Transcript Damping an e-p Instability at the LANL Proton Storage Ring

Damping an e-p Instability at the LANL
Proton Storage Ring
Rod McCrady
R. J. Macek, T. J. Zaugg, LANL
S. Assadi, C. E. Deibele, S. D. Henderson, M. A. Plum, ORNL (SNS)
J. M. Byrd, LBNL
S. Y. Lee, S. B. Walbridge, Indiana University
M. F. T. Pivi, SLAC
Journal of Applied Physics 102, 124904 (2007)
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Slide 1
Outline

Intro to the PSR and the e-p instability

Overview of the damping sytem and its performance

Details of the components

Possible factors limiting performance

More details
•
•
•

Comb filter
Bandwidth
A noise source
Summary
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Slide 2
The LANL Proton Storage Ring
H+
LINAC macropulses: ~625µs @ 20Hz to PSR
Beams to
other areas
800 MeV LINAC
H
H beam
from linac
PSR
1L Target
Accumulated
protons
Deliver 5µC
300ns-long
pulse to target
@20Hz
PSR
PSR
Accumulate ~1800 300ns-long minipulses
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Slide 3
PSR Operating Parameters
Beam kinetic energy
Betatron tunes
Incoherent tune shifts @ 5C
T
798 MeV
H, V
3.19, 2.19
H, V
H, V
Chromaticities
-0.22, -0.18
(calculated)
 -1.0
Transition gamma
T
3.1
Buncher harmonic
h
1
Buncher frequency
f
2.795 MHz
Max. RF voltage
Vrf
18 kV
Synchrotron tune @ 10kV
0
0.00042
Circumference
C
90.26 m
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Slide 4
Electron Cloud and the e-p Instability

Beam potential traps electrons

Sources of electrons
•
•
•
Scraping of beam on beampipe
Stripper foil
Residual gas ionization (small)

Beam & electrons oscillate (vertically)

Growth by secondary emission & trailing edge multipactor

Loss of stored charge
e
pipe wall
Beam
secondary electrons
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Net acceleration
Slide 5
Characteristics of the e-p Instability
Broad band
25 to 250 MHz
Rapid growth
Growth time 50s
Typical growth times
25s to 100s
Large pulse-to-pulse
variations
These data courtesy of Bob Macek
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Slide 6
Damping System Characteristics, etc.
Requirements
•
•
•
•

Fast response (short delay)
Rapid damping (high power)
Broad band (25 – 250MHz)
Constant delay vs. frequency (“flat phase response”)
Unique
•
•
Long pulse
Optimized for varying conditions

Other methods to control instability increase beam spill

Test bed for higher-power machines
•

Spallation Neutron Source (SNS) at Oak Ridge
Inexpensive prototype
•
•
•
Used some existing parts (BPM, kicker)
SNS supplied new equipment, e.g. amplifiers, LLRF components
Vertical plane only
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Slide 7
Damping System – Functional Overview
Path of a proton
around the ring
RF amp
Signal
Processing
Kicker
Pickup
Beam
Motion of a longitudinal slice of beam:
(Betatron oscillation, f=6.1 MHz)
4 turns
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Slide 8
Expected Performance
Beam orbit frequency
1 i.e.
fR

G sin  p  k
2
Damping rate:
System gain
fR
2
 p k
  p  k d / dy 
Beam parameters
Power to kicker
 sat 
 p k  nodd  90
size  
Deflection per unit
beam offset
1
e
2 Psat R
2
y sat E

d sat
Kicker shunt impedance (“effectiveness”)
For Psat=100W at ysat=0.5mm :
sat  30/ms = 1 / 33s
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Slide 9
Damping System Overview
Sensor


Input Level Control
Variable
Attenuator
Monitor

RF
Switch

Fiber Optic
Delay
 600 ns
Pre Amp
Variable
Delay
Fine Tuning
Variable
Attenuator
Gain
Control
Comb
Filter

