The Compact Linear Colider (CLIC) is designed to operate at 3 TeV centre-of-mass energy with a total luminosity of 10^35 cm^-2 s^-1. The overall system design leads to extremely demanding requirements on the bunch trains injected into the main libac at frequency of 100 Hz. In particular, the emittances of the intense bunches have to be about an order of magnitude smaller than presently achieved. We describe our approach to finding a damping ring design capable of meeting these requirements. Besides lattice design, emittance and damping rate considerations, a number of scattering and instability effects have to be incorporated into the optimisation of parameters. Among these, intra-bem scattering and the electron cloud effect are two of the most significant

Jowett, John M

Owen, H

Risselada, Thys

Zimmermann, Frank

CERN Document Server

DAMPING RINGS FOR CLIC  J.M. Jowett, T. Risselada, F. Zimmermann, CERN, Geneva, Switzerland H. Owen, CLRC Daresbury Laboratory, United Kingdom  Abstract  The Compact Linear Collider (CLIC) is designed to operate at 3 TeV centre-of-mass energy with a total luminosity of 1035 cm-2s-1.  The overall system design leads to extremely demanding requirements on the bunch trains injected into the main linac at a frequency of 100 Hz.  In particular, the emittances of the intense bunches have to be about an order of magnitude smaller than presently achieved.  We describe our approach to finding a damping ring design capable of meeting these requirements.  Besides lattice design, emittance and damping rate considerations, a number of scattering and instability effects have to be incorporated into the optimisation of parameters.  Among these, intra-beam scattering and the electron cloud effect are two of the most significant. 1 INTRODUCTION Table 1 summarises the principal parameters required of the main damping rings by the CLIC design [1] for a linear collider operating at 3 TeV centre-of-mass energy. As shown in Figure 1, the requirements on normalised emittance are significantly smaller than in other linear collider designs. The now well-established principles of damping ring lattice design [2,3,4] lead to variants of a TME arc lattice augmented with damping wigglers in straight sections.  However the resulting designs may not yield the desired performance because a variety of intensity-dependent effects―not usually taken account of in the initial design procedure―come into play.    Since a final choice has not been made for CLIC, and space is limited here, we illustrate two physical limitations on some typical lattices , indicating only their major features.  Fuller details will appear elsewhere. 2 INTRA-BEAM SCATTERING (IBS) Damping rings are usually designed so that the required output emittance is reached within the time that a given bunch train spends in the ring, usually 45 damping times.  IBS is sometimes taken into account by an iterative search for self-consistent final equilibrium emittances [7] (a fixed point of (1) below).  Here we calculate the evolution of the emittances from injection into the damping ring to subsequent extraction and show that this equilibrium does not exist.  (Our convention on the longitudinal emittance is zt σσ≈ε δ ; δσ  where zσ are the RMS fractional energy spread and bunch length.) Assuming that rapid phase mixing has already taken place and taking into account the effects of radiation damping, quantum excitation and IBS, the emittances ,,, tyx εεε of the three normal modes of single-particle motion evolve according to a set of three ordinary differential equations ( ) ( ) { }tyxT tyx ,,,,,220 ∈µεεεε+ε−ετ−=εµµµµµµ&  (1)where tyx τττ ,,  are the radiation damping times and 000 ,, tyx εεε  are the (geometric, not the normalised) equilibrium emittances as determined by radiation damping and quantum excitation in the absence of IBS.  