Beam loading and coupled-bunch instabilities from a large ring perspective D. Teytelman Dimtel, Inc., San Jose, CA, USA CEPC Workshop 2017 (Dimtel) Beam loading and instabilities November 7, 2017 1 / 24
Beam loading and coupled-bunch instabilities froma large ring perspective
D. Teytelman
Dimtel, Inc., San Jose, CA, USA
CEPC Workshop 2017
(Dimtel) Beam loading and instabilities November 7, 2017 1 / 24
Outline
1 IntroductionThe focus of this talk
2 Instabilities, Beam Loading, FeedbackRing Circumference and Coupled-Bunch InstabilitiesBeam Loading in Storage RingsBunch-by-bunch Feedback
3 Beam Loading in CEPC-ZFCC-Z Nominal ParametersPushing FCC-Z Current
(Dimtel) Beam loading and instabilities November 7, 2017 2 / 24
Outline
1 IntroductionThe focus of this talk
2 Instabilities, Beam Loading, FeedbackRing Circumference and Coupled-Bunch InstabilitiesBeam Loading in Storage RingsBunch-by-bunch Feedback
3 Beam Loading in CEPC-ZFCC-Z Nominal ParametersPushing FCC-Z Current
(Dimtel) Beam loading and instabilities November 7, 2017 3 / 24
Coupled-bunch Instabilities and Beam Loading
This talk will focus on two important effects in storage rings:I Coupled-bunch instabilities in transverse and longitudinal planes;I Transient beam loading due to non-uniform fill patterns.
Instabilities:I Beam interacts with impedances at betatron or synchrotron
sidebands of revolution harmonicsI Transverse: MωRF ± Nωrev ± ωβ
I Longitudinal: MωRF ± Nωrev ± ωs
Transient beam loading:I Driven by impedances at revolution harmonics MωRF ± Nωrev.
(Dimtel) Beam loading and instabilities November 7, 2017 4 / 24
Coupled-bunch Instabilities and Beam Loading
This talk will focus on two important effects in storage rings:I Coupled-bunch instabilities in transverse and longitudinal planes;I Transient beam loading due to non-uniform fill patterns.
Instabilities:I Beam interacts with impedances at betatron or synchrotron
sidebands of revolution harmonicsI Transverse: MωRF ± Nωrev ± ωβ
I Longitudinal: MωRF ± Nωrev ± ωs
Transient beam loading:I Driven by impedances at revolution harmonics MωRF ± Nωrev.
(Dimtel) Beam loading and instabilities November 7, 2017 4 / 24
Coupled-bunch Instabilities and Beam Loading
This talk will focus on two important effects in storage rings:I Coupled-bunch instabilities in transverse and longitudinal planes;I Transient beam loading due to non-uniform fill patterns.
Instabilities:I Beam interacts with impedances at betatron or synchrotron
sidebands of revolution harmonicsI Transverse: MωRF ± Nωrev ± ωβ
I Longitudinal: MωRF ± Nωrev ± ωs
Transient beam loading:I Driven by impedances at revolution harmonics MωRF ± Nωrev.
(Dimtel) Beam loading and instabilities November 7, 2017 4 / 24
Coupled-bunch Instabilities and Beam Loading
This talk will focus on two important effects in storage rings:I Coupled-bunch instabilities in transverse and longitudinal planes;I Transient beam loading due to non-uniform fill patterns.
Instabilities:I Beam interacts with impedances at betatron or synchrotron
sidebands of revolution harmonicsI Transverse: MωRF ± Nωrev ± ωβ
I Longitudinal: MωRF ± Nωrev ± ωs
Transient beam loading:I Driven by impedances at revolution harmonics MωRF ± Nωrev.
(Dimtel) Beam loading and instabilities November 7, 2017 4 / 24
Coupled-bunch Instabilities and Beam Loading
This talk will focus on two important effects in storage rings:I Coupled-bunch instabilities in transverse and longitudinal planes;I Transient beam loading due to non-uniform fill patterns.
Instabilities:I Beam interacts with impedances at betatron or synchrotron
sidebands of revolution harmonicsI Transverse: MωRF ± Nωrev ± ωβ
I Longitudinal: MωRF ± Nωrev ± ωs
Transient beam loading:I Driven by impedances at revolution harmonics MωRF ± Nωrev.
(Dimtel) Beam loading and instabilities November 7, 2017 4 / 24
Outline
1 IntroductionThe focus of this talk
2 Instabilities, Beam Loading, FeedbackRing Circumference and Coupled-Bunch InstabilitiesBeam Loading in Storage RingsBunch-by-bunch Feedback
3 Beam Loading in CEPC-ZFCC-Z Nominal ParametersPushing FCC-Z Current
(Dimtel) Beam loading and instabilities November 7, 2017 5 / 24
Resonant Modes and Revolution Harmonics
−400 −300 −200 −100 0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (kHz)
Imp
ed
an
ce
(a
rb.
un
its)
A 20 kHz resonance ideally“hidden” between two revolutionharmonics.1 km ring;1.5 km ring;3 km ring;10 km ring;100 km ring;In large rings narrow resonancescannot be “hidden” from thebeam.
(Dimtel) Beam loading and instabilities November 7, 2017 6 / 24
Resonant Modes and Revolution Harmonics
−400 −300 −200 −100 0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (kHz)
Imp
ed
an
ce
(a
rb.
un
its)
A 20 kHz resonance ideally“hidden” between two revolutionharmonics.1 km ring;1.5 km ring;3 km ring;10 km ring;100 km ring;In large rings narrow resonancescannot be “hidden” from thebeam.
