1. Beam dynamics studies and test facilites SLAC Accelerator Seminar January 28, 2010 Erik Adli, Department of Physics, University of Oslo and CERN

3. The Compact Linear Collider The Compact Linear Collider (CLIC): study for a Multi-TeV linear collider, with design parameters of 3 TeV COM and luminosity of 2 x 10 34 cm -2 s -1 Main linac uses normal-conducting accelerating structures with record high accelerating gradient of 100 MV/m (loaded) The rf break down rate of the structure field must be kept small (10 -7 per structure per pulse), the charge required to reach the luminosity goals must be distributed within short rf pulses to fulfill rf criteria CLIC two-beam acceleration scheme: high-power short rf pulses for main linacs are extracted from a high-intensity 100 A e - drive beam. Enables good machine efficiency (~7% wall plug to beams) 100 A drive beam CLIC two-beam acceleration scheme Recommended overview article: R. Tomas, "Overview of the Compact Linear Collider", PAC’09, Phys.Rev.ST-AB 13.014801

4. The Compact Linear Collider Main linac params: f rep = 50 Hz t train = 156 ns N = 3.7e10@2 GHz P beam = 14 MW

5. The CLIC decelerator 1 km

6. The CLIC decelerator Objective of the drive beam decelerator: Produce rf power for accelerating structures, timely and uniformly along the decelerator. Robust performance of 42 km beam line. Achieving a high energy extraction efficiency, to ensure good machine wall-plug efficiency: baseline is 90% energy extraction maximum Beam must be transported to the end with very small losses Drive Beam: 101 A, 2.4 GeV, 240 ns @ 12 GHz 1500 x 48 power extraction and transfer structures (PETS) will convert kinetic energy to rf power along 1 km decelerator sectors.  novel beam dynamic challenges for the decelerator No analogue studies for the ILC – CLIC works from scratch

7. Base line CLIC drive beam parameters Drive beam baseline parameters [CLIC parameters 2008] : E 0 = 2.4 GeV E 0 = 2.4 GeV  E / E 0 =1 %  E / E 0 =1 % I = 101 A I = 101 A f b = 12 GHz (bunch spacing d = 25 mm) f b = 12 GHz (bunch spacing d = 25 mm) t = 240 ns (2900 bunches) t = 240 ns (2900 bunches) Gaussian bunch,  z = 1 mm (FF = 0.97) Gaussian bunch,  z = 1 mm (FF = 0.97)  Nx,y  150 m   x,y  0.3 mm at  max = 3.4 mm  Nx,y  150 m   x,y  0.3 mm at  max = 3.4 mm Maximum power extraction allowed:  extr = 90 % Maximum power extraction allowed:  extr = 90 % PETS parameters Half-aperture: a 0 =11.5 mm Half-aperture: a 0 =11.5 mm R'/Q = 2294 Linac-Ohm/m R'/Q = 2294 Linac-Ohm/m L PETS = 0.21 m L PETS = 0.21 m v g = 0.45c v g = 0.45c P  (1/4) I 2 L pets 2 FF 2 ( R’/Q)  b / v g = 136 MW Resulting power power production (ss) :  = E in /E ext =  extr FF  dist 84 %  = E in /E ext =  extr FF  dist ≈ 84 % Resulting power extraction efficiency (ss) :

9. Uniform power production implies that the beam must be transported to the end with very small losses (< 1 % level). We require robust transport of the entire beam through each of the ~1 km decelerator sectors. PLACET simulations, including a specially designed PETS element (including fundamental and dipole mode wake field calculations), are the main tool for the decelerator studies. Decelerator beam dynamics studies Simulation criterion: 3  of all beam slices < ½ radius (5.8 mm) PLACET macro-particle beam model, sliced beam with tracking of 2 nd order moments

10. PETS induced energy spread The decelerator beam is very particular : the high group velocity PETS will induce a significant transient part at the head of the beam, with up to 90% energy spread at the decelerator end, as well as significant intra-bunch energy spread. To ensure reliable rf power production it is of importance that electrons of all energies are robustly transported along the lattice. Novel beam dynamics challenges. beam at decelerator end (pilot beam, w/o beam loading compensation) steady-state bunch at decelerator end (pilot beam, w/o beam loading compensation)  extr = 0.90

