Design Optimization and Impedance Sources in Low Emittance ... · Approaching TME with MBA low D H,...

Design Optimization and Impedance Sources in Low Emittance Rings

MCBI2019: ICFA mini-Workshop on Mitigation of Coherent Beam Instabilities in Particle Accelerators

23-27 September 2019, Zermatt, Switzerland Ryutaro Nagaoka (Synchrotron SOLEIL)

Content:

1. Global trend today to go for much lower gap chambers

2. Characteristics of the resultant impedances

3. Concerned collective effects and instabilities

4. Summary

Acknowledgement :

RN thanks M. Aiba (SLS), R. Bartolini (DIAMOND), M. Borland (APS), F. Cullinan (MAXIV), E.

Karantzoulis (ELETTRA), V. Smaluk (NSLS-II), M. Venturini (ALS), S. White (ESRF), H. Xu (IHEP) for

providing him with information on their (future) machines. He thanks A. Gamelin and other

colleagues at SOLEIL for helpful discussions.

Design optimization and impedance sources in low-emittance rings MCBI2019, Zermatt, Switzerland, 23-27 September 2019 02/20

1. Introduction: Why the trend today to go for low-gap chambers?

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Figure of merit and target performance of ring-based light sources:

I : Beam current, eu : Transverse emittance

2 2

0.1% x y

Photons IBrilliance

Second mrad mm BW e e

Diffraction limited electron emittance (and transversally coherent photon beam) over the main photon energy range of interest

Inversely proportional to the product of e-beam transverse emittances Linearly proportional to the e-beam intensity

We want ultra-low emittance & high e-beam intensity

Basic principle used to achieve ultra-low emittance:

MBA (Multiple Bend Achromat) instead of DBA, TBA

N: Number of bending magnets per cell

3 1 /Theoretical

H MinimumNe

Blue: Existing LSs Red: Recent & future rings

2 7


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What are the general consequences of the employed strategy on the design aspects of modern and future low-emittance rings (LERs)?

Need to approach the TME (Theoretical Minimal Emittance) condition in every dipoles

Strong quadrupole focusing everywhere (in the range of 100 T/m instead of ~20 T/m in the present generation)

Reduced magnet bore radii Smaller beam pipe half aperture b

Poorer vacuum conductance NEG coating in a large part of the ring

(D. Robin, LER2016, SOLEIL)

For ESRF-EBS, the imposed 11mm pole to pole distance for all magnets optimized for handling the synchrotron radiation

(from P. Raimondi, LER2016, Oct. 2016)


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MBA generally requires the magnet lattice to be tightly packed with dipoles, quadrupoles, sextupoles and plus all other standard elements such as flanges, BPMs, …

Chain of consequences and tendencies on e-beam dynamics: Approaching TME with MBA low DH, a, 1/trad, large natural chromaticities, … Strong sextupoles Small DA On-axis injection, Swap-out

Ultra-low emittance Significant IBS, Touschek effects Bunch lengthening with Harmonic Cavities (HCs)

Likely impact on collective effects: Enhanced impedance Z due to smaller b’s and to NEG coating (to be addressed again later)

Longer radiation damping times

Contribution of HC potential, transient beam loading effect

Comparison between ESRF and ESRF-EBS, (M. Hahn, 3ème Rencontres Nationales du Réseau Technologies du Vide, Oct. 2016)


E [GeV] b [mm] crossection remarks b [mm] crossection remarks b [mm] crossection remarks

ALS-U 2 6.5 circular Strongly focusing sections 10 circular Outer arc sections

APS-U 6 11 circular Hybrid of NEG coated Cu, Cu plated SS

with NEG strips, bare Al 3 × 8 non-circular Al chambers, 125 m in total 3 circular Al chambers, 50 m in total

DIAMOND-II 3.5 10 circular Thickness 1 mm, Chamber design at

early stage

ELETTRA-II 2 - 2.4 11 circular Cu and SS in some parts 4.5 × 20 non-circular Al NEG coated (4 and 5 m long) 3 IVU × 3 (4 m); Wiggler×2 with b = 5

mm (1.5 m) Al + NEG

ESRF-EBS 6 10 In moderate focusing sections 6.5 In strongly focusing sections 4 Straight sections

HEPS 6 11 circular Standard chambers 2.5 non-circular CPMU chamber ~4 non-circular IAU chamber

MAXIV 3 GeV 3 11 circular copper, NEG coated 4 × 18 non-circular Aluminium, EPU chambers,

NEG coated, 4 m long 2 non-circular IVUs and wiggler 2.1 m long

MAXIV 1.5 GeV 1.5 11 × 20 elliptical SS 11 × 29 non-circular SS, Arc sections 4 × 18 (or 4

× 28.5) non-circular

EPU chambers, NEG coated, 3.2 m long

NSLS-II 3 12.5 × 38 non-circular 2.5 - 3.5 non-circular IVU × 10 6.0 - 8.0 non-circular EPU × 7; DW × 3 have b = 7.5 mm

SLS-II 2.4 9 circular Design at early stage (cf. A.