(Dimtel) Beam loading and instabilities November 7, 2017 6 / 24
Resonant Modes and Revolution Harmonics
−400 −300 −200 −100 0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (kHz)
Imp
ed
an
ce
(a
rb.
un
its)
A 20 kHz resonance ideally“hidden” between two revolutionharmonics.1 km ring;1.5 km ring;3 km ring;10 km ring;100 km ring;In large rings narrow resonancescannot be “hidden” from thebeam.
(Dimtel) Beam loading and instabilities November 7, 2017 6 / 24
Resonant Modes and Revolution Harmonics
−400 −300 −200 −100 0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (kHz)
Imp
ed
an
ce
(a
rb.
un
its)
A 20 kHz resonance ideally“hidden” between two revolutionharmonics.1 km ring;1.5 km ring;3 km ring;10 km ring;100 km ring;In large rings narrow resonancescannot be “hidden” from thebeam.
(Dimtel) Beam loading and instabilities November 7, 2017 6 / 24
Resonant Modes and Revolution Harmonics
−400 −300 −200 −100 0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (kHz)
Imp
ed
an
ce
(a
rb.
un
its)
A 20 kHz resonance ideally“hidden” between two revolutionharmonics.1 km ring;1.5 km ring;3 km ring;10 km ring;100 km ring;In large rings narrow resonancescannot be “hidden” from thebeam.
(Dimtel) Beam loading and instabilities November 7, 2017 6 / 24
Resonant Modes and Revolution Harmonics
−400 −300 −200 −100 0 100 200 300 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (kHz)
Imp
ed
an
ce
(a
rb.
un
its)
A 20 kHz resonance ideally“hidden” between two revolutionharmonics.1 km ring;1.5 km ring;3 km ring;10 km ring;100 km ring;In large rings narrow resonancescannot be “hidden” from thebeam.
(Dimtel) Beam loading and instabilities November 7, 2017 6 / 24
Transverse Planes: Resistive Wall
0 100 200 300 400 500−250
−200
−150
−100
−50
0
Mode number
Gro
wth
rate
(s−
1)
Upper sideband
Lower sideband
Resistive wall impedance scaleslinearly with circumference;Impedance vs. frequency is∝ 1/
√ω;
The most unstable line is thelower betatron sideband of thefirst revolution harmonic (mode-1);Overall impedance scaling 1
ω3/2rev
;
RW growth time (in turns) scalesas ω3/2
rev .
(Dimtel) Beam loading and instabilities November 7, 2017 7 / 24
Transverse Planes: Resistive Wall
0 100 200 300 400 500−250
−200
−150
−100
−50
0
Mode number
Gro
wth
rate
(s−
1)
Upper sideband
Lower sideband
Resistive wall impedance scaleslinearly with circumference;Impedance vs. frequency is∝ 1/
√ω;
The most unstable line is thelower betatron sideband of thefirst revolution harmonic (mode-1);Overall impedance scaling 1
ω3/2rev
;
RW growth time (in turns) scalesas ω3/2
rev .
(Dimtel) Beam loading and instabilities November 7, 2017 7 / 24
Transverse Planes: Resistive Wall
0 100 200 300 400 500−250
−200
−150
−100
−50
0
Mode number
Gro
wth
rate
(s−
1)
Upper sideband
Lower sideband
Resistive wall impedance scaleslinearly with circumference;Impedance vs. frequency is∝ 1/
√ω;
The most unstable line is thelower betatron sideband of thefirst revolution harmonic (mode-1);Overall impedance scaling 1
ω3/2rev
;
RW growth time (in turns) scalesas ω3/2
rev .
(Dimtel) Beam loading and instabilities November 7, 2017 7 / 24
Transverse Planes: Resistive Wall
0 100 200 300 400 500−250
−200
−150
−100
−50
0
Mode number
Gro
wth
rate
(s−
1)
Upper sideband
Lower sideband
Resistive wall impedance scaleslinearly with circumference;Impedance vs. frequency is∝ 1/
√ω;
The most unstable line is thelower betatron sideband of thefirst revolution harmonic (mode-1);Overall impedance scaling 1
ω3/2rev
;
RW growth time (in turns) scalesas ω3/2
rev .
(Dimtel) Beam loading and instabilities November 7, 2017 7 / 24
Transverse Planes: Resistive Wall
0 100 200 300 400 500−250
−200
−150
−100
−50
0
Mode number
Gro
wth
rate
(s−
1)
Upper sideband
Lower sideband
Resistive wall impedance scaleslinearly with circumference;Impedance vs. frequency is∝ 1/
√ω;
The most unstable line is thelower betatron sideband of thefirst revolution harmonic (mode-1);Overall impedance scaling 1
ω3/2rev
;
RW growth time (in turns) scalesas ω3/2
rev .
(Dimtel) Beam loading and instabilities November 7, 2017 7 / 24
Outline
1 IntroductionThe focus of this talk
2 Instabilities, Beam Loading, FeedbackRing Circumference and Coupled-Bunch InstabilitiesBeam Loading in Storage RingsBunch-by-bunch Feedback
3 Beam Loading in CEPC-ZFCC-Z Nominal ParametersPushing FCC-Z Current
(Dimtel) Beam loading and instabilities November 7, 2017 8 / 24
Beam/Cavity Interaction
loops
RF feedback
dynamics
Longitudinal
Generator
C R L
Beam
~IG
~VC
~IB
RLC model of the acceleratingcavity with two input currents:generator and beam;Cavity voltage ~VC is defined bythe sum current;Low loading (~IB ~IG) — cavityvoltage is mostly defined by thegenerator current;High loading — cavity voltage isstrongly affected by beam current;“Feedback loop” from cavityvoltage to beam current and backto cavity voltage.
