1. Some Timing Aspects for ILC Heiko Ehrlichmann DESY GDE, Frascati, December 2005

2. 2 central component: the damping rings are defining the ILC timing are defining some global ILC parameters could provide some flexibility together with an undulator based positron generation also the ILC geometry is influenced => damping ring parameters should be well chosen!

3. 3 some general points the damping ring circumference C is given by the HF wavelength HF and the harmonic number h ( = number of HF-buckets) C = h HF (assuming that all particles have the speed of light) usually not all HF buckets are used, but only a fraction, giving the number of equally spaced buckets N B (not mandatory) N B = h / i the bucket distance in the damping ring t(DR) has to be a multiple of one HF bucket distance t HF (DR) t(DR) = i t HF (DR) = i / f HF (DR) bunch distance in the damping ring t(DR) is much smaller than bunch distance in the LINAC t(L) => “compressed” storage of the desired LINAC pulse train to produce the pulse train bunch structure the damping ring ejection will run with a certain feed k(-> decompression) t(L) = k t(DR) the ejected bunch pattern has to fit to the LINAC HF buckets t(L) = j t HF (L)

4. 4 damping ring ejection as an easy example: damping ring for N B =100 filled buckets compression factor = ejection feed k=10 => after one revolution an already emptied bucket will be reached “step solution” allow a step in k after each revolution -> in our example: 9x k=10, 1x k=11, 9x k=10, 1x k=11 etc. => different bunch distances in the LINAC pulse train, k not constant => neglected (but still a solution) “filled solution” no common divider for k and N B always fulfilled for N B = prime number or k = prime number and not divider of N B -> in our example: e.g. NB = 101 or k =11, but also k = 9 => restrictions for N B and k N B = p k + e => restrictions for N B and k N B = p k + e special case: N B = p k +/- 1 => constant bucket feed per damping ring revolution of exact one bucket d = k - e = -/+1

5. 5 once the circumference is fixed filled solution (e.g. TESLA TDR) both rise time and fall time of the ejection (and injection) kicker pulses must be shorter than the bucket distance t(DR) k can be changed, as long as the restrictions are satisfied ( simply the bucket feed d will vary) -> flexibility in LINAC bunch distance and HF pulse length -> in our example: NB = 100, k=...,7,9, 11,13,17,.... N B can be changed, as long as h = N B i stays constant -> flexibility in DR bunch distance and number of bunches => h should contain many dividers i a desired gap in the LINAC pulse train can be produced with single missing bunches in the damping ring an artificial single gap of empty buckets in the damping ring would transform into missing single bunches in the LINAC pulse train special case: p equidistant gaps, fixed ejection feed k and N B = p k +/- 1 special case: p equidistant gaps, fixed ejection feed k and N B = p k +/- 1 -> “gap solution” the gaps are transformed to a shorter overall bunch train

6. 6 once the circumference is fixed gap solution (fixed bucket feed per revolution d + empty buckets) k can be changed, as long as p k stays constant -> in our example: NB = 101, k p=10 10, 5 20, 20 5, 50 2, 2 50 -> some flexibility bucket number N B is nearly fixed h = i N B = i (p k + 1) = const p artificial gaps of empty buckets can be implemented without creation of missing single bunches in the LINAC pulse train + ejection of always the bunch before the gap + ejection of always the bunch before the gap -> more freedom for kicker pulse needs -> only the rise time of the ejection kicker pulses must be shorter than the bucket distance t(DR) (with re-injection bucket feed g) as before: a desired gap in the LINAC pulse train can be produced with single missing bunches in the damping ring

7. 7 damping ring HF frequency as mentioned already above: the ejected bunch pattern has to fit to the LINAC HF buckets t(L) = j t HF (L) = k t(DR) = k i t HF (DR) => for flexibility in N B, especially for the filled solution, a good choice of the HF frequency of the damping ring is important f HF (L) / f HF (DR) = j / (k i) f HF (L) / f HF (DR) = j / (k i) => flexibility in k and i is determined f HF (L) given: 1.3GHzexamples f HF (L) given: 1.3GHzexamples j / (k i) = 2 f HF (DR)= 650MHz j / (k i) = 2 f HF (DR)= 650MHz = 3= 433MHz = 4= 325MHz = 5/2= 520MHz =13/5= 500MHz (not necessarily equal in both damping rings)

