Braun H-H

Korostelev M

Papaphilippou Y

English

ePubs: the open archive for STFC research publications

PARAMETER SCAN FOR THE CLIC DAMPING RINGSY. Papaphilippou, H.H. Braun, CERN, Geneva, SwitzerlandM. Korostelev Cockroft Institute, UKAbstractTriggered by the RF frequency reduction of the CLICmain linac cavities, the damping ring parameters had tobe reevaluated and the rings’ performance adapted to thenew luminosity requirements. In view of a staged approachfor reaching the ultimate energy of the collider, the depen-dence of the rings output emittances under the influence ofIntrabeam Scattering is evaluated with respect to differentbeam characteristics such as bunch population, beam en-ergy, coupling and longitudinal beam characteristics.CLIC DAMPING RINGS PARAMETERSSince 2005, the design and layout of the CLIC damp-ing rings (DR) have not substantially changed [1]. Theirperformance was further optimized to achieve the tar-get normalized emittances at their output. These studieswere principally documented in the PhD thesis of M. Ko-rostelev [2] which describes the baseline design. At a laterstage, and in view of the change in the main CLIC struc-tures, the impact of the imposed new parameters in the DRoutput emittances was studied but without a further opti-mization of their performance. The actual DR parametersare displayed in Table 1.The electron and positron bunches with energy of2.424 GeV are injected into the two rings whose layout is ofracetrack shape. The two arcs are filled with 1.8 m long the-oretical minimum emittance (TME) cells and the straightsections contain FODO cells with damping wigglers. Azone for injection and extraction is included after the dis-persion suppressor of one of the arcs. The total length ofthe ring was slightly increased to 365.2m by raising the to-tal number of TME cells to 100 and reducing some spacein the dispersion suppressors. The phase advance per TMEcell was kept to 210◦ in the horizontal and 90◦ in the verti-cal plane, providing a detuning factor of 1.8, defined as theratio between the achieved emittance with respect to theminimum emittance of the corresponding TME cell. Thechromaticity is controlled by two sextupole families.The previous injection and extraction procedure wasbased on an interleaved bunch train scheme where two pairsof two bunch trains were injected and extracted simultane-ously and than recombined with the help of a delay loopand RF deflectors. This scheme had the interesting featureof doubling the bunch spacing in the DR, thus reducing theeffect of electron cloud and fast ion instabilities. This so-lution was abandoned due to its complexity. At the sametime, the reduction of the repetition rate from 150 to 50 Hzleaves enough time (20 ms) for the emittances to reach theirParameter [unit] symbol old value new value(2005) (2007)beam energy [GeV] Eb 2.424 2.424circumference [m] C 360 365.2bunch population [109] N 2.56 3.70 ×1.1bunch spacing [ns] Tsep 0.533 0.5bunches per train Nb 110 312number of trains Ntrain 4 1store time / train [ms] tstore 13.3 20rms bunch length [mm] σz 1.547 1.53rms momentum spread [%] σδ 0.126 0.143final hor. emittance [nm] γx 550 381hor. emittance w/o IBS [nm] γx0 134 84final vert. emittance [nm] γy 3.3 4.1coupling [%] κ 0.6 0.13vertical dispersion invariant Hy 0 0.248no. of arc bends nbend 96 100arc-dipole field [T] Bbend 0.932 0.932length of arc dipole [m] lbend 0.545 0.545arc beam pipe radius [cm] barc 2 2number of wigglers nw 76 76wiggler field [T] Bw 1.7 2.5length of wiggler [m] lw 2.0 2.0wiggler period [cm] λw 10 5wiggler half gap [cm] bw 0.6 0.5mom. compaction [10−4] αc 0.796 0.804synchrotron tune Qs 0.005 0.004horizontal betatron tune Qx 69.82 69.84vertical betatron tune Qy 34.86 33.80RF frequency [GHz] fRF 1.875 2energy loss / turn [MeV] U0 2.074 3.857RF voltage [MV] VRF 2.39 4.115h/v/l damping time [ms] τx/τy ,/τs 2.8/2.8/1.4 1.5/1.5/0.76revolution time [μs] Trev 1.2 1.2repetition rate [Hz] frep 150 50Table 1: CLIC damping rings parameters as registered inthe 2005 note and new parameters after the main RF struc-ture redesign.equilibrium. The injection and extraction process is quitesimple with only one pulse stored in the damping ring percycle. The change of parameters in the main CLIC cavi-ties increased the bunch spacing to almost the same levelas for the interleaved scheme. The number of bunches withthe above mentioned bunch spacing fill 13 % of the rings.Note finally the increase of the RF frequency to 2 GHz.A further reduction of the