(Dimtel) Beam loading and instabilities November 7, 2017 9 / 24
Beam/Cavity Interaction
loops
RF feedback
dynamics
Longitudinal
Generator
C R L
Beam
~IG
~VC
~IB
RLC model of the acceleratingcavity with two input currents:generator and beam;Cavity voltage ~VC is defined bythe sum current;Low loading (~IB ~IG) — cavityvoltage is mostly defined by thegenerator current;High loading — cavity voltage isstrongly affected by beam current;“Feedback loop” from cavityvoltage to beam current and backto cavity voltage.
(Dimtel) Beam loading and instabilities November 7, 2017 9 / 24
Beam/Cavity Interaction
loops
RF feedback
dynamics
Longitudinal
Generator
C R L
Beam
~IG
~VC
~IB
RLC model of the acceleratingcavity with two input currents:generator and beam;Cavity voltage ~VC is defined bythe sum current;Low loading (~IB ~IG) — cavityvoltage is mostly defined by thegenerator current;High loading — cavity voltage isstrongly affected by beam current;“Feedback loop” from cavityvoltage to beam current and backto cavity voltage.
(Dimtel) Beam loading and instabilities November 7, 2017 9 / 24
Beam/Cavity Interaction
loops
RF feedback
dynamics
Longitudinal
Generator
C R L
Beam
~IG
~VC
~IB
RLC model of the acceleratingcavity with two input currents:generator and beam;Cavity voltage ~VC is defined bythe sum current;Low loading (~IB ~IG) — cavityvoltage is mostly defined by thegenerator current;High loading — cavity voltage isstrongly affected by beam current;“Feedback loop” from cavityvoltage to beam current and backto cavity voltage.
(Dimtel) Beam loading and instabilities November 7, 2017 9 / 24
Beam/Cavity Interaction
loops
RF feedback
dynamics
Longitudinal
Generator
C R L
Beam
~IG
~VC
~IB
RLC model of the acceleratingcavity with two input currents:generator and beam;Cavity voltage ~VC is defined bythe sum current;Low loading (~IB ~IG) — cavityvoltage is mostly defined by thegenerator current;High loading — cavity voltage isstrongly affected by beam current;“Feedback loop” from cavityvoltage to beam current and backto cavity voltage.
(Dimtel) Beam loading and instabilities November 7, 2017 9 / 24
Why Worry about Beam Loading
Two main effects of heavy beam loading in large rings:I Synchronous phase transients;I Longitudinal coupled-bunch instabilities driven by the RF cavity
fundamental impedanceTransient effects depend on
I Total beam loading;I Fill pattern.
Fill patterns can be designed to mitigate transient effects;But longitudinal instabilities due to the fundamental impedanceremain an issue even with completely uniform fills;Reducing beam loading in the RF system design helps bothissues.
(Dimtel) Beam loading and instabilities November 7, 2017 10 / 24
Why Worry about Beam Loading
Two main effects of heavy beam loading in large rings:I Transient modulation of longitudinal optics;I Longitudinal coupled-bunch instabilities driven by the RF cavity
fundamental impedanceTransient effects depend on
I Total beam loading;I Fill pattern.
Fill patterns can be designed to mitigate transient effects;But longitudinal instabilities due to the fundamental impedanceremain an issue even with completely uniform fills;Reducing beam loading in the RF system design helps bothissues.
(Dimtel) Beam loading and instabilities November 7, 2017 10 / 24
Why Worry about Beam Loading
Two main effects of heavy beam loading in large rings:I Transient modulation of longitudinal optics;I Longitudinal coupled-bunch instabilities driven by the RF cavity
fundamental impedanceTransient effects depend on
I Total beam loading;I Fill pattern.
Fill patterns can be designed to mitigate transient effects;But longitudinal instabilities due to the fundamental impedanceremain an issue even with completely uniform fills;Reducing beam loading in the RF system design helps bothissues.
(Dimtel) Beam loading and instabilities November 7, 2017 10 / 24
Why Worry about Beam Loading
Two main effects of heavy beam loading in large rings:I Transient modulation of longitudinal optics;I Longitudinal coupled-bunch instabilities driven by the RF cavity
fundamental impedanceTransient effects depend on
I Total beam loading;I Fill pattern.
Fill patterns can be designed to mitigate transient effects;But longitudinal instabilities due to the fundamental impedanceremain an issue even with completely uniform fills;Reducing beam loading in the RF system design helps bothissues.
(Dimtel) Beam loading and instabilities November 7, 2017 10 / 24
Why Worry about Beam Loading
Two main effects of heavy beam loading in large rings:I Transient modulation of longitudinal optics;I Longitudinal coupled-bunch instabilities driven by the RF cavity
fundamental impedanceTransient effects depend on
I Total beam loading;I Fill pattern.
Fill patterns can be designed to mitigate transient effects;But longitudinal instabilities due to the fundamental impedanceremain an issue even with completely uniform fills;Reducing beam loading in the RF system design helps bothissues.
(Dimtel) Beam loading and instabilities November 7, 2017 10 / 24
Why Worry about Beam Loading
Two main effects of heavy beam loading in large rings:I Transient modulation of longitudinal optics;I Longitudinal coupled-bunch instabilities driven by the RF cavity
fundamental impedanceTransient effects depend on
I Total beam loading;I Fill pattern.