8. 8 different circumferences the collisions should always take place at the IP => the bunch train structure must be equal: t(L) e+ = t(L) e- k e+ i e+ t HF (DR) e+ = k e- i e- t HF (DR) e- C = h c t HF (DR) = i N B c t HF (DR) for the step solution: impossible, since the steps in k would appear at different bunch train positions impossible, since the steps in k would appear at different bunch train positions for the filled solution: possible if both N Be+ and N Be- are prime numbers -> by definition without flexibility in N B -> missing bunches in the larger ring -> in our example: N Be- = 101, N Be+ = 199 for a nearly doubled circumference impossible, if k should be a prime number impossible, if k should be a prime number

9. 9 different circumferences k e+ i e+ t HF (DR) e+ = k e- i e- t HF (DR) e- for the gap solution: with unchanged bunch distance: with unchanged bunch distance: t HF (DR) e+ = t HF (DR) e-, i e+ = i e- => k e+ = k e- p e+ = z p e- (z = circumference factor, not necessarily an integer ) => C e+ = z C e- + (1 - z) i HF => possible (e.g. C e+ = 2 C e- impossible, but C e+ = 2 C e- - i HF ) (e.g. C e+ = 2 C e- impossible, but C e+ = 2 C e- - i HF ) with changed bunch distance: with changed bunch distance: t(DR) e+ = z t(DR) e- => k e+ = k e- / z => p e+ = z p e- => C e+ = z C e- => possible (e.g. C e+ = 2 C e- possible ) restriction: k must be dividable by z

10. 10 example for flexibility k:k:k:k:1719 23 T HF (ms): 0.9881.105 1.338 i NBNBNBNB t(DR) (ns) t(L) (ns) 384006.92117.7131.5 159.2 463009.23156.9175.4 212.3 5504011.54196.1219.2 265.4 6420013.85235.4263.1 318.5 7360016.15274.6306.9 371.5 8315018.46313.8350.7 424.6 9280020.77353.1394.6 477.7 10252023.08392.3438.5 530.8 long damping ring: C = 17.434km(h = 25200, f HF (DR ) = 433MHz) some of the possible operation parameters: high flexibility in number of bunches + bunch distance in the DR bunch distance in the LINAC + overall bunch train length -> just by changing the DR timing between two cycles

11. 11 examples for flexibility C = 6.477km(h = 10802, f HF (DR ) = 500MHz) N B = 5400, t(DR) = 4ns some of the possible operation parameters: some flexibility in bunch distance in the LINAC + resulting changes in bunch number + resulting changes in bunch number -> also just by changing the DR timing between two cycles by (trivial) omitting of bunches the number of bunches is changed, but not the number of buckets the bunch distance in the damping ring is fixed p k t(L) (ns) t(L) (ns) T HF (ms): T HF (ms): N (e=20) N (e=20) 60903601.5124200 72753001.1883960 90602400.8643600 108502000.6483240 C = 6.643km(h = 14403, f HF (DR ) = 650MHz) N B = 4800, t(DR) = 4.61ns some of the possible operation parameters: pk t(L) (ns) t(L) (ns) T HF (ms): T HF (ms): N (e=20) N (e=20)6080369.21.3293600 6475346.11.2183520 7564295.40.9743300 8060276.90.8863200 9650230.80.6642880

12. 12 consequences up to now if some flexibility is required the damping ring parameters HF frequency HF frequency harmonic number and thus circumference harmonic number and thus circumference should be well chosen filled solution more changes in global parameters allowed during operation more changes in global parameters allowed during operation the circumference is given by the kicker pulse needs the circumference is given by the kicker pulse needs both rings should have the same circumference both rings should have the same circumference probably two long rings are better probably two long rings are better gap solution easier adjustment for kicker pulse needs easier adjustment for kicker pulse needs (especially for asymmetric pulse shapes) requires fixed number of buckets requires fixed number of buckets different circumferences are possible different circumferences are possible

13. 13 re-injection with independent particle sources the re-injection of ejected bunches can be done every time (between immediately or after one complete ejection cycle) in the gap solution one might refill with a deliberate bunch feed d for the ejection kicker pulse needs with the undulator based positron source the particle generation time is given by the electron LINAC timing always an already ejected bucket has to be refilled => the path length of the positron transport line must fit to the damping ring timing most flexible solution: self reproduction => an ejected positron bunch is refilled by it’s own electron partner essential for single bunch ejection (commissioning scenario, pilot bunches, machine protection system.....)

