Impedance Calculation and Minimisation for Low Emittance Rings(LERs) T.F. Günzel 3rd Low Emittance Ring Workshop 8-10th July Thomas Günzel, III LER

Outline: Different LERs in comparison General effects of a smaller beam pipe Further Impedance relevant properties of LERs Computations for the MAX-IV 3GeV ring cavity tapers bellows double flange cavity BPM buttons The risk of Microwave instability Minimisation respectively optimisation of Impedance Conclusions Thomas Günzel, III LER

Projects in comparison [1] [2] [3,4,5] [6] [7,8] small emittances smaller beam sizes longer damping times small momentum compaction factor smaller bunch length smaller synchrotron frequency Smaller beam pipe radius (b) LSs come closer to the sub-mm regime in terms of bunch length already studied for FELs Thomas Günzel, III LER

Projects in comparison the Boussard criterion imposes tighter limits on the long. impedance budget (knowing that it is only indicative) The chamber cut-off frequency reaches about 10GHz or more. The search for dangerous trapped modes has to be extended up that frequency. small beam size and often large circumference makes space charge larger than the synchrotron frequency for all (here studied) LE-rings. large ratio of space charge to synchrotron can change trans. beam dynamics[9]. Thomas Günzel, III LER

Effects of a smaller beam pipe(+) For synchrotron light sources and damping rings which contain many low-gap chambers it reduces the impedance of the tapers: According to K.Yokoya[10]: The difference b-d gets smaller, significant reduction of the imaginary part and A.Blednykh & S.Krinsky(2010)[11]: b d L Long. Impedance of low-gap chambers can be significantly reduced by choosing long tapers Thomas Günzel, III LER

Effects of a smaller beam pipe(-) Zlong respectively loss factor κL depend ~b-1 (or b-2) on vert. chamber size Step regime (Zotter&Kheifets[12]) small step (Blednyhk & Krinsky[11]) Cavity regime according to diffraction model (Zotter&Kheifets[12]): Slits in a circular chamber (Stupakov [13], Kurennoy[14]): Long. Resistive wall: These adverse effects concern above all bellows, absorbers, flanges slits and BPMs. Heatload can become a hot issue! Thomas Günzel, III LER

Effects of a smaller beam pipe (trans.) Positive effects: Less steep tapers for low-gap chambers (according to K.Yokoya [10]): Negative effects: In general: Slits and holes: Strong resistive wall: Depending on ß-fct and pipe material the std vacuum chamber contributes to ßZtotal sensibly Not only with a smaller beam pipe, also with a smaller bunch length the kicks get larger! Transverse kicks can deteriorate the vertical emittance (but only in extreme cases) Thomas Günzel, III LER

Vertical emittance growth due to kicks This effect has been studied with bunches in sub-mm range for X-FELs. by Dohlus, Zagorodnov, Zagorodnova[15]. With (CLIC-damping ring): ε0y=1pm ß =2m Nee=0.66nC krms = 1000V/(pCm) (produced by low-gap damping wigglers) this value is quite large, but with a long ID and short bunch possible <y’2c>0.5 = 2.3·10-7m Δε0y/εy0  5% wiggler wiggler Fortunately for the other LER’s it is sensibly smaller. Thomas Günzel, III LER

Further impedance relevant properties of LERs In difference to 3rd generation LSs the space inside and between the magnets is very limited which does not allow a large number of special elements. Therefore the number of elements (bellows, flanges and vacuum slits etc.) creating high impedance is in general smaller than for existing SRs. Example: The MAX-IV ring will contain: 260 flanges 200 BPMs 60 bellows in 528m circumference The existing ESRF SR contains: 550 flanges 224 BPMs very modular vacuum system 290 bellows in 844m circumference The strongest challenges are the Microwave Instability and heatload. Transverse resistive wall and Head-Tail instability are also important but can be damped with a transverse feedback system or with bunch lengthening via HCavity. Thomas Günzel, III LER

