Some Timing Aspects for ILC

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

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. some general points • the damping ring circumference C is given by the HF wavelength lHFand the harmonic number h ( = number of HF-buckets) C = h lHF (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 NB(not mandatory) NB = h / i • the bucket distance in the damping ring t(DR) has to be a multiple of one HF bucket distance tHF(DR) t(DR) = i tHF(DR) = i / fHF(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 tHF(L)

4. damping ring ejection as an easy example: • damping ring for NB=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, knot constant => neglected (but still a solution) “filled solution” no common divider for k and NB always fulfilled for NB= prime number or k = prime number and not divider of NB -> in our example: e.g. NB = 101 or k =11, but also k = 9 => restrictions forNB and kNB= p k + e special case:NB= p k +/- 1 => constant bucket feed per damping ring revolution of exact one bucket d= k - e = -/+1

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 distancet(DR) • kcan 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 -> inour example: NB = 100, k=...,7 ,9, 11 ,13 ,17 ,.... • NBcan be changed, as long as h =NBi stays constant -> flexibility in DR bunch distance and number of bunches =>hshould contain many dividersi • 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 NB = p k +/- 1 -> “gap solution”the gaps are transformed to a shorter overall bunch train

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 NBis nearly fixed h= i NB= 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 -> more freedom for kicker pulse needs -> only the rise time of the ejection kicker pulses must be shorter than the bucket distancet(DR) (withre-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. damping ring HF frequency as mentioned already above: the ejected bunch pattern has to fit to the LINAC HF buckets t(L) = j tHF(L) = k t(DR) = k i tHF(DR) => for flexibility in NB, especially for the filled solution, a good choice of the HF frequency of the damping ring is important fHF(L) / fHF(DR) = j / (k i) => flexibility in k and i is determined fHF(L)given: 1.3GHz examples j / (k i) = 2 fHF(DR)= 650MHz = 3 = 433MHz = 4 = 325MHz = 5/2 = 520MHz =13/5=500MHz (not necessarily equal in both damping rings)

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- ke+ ie+ tHF(DR)e+= ke- ie- tHF(DR)e- C = h ctHF(DR) = i NBctHF(DR) • for the step solution: • impossible, since the steps in k would appear at different bunch train positions • for the filled solution: possible if both NBe+ and NBe- are prime numbers -> by definition without flexibilityinNB -> missing bunches in the larger ring -> in our example:NBe- = 101, NBe+ = 199 for a nearly doubled circumference • impossible, if k should be a prime number

9. different circumferences ke+ ie+ tHF(DR)e+= ke- ie- tHF(DR)e- • for the gap solution: • with unchanged bunch distance: tHF(DR)e+ =tHF(DR)e- , ie+= ie- => ke+= ke- pe+= z pe- (z= circumference factor, not necessarily an integer) =>Ce+= z Ce-+ (1 - z) i lHF => possible (e.g. Ce+= 2 Ce-impossible, but Ce+= 2 Ce-- i lHF ) • with changed bunch distance: t(DR)e+ =zt(DR)e-=> ke+= ke-/ z => pe+= z pe- =>Ce+= z Ce-=> possible (e.g. Ce+= 2 Ce-possible) restriction:kmust be dividable byz

10. example for flexibility long damping ring: C = 17.434km (h = 25200, fHF(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. examples for flexibility C = 6.477km (h = 10802, fHF(DR ) = 500MHz) NB = 5400 , t(DR) = 4ns some of the possible operation parameters: some flexibility in • bunch distance in the LINAC + 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 C = 6.643km (h = 14403, fHF(DR ) = 650MHz) NB = 4800 , t(DR) = 4.61ns some of the possible operation parameters:

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

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. 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. path length restriction 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 ilHF => geometry restriction reduced, but operation flexibility also(k fixed) • for the gap solution: D multiple of (g+k) ilHF => operation flexibility is reduced anyhow (k, NB), 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. some additional comments • second IP at a different longitudinal position the path length equation is valid for both IP’s 1. IP distance= ct(L) = c kt(DR) => k fixedby 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. 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 • if the kicker pulse fall time is expected to be long => gaps for the kicker pulse needs accept the reduced flexibility