SPS Impedance-driven Instability with Space Charge at Q26 · Q26 ResultsforQ20: TMCIthresholddoesnotchangemuch! only impedance: TMCIbetweenazimuthalmodes-2and-3(radialmode0) impedance

SPS Impedance-driven Instabilitywith Space Charge at Q26

Adrian Oeftiger

CERN – Space Charge Working Group Meeting9 October 2018

Overview

Outline:1 Overview: Past Results for Q20+Q26 Optics2 PyHEADTAIL Simulations for Q26

Continuation of study based on previous presentations:

SC WG meeting 17 August 2017 HSC section meeting 5 March 2018 HSC section meeting 9 April 2018 SC WG meeting 12 June 2018 HSC section meeting 10 September 2018

1 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018

https://indico.cern.ch/event/704695/

https://indico.cern.ch/event/709338/contributions/2913824/attachments/1610293/2557757/oeftiger_TMCI_SPS_SC.pdf




1. Overview:Past Results for Q20+Q26 Optics

SPS Measurements vs. Simulations (Impedance only)

Threshold measurements fit predictions from impedance-only simulations:

Nth ∝|η|εzβy

(1)

figure from H. Bartosik et al., "TMCI thresholds for LHC single bunches in the CERN SPS and comparison with simulations", IPAC 2014


Reminder: Q20 Case

Last space charge working group presentation : treating Q20 case!in general, Q20 higher TMCI threshold than Q26 (η

∣∣Q20 > η

∣∣Q26)

=⇒ synchrotron motion much faster in Q20:Qs

∣∣Q20 ≈ 1/60À 1/300≈Qs

∣∣Q26

−→ space charge parameter q =∆QSC,spreadx ,y /(2Qs ) expresses relative

strength of space charge w.r.t. TMCI

=⇒ relative impact of space charge much lower for Q20:q∣∣Q20 ≈ 5¿ 27≈ q

∣∣Q26

Results for Q20: TMCI threshold does not change much!only impedance:TMCI between azimuthal modes -2 and -3 (radial mode 0)impedance + space charge:TMCI between azimuthal modes 1 and 2 (radial mode 1)



Reminder: Q20 Case


∣∣Q20 > η

∣∣Q26)


∣∣Q20 ≈ 1/60À 1/300≈Qs

∣∣Q26




∣∣Q26




Reminder: Q20 Case


∣∣Q20 > η

∣∣Q26)


∣∣Q20 ≈ 1/60À 1/300≈Qs

∣∣Q26




∣∣Q26




Where are we at?... I

Comparing measurements to wakefield simulations with HEADTAIL:

figure from H. Bartosik et al., "TMCI thresholds for LHC single bunches in the CERN SPS and comparison with simulations", IPAC 2014


Where are we at?... II

Comparing measurements to wakefield simulations with HEADTAIL:−→ Q20 traces indeed look similar, confirmed in PyHEADTAIL

simulations with space charge (see last SC WG presentation):

0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8z [m]

60

40

20

0

20

40

60

BPM

ver

tical

sign

al [a

.u.]

(a) no space charge

0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8z [m]

200150100

500

50100150200

BPM

ver

tical

sign

al [a

.u.]

(b) including space charge

Figure: Q20 PyHEADTAIL simulations

Q26 discussion between Elias Métral and Alexey Burov:−→ measurement trace excursion shifted towards bunch tail−→ impedance-only simulation symmetric about bucket centre=⇒ suspicion: space charge might be missing ingredient?


Where are we at?... II

Comparing measurements to wakefield simulations with HEADTAIL:−→ Q20 traces indeed look similar, confirmed in PyHEADTAIL

simulations with space charge (see last SC WG presentation):

0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8z [m]

60

40

20

0

20

40

60

BPM

ver

tical

sign

al [a

.u.]

(a) no space charge

0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8z [m]

200150100

500

50100150200

BPM

ver

tical

sign

al [a

.u.]