The three equations are coupled through the IBS growth times ( )tyxT εεεµ ,,  which are non-linear functions [7] of the emittances and other beam parameters including the beam energy, E, and bunch population, Nb..  In the present 1.5 2 2.5 3 3.5 4 4.5 5EêGeV1. ×10−131. ×10−121. ×10−111. ×10−101. ×10−91. ×10−8εêmATF achieveNLC e+main TESLA e+CLIC 1 TeVATF achieveNLC e+mainTESLA e+CLIC 1 TeVFigure 1: Geometric emittances vs. energy at the output of the main damping rings in various linear collider designs [3,4,5].  Values attained at the KEK ATF [6] are also shown.  The 3 TeV CLIC requirements are plotted as blue (horizontal) and red (vertical) curves. Quantity Symbol Value Bunch population Nb 9101.4 ×  No. of bunches/train kbt 154 Repetition frequency rf  100 Hz Horizontal emittance xγε  m105.4 7−×  Vertical emittance  yγε  m103 9−×  Bunch spacing bl  0.2 m Min. kicker rise time 25 ns Table 1: Beam parameters required for 3 TeV CLIC 0-7803-7191-7/01/$10.00 ©2001 IEEE. 4065Proceedings of the 2001 Particle Accelerator Conference, Chicagocalculation, we use the MAD [10] implementation of the Bjorken-Mtingwa theory [8], to sum local values of ( )tyxT εεεµ ,,  over all elements of our lattices.  We pause to acknowledge that the MAD implementation of this theory has some limitations deriving from the common bias towards flat, uncoupled machines.  However our damping rings closely approximate this archetype. The numerical integration of the system (1) is carried out by Mathematicas NDSolve function [9] using dynamic programming to minimise the solicitation of MAD via the Madtomma [11] interface. One of our first damping ring lattices (drv16) at 1.98 GeV had circumference m 538=C , including, besides the usual TME arcs, some 60 m of insertions containing 10.8 m of wigglers with a peak field of 1.8 T; neglecting IBS, this machine achieves the required xε .   Another ring (drscale10),designed for 4.63 GeV, had similar straight sections but many more arc cells, giving a circumference of  m 2419=C ; neglecting IBS, this machine betters the required xε  by a factor 2.     The evolutions of the emittances for these two rings are shown in Figure 2.  In drv16, xε and yε stay an order of magnitude above the required value while in drscale10 they get within a factor ≈3.  In both cases, xε begins to grow again as yε  damps below a certain value. IBS is significant only for yx εε ,  and then only when the injected emittances have damped sufficiently.  This suggests that changes of the damping partition numbers at the expense of the longitudinal damping could be beneficial by slowing the damping of tε .  Moreover, these calculations are arguably pessimistic for they do not include collective effects such as potential well or turbulent bunch lengthening that may sustain a larger tε for longer.  3 ELECTRON CLOUD We consider a set of typical parameters listed in Tables 1 and 2, assuming that both wiggler and arcs are equipped with an antechamber, which absorbs 95% of the photons. Only the remaining 5% contribute to the electron cloud generation via photoemission, with a supposed photoelectron yield of 5% per absorbed photon. We further assume that 10% of the photons escaping the antechamber are reflected towards the top and bottom of the beam pipe, whereas the other 90% remain confined within a narrow outward cone. A photoelectron that impinges on the wall may be lost, reflected or produce true secondary electrons. The maximum secondary emission yield for perpendicular incidence will vary as a function of electron bombardment. We consider values of maxδ  between 1.7 and 1.1.  The dominant region of synchrotron radiation will be the long wiggler sections. Typical wiggler parameters are also given in the Table 2. In addition, there is of course synchrotron radiation in the arcs.  0.02 0.04 0.06 0.08 0.1 0.12 0.14tês-12-11-10-8-7-6-5log10HeêmL"drv116" 0.02 0.04 0.06 0.08 0.1tês-12-10-6log10HeêmL"drscale10" Figure 2: Evolution of xε  (blue), yε (red) and tε (black) from injection to extraction (5 damping times).  