1. The CLIC Decelerator Beam Dynamics
3rd CLIC Advisory Committee (CLIC-ACE)
Erik Adli, CERN/University of Oslo, September 2008

2. Outline Intro Longitudinal dynamics / power production (short)
Transverse dynamics
Sources of envelope growth
PETS
Short summary of work with PETS
Effect of transverse wakes
Alignment tolerances
Beam Based Alignment
Drive beam generation
Failure Modes (short / selected topics)
TBL

3. Intro

4. The objective of the decelerator:
The CLIC decelerator
CLIC decelerator (one sector)
The objective of the decelerator:
Produce the correct power for accelerating structures, timely and uniformly along the decelerator, while achieving a high extraction efficiency
Uniform power production implies that the beam must be transported to the end with very small losses

5. Lattice 24 decelerator sectors per main linac
Varying sector length due to number and size of main linac quadrupoles
Baseline for PETS: longest sector (1050 meter) with a PETS fill-factor of 71% ("worst case for beam dynamics")
Tight FODO focusing (large energy acceptance, low beta)
Lowest energy particles see phase-advance m90 (higher energy sees weaker focussing)

6. Baseline parameters for this study
Baseline parameters from [CLIC paramaters 2008]
E0  2.4 GeV
sE=0 in most simulations (because sE of few % is insignificant wrt. the energy spread due to deceleration)
I  100 A
d = 25 mm (bunch spacing, fb = 12 GHz)
t  240 ns (2900 bunches)
Gaussian bunch, z  1 mm
eN  150 mm  x,y  0.3 mm (at bmax)
Simulation tool: PLACET (D. Schulte)

7. Longitudinal dynamics

8. PETS energy extraction
Single particle energy loss:
example for Gaussian bunch
PETS longitudinal d-wake, including group velocity:
field builds up linearly (and stepwise, for point-like bunches)
Energy loss from leading bunches + single bunch component:
Approx: sb component equal to mb, and linear field increase:
if mb assumption is good, wake function is recognized for particle energy loss of z
Integrating DE over bunch gives second
form factor, and times fb gives extr. power:
(x 1/2 for linac-Ohms)

9. The effect of deceleration
l(z) E
S=(E-Ě) / E
= 90% Ě
Ě = E(1-S)
=E-NPETSDÊ = 24 MeV
tb = 83ps
sz = 1mm
tfill = (LPETS/vg)(1-bg) g = 1ns
tz = 3ps
Power extracted from beam (ss) :
P  (1/4) I2 Lpets2 FF2 (R’/Q) wb / vg = 135 MW
Transport of the decelerator beam becomes more challenging with increasing S and decreasing Ě – in this study S=90% used
Power extraction efficiency (ss) :
h = Ein/Eext = S FF hdist = 84%

10. Transverse dynamics
How to keep the entire beam (particles of all energies) within the vacuum chamber, along all the decelerator

11. Metrics
Because of the minimum-loss requirement we use as metric the 3-sigma envelope for the worst particle, defined as :
Simulation criterion for minimum-loss transport: r < ½a0 =5.75 mm
Factor ½ : margin for unmodelled higher order fields (especially wake fields!)
Requiring pclic=99% accelerator sectors  psector=99.98% of machines should satisfy this criterion (!)

12. Simulation overview
The following effects are included in the transverse dynamics studies
PETS model (baseline)
Transverse wakes (long and short range)
RF-kicks
Adiabatic undamping
Lattice component misalignment (baseline)
PETS misalignment (offset, angle)
Quadrupole misalignment (offset, angle)
BPM misalignment (offset, angle)
BEAM perturbations (studied separately)
Beam offset
Beam jitter

13. Results: baseline
Beam envelope, r, for baseline (incl. component misalignment) :
In order to improve the situation we first disentangle the contributions to the beam envelope

14. Minimum final envelope
Initial beam: modelled as slices with given energy and transverse distribution
Ad. undamping in a perfect machine
Relative orientation of distribution: irrelevant for r
we don't care about "chromaticity"
not necessarily useful to study emittance growth
To study increase fo beam envelope it is useful to work with a "pencil beam" of centroid only, where centroid envelope is den. rc

15. The effect of quadrupole kicks
Thus: quadrupole kicks alone drives the beam envelope above our limit (perhaps a bit surprinsingly)