Fill patterns can be designed to mitigate transient effects;But longitudinal instabilities due to the fundamental impedanceremain an issue even with completely uniform fills;Reducing beam loading in the RF system design helps bothissues.
(Dimtel) Beam loading and instabilities November 7, 2017 10 / 24
Why Worry about Beam Loading
Two main effects of heavy beam loading in large rings:I Transient modulation of longitudinal optics;I Longitudinal coupled-bunch instabilities driven by the RF cavity
fundamental impedanceTransient effects depend on
I Total beam loading;I Fill pattern.
Fill patterns can be designed to mitigate transient effects;But longitudinal instabilities due to the fundamental impedanceremain an issue even with completely uniform fills;Reducing beam loading in the RF system design helps bothissues.
(Dimtel) Beam loading and instabilities November 7, 2017 10 / 24
Ring Circumference and Beam Loading
Photo/image credit: CERN, SLAC
People don’t build multi-kilometerrings just to spend money;Large circumference — very highenergy;Or very high current;Or both.Large circumference meansheavy beam loading of the RFsystem.
(Dimtel) Beam loading and instabilities November 7, 2017 11 / 24
Ring Circumference and Beam Loading
Photo/image credit: CERN, SLAC
People don’t build multi-kilometerrings just to spend money;Large circumference — very highenergy;Or very high current;Or both.Large circumference meansheavy beam loading of the RFsystem.
(Dimtel) Beam loading and instabilities November 7, 2017 11 / 24
Ring Circumference and Beam Loading
Photo/image credit: CERN, SLAC
People don’t build multi-kilometerrings just to spend money;Large circumference — very highenergy;Or very high current;Or both.Large circumference meansheavy beam loading of the RFsystem.
(Dimtel) Beam loading and instabilities November 7, 2017 11 / 24
Ring Circumference and Beam Loading
Photo/image credit: CERN, SLAC
People don’t build multi-kilometerrings just to spend money;Large circumference — very highenergy;Or very high current;Or both.Large circumference meansheavy beam loading of the RFsystem.
(Dimtel) Beam loading and instabilities November 7, 2017 11 / 24
Ring Circumference and Beam Loading
Photo/image credit: CERN, SLAC
People don’t build multi-kilometerrings just to spend money;Large circumference — very highenergy;Or very high current;Or both.Large circumference meansheavy beam loading of the RFsystem.
(Dimtel) Beam loading and instabilities November 7, 2017 11 / 24
Cavity Detuning and Longitudinal Stability
−1.5 −1 −0.5 0 0.5 1 1.50
500
1000
1500
2000
Frequency offset from ωrf, revolution harmonics
ℜ(Z
), k
Ω
−1.5 −1 −0.5 0 0.5 1 1.5−2000
−1000
0
1000
2000
Eigenmode numberEffective d
rivin
g im
pedance, kΩ
Growth rate for mode -1 is∝ Z (ωrf − ωrev + ωs)− Z (ωrf +ωrev − ωs);Symmetric on resonance;Growth rates peak whenfundamental crossesrevolution harmonics;Need RF feedback to reducethe effective impedance.
(Dimtel) Beam loading and instabilities November 7, 2017 12 / 24
Cavity Detuning and Longitudinal Stability
−1.5 −1 −0.5 0 0.5 1 1.50
500
1000
1500
2000
Frequency offset from ωrf, revolution harmonics
ℜ(Z
), k
Ω
−1.5 −1 −0.5 0 0.5 1 1.5−2000
−1000
0
1000
2000
Eigenmode numberEffective d
rivin
g im
pedance, kΩ
Growth rate for mode -1 is∝ Z (ωrf − ωrev + ωs)− Z (ωrf +ωrev − ωs);Symmetric on resonance;Growth rates peak whenfundamental crossesrevolution harmonics;Need RF feedback to reducethe effective impedance.
(Dimtel) Beam loading and instabilities November 7, 2017 12 / 24
Cavity Detuning and Longitudinal Stability
−1.5 −1 −0.5 0 0.5 1 1.50
500
1000
1500
2000
Frequency offset from ωrf, revolution harmonics
ℜ(Z
), k
Ω
−1.5 −1 −0.5 0 0.5 1 1.5−2000
−1000
0
1000
2000
Eigenmode numberEffective d
rivin
g im
pedance, kΩ
Growth rate for mode -1 is∝ Z (ωrf − ωrev + ωs)− Z (ωrf +ωrev − ωs);Symmetric on resonance;Growth rates peak whenfundamental crossesrevolution harmonics;Need RF feedback to reducethe effective impedance.
(Dimtel) Beam loading and instabilities November 7, 2017 12 / 24
Cavity Detuning and Longitudinal Stability
−1.5 −1 −0.5 0 0.5 1 1.50
500
1000
1500
2000
Frequency offset from ωrf, revolution harmonics
ℜ(Z
), k
Ω
−1.5 −1 −0.5 0 0.5 1 1.5−2000
−1000
0
1000
2000
Eigenmode numberEffective d
rivin
g im
pedance, kΩ
Growth rate for mode -1 is∝ Z (ωrf − ωrev + ωs)− Z (ωrf +ωrev − ωs);Symmetric on resonance;Growth rates peak whenfundamental crossesrevolution harmonics;Need RF feedback to reducethe effective impedance.