(b) including space charge

Figure: Q20 PyHEADTAIL simulations

Q26 discussion between Elias Métral and Alexey Burov:−→ measurement trace excursion shifted towards bunch tail−→ impedance-only simulation symmetric about bucket centre=⇒ suspicion: space charge might be missing ingredient?


2. PyHEADTAIL Simulations for Q26

SPS Parameters

parameter valueinjection energy p0 = 26GeV

intensity 0<N < 1.25×1011

transverse tunes Qx ,y = (26.13,26.18)chromaticity Q′

x ,y = 0synchrotron tune Qs = 3.24×10−3

momentum compaction αc = 1.92×10−3

bunch length σz = 21cmRF voltage1 VRF = 600kV

longit. emittance1 εz = 0.23eVs

Table: Q26 parameters following Benoit’s thesis, Table B.4

−→ single bunch, linear synchrotron motion−→ no damper, no octupole currents, no dispersion−→ idealised broad-band resonator impedance model (Chao Eq. (2.82)):

Rshunt = 10×106Ω/m, f = 1GHz, Q = 1−→ only kick in vertical plane and only dipolar impedance

1from Qs fixed =⇒ VRF =Q2s 2πp0βc/(ehη) → matched σδ = 1.0×10−3 and not Benoit’s 0.93×10−36 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018

Instability: Complex Tune Shift

0.0 0.2 0.4 0.6 0.8 1.0 1.2Intensity [1e11 ppb]

25

0

25

50

75

100

125

150

175

200

Verti

cal g

rowt

h ra

te [1

/s]

centroid fitemittance fit

Rise times at Q ′x, y = 0

extract tune shift from ⟨y⟩ > 17.5µm and before ∆εx ,y > 500%=⇒ threshold intensity for mode -2/-3 coupling:

Nth > 6.2×1010ppb

(Benoit found Nth > 6.7×1010ppb)−→ emittance fitting OK for mode -2/-3 coupling but not OK for mode

0/-1 coupling+decoupling (20000 turns are not long enough for theemittance to grow exponentially yet)


Set-up PyHEADTAIL with Space Charge

Set-up of space charge with PIC:3×106macro-particlessmooth approximation (constant beta functions around machine)200 space charge kicks along ringsimulate for 20000 turns1 impedance kick per turn with 500 slices2.5D space charge PIC: 100 transverse grids equally distributed over6σz along bunch line charge density to solve free-space Poisson eq.−→ transverse grid size fixed to 10 or 20σx ,y total width (128×128 cells)

3 cross-check with 3D model: same qualitative behaviour with growinginstability towards end of bunch at 9×106macro-particles and 300longitudinal mesh points (2.5D PIC resolution ×3)!


Intensity Scan: Gaussian Tune Spread

scale emittances with intensity εx ,y ∝N=⇒ fixed maximum Gaussian tune spread due to direct space charge

∆QSCx ,y

∣∣∣z=0 = 0.175

0.0 0.5 1.0 1.5 2.0 2.5intensity N [1011 ppb]

0.08

0.10

0.12

0.14

0.16

0.18

QSC

LIU nominalN = 2.57 × 1011

horizontal (x)vertical (y)

54.04

54.06

54.08

54.10

54.12

QSC

/Qs

Initial (6D-Gaussian) directspace charge tune spread

∆QSCx ,y = rpN

(2π)3/2β2γ3σz×∮

dsβx ,y (s)

σx ,y (s) (σx (s)+σy (s))

σx ,y =√βx ,y εx ,y

βγ


Results with Space Chargebelow “no-SC” Threshold

TMCI Threshold: With Space Charge

N = 2.0×1010ppb: instability?

0.6 0.4 0.2 0.0 0.2 0.4 0.6Position [m]

3

2

1

0

1

2

Verti

cal s

igna

l [ar

b. u

nits

]

Vertical pick-up signal

N = 3.0×1010ppb: unstable...

0.6 0.4 0.2 0.0 0.2 0.4 0.6Position [m]

30

20

10

0

10

20

30

Verti

cal s

igna

l [ar

b. u

nits

]



TMCI Threshold: No Space Charge

N = 2.0×1010ppb: stable!