Simulations (limited to long. Impedance) carried out with GdfidL (W. Bruns)[16] wake field (up to 8m) and subsequent coupling impedance computation (T-domain) bunch length 4mm and step size 0.2mm eigen mode computation in most cases up to 10.4GHz (F-domain) computation of the shunt impedance and quality factor of the found modes by material assignment to different parts of the geometry (some simplifications applied) The wake field computation was done to support the eigen mode computation to provide an input for tracking simulation in long. phase space (MW-instability) In order to comply with both requirements is a tremendous amount of computation. The data is shown in a logarithmic presentation of coupling impedance and the shunt impedance of each mode. The shunt impedance is multiplied by the quantity of the corresponding element in the ring. On top of it the threshold curves for LCBIs are plotted for 1) 20ps gaussian bunch, 2) 40ps gaussian bunch and 3) 187ps bunch with HCavity Both scales (left: coupling impedance and right: shunt impedance) are identical Thomas Günzel, III LER

the cavity was simulated apart (and won’t be shown) Cavity taper (MAX-IV) Tapers to low-gap chambers are smoother, but tapers to the cavities not 152mm 39.5mm the cavity was simulated apart (and won’t be shown) a pipe of 50mm radius was placed between the tapers instead. Thomas Günzel, III LER

Cavity taper (MAX-IV) upstream taper 39.3mm upstream taper 127mm 4mm bunch 4mm bunch many modes at rather high frequency some already above threshold (20ps gaussian bunch) as more cavities installed as more dangerous they are Q only considers wall dissipation longer taper reduces shunt impedance slower damping reduces margin further Thomas Günzel, III LER

Standard bellows (MAX-IV) 15 elements (there are more of diff. type) the discontinuity has triangular shape According to Kurennoy et al.’s theory [17] of discontinuities: close to the cut-off at 9.16GHz Ψ susceptibility discontinuity in the beam pipe e- 2b A effect of the slits seems to be less important Thomas Günzel, III LER

Standard bellows (MAX-IV) resonance rather close to the cut-off Q-value only based on wall dissipation radiation contribution to Q? f=9.07GHz Rs=167Ω 4mm bunch For many bellows in the ring such a resonance can become dangerous (in MAX-IV the number is limited though). Thomas Günzel, III LER

BPM block sandwiched by a double flange (MAX-IV) resides on each side of the majority of the vacuum chambers (120x) taper (11->12.5) taper (12.5->11) absorber protects BPM block bellow (w/o buttons) flange It is a swallow cavity which allows modes to get trapped taper pair necessary to protect the BPM block from synchrotron radiation dispose of enough space for the buttons Thomas Günzel, III LER

BPM block sandwiched by double flange main peak @5.6GHz double resonance of in total 98Ω peak contributes to MW f=9.82GHz f=9.34GHz Rs=3180Ω Rs=466Ω peak contributes to MW 4mm bunch Thomas Günzel, III LER

BPM button (MAX-IV) 4mm bunch The small radius of the buttoms leads to no external load no radiation loss considered peak contributes to MW The small radius of the buttoms leads to a resonance at rather high frequency[18]: large shunt impedance Rs = 105Ω but does not increase heatload 4mm bunch The Power loss is not very high and can, if necessary, be diminished by using Ag- or Au-buttons Thomas Günzel, III LER

In the round MAX-IV chamber there no asymmetry anymore BPM button (MAX-IV) High shunt impedance, what does it mean? Due to asymmetric position in rectang. pipe the Rs of the ALBA button is small. In the round MAX-IV chamber there no asymmetry anymore ALBA button in MAX-IV chamber the material mainly determines the Rs, the button radius the peak frequency it is (R/Q) which enters in the computation of the MW-instability Kurennoy’s theory of discontinuities[17]: Rs=370Ω no external load no radiation loss considered Imagine 250 BPMs with Rs=400 =0.1M  In case of high Rs and numerous BPMs LCB-instability threshold could be exceeded. However, for small buttons (high freq.resonance) the threshold is high so that the risk is rather limited. Thomas Günzel, III LER

The risk of the Microwave instability(MAX-IV) The computation of the Microwave Instability for MAX-IV was presented in the paper of M.Klein, R.Nagaoka, G.Skripka, P.F.Tavares and E.J.Wallen[19]. 5.6GHz: resonance in the double flange 9.8GHz: resonance in the double flange cavity 15.9GHz: resonance in the BPMs however the resonance of biggest adverse effect is broadband (not shown here) However, in several other LER’s the peak current is even higher. Despite the long bunches the found MW-threshold is rather close (3.5mA) to the single bunch current 2.84mA MAX-IV made the choice to use high current in long bunches (lengthened by a harmonic cavity). BPM resonances cannot be avoided. Flange resonances could be short-circuited. Thomas Günzel, III LER