horizontal emittance isachieved with the inclusion of 76 damping wigglers. Withthe previous set of parameters, the target transverse emit-tance was not reached due to the strong effect of IBS whichincreases the horizontal output emittance by almost a factorof 5 with respect to the equilibrium emittance. It was thusnecessary to choose higher wiggler fields, above the satu-ration level of iron dominated magnets, and shorter wigglerProceedings of EPAC08, Genoa, Italy MOPP06003 Linear Colliders, Lepton Accelerators and New Acceleration Techniques A10 Damping Rings679wavelengths. In the present design, the wiggler field is of2.5 T with a period of 5 cm [3], which necessitates super-conducting materials for achieving it. With these wigglerparameters, the achieved normalized horizontal emittanceat the damping rings output drops below 400 nm.The change in the wigglers’ parameters triggered theincrease of the energy loss per turn and the decrease ofthe damping times. In this respect, the RF voltage hadto increase to 4.1MV in order to provide enough energyrecovery while keeping the longitudinal emittance below5000 eV. m. The vertical tune of the DR had to be reducedby a unit to accommodate the wigglers’ field change.The previous parameter set included the influence ofmisalignments on the vertical emittance which was con-sidered to be dominated by coupling with a coefficient of0.6 %. A detailed study of alignment tolerances and theirinfluence to the vertical emittance was undertaken [2] andshowed that the vertical emittance growth is dominated byvertical dispersion and less by coupling. The evaluation ofvertical emittance value of 4.1 nm quoted in the latest pa-rameter set includes this non-vanishing dispersion invariantfor the vertical plane, and uses the complete set of coupleddifferential equations for evaluating the effect of IBS.SCALING OF PARAMETERSBunch chargeFigure 1 presents the dependence of the transverse emit-tances with respect to bunch charge. The horizontal emit-tance scales linearly with the square root of the bunchcharge (for high charges) and inversely with the square rootof the longitudinal emittance, i.e. x ∝√Ns. The verti-cal and longitudinal emittance have a much weaker depen-dence to the bunch charge and actually of the same order.As the bunch charge changes, the vertical and longitudinalemittance seem to be linear with each other. This confirmsthat the vertical emittance is dominated by vertical disper-sion and not coupling.The change of the CLIC RF structure design parameters,had a major impact on the bunch charge which increasedby a factor of 1.6, including a 10 % margin for losses inthe downstream injector systems. Taking into account theprevious scaling, the impact of the increased bunch chargeto the horizontal and vertical emittance was small and wellwithin the target values.Longitudinal emittanceThe longitudinal emittance can be controlled by the RFvoltage, with a lower limit given by the energy loss per turn.We consider to relax the longitudinal emittance of 5 keV.mrequired by the downstream linac. The longitudinal emit-tance can be increased up to 9keV.m, by decreasing the RFvoltage, while keeping the same bunch charge (Fig. 2). Thehorizontal emittance presents the inverse square root de-pendence shown before and can be reduced by 25 %. TheFigure 1: Horizontal and vertical emittance dependence onbunch charge270 290 310 330 350 370 390 410 430 2.70 2.90 3.10 3.30 3.50 3.70 3.90 4.10 4.30 4000 5000 6000 7000 8000 9000 10000 Horizontal emittance [nm] Vertical emittance [nm] Longitudinal emittance [eV m] Vertical Horizontal Figure 2: Horizontal (blue) and vertical (red) emittance de-pendence on longitudinal emittance.dependence of the vertical emittance is much weaker andscaled as y ∝ −1/7s .EnergyThe “zero-current” equilibrium emittance is written asx;0 =Cqγ212(Jx + Fw)(θ3√15r +Fw|B3w|λ3w〈βx〉16(Bρ)3)(1)with the relative damping factor Fw = LwB2w4π(Bρ)B and r theTME detuning factor. Assume that the damping partitionnumber Jx = 1 (no gradient in dipoles) and that the bend-ing angle θ = Lρ and the bending field are constant. Asthe bending radius is proportional to the energy, the dipolelength and the circumference should be scaled in the sameway. Scaling the total wiggler length as Lw ∝ γ, makesthe relative damping factor energy independent.The average beta function in a wiggler FODO cell is〈βx〉 = 2 3f2−L2w3√f2−L2wand scales as the wiggler length orthe energy, considering constant focusing strength. Keep-ing the wiggler