0.6 0.4 0.2 0.0 0.2 0.4 0.6Position [m]

0.2

0.0

0.2

0.4

Verti

cal s

igna

l [ar

b. u

nits

]


N = 3.0×1010ppb: stable!

0.6 0.4 0.2 0.0 0.2 0.4 0.6Position [m]

0.4

0.2

0.0

0.2

0.4

Verti

cal s

igna

l [ar

b. u

nits

]



Comparing Initial Intrabunch Motion

Intrabunch Motion: N = 3.0×1010ppb

N = 3.0×1010ppb: no space charge

N = 3.0×1010ppb: with space charge





B note shift of trace excursion towards bunch tail!=⇒ space charge is indeed possible explanation for this shift!






Centroid Movement Comparison

(a) no space charge, N = 3×1010ppb (b) including space charge, N = 3×1010ppb

−→ extracting rise time from centroid motion not straight-forward!



(c) no space charge, N = 3×1010ppb (d) including space charge, N = 7×1010ppb




(e) no space charge, N = 3×1010ppb (f) including space charge, N = 1×1011ppb



Summary for RBBR = 10MΩ/m

Instability: Complex Tune Shift with Space Charge

0.0 0.2 0.4 0.6 0.8 1.0 1.2Intensity [1e11 ppb]

0

25

50

75

100

125

150

175

200

Grow

th ra

te [1

/s]

HorizontalVertical


extract tune shift from εy > 1.01εy∣∣initial

B when emittance changes, space charge conditions change!...−→ also, emittance did not grow (yet) for low intensities?real tune shift remains around shifted mode 0 in first 400 turns(frequency analysis with Sussix)


Instability: Complex Tune Shift WITHOUT Space Charge

0.0 0.2 0.4 0.6 0.8 1.0 1.2Intensity [1e11 ppb]

25

0

25

50

75

100

125

150

175

200

Grow

th ra

te [1

/s]

HorizontalVertical



RBBR = 20MΩ/mNo Space Charge

Comparison to Giovanni Rumolo’s HEADTAIL Simulations

Cross-check with previous HEADTAIL simulations2 by Giovanni Rumolo:

(a) PyHEADTAIL (b) HEADTAIL (GiovanniR)

−→ shift of coherent motion towards bunch tail observed also forno-space-charge case but higher shunt impedance!

=⇒ space charge not the only explanation for this shift!

2differences: σz = 0.2m smaller by 5%, σδ = 0.93 smaller by 7%, Dx = 1.2m (noneconsidered in PyHEADTAIL), approx. exchanging tunes: Qx = 26.185 and Qy = 26.13


Intrabunch Motion: RBBR = 20MΩ/m, No SC




Intrabunch Motion: RBBR = 20MΩ/m, No SC




Centroid Movement Comparison: RBBR = 20MΩ/m, No SC

(a) no space charge, N = 3×1010ppb (b) no space charge, N = 7×1010ppb

(c) no space charge, N = 1×1011ppb (d) no space charge, N = 1.2×1011ppb


Summary & Conclusion

We found that...Q20 shows a minor change when including space charge in thesimulation model (relatively weak, q = 5)−→ qualitatively compatible with observations in real machineQ26 shows a qualitatively different behaviour when including spacecharge (stronger, q = 27):

additional instability below no-SC TMCI threshold with space charge!(i.) space charge as well as (ii.) higher broad-band shunt impedanceboth lead to trace excursion shift towards bunch tail

Open questions:What is this Q26 SC below-TMCI instability?Possible criterion to distuingish space charge impact from impedanceonly, observable in experiment?


Q26 RBBR = 10MΩ/m Space Charge: Centroid Evolution


Thank you for your attention!

Documents

SPS Impedance-driven Instability with Space Charge at Q26 · Q26 ResultsforQ20: TMCIthresholddoesnotchangemuch! only impedance: TMCIbetweenazimuthalmodes-2and-3(radialmode0) impedance