Zandonella's talk)

SOLEIL-U 2.75 5 to 8? circular? Likely be NEG coated

● Vacuum chamber aperture and some other characteristics for several recently constructed and future rings

Principal vertical half aperture b adopted in several existing and future light sources

versus their machine energies


2. Characteristics of the resultant impedances

Images taken from Alex Chao textbook

Both geometric and resistive-wall impedances grow larger for smaller vacuum chamber apertures

General dependence of Z on the chamber (half) aperture b:

- Longitudinal impedance (roughly) b-1 + higher

- Transverse geometric impedance (roughly) b-2 + higher

- Transverse RW impedance b-3

cf) Impedance of a hole on the chamber: (S. Kurennoy, EPAC94)

/ / 0 02 2 2 4

( ) ( )( ) , ( ) cos( )

4

m e m eh h bZ iZ Z iZ a

c b b

a a a a

General contributors: - Tapers, BPMs, shielded bellows, flanges, cavities, kickers,

absorbers, scrapers, resistive-wall (RW), …

Standard infinite thick RW model for a circular chamber cross section (rr: electric resistivity)

Extensions made to - Finite thickness wall - Multilayers - Short-range (high frequencies) - Non-circular cross section


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Evaluation and optimization of geometric impedances:

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(Above) Malfunctioning of button electrodes encountered at SOLEIL are likely caused by beam heating due to the trapped mode at ~8 GHz

(Right) RF Shielding foil helped drastically to suppress the flange impedance. However, its possible mis-positioning at interventions may cause serious heating

Bell-shaped BPM button developed at SIRIUS, optimized to increase the button cut-off frequency without losing the button sensitivity (A.R.D Rodrigues et al., IPAC2015).

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Impedance of NEG coated chambers: For low-emittance rings that require low-gap chambers, NEG is very helpful for vacuum pumping Successfully applied to ESRF, ELETTRA, SOLEIL, MAXIV, …

However, characteristics of ZNEG and its impact on beam must be well understood Early studies indicated that ~1 mm thick NEG coating has an effect; (R. Nagaoka, EPAC 2004, Lucerne)

(ReZ)NEG (ReZ)substrate, (ImZ)NEG 2(ImZ)substrate

in the frequency range below ~20 GHz, when the resistivity rNEG > rsubstrate

Instability thresholds would not be directly affected by NEG

- Bunch lengthening, coherent and incoherent tune shifts may be enhanced

- Measurement made at ELETTRA and SOLEIL are in (qualitative) agreement with theory


Experimental study of NEG electric conductivity versus frequency (E. Koukovivi-Platia et al., PRAB 20,011002 (2017))

“columnar”

“dense”

Experimental study of surface resistivity of two types of NEG (O. B. Malyshev et al., NIM A844 (2017) 99–107)

Detuning by ~2 observed at ELETTRA for a NEG-coated chamber as compared with those w/o coating. (E. Karantzoulis, V. Smaluk, L. Tosi, PRSTAB 6, 030703 (2003))

Surface roughness impedance :

Correlated bumps in the small angle approximation + measurement (G. Stupakov et al., PRSTA 2, 060701)

Measured surface roughness of a NEG coated Al chamber at SOLEIL (M. Thomasset, Optics group)

at low frequencies k << 1/h (h: Height of uncorrelated bumps)

Uncorrelated bump model is considered to largely overestimate the true roughness impedance (K.L.F. Bane, EPAC2004, Lucerne)

3

// 0

2

( )

4

Z k Z hi

k b


Metallic coated ceramic chambers:

Heating of ceramic chambers has rather frequently been reported (MAXIV, NSLS-II, …)

EM field matching with different metallic layers can be extended to include dielectric materials (e.g. R. Nagaoka, EPAC2006, Edinburgh)

Thickness of metallic coating

Image current flow in the metallic coating of the ceramic chamber

Horizontal distribution of power

density on the flat chamber wall


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Impedance budget obtained for (the future machine) SIRIUS (left: longitudinal, right: transverse) (F.-E. De Sá, LER2016)

Numerical evaluation of Zs / Construction of Z- budget:

- Using 3D EM solvers (CST microwave studio, GdfidL, ECHO3D, …)

- Analytical methods for resistive-wall and di-electric (ceramic) chambers

- Multi-layer RW (non-circular) chambers ImpedanceWake2D (IW2D) developed at CERN

ex) Impedance budget evaluated for SIRIUS:

- Dominance of RW impedance (as compared to older machines)

- ImZ > 2ReZ in practically the entire range due to NEG coating

- Machine is inductive (as always) at low frequencies


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Discrepancies found between calculated and measured impedance in different machines and investigations on their origins (V. Smaluk, NIM A888 (2018) 22–30)

Comparison of (ZL//n)eff and (ImZy)eff made over some 15 rings (LSs and colliders)

Though some agree to 20-30%, the majority have more than 100% of discrepancies

To pursue the possible origins of discrepancies, the following three possibilities were numerically studied with simple pillbox cavities (using ECHO):