characteristics constant, the second term ofthe equation (1) is energy independent whereas the first isscaled with the square of the energy. This term will dom-inate for high-energies, so that the horizontal normalizedemittance is x;0 ∝ γ3.The normalized longitudinal emittance is s =γσsσδm0c2. The rms bunch length can be written asMOPP060 Proceedings of EPAC08, Genoa, Italy03 Linear Colliders, Lepton Accelerators and New Acceleration Techniques680A10 Damping Ringsσs =c|η|ωsσδm0c2, with the slippage factor approximatelyequal to the momentum compaction factor for leptons:η ≈ αp = 3π2(4√159)2/3(Bρ)(1 + Fw)2/3C|B|γ2 ×(γx;0Cq− Fw|B3w|λ2w〈βx〉γ3192(Bρ)3(Jw + Fw))2/3 √5 + √2r − 12/3r.Under the assumptions made for the scaling of the“zero-current” equilibrium emittance, the momentum com-paction factor is energy independent. The rms momen-tum spread is proportional to σδm0c2 =√Cqγ2Jsρ ∝√γ.Finally the synchrotron frequency is written as ωs =cC√2πhαp(eVˆ 2−U20 )1/2m0c2. Taking into account that the har-monic number is proportional to the circumference andtherefore to the energy, based on our previous considera-tion, and assuming an increase of the RF voltage with theenergy loss per turn, the synchrotron frequency is ω s ∝1√γ . This makes the rms bunch length linear with the en-ergy and finally the longitudinal normalised emittance iss;0 ∝ γ5/2. The horizontal damping time is expressedas τx = 3BρC2πrecγ3B(Jw+Fw) and thus it is inversely propor-tional to the energy.Under the influence of IBS, it is difficult to find an an-alytical scaling due to the complexity of the growth rateformulas. Using the previous scaling laws and withoutredesigning a new lattice, a numerical scaling can be ob-tained, by integrating the same set of coupled differenceequations of the standard IBS theory. In Fig. 3, the depen-dence of horizontal and longitudinal emittance with respectto the energy is plotted. This gives that the longitudinal andhorizontal emittance scale approximately as s ∝ γ4 andx ∝ γ−2. Note that they still respect the inverse squareroot scaling with each other.Figure 3: Horizontal (blue) and longitudinal (green) emit-tance dependence on the energy.The horizontal emittance dependence with the energyfor constant longitudinal emittance is presented in Fig. 4.There seem to be two regimes: for higher energies, wherethe effect of IBS should become smaller, it increases fol-lowing a power law, similar to the one of the “zero-current”equilibrium emittance. For small energies where the ef-fect of IBS dominates, the horizontal emittance is almostinversely proportional to the energy. The energy provid-ing the minimum emittance is around the one of the CLICdamping rings.??????????????? ? ? ? 	? 	? ??		???	?	?Figure 4: Horizontal emittance dependence on the energywhile keeping a constant longitudinal emittance.The vertical emittance dependence to the energy isshown in Fig. 5. The top curve is for varying longitudi-nal emittance whereas in the bottom curve the longitudinalemittance is kept constant. In the former case, the verticalemittance follows a quadratic polynomial law with the en-ergy. As before, the minimum vertical emittance is closeto the energy of the CLIC damping rings. In the lattercase, it scales linearly with the energy for high energies,thus the geometrical emittance is energy independent. Thiscomes from the fact that the vertical emittance dependsmostly on the alignement tolerances which are energy in-dependent. For low energies the vertical normalized emit-tance seems to saturate to a constant value which meansthat when the IBS becomes strong, the vertical geometricalemittance should be inversely proportional to the energy.Considering a low energy version of the CLIC project,the scaling laws presented in this paper can be used forproviding conservative emittances for the DR, based on ex-isting designs of future light sources [4].Figure 5: Vertical emittance dependence on the energy.The bottom curve corresponds to constant longitudinalemittance.REFERENCES[1] F.Tecker (ed.), et al, CLIC note 764, to be published.[2] M.Korostelev, PhD thesis, EPFL, 2006.[3] S. Casalbuoni, et al., PAC07, Albuquerque, USA, 2007.[4] Y. Papaphilippou, et al., CLIC note, in preparation.Proceedings of EPAC08, Genoa, Italy MOPP06003 Linear Colliders, Lepton Accelerators and New Acceleration Techniques A10 Damping Rings681

Parameter scan for the CLIC Damping Rings

Abstract

Similar works

Full text

Available Versions

ePubs: the open archive for STFC research publications