Impedance and instabilities of low gap chambers · Approaching TME with MBA low D H, a, 1/t rad,...

Impedance and instabilities of low gap chambers

ALERT2019: 3rd Topical Workshop on Advanced Low Emittance Rings Technology 2019 10-12 July 2019, Epirus Palace Hotel, Ioannina, Greece

Ryutaro Nagaoka (Synchrotron SOLEIL)

Content:

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

2. Characteristics of the resultant impedances

3. Concerned collective effects/instabilities and their mitigations

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 also thanks Ahmad Najlaoui (a

trainee student at SOLEIL) and A. Gamelin for their contributions in impedance calculations and

other colleagues at SOLEIL for helpful discussions.

Impedance and instabilities of low gap chambers ALERT2019, Ioannina, Greece, 10-12 July 2019 02/27

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 ultra-low emittance e-ring (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 & NGLRs

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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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.

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


Unshielded flange

Taper: b bmin = 3 mm

BPM

A numerical study of the dependence of Z on vertical half aperture “b”: GdfidL, stepsize: 0.12 – 0.3 mm, sigmaL = 6 mm


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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


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-1 Im( ) [m ]2 /

eff eff

QK l Z

E et

0

0 0

( ) ( )( ) ( ) cos ( ) ( )

/ 2sin

s sQy s y s s

E e

m m

Accurate beam-based local impedance measurement

Using orbit response to a transverse wake-induced kick

Q = Q2 – Q1, y = y2 - y1, y1, y2 : local bumps created with bunches having charges Q1 and Q2

Current-dependence of BPMs minimized by subtracting off the reference orbits y10 and y20 measured with Q1 and Q2 Excellent agreement obtained for transverse

kick factor vs ID gap (V. Smaluk et al., PRSTAB 17,074402 (2014))

Using turn-by-turn BPMs and a pinger

Effective focusing strength Keff created by the transverse wake is measured by fitting the betatron phase distortion

Elaborated applications in modern LSs using advanced BPM electronics

Synchronization of bunches with the pinger pulse shape (M. Carlà et al., PRSTAB 19,121002 (2016))

These methods could also help us evaluate interference effects of wakes experimentally


3. Concerned collective effects/instabilities and their mitigations

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3. 1 Instabilities and collective effects


feedback saturation

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

A melted RF finger (SOLEIL) Melted BPM button in PEP-II

1) Beam-induced heating of vacuum components

… 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

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2) Bunch lengthening

Measured bunch lengthening in the MAXIV 3 GeV ring. The fit to the PWD formula gives |ZL/n|eff = 0.98 W , while 0.1 W was predicted. NEG and IBS contributions have been found non-negligible. (F. Cullinan et al., LER2018, CERN)

Most machines have predominant inductive impedance Zinductive at low frequencies, with which

Longitudinal bunch profile deforms in the so-called PWD regime without changing the p/p profile:

If one is above transition,

a > 0 Zinductive lengthens the bunch

a < 0 Zinductive shortens the bunch

As many LERs are interested in lengthening the bunch, the wake-induced lengthening should rather be beneficial

Impact of PWD on microwave, head-tail, RW must be well understood, especially for LERs that have small a or a < 0 due to antibends

/ /

3

300 0

0

( )2

1( ) ( )

4 cos ( )

effl l

l lrf s

s

ZiI

n

V h e

a

l0, e, s0: Zero current bunch length, energy spread and synchrotron (angular) frequency, I: Bunch current, h: Harmonic number, 0: Revolution (angular) frequency, s: Synchronous phase


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3) 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 = zr

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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5) TMCI, head-tail instabilities

For most LERs, the TMCI threshold is fairly low - Strong detuning of mode 0 due to large Zinductive and Zresistive that couples modes 0 and -1

- Quasi no coupling observed at MAXIV Strong transverse nonlinearity (ADTS) suspected as origin

Shifting of chromaticity x to larger positive values generally increases Ithreshold of head-tail (HT) instability (at the cost of losing the dynamic acceptance in most cases)

Collective beam dynamics at high x and Ibunch is more involved than the classical HT - Post HT theory developed at the ESRF (Ph. Kernel et al., EPAC 2000)

- Recent study in the Fokker-Planck formalism (R. Lindberg, PRAB 19,124402 (2016))

- For a LER with a < 0, the role of x > 0 and x < 0 changes

Investigation of TMCI with no strong coupling observed at MAXIV, (F. Cullinan et al, LER2018, CERN)

m=-1 distribution peaked in L-phase space at where coherent tune equals s

A new type of TMCI discovered in the presence of bunch lengthening cavities (M. Venturini, LER2018, CERN)