11. Beam transport and focusing strategy Focusing strategy: lowest energy particles ideally see constant phase-advance  90  Focusing strategy: lowest energy particles ideally see constant phase-advance  90  Higher energy particles see phase-advance varying from  90  to  10  (towards the end of the lattice) Higher energy particles see phase-advance varying from  90  to  10  (towards the end of the lattice) Perfect machine and beam : high energy envelope contain in low energy envelope Perfect machine and beam : high energy envelope contain in low energy envelope Energy acceptance (e.g. of generated halo particles) only -3% of E 0 at the entrance; but increasing along the lattice Energy acceptance (e.g. of generated halo particles) only -3% of E 0 at the entrance; but increasing along the lattice Implies that each of the (~ 40'000) quadrupoles should ideally have a different gradient Implies that each of the (~ 40'000) quadrupoles should ideally have a different gradient Least decelerated and most decelerated particle along the lattice : least dec. has a tune of ≈70, and an increase of  of  Fmax (E 0 )/ F0 = 4.4 most dec. has a tune of ≈135, and an increase of action of J max (E0) / J 0 =  0 / f = 10 3- envelope for perfect machine: r ad = 3.3 mm

13. PETS: effect on drive beam Strong PETS higher-order of the modes combined with the very high drive beam current : strong wake field effects, which must be studies carefully. Reminder: PETS design (from Igor Syratchev, CERN) : Full simulation of PETS HOM fields, for a single driving bunch. Courtesy of A. Candel (SLAC).

14. Transverse wake calculations Fundamental mode longitudinal field builds up and provides rf power. Transverse integrated field, induced by beam dipole moment, will deflect particles. Ultra-relativistic approximation: average integrated transverse force, evaluated in a frame moving with the particle: wake function per unit length, W' T (z). Dipole wake: force ~ offset of driving particle. Transverse impedance spectrum : rf simulation and reconstruction PLACET PETS elements: time-domain implementation allows to implement an artbitrary number of high-group velocity HOM modes, to regenerate the calculated HOM spectrum from rf simulations.

15. Beam dynamics challenge: dipole wake Principal effect of dipole wake: resonant linear increase of betatron amplitude of driven particle. Sufficient mitigation of transverse electro- magnetic forces, due to the PETS dipole wake, has been a major challenge for the two-beam accelerator concept. The natural amplification due to the dipole wake is large, but the PETS induced energy spread mitigates the amplification. However, this constrains however the PETS design: Decoherence due to intra-bunch energy spread, with respect to point-like bunches Rf power production is proportional with (R'/Q) / v g = const. However, PETS with too low group velocity do not develop energy spread fast enough to decohere the wake build-up

16. Dipole wake: PETS baseline design reached Large series of potential PETS design variants have been examined for robust mitigation of the transverse wake, for all beam modes, and injection errors. After thorough cooperation rf experts and EA, a PETS baseline indicating adequate wake mitigation, has been secured. [I. Syratchev, D. Schulte, EA and M. Taborelli, "High RF Power Production for CLIC", Proceedings of the 22nd IEEE Particle Accelerator Conference, 2007]

18. Beam dynamics challenge: orbit correction Second challenge is the effect of machine misalignment. In particular: kicks from misaligned quadrupoles might drive beam envelope far out of vacuum chamber, even for very tight pre-alignment of 20 m. Estimate for uncorrected machine sets scale : Beam transport for ideal injection into a misaligned machineBeam transport for ideal inj. into a 1-to-1 corrected machine 90% energy spread of decelerator beam poses a challenge for beam transport : Dispersive trajectories of higher / lower energy particles : 1-to-1 correction does only properly correct the beam centroid properly. With 1000 quadrupoles and 20 m rms offset, the expected centroid envelope is ca. 4 mm.

