5.7 mT.  Rough calculations for the 150 turns-78 mm gap correctors I = 2.34 A.  3 rms of z-corrector strengths = 0.33 mrad B = 4.3 mT. However Corrector PS should take into account the 0.5 mm/mrad error possibility as a safety margin. In this case:  3rms of x-corrector strengths = 0.96 mrad B = 15.3 mT I = 6.33 A. FEMM code calculations (by Sofian) gave I = 6.9 A  3rms of z-corrector strengths = 0.84 mrad B = 10.8 mT. FEMM code calculations (by Sofian) gave I = 850 A.turn

7. SESAME – TAC 2012: M. Attal Injection into the Booster Inj. Kicker pulse is 4µs with decay time ~ 2.7µs. It moves the orbit to x = -25 mm @ injection septum. The 2 µs microtron beam is injected into the booster at x = -25 mm. Microtron beam pulse Thickness of septum sheet = 0.1 mm

8. SESAME – TAC 2012: M. Attal To simulate the real shape of the measured kick, some data points are extracted from the measured pulse curve & fitted to a function that is used to evaluate the kick After each turn in the booster (  = 0.128 µs) The -4.9 mrad kick decays to zero after 21 turns. The length of microtron beam pulse (2µs) is comparable to that of the kicker pulse decay time (~ 2.7µs) The microtron beam pulse can be divided into slices which see different kicks and execute different injection behaviors.

9. SESAME – TAC 2012: M. Attal Injecting at peak of the kick (  = -4.905 mrad -   -4.126 mrad) causes the beam slice to get lost completely at the septum sheet in the first 3 turns, regardless of the injection angle. The full beam size (~ 10 mm) is used in the injection. The working point (Q x = 2.2, Q z = 2.13) On the other hand, injecting at the tail of the kick (  = 0.0148 mrad) causes the beam slice also to get lost completely at the septum sheet in the 5 th turn.

10. SESAME – TAC 2012: M. Attal Between the above two limits the beam losses will be different for each slice of the beam depending on the kick value seen by that slice. This injection is done @ zero angle. It can be seen that the microtron beam should be injected at t = 0.64  s from the peak of injection kicker pulse.

11. SESAME – TAC 2012: M. Attal The injection efficiency can be enhanced by injecting the beam with angles > zero. The different slices have their largest injection efficiencies at different angle ranges, however the injection angles range (0.44 mrad – 0.5 mrad) is common and gives the largest compromised efficiency. I should mention that ~ the full beam

12. SESAME – TAC 2012: M. Attal The Tolerance in Injection Septum Power Supply The slice of maximum injection efficiency is considered in these Calculations. Injection efficiency is further reduced for 0.44 >  inj > 0.5 mrad. The target of zero more losses The allowed error in injection angle is  inj = ± 0.03 mrad.  V = ±13.5 V in the Power Supply of the injection septum. Since the needed bending voltage @ 22.5MeV = 112.357 kV  V/V = 1.2 x10 -4.

13. SESAME – TAC 2012: M. Attal The Booster Dipole Current Ramping Form Old proposed curve New proposed curve 00.4510.501 Ramping time (s)

14. SESAME – TAC 2012: M. Attal The Booster Ramping Form  Black: the old proposed ramping curve (normalized by 1050 A).  Red: the new proposed ramping curve (normalized by 1050 A).  Blue: suggested alternative ramping curve f(t) = 0.5(1 – cos(wt)). The proposed ramping curves The induced sextuole component

15. SESAME – TAC 2012: M. Attal The Booster Ramping Curve Red: proposed ramping curve Red: the corresponding induced sext. field Blue: 0.5(1 – cos(wt)) ramping curve Blue: the corresponding induced sext. field  The induced sextupole component is calculated using analytical formula, in which F =1.3 for a vacuum chamber 70mm x 30 mm.

16. SESAME – TAC 2012: M. Attal Energy rampingDipole filed ramping Dipole field & Energy Ramping Curves  f(t) = 0.5(1 – cos(wt)) using w = 2  *1  B(t) = Bi + (Be – Bi) f(t) using Bi = 0.0284 T, Be = 1.0092 T  E(t) = B(t)*rho* 0.299792458 using rho = 2.6642 m

17. SESAME – TAC 2012: M. Attal Dynamic Effect of the Eddy Current Induced Sextupole Component The max. sext. integrated strength in each dipole SL = 0.715*1.395 = 1 m^-2 The sextupole component was scaled to FEMM result by changing F (conservative assumption)

18. SESAME – TAC 2012: M. Attal Each sextupole component is distributed into 6 slices over each dipole.

19. SESAME – TAC 2012: M. Attal Effect of Eddy Current Sextupole comp. on On-Momentum Dynamics  The blue box & red lines represent limitations of vacuum chamber and injection septum respectively.  The 100,000 turn tracked particle is still stable within the physical acceptance.

20. SESAME – TAC 2012: M. Attal Effect of Eddy Current Sextupole comp. on Off-Momentum Dynamics  Natural chromaticities  x = -0.8512 and  z = -3.183.  Sextupole component changes chromaticities to  x = 5.8 and  z = -20.12

21. SESAME – TAC 2012: M. Attal Effect of Eddy Current Sextupole comp. on Off-Momentum Dynamics  3 rms of beam energy spread = 2 e-3, whereas vac. cham. energy accept. = 5.8 e-3  The ± 2e-3 & ± 5.8e-3 particles are still stable within the physical acceptance

22. SESAME – TAC 2012: M. Attal Thank you