16. Results: baseline Base + case w/o transverse wakes
Quadrupole kicks alone + undamping already leads to unacceptable beam envelope

17. Transverse dynamics - PETS

18. PLACET input: dipole wake function
PETS Impedance simulated and a set of discrete dipole modes are extracted to represent the impedance (I. Syratchev)
Each mode implemented in PLACET (fT, wT, QT, bT) and included in the PETS element (D. Schulte)
Slide: I. Syratchev

19. Input to PETS design
During the 12 GHz PETS design, beam dynamics simulations were done in an iterative process with the PETS design to ensure small amplification due to transverse wakes

20. Origin of wake amplification
Further investigation shows the amplification of the envelope occurs towards the end of the bunch
-> mainly the single bunch wake that drives the amplification
Collorary: since single bunch wake is sine-like, shorter bunch-length might reduce wake amplification significantly

21. Instabilities along the beam
NB: Q-factor larger than the nominal increase multi-bunch wake and might lead to instability along the beam
Here illustrater for Q=Q0 and Q=2Q0
Deemed unacceptable (even if centroid rc envelope is constrained)
NB: trapped modes***
Q=2Q0
Q=Q0

22. Conclusion: PETS design
Effect PETS transverse wakes mitigated efficiently for nominal PETS parameters
Stability sensitive to higher Q values

23. Alignment tolerances

24. (the rest of presentation: baseline parameters)
Procedure
(the rest of presentation: baseline parameters)
We want to specify lattice element alignment tolerances
We require that no single misalignment should drive our centroid (pencil beam) envelope more than 1 mm, rc < 1 mm (max. of 100 machines)

25. Limits

26. Quadrupoles
effect
limit of static alignment
Update table ***

27. Beam-based alignment

28. 1-to-1 steering
Using simple 1-to-1 steering (SC) forces the beam centroid through the center of each BPM
We assume a BPM accuracy of 20um (limited mainly by static alignment?)
As result the centroid also passed in the order of *** um from each quad

29. Results 1-2-1 steering Even if ***
[plot of distribution over machines]

30. Dispersion-free steering
1-to-1 correction does not give an adequate steering due to the large variation of dispersive trajectories
We therefore seek to minimize the dispersive trajectories by applying Dispersion-Free Steering (DFS, [Raubenheim** and Ruth, ***]
Our implementation minimized
We want a difference trajectory with large leverage

31. DFS: test-beam generation
Advantages with this method
quadrupole strengths are kept constant
main-beam and test-beam can be combined in one pulse
Large energy-leverage

32. Results: DFS
Start of lattice: DFS not effective, due to the small energy difference of the test-beam, but does not matter since ***

33. Current jitter Dispersion-free steering:
Dependence on current, versus bins
Lowest energy particles: XX phase-space revolutions
Highest energy partices: YY phase-space revolutions
DFS technique will be performed in bins, with a max. size depending on the current difference
need to perform DFS technique in bins

34. Decelerator: discussion and conclusion

35. Not included in the simulations
Resistive-wall wake
The following estimate
Higher-order wakes
Effect should be limited within r < ½a0 (but probably worth looking further into)
Longitudinal effects and phase jitter
Some work in [D. Schulte]
On-going work
Halo simulations
On-going work by I. Ahmed

36. Failure modes
Selected topics

37. Quadrupole failure

38. PETS: estimation of accepted break down voltage

39. PETS: effect of inhibition
"Petsonov"
Simulated as R/Q=0, QT=2QT0 (worst-case)
the lack of deceleration leads to higher minimum beam energy and thus less adiabatic undamping and less energy spread
dipole wake kicks increase; for a steered trajectory the change of kicks will in addition spoil the steering
the coherence of the beam energy will increase, and thus also the coherent build up of tranverse wakes

40. TBL versus the decelerator

41. From Model to Reality 1: The Test Beam Line (TBL)
The Test Beam Line (TBL) is under construction as part of the CLIC Test Facility 3 (CTF3). TBL will be a first prototype for the CLIC decelerator. The targets are, among others, to investigate beam stability and minimum-loss transport during deceleration with high power extraction efficiency. In addition the TBL will serve as test-bed for Beam-Based Alignment of a decelerated beam, and as a general benchmarking of the simulation codes.

42. TBL versus CLIC - parameters

43. Effect of quadrupole kicks

44. Wake amplification