Minimisation of Impedance The requirements of the mechanical engineering do not allow a large margin for optimisation One of the constraints is to cope with the heatload of the synchrotron radiation Due to the limited space large geometrical variation is anyway not possible. Trans. collective effects benefit from lower β-functions in LER’s compared to existing SRs. However, the shown examples give some indications: For optimisation analytical parametrisation of the impedance is recommended. The cavity taper shows: use long tapers for cavities and low-gap chambers By-pass/short-circuit the flanges (NSLS-II [18] and Soleil [20] do it) Cavities, even rather swallow ones, have to be avoided. If steps are necessary, make them as soft as possible. Use well conducting material in order to reduce heatload of BPMs and other sensitive elements reduce the number of critical elements (less pump slits, bellows, BPMs etc.) For RW: use of NEG-coated Al or Cu all along the ring Another approach is to optimise the input parameters of the Boussard criterion: choose a moderate peak current (increasing the harmonic number and/or using longer bunches) tune the RF-system so that it reduces rather the synchrotron tune instead of bunch length favor machines of higher energy choose lattices which avoid a rather low momentum compaction factor  Thomas Günzel, III LER

Conclusions Lower β-functions, less special vac.elements and less steep tapers alleviate collective effects of LERs. Nevertheless I consider the MW-instability as one of the greatest challenges. Minimisation of impedance should be done with respect to the most dangerous collective effect Some collective effects can be afforded, others not. The computation of thresholds and other intensity-related collective effects is by far exact, often the discrepancy between the computed and measured effects is significant. Examples: Transverse impedance budget of Soleil[21] and ESRF[22] is 50-66% of the impedance that was measured. So far worst case estimations were in most cases sufficient. This will certainly change for LER’s. The key parameter of a resonance Rshunt=(R/Q)·Q depends on Q. It determines the threshold of the multi-bunch instabilities. However, the quality factor Q is only approximately known. Q gets contributions from wall dissipation, radiation and possibly external load. Thomas Günzel, III LER

References [1]S.Leemann et al.“Beam dynamics and expected performance of Sweden’s new SR LS:MAX-IV”,PRSTAB12 120701(2009) [2] ESRF Upgrade Programme II (2015-2019), White Paper [3] K.Soutome, LER-workshop 2011 [4]T.Watanabe et al., THPC032, IPAC’11 [5] T.Watanabe, talk on the FLS 2010 at SLAC [6] CDR-CLIC CERN-12-007 [7] K.Bane et al.”A design report of the baseline for PEP-X”, SLAC-PUB-13999, PUB-14785 [8] Y.Cai et al.,”PEP-X, an ultimate storage ring based on 4th order geometric achromats”,SLAC- [9] M.Blaskiewicz,”Fast Head-tail instability with space charge”, PRST-AB 1,044201 (1998) [10] K.Yokoya,”Impedance of slowly tapered structures”,CERN SL/90-88(AP), 1990 [11]Blednykh & Krinsky, “Loss factor of short bunches in azimuthally symmetric tapered struct.” PRST-AB 13,064401(2010) [12]B.Zotter&S.Kheifets,”Impedance and wakes in HE particle accelerators”, World Scientific(98) [13] G.Stupakov, Phys.Rev.E 51,3,(95) 3515 [14] S.Kurennoy, Part. Accel. 39,1,(1992) [15] Dohlus et al.,”Impedance of Collimators in the Euro-XFEL”, TESLA-FEL-2010-04, [16] GdfidL, electromagnetic 3D-solver,Warner Bruns, www.gdfidl.de [17] S.Kurennoy et al.,”Coupling impedance of small discontinuities, a general approach”, Phys.Rev.E Vol.52(4),1995 [18] A.Blednykh,”Beam impedance and Heating for several important NSLS-II components”, Miniworkshop,Diamond Jan.13 [19] M.Klein et al.,”Study of collective beam instabilities for MAX-IV 3GeV-ring”, IPAC13 [20] R.Nagaoka,”Numerical Evaluation of geometric Impedance for Soleil”, EPAC’04, p.2041 [21] R.Nagaoka et al., “Beam Instability Obversations and Analysis at Soleil”, PAC’07 [22] T.F.Guenzel, “The transverse coupling impedance of the storage ring at the ESRF”, PRSTAB,9,114402(2006) Thomas Günzel, III LER

Thank you for your attention ! Thomas Günzel, III LER