14. 14 ILC geometry (positron part) C = circumference of the damping ring L = distance between the IP and the beginning of the linear tunnel (BDS, LINAC, BC…) T1 = distance between the IP and the damping ring T2 = distance between the damping ring and the beginning of the 180° return arc B = pass length of the 180° return arc A = linear tunnel length between both 180° return arc ends b = additional path length for the IP bypass line, artificial detours somewhere in the positron transport line or other reasons (e.g. also for particle velocity differing from c) D = damping ring bucket feed length for the re-injected bunch (D=0 for self reproduction in the filled solution) => n C + D = 2 L + (B-A) + b

15. 15 path length restriction n C + D = 2 L + (B-A) + b n C + D = 2 L + (B-A) + b independent of the damping ring shape or position along the LINAC valid for all ILC stages: 500GeV, 1TeV upgrade... (B-A) + b -> detour path lengths, e.g. due to 180° return arc -> small in comparison to U or L -> geometry can be used for path length adjustment for self reproducing fills (filled solution): D = 0 => strong geometry restriction, but high operation flexibility for non-reproducing filled solution: D multiple of k i HF => geometry restriction reduced, but operation flexibility also (k fixed) for the gap solution: D multiple of (g + k) i HF => operation flexibility is reduced anyhow (k, N B ), some geometry restrictions, also the bucket feed g will be fixed in general all geometry conditions can be satisfied with artificial detours, maybe adjustable during operation-> costs?

16. 16 some additional comments second IP at a different longitudinal position the path length equation is valid for both IP’s 1. IP distance = c t(L) = c k t(DR) => k fixed by geometry 2. switch able additional path length in the positron transport, just compensating the IP distance effect HF frequency changes during the damping times could be used for shifting bunch patters between two LINAC pulses, but are not able to relax the flexibility or geometry restrictions the exact IP position can be adjusted by the LINAC HF phases since the damping ring HF phases must fit to the corresponding LINAC HF phases and the positron generation “phase” is determined by the electron LINAC HF phase, an adjustment of the damping ring injection phase is only possible with positron path length adjustment

17. 17 conclusions if the overall kicker pulse length can be small and a high flexibility in operation parameter choice is required => long damping rings with equal circumference, every bucket filled accept strong design parameter restrictions accept strong design parameter restrictions if the kicker pulse fall time is expected to be long => gaps for the kicker pulse needs accept the reduced flexibility accept the reduced flexibility

18. 18 only one kicker system in case of circular damping rings (small tunnel overlap with the LINAC) one kicker system could be used for ejection and re- injection (two independent septa) the timing shift between the ejection pulse sequence and the re- injection pulse sequence is constant for the gap solution and depends on the kicker feed k for the filled solution a “double” kicker system with two parts and 180° phase advance and the septum in between could be used for compensation of long kicker pulses (180° bump) a special case would be the synchronous ejection and re-injection within one kicker pulse, using e.g. neighbored HF buckets (by definition a bunch pattern cannot be self reproducing) => the path length has to be well adjusted to the corresponding special set of parameters (no flexibility)

19. 19 damping ring position long damping rings, filled solution due to cost reasons maybe a dogbone shape is preferable, using the LINAC tunnel => one of each bending sections can be used for the required (and independent) 180° return arcs => damping rings at both ends of the ILC preferable for damping rings in a separate tunnel the position is a free parameter maybe cost reduction by putting both rings in the same tunnel then: coupling possibilities -> use both rings together for electrons or positrons -> use the electron ring for positrons in case of technical problems with the positron ring -> operate the positron ring with electrons during commissioning as keep alive solution, when positrons are not available

20. 20 switch yard for using the e- ring with e+ for using the e+ ring with e- bypass lines mirrored view for better visibility, both rings of course in tunnel all switches can be slow (DC) all switches can be slow (DC) only for using both rings for positrons a fast switch is needed only for using both rings for positrons a fast switch is needed