SPS Impedance-driven Instability with Space Charge at Q26 · Q26 ResultsforQ20:...
Transcript of SPS Impedance-driven Instability with Space Charge at Q26 · Q26 ResultsforQ20:...
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
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
2 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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)
3 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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)
3 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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)
3 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
4 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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?
5 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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?
5 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
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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)
7 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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)!
8 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
9 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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]
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20
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Verti
cal s
igna
l [ar
b. u
nits
]
Vertical pick-up signal
10 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
]
Vertical pick-up signal
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
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Vertical pick-up signal
11 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Comparing Initial Intrabunch Motion
Intrabunch Motion: N = 3.0×1010ppb
N = 3.0×1010ppb: no space charge
N = 3.0×1010ppb: with space charge
12 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Intrabunch Motion: N = 7.0×1010ppb
N = 7.0×1010ppb: no space charge
N = 7.0×1010ppb: with space charge
B note shift of trace excursion towards bunch tail!=⇒ space charge is indeed possible explanation for this shift!
13 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Intrabunch Motion: N = 1.0×1011ppb
N = 1.0×1011ppb: no space charge
N = 1.0×1011ppb: with space charge
14 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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!
15 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Centroid Movement Comparison
(c) no space charge, N = 3×1010ppb (d) including space charge, N = 7×1010ppb
−→ extracting rise time from centroid motion not straight-forward!
15 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Centroid Movement Comparison
(e) no space charge, N = 3×1010ppb (f) including space charge, N = 1×1011ppb
−→ extracting rise time from centroid motion not straight-forward!
15 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
Rise times at Q ′x, y = 0
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)
16 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
Rise times at Q ′x, y = 0
17 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
18 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Intrabunch Motion: RBBR = 20MΩ/m, No SC
N = 3.0×1010ppb: no space charge
N = 7.0×1010ppb: no space charge
19 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Intrabunch Motion: RBBR = 20MΩ/m, No SC
N = 1.0×1011ppb: no space charge
N = 1.2×1011ppb: no space charge
20 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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
21 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
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?
22 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Q26 RBBR = 10MΩ/m Space Charge: Centroid Evolution
23 of 23 Adrian Oeftiger SPS Q26: TMCI with SC – 9 October 2018
Thank you for your attention!