Dashed lines correspond to the absence of IBS.   Quantity Symbol Value Beam energy E 3.5 GeV RMS bunch length zσ  5 mm RMS horiz. beam size xσ  18 µm RMS vertical beam size yσ  1.5 µm Average β-function yβ  5 m Wiggler period wλ  0.2 m Peak field in wigglers wB  1 T Wiggler deflection θw 4.1 mrad Arc dipole field arcB  0.015 T Chamber radius yxh ,  5 mm Primary electron rate in wigglers dsd e /λ  0.075/ e+/m Primary e- rate in arc dsd e /λ  0.0025/ e+/m Photon reflectivity R 10% Max. secondary emission yield maxδ  1.11.7 Energy at maxδ  maxε  300 eV Max. probability of elastic reflection E,elδ  0.56 Width of elastic reflection elσ  52 eV Table 2: Parameters for electron cloud simulation 4066Proceedings of the 2001 Particle Accelerator Conference, Chicago We simulate the electron cloud build-up for (1) a field-free region, (2) a bending field, (3) a periodic wiggler field, in all three cases considering a beam pipe illuminated by the wiggler radiation, and (4) for an arc dipole section, where the number of photoelectrons is reduced.  Simulations results are shown in Figure 3. The line density along the bunch train saturates at values of order 1010 m-1. We note that the electron density is higher in the wigglers because of the larger number of primary photoelectrons. The difference between the periodic wiggler magnet and a uniform dipole field (also simulated but not shown) is small, assuming the same primary electron production rate. The central density near the beam attains values up to a few 1014 m-3, a hundred times higher than the simulated and measured densities for the SPS or the two B factories, indicating that the electron cloud can pose a severe problem for damping rings.  The threshold density for the single-bunch TMCI instability driven by the cloud can be estimated as [12] yese CrQβπγ≈ρ 2TMCth,  (2)With m5  km,2 ≈β≈ yC and ,02.0≈sQ we obtain m103 12TMCth, ×≈ρe , 10100 smaller than in Figure 3. The coherent tune shift due to the cloud [13,14] is γρβ≈∆2,,eeyxyxCrQ  (3)which, with the same parameters and 3-14 m10≈eρ , evaluates to 2.0, ≈∆ yxQ .  The incoherent tune spread can be several times larger still [13,14]. 4 CONCLUSIONS Damping rings for high-energy linear colliders like CLIC can suffer from severe electron cloud effects.  Intra-beam scattering is also a major problem but can be taken account of in the design of the rings. 5 REFERENCES [1] CLIC Study Team, A 3 TeV e+e- Linear Collider based on CLIC Technology, CERN 2000-005 (2000). [2] J.-P. Potier, L. Rivkin,  PAC97, Vancouver, 1997. [3] J.-P. Potier, T. Risselada, EPAC2000, Vienna, 2000. [4] P. Emma, T. Raubenheimer, Phys. Rev. Special Topics Accelerators and Beams 4, 021001 (2001). [5] TESLA Technical Design Report, DESY 2001. [6] K. Kubo,  HEACC01, Tsukuba 2001. [7]A. Piwinski in A.W. Chao, M. Tigner (Eds.), Handbook of Accelerator Physics and Engineering, World Scientific, Singapore 1999. [8] J.D. Bjorken, S.K. Mtingwa, Particle Accelerators 13 (1983) 115. [9] S. Wolfram, The Mathematica Book, 4th ed., (Wolfram Media/Cambridge Unv. Press) 1999. [10] http://wwwslap.cern.ch/mad/ [11] http://cern.ch/jowett/Madtomma/  [12] K. Ohmi and F. Zimmermann, Phys. Rev. Letters 85, p. 3821 (2000). [13] M. Furman and A. Zholents, PAC99, (1999). [14] F. Zimmermann, in CERN-SL-2001-003-DI (2001).  Figure 3:  Evolution of electron cloud density (top row) and central cloud density (bottom row) as a function of time during the passage of the 154 bunch train through an arc chamber, a field free region adjacent to a wiggler  and a periodic wiggler magnet.  Results are shown for four different values of maxδ are shown (colours) and elastic electron scattering is included. 4067Proceedings of the 2001 Particle Accelerator Conference, Chicago

Damping rings for CLIC

Abstract

Similar works

Full text

Available Versions

CERN Document Server

The University of Manchester - Institutional Repository