International Task Force Joint Meeting: Discussion on
TMCI and impedance matters
M. Migliorati
on behalf of the TMCI sub-group of the SuperKEKB International TaskForceTMCI sub-group core members• Contact person: Mauro Migliorati (SAPIENZA - Università di Roma)• Sub-contact person: Takuya Ishibashi (KEK, vacuum system incl.
collimator)• Kazuhito Ohmi (KEK, beam dynamics)• Demin Zhou (KEK, beam dynamics)• Shinji Terui (KEK, vacuum system incl. collimator)
A first meeting has been held on 27/8/2021 with the following presentations:• Introduction of TMCI members, collimators, tune shift and instability
measurements - Speaker: Takuya ISHIBASHI (KEK ACCL)• Impedance and wakefield model - Speaker: Demin ZHOU (KEK ACCL)• TMCI and localized impedance - Speaker: Kazuhito OHMI (KEK ACCL)The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 2

TMCI sub-group people
Mailing list of the group to share and discuss topics about TMCI:
skb-itf-tmci@ml.post.kek.jp
To join the TMCI sub-group, send an email to takuya.ishibashi@kek.jp.
Members of the mailing list (27/8/2021)
Kazuro Furukawa (KEK)
Makoto Tobiyama (KEK)
Mauro Migliorati (University of Rome/INFN)
Mika Maszawa (KEK)
Rogelio Tomas (CERN)
Tadashi Koseki (KEK)
Takuya Ishibashi (KEK)
Tor Raubenheimer (SLAC/Stanford University)
Yusuke Suetsugu (KEK)The 25th KEKB Accelerator Review
Committee

Emanuela Carideo (CERN PhD)
Nicolas Mounet (CERN)
Demin Zhou (KEK)
Kazuhito Ohmi (KEK)
Mikhail Zobov (INFN – LNF)
Shinji Terui (KEK)
Hiroyuki Nakayama (KEK)
Frank Zimmerman (CERN)
Yoshihiro Funakoshi (KEK)
Katsunobu Oide (KEK)02/09/2021

Pag. 3

Goals of the TMCI sub-group• Understand the observed transverse blow-up under different machineconditions• Build a machine impedance model able to reproduce the instability• Find some solutions to mitigate the instability
There could be three main activities:
1) Machine studies2) Impedance model and simulations
3) Theoretical activity
For each of these activities we need to identify a person in charge andmanpower.
Of course interactions with the other subgroups are fundamental.
Some people are and can be involved in the other subgroups.
The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 4

TMCI: theory• The Vlasov equation describes the collective behaviour of amultiparticle system under the influence of electromagnetic forces.

The steps to study the Vlasov equation in case of instability are generally
the following:1) Use a perturbation method:2) Introduce the transverse force induced by the wakefields
3) Expand the perturbation as sum of coherent modes of oscillations
The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 5TMCI: theory
The characteristics of the transverse coherent modes are the following:• the bunch is supposed to have only a dipole moment in thetransverse plane• This dipole moment is not constant longitudinally. Depending on thelongitudinal mode number , its longitudinal structure may be simple
or complicatedFrom A. Chao book
m=0

m=1

m=2

• The modes are called transverse modes, but
the transverse structure is a pure dipole and themain task is to find their longitudinal structure• the Vlasov equation needs to take into accountboth the transverse and the longitudinal phasespaces. Fortunately, however, the transverse
structure of the beam is simple

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 6TMCI: theory
4. There are several methods to solve the Vlasov equation.
5. In general an infinite set of linear equations is obtained. Theeigenvalues represent the coherent frequencies and theeigenvectors the corresponding modes.
6. The eigenvalue system is of the kind

The matrix elements depend also on chromaticity. When this is zero, theonly instability for low intensity beams is due to high Q resonators. If thechromaticity is different from zero, single azimuthal modes can beunstable (differently from the longitudinal case). This instability is called
head-tail instability. This is not an intensity threshold mechanism and canoccur even at low intensity.
The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 7

TMCI: example at high intensity• At high intensity we need to solve the eigenvalue system andcoupling between different azimuthal modes can occur
Frequencies
of somecoherent
oscillation
modes
obtained with
PyHEADTAIL
tracking codeby performing
the FFT ofover all themacroparticles
Mitigation of Coherent Beam Instabilities inparticle accelerators

23/09/2019

Pag. 8TMCI: example at high intensity• At high intensity we need to solve the eigenvalue system andcoupling between different azimuthal modes can occur
Blackpoints: E.
Métral,GALACTIC
Vlasovsolver
NB: in the past
MOSES codefrom Y. H. Chinand, more
recently, theNHT from A.
Burov andDELPHI fromN. Mounet are often used.
Mitigation of Coherent Beam Instabilities inparticle accelerators

23/09/2019

Pag. 9Observations and some results of the studies
related to TMCI
Instability threshold

S. Terui: Particle Accelerator Society Japan

Verticaltune shift

With a slope of 0.0089/mA, a tune shift ofthe order of half the synchrotron tune() is reached with a currentof about 1.24 mA.
From direct observations, the beam size
blow-up is in the order of ~0.9 mA(depending on the betatron tune,chromaticity, …)

slope ∼ 0.0089/mA
The 25th KEKB Accelerator Review
Committee

The tune shift value gives a larger
threshold than blow-up observations. The
instability doesn’t seem to be due to acoupling of modes 0 and -1.
02/09/2021

Pag. 10Observations and some results of the studies
related to TMCI
Possible explanations on discrepancy:• Localized impedance• Missing impedance sources• Effect of longitudinal impedance which modifies synchrotron tune (potential
well distortion and/or microwave)• Other effects (extension of TMCI, as: detuning impedance, nonlinear
chromaticity, synchro-betatron resonances and x-y coupling, space charge,…)• A combination of the above effects?