(Dimtel) Beam loading and instabilities November 7, 2017 12 / 24
Cavity Detuning and Longitudinal Stability
−1.5 −1 −0.5 0 0.5 1 1.50
500
1000
1500
2000
Frequency offset from ωrf, revolution harmonics
ℜ(Z
), k
Ω
−1.5 −1 −0.5 0 0.5 1 1.5−2000
−1000
0
1000
2000
Eigenmode numberEffective d
rivin
g im
pedance, kΩ
Growth rate for mode -1 is∝ Z (ωrf − ωrev + ωs)− Z (ωrf +ωrev − ωs);Symmetric on resonance;Growth rates peak whenfundamental crossesrevolution harmonics;Need RF feedback to reducethe effective impedance.
(Dimtel) Beam loading and instabilities November 7, 2017 12 / 24
Cavity Detuning and Longitudinal Stability
−1.5 −1 −0.5 0 0.5 1 1.50
500
1000
1500
2000
Frequency offset from ωrf, revolution harmonics
ℜ(Z
), k
Ω
−1.5 −1 −0.5 0 0.5 1 1.5−2000
−1000
0
1000
2000
Eigenmode numberEffective d
rivin
g im
pedance, kΩ
Growth rate for mode -1 is∝ Z (ωrf − ωrev + ωs)− Z (ωrf +ωrev − ωs);Symmetric on resonance;Growth rates peak whenfundamental crossesrevolution harmonics;Need RF feedback to reducethe effective impedance.
(Dimtel) Beam loading and instabilities November 7, 2017 12 / 24
Mitigating Beam Loading in Design
Cavity detuning
ωd =∣∣∣ωrfI0
Vc
RQ cosφb
∣∣∣Minimize the number of cavities:
I Reduces fundamental impedance interacting with the beam;I Limited by the maximum coupler power and/or the maximum cavity
voltage.Minimize detuning:
I Cavities with low R/Q;I Lower RF frequencies are preferable, especially when coupler
limited.
(Dimtel) Beam loading and instabilities November 7, 2017 13 / 24
Mitigating Beam Loading in Design
Cavity detuning
ωd =∣∣∣ωrfI0
Vc
RQ cosφb
∣∣∣Minimize the number of cavities:
I Reduces fundamental impedance interacting with the beam;I Limited by the maximum coupler power and/or the maximum cavity
voltage.Minimize detuning:
I Cavities with low R/Q;I Lower RF frequencies are preferable, especially when coupler
limited.
(Dimtel) Beam loading and instabilities November 7, 2017 13 / 24
Outline
1 IntroductionThe focus of this talk
2 Instabilities, Beam Loading, FeedbackRing Circumference and Coupled-Bunch InstabilitiesBeam Loading in Storage RingsBunch-by-bunch Feedback
3 Beam Loading in CEPC-ZFCC-Z Nominal ParametersPushing FCC-Z Current
(Dimtel) Beam loading and instabilities November 7, 2017 14 / 24
Bunch-by-bunch Feedback
DefinitionIn bunch-by-bunch feedback approach the actuator signal for a givenbunch depends only on the past motion of that bunch.
Controller
Beam Kicker structure
Back−endFront−end
SensorBPM Actuator
Bunches are processed sequentially.Correction kicks are applied one turn later.
(Dimtel) Beam loading and instabilities November 7, 2017 15 / 24
Feedback Control Limits: Transverse
For single pickup/single kicker topology the maximum growth ratethat can be controlled is limited by the response delay (time frommeasuring bunch position error to correction kick acting on thesame bunch on a later turn).Rule of thumb for robust operation: λcl ≥ −λol.Fast damping in time domain corresponds to wide bandwidth inthe frequency domain→ feedback induced noise can be an issuein the vertical plane.For fractional tunes in 0.2–0.4 range the limit is around 10 turnsgrowth time (with 10 turns closed-loop damping time);Tunes close to integer or half-integer require the feedback withsignals from many past turns, slower damping.
(Dimtel) Beam loading and instabilities November 7, 2017 16 / 24
Feedback Control Limits: Transverse
For single pickup/single kicker topology the maximum growth ratethat can be controlled is limited by the response delay (time frommeasuring bunch position error to correction kick acting on thesame bunch on a later turn).Rule of thumb for robust operation: λcl ≥ −λol.Fast damping in time domain corresponds to wide bandwidth inthe frequency domain→ feedback induced noise can be an issuein the vertical plane.For fractional tunes in 0.2–0.4 range the limit is around 10 turnsgrowth time (with 10 turns closed-loop damping time);Tunes close to integer or half-integer require the feedback withsignals from many past turns, slower damping.
(Dimtel) Beam loading and instabilities November 7, 2017 16 / 24
Feedback Control Limits: Transverse
For single pickup/single kicker topology the maximum growth ratethat can be controlled is limited by the response delay (time frommeasuring bunch position error to correction kick acting on thesame bunch on a later turn).Rule of thumb for robust operation: λcl ≥ −λol.Fast damping in time domain corresponds to wide bandwidth inthe frequency domain→ feedback induced noise can be an issuein the vertical plane.For fractional tunes in 0.2–0.4 range the limit is around 10 turnsgrowth time (with 10 turns closed-loop damping time);Tunes close to integer or half-integer require the feedback withsignals from many past turns, slower damping.
(Dimtel) Beam loading and instabilities November 7, 2017 16 / 24
Feedback Control Limits: Transverse
For single pickup/single kicker topology the maximum growth ratethat can be controlled is limited by the response delay (time frommeasuring bunch position error to correction kick acting on thesame bunch on a later turn).Rule of thumb for robust operation: λcl ≥ −λol.Fast damping in time domain corresponds to wide bandwidth inthe frequency domain→ feedback induced noise can be an issuein the vertical plane.For fractional tunes in 0.2–0.4 range the limit is around 10 turnsgrowth time (with 10 turns closed-loop damping time);Tunes close to integer or half-integer require the feedback withsignals from many past turns, slower damping.