1) Interference of wake fields, 2) Computation mesh size, 3) Impedance bandwidth

Results indicate that while the mesh size and impedance bandwidth influence by typically less than 10%, the interference causes more than 100% of variations

Interferences are likely to be enhanced for LERs as both b and the spacing between objects get furthermore reduced

Comparison of (ZL//n)eff Numerical evaluation of a single and double pillbox cavities

Deviation from the sum of two cavities


3. Concerned collective effects and instabilities

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feedback saturation

Measured beam loss at 500 mA White: Beam, Red: TFB kick

A melted RF finger (SOLEIL)

… Probably the most concerned collective effect for LERs with low-gap chambers, as a single component can seriously damage the machine operation

- FBII (Fast Beam-Ion Instability) that blocks from operating the ring in ¾ filling at 500 mA at SOLEIL is considered to be due to beam-induced heating of (some unknown) vacuum components

- Loss factors and trapped modes must be carefully studied from the geometric and metallic coating impedance of each vacuum component, and the results need be evaluated in terms of “heat (temperature)” involving drafting office engineers


● Beam-induced heating pf vacuum components

● Transverse single bunch instabilities (TMCI, head-tail and post-head-tail)

Transition from headtail to post-headtail observed at the ESRF (Ph. Kernel et al., EPAC2000)

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● Microwave and CSR instabilities

- Microwave instability is a longitudinal single bunch instability involving both energy spread widening and bunch lengthening (without beam losses)

- (High frequency) ReZ// is considered responsible, which could either be Zmachine and/or ZCSR

- The instability must be avoided in rings that make use of higher harmonics of undulator spectra

- For future low-emittance rings employing MBA lattice in which shielding effectively works better (bending radius r larger & vertical aperture h smaller), the CSR instability should not be a big concern (P = szr

1/2/h1/2)

- However, enhanced Zmachine due to reduced b and NEG coating would necessitate careful studies of microwave instability beforehand

Measured microwave threshold at the ESRF Degradation of undulator higher-harmonic spectra with beam energy spread widening (H. Abualrob et al., IPAC 2012)


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● Resistive-wall (RW) instability

Studies of stabilizing effect of HC lengthening on RW instability

- A transverse multibunch instability driven essentially by ZRW due to the long-range nature of ZRW

- As the chamber aperture b tends to diminish for LERs and ZRW b-3, most LERs are seriously

impacted by this instability (Ithreshold usually very low at x = 0)

- Thanks to the HT damping induced by ZBBR, the instability (driven by lower-order HT modes) may

be damped by shifting x to positive

- Bunch-by-bunch feedback generally works well in suppressing the instability

- Bunch lengthening by HCs also appears effective in stabilizing the instability Studies ongoing

to clarify the physical mechanisms

(F. Cullinan et al., PRAB 19, 124401 (2016))

Evolution of m = 0 spectrum from single-peaked to double-peaked as x is increased


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● Resistive-wall (RW) instability (cont’d)

- Analysis with a linearised Vlasov equation solver in the case of SOLEIL:

Dependence on: ZRW, ZBB and f = 2b (chamber inner diameter)

Only with ZRW

Necessity to carry out more detailed studies including among others;

- ZBB

- Bunch-by-bunch transverse feedback - Local optics variation - Optics nonlinearity - HHC lengthening (if used)


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● Incoherent tune shifts due to non-circular RW chambers

(P. Brunelle et al., PRAB 19,044401 (2016))

- Non-circular (flat) chambers induce quadrupole wakes

- Introduce non-negligible current-dependent optics distortions

- Studies at SOLEIL indicate that the betatron tune shifts in an intense bunch of 20 mA get nearly 20 times larger than in multibunch at 500 mA

- NEG coating likely enhances tune shifts


4. Summary

● A clear trend that future LERs adopt vacuum chambers with significantly reduced aperture b

● As the wakefields scale as b-n (n 1), their sensitivity to the sources of impedance can only be larger A big effort needed to keep the machine impedance on the same level as before

● Innovative vacuum components designs, including coating technology, needed in collaboration with machine physicists to keep machine heating and beam instability under control

● Special efforts required to; - avoid heating due to ceramic chambers and trapped modes - develop means to cleverly evacuate generated heat without damaging vacuum components

● Due to its b-3 dependence, the contribution of the transverse RW impedance to the total

impedance budget shall be dominating

e.g. SOLEIL case: If bstandard = 12.5 mm 5 mm, ZRW shall be (12.5/5)3 = 15.6 times larger ● NEG coating would non-negligibly enhance Z, but its impact should be appear via ImZ (i.e.

bunch lengthening, coherent tune shifts, …) as long as the beam is only sensitive to Zlow_frequency

● The cross section of low-gap chambers better be round to avoid quadrupolar wakes that may

spoil the ultra low-emittance tuning especially for high intensity bunches ● Due to low gaps and to proximity of vacuum components in future rings, the possibility of

wakes interference may be carefully looked at


Design Optimization and Impedance Sources in Low Emittance ... · Approaching TME with MBA low D H,...

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