The 25th KEKB Accelerator ReviewCommittee

02/09/2021

Pag. 11

Observations and some results of the studies
related to TMCIThe beam dynamics is quite complicated. Chromaticity (and tune) dependence(from S. Terui):• When the vertical tune is 0.56, the current threshold (determined by a beam
size blow-up) does not change with chromaticity• When the vertical tune is > 0.6, the current threshold increases withchromaticity (1.4 4.4). But injection efficiency is sometimes reduced• When the vertical tune is 0.59, the current threshold increases (0.9 1.0mA) with chromaticity (1.4 4.4) and bunch by bunch feedback gain is +12
dB. But background noise in Belle2 increases• When the vertical tune is 0.59, the current threshold increases(0.9 1.12mA) when the vertical chromaticity is negative (-0.4) and bunch by bunch
feedback gain is +12 dB
The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 12

Some results on collective effects and tune shift
The work on impedance model for KEKB and SuperKEKB was done by D.
Zhou together with colleagues of hardware and collimation groups.
The longitudinal impedance budget was constructed with design configurations.
D. Zhou et al., Impedance calculation and simulation of microwave instability for themain rings of SuperKEKB, in Proceedings of IPAC'14, Dresden, Germany
Total longitudinal wake of 0.5 mm Gaussian bunch

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 13

Some results on collective effects and tune shift
With PyHEADTAIL we started some simulations of collective effects by using
the machine impedance model for both the longitudinal and transverse cases.
The longitudinal case was simulated to check if the code was in agreement withstudies performed by D. Zhou. Some differences in the microwave threshold
are due to the way of treating the CSR.

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 14

Some results on collective effects and tune shift
Transverse case: wakefield model (D. Zhou)
Short-bunch (0.5mm) wakefield of allcomponents in 2016 (Phase-1 ofSuperKEKB commissioning).
Some limitations:This is simply a sum of all wakes together.
No weighting over beta functions was done.
The model is old and can be far from thecurrent machine condition. The maindifference is from collimators, which arebelieved to be the main sources of theTMCI threshold.
In this model the dipolar and quadrupolar
wakes were not separated.
The new impedance model is underdevelopment.
The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 15

Some results on collective effects and tune shift
By multiplying by 16 the transverse wakefield, tune shift and TMCI thresholdobtained by PyHEADTAIL are the following (The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 16

Some results on collective effects and tune shift
Effect of longitudinal wake on transverse one (The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 17

Some results on collective effects and tune shift
Effect of longitudinal wake on transverse one: case of FCC-ee

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 18

Some results on collective effects and tune shift
Question of localized impedance

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 19

Some results on collective effects and tune shift
Effect of localized impedance. Same wake and input but

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 20

Some results on collective effects and tune shift
Effect of localized impedance. Same wake and input but

0.8 mAThe 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 21

TMCI in other machines
EPAC 98

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 22

TMCI in other machines
EPAC 98

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 23

TMCI in other machines

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 24

TMCI in other machines
The new synchrotrons can be limited by TMCI due to their small vacuum chambersize.
This is mainly for the regimes with small number of bunches and high intensity. In
the multi-bunch regimes, generally, this is not a problem (low charge).
In most cases the chromaticity helps to increase the TMCI threshold but ...
Y. H. Chin, A. W. Chao, M. M. Blaskiewicz, Y. Shobuda, Phys Rev AB 20, 071003(2017)The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 25

TMCI in other machines

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 26

Actions and Countermeasures• Develop an impedance model able to reproduce the observations• Machine studies: betatron tune scan, chromaticity, etc.
• Increase/change of synchrotron frequency (for both TMCI and localizedimpedance)• Decrease the beta function at the collimators’ position, …
• Nonlinear tapering of collimators (see, e. g.
https://accelconf.web.cern.ch/p07/PAPERS/WEOAC04.PDF). Some issues
could remain, in particular due to the reliability of accuracy ofelectromagnetic codes with very small gaps

The 25th KEKB Accelerator Review
Committee

02/09/2021

Pag. 27

Actions and Countermeasures• Develop an impedance model able to reproduce the observations• Machine studies: betatron tune scan, chromaticity, etc.
• Increase/change of synchrotron frequency (for both TMCI and localizedimpedance)• Decrease the beta function at the collimators’ position, …
• Nonlinear tapering of collimators (see, e. g.
https://accelconf.web.cern.ch/p07/PAPERS/WEOAC04.PDF). Some issues
could remain, in particular due to the reliability of accuracy ofelectromagnetic codes with very small gaps

The 25th KEKB Accelerator ReviewCommittee

02/09/2021

Pag. 28