(Dimtel) Beam loading and instabilities November 7, 2017 16 / 24
Feedback Control Limits: Longitudinal
Measure longitudinal position (time of arrival), correct energy;To generate required 90 phase shift the feedback must observeat least half synchrotron period;Fastest growth times on the order of 1–2 synchrotron periods.
(Dimtel) Beam loading and instabilities November 7, 2017 17 / 24
Feedback Control Limits: Longitudinal
Measure longitudinal position (time of arrival), correct energy;To generate required 90 phase shift the feedback must observeat least half synchrotron period;Fastest growth times on the order of 1–2 synchrotron periods.
(Dimtel) Beam loading and instabilities November 7, 2017 17 / 24
Feedback Control Limits: Longitudinal
Measure longitudinal position (time of arrival), correct energy;To generate required 90 phase shift the feedback must observeat least half synchrotron period;Fastest growth times on the order of 1–2 synchrotron periods.
(Dimtel) Beam loading and instabilities November 7, 2017 17 / 24
Longitudinal Example from ANKA
0
0.550100
150
0
0.2
0.4
Time (ms)
a) Osc. Envelopes in Time Domain
Bunch No.
de
g@
RF
0
0.5
0
100
0
0.05
0.1
Time (ms)
b) Evolution of Modes
Mode No.
de
g@
RF
44.5 45 45.536.19
36.2
36.21
36.22
36.23
36.24
Mode No.
Fre
qu
en
cy (
kH
z)
c) Oscillation freqs (pre−brkpt)
44 44.5 45 45.5 46
15.6099
15.6099
15.6099
15.6099
15.6099
15.6099
15.6099
Mode No.
Ra
te
(1
/ms)
d) Growth Rates (pre−brkpt)
44.5 45 45.536.25
36.3
36.35
36.4
36.45
36.5
Mode No.
Fre
qu
en
cy (
kH
z)
e) Oscillation freqs (post−brkpt)
44 44.5 45 45.5 46
−35.4292
−35.4292
−35.4292
−35.4292
Mode No.
Ra
te
(1
/ms)
f) Growth Rates (post−brkpt)
ANKA:mar0516/143812: Io= 138.0587mA, Dsamp= 2, ShifGain= 4, Nbun= 184,At Fs: G1= 119.0572, G2= 0, Ph1= −76.5927, Ph2= 0, Brkpt= 240, Calib= 34.252.
Measured while cavity tuningwalks an HOM onto asynchrotron sideband;Growth time is 2.3Ts, dampingtime is Ts;Filter is 2/3 of a synchrotronperiod.
(Dimtel) Beam loading and instabilities November 7, 2017 18 / 24
Longitudinal Example from ANKA
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Time (ms)
deg@
RF
mar0516/143812 Data, Fit and Error for Mode #45
Data
Fit
Error Measured while cavity tuningwalks an HOM onto asynchrotron sideband;Growth time is 2.3Ts, dampingtime is Ts;Filter is 2/3 of a synchrotronperiod.
(Dimtel) Beam loading and instabilities November 7, 2017 18 / 24
Longitudinal Example from ANKA
0 10 20 30 40 50−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Time (turns)
Coeffic
ient
Measured while cavity tuningwalks an HOM onto asynchrotron sideband;Growth time is 2.3Ts, dampingtime is Ts;Filter is 2/3 of a synchrotronperiod.
(Dimtel) Beam loading and instabilities November 7, 2017 18 / 24
ParametersJ. Gao, “CEPC accelerator CDR - status”,J. Zhai, “CEPC SRF system study”
Parameter ValueEnergy 45.5 GeVEnergy loss per turn 35 MeVMomentum compaction 1.14× 10−5
Energy spread 3.7× 10−4
Radiation damping time 433 msGap voltage 53 MVHarmonic number 216664Buckets filled 10725R/Q 106.5 ΩQ0 1010
Coupling factor1 26657
1Optimized for zero reflected power at 83.7 mA(Dimtel) Beam loading and instabilities November 7, 2017 19 / 24
Outline
1 IntroductionThe focus of this talk
2 Instabilities, Beam Loading, FeedbackRing Circumference and Coupled-Bunch InstabilitiesBeam Loading in Storage RingsBunch-by-bunch Feedback
3 Beam Loading in CEPC-ZFCC-Z Nominal ParametersPushing FCC-Z Current
(Dimtel) Beam loading and instabilities November 7, 2017 20 / 24
Beam Loading Effects
0 50 100 150 200 250 300 350−1.5
−1
−0.5
0
0.5
1
Time (µs)
Phase (
deg@
RF
)
Transient is 2.0854 degrees peak−to−peak
0 50 100 150 200 250 300 3500
1
2
3
4
5
6
7
8x 10
−3
Time (µs)
Bunch c
urr
ent (m
A)
CEPC−Z; 12/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.0837 A; CEPC−Z−1% fill
Nominal CEPC-Z, no parkedcavities, 1 kHz detuning;Small gap transient;Bunch length modulation is alsosmall;Growth rates are moderate (mode-1 at ≈ 3Ts), but mode 0 is tuneshifted nearly to DC, on the vergeof high-current Robinsoninstability;With moderate direct loop gain of10, all modes are stabilized.