19. Dispersion-free steering We seek to improve the situation by imposing that particles of different energy shall all follow same trajectory – i.e. minimizing the energy dependence of the trajectories. We propose a scheme based on drive beam bunch- manipulation and exploiting PETS beam loading, to generate a test-beam. Beam transport for ideal inj. into a dispersion-free steered machine Energy profile of main beam and example test-beam [EA and D. Schulte, “Beam-Based Alignment for the CLIC Decelerator”, EPAC’08]

20. Performance of beam-based alignment Results of simulation including the combined effects of wake fields and misalignment for base line parameters :  quad =  BPM = 20 m, 1 mrad  BPM,res = 2 m nominal GdfidL wake level (Q=Q 0 ) quadrupole mover step size 1 m 3-  envelope of 500 simulated machines (worst case)

22. Lattice component specifications are driven by wake mitigation and correction strategies Need tight focusing for sufficient wake mitigation. - Baseline: one quadrupole per meter ( = 1.25 m) Need sufficent component alignment precision for initial correction. - Baseline: BPM and quadrupole alignment of 20 um Need sufficient BPM precision for dispersion-free steering performance - Baseline: BPM precision of 2 um Beam envelopes for decelerator baseline, 1-to-1 correction, and dispersion-free steering – worst of 500 machinesSpecifications ToleranceValueComment PETS offset 100  m r c < 1 mm fulfilled PETS angles~ 1 mradr c < 1 mm fulfilled Quad angles~ 1 mradr c < 1 mm fulfilled Quad offset 20  m Must be small to be able to transport alignment beam BPM accuracy (incl. static misalignment and elec. error) 20  m Must be small to be able to perform initial correction BPM precision (diff. measurement) ~ 2  m Allows efficient suppression envelope growth due to dispersive trajectories ToleranceValueComment Quadrupole position jitter 1  m r/r 0 < 5 % Quadrupole field ripple 1  10 -3 r/r 0 < 5 % Current jitter< 1%Stability req. only – RF power constraints might be tighter. Beta mismatch, d  ~10 %r/r 0 < 5 % Dynamic tolerances Static tolerances Ultimate goal of beam dynamics studies: pin-point component specification

24. CLIC Test Facility 3 The CLIC Test Facility 3 is designed to demonstrate the CLIC two-beam acceleration scheme and drive beam generation (12 GHz 28 A pulse), including : - fully loaded linac ( > 90% energy transfer demonstrated) - bunch combination (2 x 4 combination, total of 26 A, demonstrated) - CLIC experimental area with test of two-beam acceleration and deceleration [S. Bettoni et al., "Achievements in CTF3 and Commissioning Status", PAC'09, 2009]

25. Decelerator test-facilities Decelerator sector: ~ 1 km, 90% of energy extracted Two-beam Test Stand: test the characteristics of a single PETS Test Beam Line: test of beam transport where a large fraction of the energy is extracted, under betatron motion (16 PETS) CLEX

26. Two-beam Test Stand PETS experiments The first 12 GHz CLIC PETS prototype (2008) is tested with beam in the Two-beam Test Stand CLIC Test Facility 3 at CERN : CLIC 12 GHz PETS prototype The CTF3 Two-beam Test Stand experiment (University of Uppsala, Sweden) CLIC Experimental Area I. Syratchev, EA et al.,"High-Power Testing of X-Band CLIC Power Generating Structures" PAC'09, 2009

27. TBTS: experimental set-up and field recirculation To facilitate large power production with available CTF3 current, the Two- beam Test Stand produced rf field is recirculated back into the PETS : The formulae for PETS field, power and voltage have been extended to include recirculation : The Two-beam Test Stand is equipped with four rf windows (diode and I/Q) and five inductive BPMs, including one in a spectrometer line. Allows for precision measurement and correlation of both the electron beam and the rf power. The Two-beam Test Stand in its "PETS only " configuration

28. TBTS: experimental results Using the developed theoretical framework, the data from the 2008 Two-beam Test Stand has been analysed, in particular rf power, rf phase and beam energy loss has been measured and compared with theory expectations. Statistics: rms disagreement lies within 10% for 75% quartile for power reconstructions and within 20% for energy reconstructions. The analytical model, derived from basic principles, yield a good agreement and understanding of the physics of resonant power production with recirculation, and a basis for detecting break down. [EA et al. "First Beam Tests of the CLIC Power Extraction Structure in the Two-beam Test Stand", proceedings of DIPAC'2009].