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6) 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 = 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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7) 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


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9) Ion-induced instability

Many 2nd generation SLSs (such as PF-KEK, NSLS-VUV ring, SuperACO, Aladin …) suffered from ion-trapping

Ion trapping could induce beam blow-up, beam pulsation, reduction of lifetime, …

Positron operation was considered (SuperACO, PF-KEK, APS, …) to avoid ion trapping

Modern LSs seem to suffer much less from ion trapping, due presumably to improved vacuum pressure and lower emittance

For LERs storing a high intensity and low emittance beam, however, a “single pass” interaction (FBII) between the two beams may become strong enough to jeopardise the performance.

At SOLEIL, FBII arises due to local outgassing produced by beam-induced heating of vacuum components and provokes beam losses

Critical mass calculated for SOLEIL. Left: eH = 4 nm. Right: eH = 200 pm.


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3. 2 Mitigations

1) Minimization of coupling impedance

Some typical examples:

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).

“Zero-impedance” flange developed at SIRIUS (R.M. Seraphim et al., IPAC2015)

Short-circuited flange developed at SOLEIL. The metallic sheet (green) inserted between the two plates effectively shields the cavity-like structure (R. Nagaoka et al., EPAC2004).

Original design (at SOLEIL) created a too large kloss due to trapped modes Button thickness was increased to reduce kloss by a factor of 2, instead of reducing the button diameter (R. Nagaoka et al., EPAC2006)


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2) Bunch-by-bunch feedback

It is one of the most efficient methods in suppressing CM-motion-driven beam instabilities:

- Longitudinal: HOM-driven coupled-bunch

- Transverse: TMCI, head-tail (low-order), RW, HOM-driven coupled-bunch, beam-ion, …

Technology is well established in fast detection of CM, signal processing (processors available on the market), and deflections

Feedback performance appears to be generally satisfactory against RW instability at high current multibunch:

In transverse single bunch, the performance appears to depend much on the nature (regime) of instability More studies required

Experimental/numerical studies made at DIAMOND (E. Koukovini-Platia et al., LER2016)


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3) Chromaticity shifting

5) Beam filling with gaps

Positive effects Negative effects

Damps lower-order head-tail

modes (m = 0, -1, …)

Excites higher-order headtail modes

Reduces dynamic acceptances

Poorer injection rate

Touschek lifetime drops

Promotes Landau damping due to

tune spreads = x(p/p) Loss of CM motions

Reduces of feedback efficiency Increases certain instability

thresholds

(Laclare, J. L. “Bunched Beam Coherent Instabilities”,CERN 87–03)

If a < 0 x < 0 gives head-tail damping

A large enough gap normally clears trapped ions

Division of a bunch train into many short pieces with a certain gap in between suppresses Fast Beam-Ion Instability (FBII) (cf. right figure)

With passive Harmonic Cavities (HC)s, unsymmetrical fills may induce transient beam loading and may not be compatible with bunch lengthening constraints

Simulation studies of FBII (L. Wang et al., PRSTAB 14, 084401 (2011))


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), whether geometric or resistive-wall, their sensitivity to the sources of impedance can only be larger. A big effort required if we want 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

● Bunch lengthening with HHC should in general help ease the above issues via; - Reduction of beam interaction with high frequency impedance - Synchrotron tune spread enhancing Landau damping

● Due to its b-3 dependence As regards the transverse RW impedance, its signifies that its

contribution 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 ● Chambers with better electric conductivity and machine optics with generally reduced average

could compensate the strong RW effect to a certain extent



● Gravity of the enhanced Z would depend on the operation modes (beam filling, total current) and on the desired beam quality Most challenging if high bunch current without bunch lengthening is targeted If e = e0 is to be met, efforts needed to push (Ith)microwave > Iope

● RW and transverse single bunch instabilities are likely to get strongly excited Bunch-by-bunch TFB would be indispensable for machine operation

● Advanced beam instability simulation that can handle Bunch by bunch feedback / Single particle nonlinear dynamics (incoherent tune shifts) / Element-by-element transformation (instead of 1-turn) / Arbitrary beam filling

become important to assure high beam current operation against strong RW effects

(cf. Importance of this kind of simulations already pointed out by APS and IHEP groups studying the swap-out injection of high current bunches) ● 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

● Save specific need, the cross section of a low-gap chamber 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

Impedance and instabilities of low gap chambers · Approaching TME with MBA low D H, a, 1/t rad,...

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