(Dimtel) Beam loading and instabilities November 7, 2017 21 / 24
Beam Loading Effects
0 50 100 150 200 250 300 350−1.5
−1
−0.5
0
0.5
1
Time (µs)
Phase (
deg@
RF
)
Transient is 2.0854 degrees peak−to−peak
0 50 100 150 200 250 300 3500
1
2
3
4
5
6
7
8x 10
−3
Time (µs)
Bunch c
urr
ent (m
A)
CEPC−Z; 12/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.0837 A; CEPC−Z−1% fill
Nominal CEPC-Z, no parkedcavities, 1 kHz detuning;Small gap transient;Bunch length modulation is alsosmall;Growth rates are moderate (mode-1 at ≈ 3Ts), but mode 0 is tuneshifted nearly to DC, on the vergeof high-current Robinsoninstability;With moderate direct loop gain of10, all modes are stabilized.
(Dimtel) Beam loading and instabilities November 7, 2017 21 / 24
Beam Loading Effects
0 50 100 150 200 250 300 3503.6
3.605
3.61
3.615
3.62
3.625
3.63
3.635
3.64
Time (µs)
Bunch length
(m
m)
Peak−to−peak bunch length spead 0.72%
Nominal CEPC-Z, no parkedcavities, 1 kHz detuning;Small gap transient;Bunch length modulation is alsosmall;Growth rates are moderate (mode-1 at ≈ 3Ts), but mode 0 is tuneshifted nearly to DC, on the vergeof high-current Robinsoninstability;With moderate direct loop gain of10, all modes are stabilized.
(Dimtel) Beam loading and instabilities November 7, 2017 21 / 24
Beam Loading Effects
−10 −5 0 5 10−30
−20
−10
0
10
20
Mode number
Gro
wth
rate
(s−
1)
CEPC−Z; 12/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.0837 A; CEPC−Z−1% fill
−10 −5 0 5 10−60
−50
−40
−30
−20
−10
0
10
Mode number
Fre
quency s
hift (H
z)
SSM (stable)
SSM (unstable)
Analytical
SSM (stable)
SSM (unstable)
Analytical
Nominal CEPC-Z, no parkedcavities, 1 kHz detuning;Small gap transient;Bunch length modulation is alsosmall;Growth rates are moderate (mode-1 at ≈ 3Ts), but mode 0 is tuneshifted nearly to DC, on the vergeof high-current Robinsoninstability;With moderate direct loop gain of10, all modes are stabilized.
(Dimtel) Beam loading and instabilities November 7, 2017 21 / 24
Beam Loading Effects
−10 −5 0 5 10−30
−20
−10
0
10
20
Mode number
Gro
wth
rate
(s−
1)
CEPC−Z; 12/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.0837 A; CEPC−Z−1% fill
−10 −5 0 5 10−60
−50
−40
−30
−20
−10
0
10
Mode number
Fre
quency s
hift (H
z)
SSM (stable)
SSM (unstable)
Analytical
SSM (stable)
SSM (unstable)
Analytical
Nominal CEPC-Z, no parkedcavities, 1 kHz detuning;Small gap transient;Bunch length modulation is alsosmall;Growth rates are moderate (mode-1 at ≈ 3Ts), but mode 0 is tuneshifted nearly to DC, on the vergeof high-current Robinsoninstability;With moderate direct loop gain of10, all modes are stabilized.
(Dimtel) Beam loading and instabilities November 7, 2017 21 / 24
Outline
1 IntroductionThe focus of this talk
2 Instabilities, Beam Loading, FeedbackRing Circumference and Coupled-Bunch InstabilitiesBeam Loading in Storage RingsBunch-by-bunch Feedback
3 Beam Loading in CEPC-ZFCC-Z Nominal ParametersPushing FCC-Z Current
(Dimtel) Beam loading and instabilities November 7, 2017 22 / 24
From 12 to 24 Cavities
0 50 100 150 200 250 300 350−6
−4
−2
0
2
4
Time (µs)
Phase (
deg@
RF
)
Transient is 7.6666 degrees peak−to−peak
0 50 100 150 200 250 300 3500
0.005
0.01
0.015
Time (µs)
Bunch c
urr
ent (m
A)
CEPC−Z; 24/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.157 A; CEPC−Z−1% fill
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
From 12 to 24 Cavities
0 50 100 150 200 250 300 350−6
−4
−2
0
2
4
Time (µs)
Phase (
deg@
RF
)
Transient is 7.6666 degrees peak−to−peak
0 50 100 150 200 250 300 3500
0.005
0.01
0.015
Time (µs)
Bunch c
urr
ent (m
A)
CEPC−Z; 24/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.157 A; CEPC−Z−1% fill
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
From 12 to 24 Cavities
−10 −5 0 5 10−200
−150
−100
−50
0
50
100
150
200
Mode number
Gro
wth
ra
te (
s−1)
CEPC−Z; 24/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.157 A; CEPC−Z−1% fill
−10 −5 0 5 10−60
−50
−40
−30
−20
−10
0
10
Mode number
Fre
qu
en
cy s
hift
(Hz)
SSM (stable)
SSM (unstable)
Analytical
SSM (stable)
SSM (unstable)
Analytical
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
From 12 to 24 Cavities
−10 −5 0 5 10−200
−150
−100
−50
0
50
100
150
200
Mode number
Gro
wth
ra
te (
s−1)
CEPC−Z; 24/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.157 A; CEPC−Z−1% fill
−10 −5 0 5 10−60
−50
−40
−30
−20
−10
0
10
Mode number
Fre
qu
en
cy s
hift
(Hz)
SSM (stable)
SSM (unstable)
Analytical
SSM (stable)
SSM (unstable)
Analytical
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
From 12 to 24 Cavities
−10 −5 0 5 10−5
−4
−3
−2
−1
0
Mode number
Gro
wth
rate
(s−
1)
CEPC−Z; 24/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.157 A; CEPC−Z−1% fill
−10 −5 0 5 10−60
−50
−40
−30
−20
−10
0
10
Mode number
Fre
quency s
hift (H
z)
SSM (stable)
SSM (unstable)
Analytical
SSM (stable)
SSM (unstable)
Analytical
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
From 12 to 24 Cavities