29. TBTS break down Example of pulses with observed pulse shortening. Precise measurement of rf amplitude and phase will be used to bunchmark rf breakdown physics (work in progress)

30. Test Beam Line Test Beam Line: Transport of the 28 A CTF3 Drive Beam, while extracting more than 50% of the energy using 16 PETS, each producing CLIC level rf power, with small loss level. Test Beam Line – End of 2009 Parameters CLIC versus TBL Optimized segmented dump for complete energy measurement Quadrupole movers (CIEMAT) Precision inductive BPMs (IFIC ES.) Loss monitors (Cockroft I.)

31. Test Beam Line: experiments Precision correlation of 1) expected energy extraction (from intensity and bunch form), 2) rf power measurement and 3) dump energy measurements. Precision correlations (aiming for ~ 5 %) will show - that we fully understand and can operate the drive beam rf power generation - that neither wakes nor energy spread impede transport (loss monitoring) - performance tests of first series of 12 GHz PETS and couplers Test of the proposed decelerator orbit correction-schemes, using bunch manipulation and exploitation of the beam loading -proof of principle demonstration for decelerator correction -performance tests of BPMs and quadrupole movers Potential verification of resonant wake build-up (might require resonant kickers/BPMs) Benchmarking of drive beam / PETS part of the PLACET code 3

32. As a test-case for the Dispersion-Free Steering, was applied to the CTF3 fully loaded linac : Test-case with large simulated BPM offsets was defined : Steering close to real center trajectory instead of (artifically) offset BPM centers in practice: DFS indicate where problems are located Disperison reduced by a factor 3 with respect to 1-to-1 CTF3 linac: Dispersion-free steering CTF3 linac structures [EA et al., “Status of an Automatic Beam Steering for the CLIC Test Facility 3”, Proceedings of Linac’08]

34. Conclusions Decelerator: novel beam dynamics challenges due to the 90% energy extraction 42 km of beam line as the rf power source: must ensure robust beam transport Simulation studies show satisfactory performance for the decelerator, following from - sufficient mitigation of PETS wakes - dispersion-free correction scheme - tight, but feasible, component tolerances Important issues still remain, but are being adressed: - experiment tests of beam transport with large energy extraction - machine protection issues related to the 100 A beam - vacuum and other technical considerations Thank you for your attention For more details about the CLIC decelerator: see EA, "A Study of the Beam Physics in the CLIC Decelerator", Ph.D. thesis, University of Oslo (2009) http://eadli.home.cern.ch/eadli/clic_decelerator_thesis.pdf

36. TBTS break down

37. Effect on reducing number of BPMs N=1N=2 N=3N=4 (perfect BPMs and single machine simulated, for illustration purposes)

38. PETS: effect of inhibition Effect of inhibition on the beam dynamics: 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 transverse wakes "Petsonov": on/off mechanism Simulated as R/Q=0, Q T =2Q T0 (worst-case) Negligible effect on beam envelope for up to 1/3 of all PETS inhibited, and even more for a DFS steered machine A number of random PETS inhibited (averaged over 100 seeds)

39. PETS: estimation of accepted break down voltage Maximum accepted transverse voltage accepted if we require r c < 1 mm due to this kick

40. Quadrupole jitter and failure Losses as function of random quad failure Envelope increase as function of quad jitter

41. Lattice focusing For a given optics 3% change, or more, in initial current or energy will induce losses

42. TBL energy extraction

43. Two-beam Test Stand TBTS: the primary test-bed for single PETS performance Particular interest for the decelerator studies: verification of transverse wake : - measurement of beam deflection, TBTS kick angle measurement precision of 10 urad (expected kick; few 10 urad/mm centroid offset (5 A) ) – first benchmarking of PETS code - direct measurement of transverse wake with rf antennas On-going work

44. Illustration of two-beam acceleration Animation provided by A. Candel, Stanford Linear Accelerator Centre, using code T3P