−300 −200 −100 0 100 200 3000
2000
4000
6000
8000
10000
12000
Frequency offset (kHz)
ℜ(Z
) (k
Ω)
−300 −200 −100 0 100 200 300−6000
−4000
−2000
0
2000
4000
6000
Frequency offset (kHz)
ℑ(Z
) (k
Ω)
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
From 12 to 24 Cavities
−300 −200 −100 0 100 200 3000
50
100
150
200
250
300
350
Frequency offset (kHz)
ℜ(Z
) (k
Ω)
−300 −200 −100 0 100 200 300−400
−300
−200
−100
0
100
200
300
400
Frequency offset (kHz)
ℑ(Z
) (k
Ω)
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
From 12 to 24 Cavities
−100 −50 0 50 100−2.7
−2.6
−2.5
−2.4
−2.3
−2.2
−2.1
−2
−1.9
Mode number
Gro
wth
ra
te (
s−1)
CEPC−Z; 24/0 powered/parked cavities; Vgap
= 53 MV; I0 = 0.157 A; CEPC−Z−1% fill
−100 −50 0 50 100−0.05
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
Mode number
Fre
qu
en
cy s
hift
(Hz)
157 mA, 3.7 kHz detuning;Gap transient still acceptable;Fastest growth time is 6 ms, athird of synchrotron period;With optimal direct loop gain of 30instabilities are suppressed;Zoom in to see all modes atradiation damping;6.5 kHz open-loop;446 kHz closed-loop;Some small mismatches at higherfrequencies.
(Dimtel) Beam loading and instabilities November 7, 2017 23 / 24
Summary
Even at low currents CEPC-Z is heavily beam loaded;RF system design should be driven by the beam loading andlongitudinal stability considerations;RF feedback loops will be needed to provide beam/cavity stability;Fundamental impedance is large, but very tightly controlled, CBIdriving impedance reduction is straightforward;Cavity HOMs are relatively unpredictable, need to be damped tolevels, manageable by the bunch-by-bunch feedback.Gap transient response cannot be controlled by RF feedback(high peak power), need to manage fill pattern gaps.
(Dimtel) Beam loading and instabilities November 7, 2017 24 / 24
Summary
Even at low currents CEPC-Z is heavily beam loaded;RF system design should be driven by the beam loading andlongitudinal stability considerations;RF feedback loops will be needed to provide beam/cavity stability;Fundamental impedance is large, but very tightly controlled, CBIdriving impedance reduction is straightforward;Cavity HOMs are relatively unpredictable, need to be damped tolevels, manageable by the bunch-by-bunch feedback.Gap transient response cannot be controlled by RF feedback(high peak power), need to manage fill pattern gaps.
(Dimtel) Beam loading and instabilities November 7, 2017 24 / 24
Summary
Even at low currents CEPC-Z is heavily beam loaded;RF system design should be driven by the beam loading andlongitudinal stability considerations;RF feedback loops will be needed to provide beam/cavity stability;Fundamental impedance is large, but very tightly controlled, CBIdriving impedance reduction is straightforward;Cavity HOMs are relatively unpredictable, need to be damped tolevels, manageable by the bunch-by-bunch feedback.Gap transient response cannot be controlled by RF feedback(high peak power), need to manage fill pattern gaps.
(Dimtel) Beam loading and instabilities November 7, 2017 24 / 24
Summary
Even at low currents CEPC-Z is heavily beam loaded;RF system design should be driven by the beam loading andlongitudinal stability considerations;RF feedback loops will be needed to provide beam/cavity stability;Fundamental impedance is large, but very tightly controlled, CBIdriving impedance reduction is straightforward;Cavity HOMs are relatively unpredictable, need to be damped tolevels, manageable by the bunch-by-bunch feedback.Gap transient response cannot be controlled by RF feedback(high peak power), need to manage fill pattern gaps.
(Dimtel) Beam loading and instabilities November 7, 2017 24 / 24
Summary
Even at low currents CEPC-Z is heavily beam loaded;RF system design should be driven by the beam loading andlongitudinal stability considerations;RF feedback loops will be needed to provide beam/cavity stability;Fundamental impedance is large, but very tightly controlled, CBIdriving impedance reduction is straightforward;Cavity HOMs are relatively unpredictable, need to be damped tolevels, manageable by the bunch-by-bunch feedback.Gap transient response cannot be controlled by RF feedback(high peak power), need to manage fill pattern gaps.
(Dimtel) Beam loading and instabilities November 7, 2017 24 / 24
Summary
Even at low currents CEPC-Z is heavily beam loaded;RF system design should be driven by the beam loading andlongitudinal stability considerations;RF feedback loops will be needed to provide beam/cavity stability;Fundamental impedance is large, but very tightly controlled, CBIdriving impedance reduction is straightforward;Cavity HOMs are relatively unpredictable, need to be damped tolevels, manageable by the bunch-by-bunch feedback.Gap transient response cannot be controlled by RF feedback(high peak power), need to manage fill pattern gaps.
(Dimtel) Beam loading and instabilities November 7, 2017 24 / 24