Power Amps
Beam Kicker
Sensor and kicker are in the beam tunnel
Everything else is “upstairs” about 100 away
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Slide 10
Demonstration of Performance of the Damping System
Quantitative measure of performance:
Buncher voltage at threshold of instability
is reduced by 30% with the damper on
Buncher Field
Maintains beam bunch
Increases energy spread
lower energy
higher energy
Unstable oscillations “decohere” (Landau damping)
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Slide 11
System Performance
System provides 30% improvement
Why isn’t performance better?
Power?
Bandwidth?
Signal fidelity?
Horizontal instability?
Beam dynamics / nature of the instability?
Other?
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Slide 12
Damp-Grow-Damp Experiments – Exploring System Performance
Allow instability to grow, then turn
damper back on
Instability is damped
… then it returns!
Why?
No evidence of horizontal instability:
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Slide 13
Damp-Grow-Damp Experiments – Exploring System Performance
Bandwidth probably isn’t the problem:
There seems to be more power available:
Beam in the gap exacerbates electron
cloud build-up
Reduction of buncher voltage may not be
the best measure of performance
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Slide 14
Damping System Details – Beam Position Sensor
Signal at upstream end:
Signal minus time-delayed copy
 90 phase shift
sin t  sin  (t   )  2 cos(t   / 2) sin  / 2
cos t
sin t
This looks like differentiation:
(in the band of interest)
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d
sin t   cos t
dt
Slide 15
Damping System Details – Vertical Difference Signal
Signal out: Top minus Bottom
Broad-band (1 – 500 MHz)
Rapid processing ( 1 ns)
Beam position:
so
z
v T  B

v T  B
and
v  i
v  z  i
 Longitudinal “noise” in
the feedback signal
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Slide 16
System Details – Fiber Optic Delay

Long delay needed
•
700ns in addition to what is intrinsic to the system

Severe dispersion and attenuation in that much copper cable

Fiber optic link used instead

“Switchboard” reconfigurable
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Slide 17
Damping System Details – Power Amplifiers
Phase flatness is poor for f < 20MHz
Gain is lower than expected
50
Two of these
(1 for each kicker electrode)
Phase (deg)
40
48
30
46
20
44
10
0
42
-10
40
0
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Amplitude (dB)
50
Power Amplifier (0dBm)
50 100 150 200 250 300
f (MHz)
Slide 18
Damping System Details – Beam Kicker
Originally a stripline BPM
Kick power flows upstream
Length = 37cm
Shorter kicker  higher frequencies
Effective shunt impedance:
2
 L(1   ) 
 2 g  c 

R  2 Z L 
 sin 2 
 d


2c

(for parallel-plate geometry)
Z L : Load impedance
g  : Geometry factor ( 1)
c : Beam speed
d : Electrode separation
L : Electrode length
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Slide 19
Factors Possibly Limiting Performance of the System

Beam in the gap

Horizontal instability

Power
•
•

Coherent tune shift
•

90 shift
 i(t)
Bandwidth
•
•

10 to 15 % effect
v signal
•
•

Amplifiers
>1 kickers
Amplifiers
Kicker
Phase shifts
•
•
10 here and there can add up
Cables, amplifiers, delay box
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Slide 20
Beam in the Gap
A clean gap to allow extraction
kickers to turn on
Not-so-clean gap
Holds on to electron cloud
Also allows electron cloud to
dissipate as the gap passes by
Exacerbates instability
(We’ve done experiments on this)
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Slide 21
Horizontal Instability

We damped the vertical oscillations only
•

Horizontal instability is expected
•
•
•

Because the instability is seen there
But threshold intensity for vertical instability is lower than for horizontal
Threshold intensity  tune Neuffer et al, “Observations of a fast transverse instability in the PSR”
NIM A321 (1992) 1-12
QH > Qv (3.2 vs. 2.2)
We see signs of this when the vertical instability is damped
Maybe:
Horizontal
instability
Electron
Cloud
Vertical damping enabled,
Buncher set at threshold
Vertical
instability
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Slide 22
More Kick Power Using More Kickers
2  amplifier power  2  damping rate
2  # kickers  2  damping rate
This is on our wish list …
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Slide 23
Phase Errors
Cables from amplifiers to kicker
2 Cables
0
-5
Phase (deg)
Phase (deg)
0
-10
-5
-10
-15
-15
-20
-20
0
Delay Box
50 100 150 200 250 300
f (MHz)
0
50 100 150 200 250 300
f (MHz)
SNS is developing a digital LLRF system
FIR filters can correct these problems
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Slide 24
The 90 Phase Shift in the Vertical Difference Signal
For phase flatness, want a low f3dB
v signal  derivative of beam position
 Use an integrator
R
Vin
Vout
1/  90
well above f3dB
… but 1/ removes signal !
C
Other ideas:
Differentiator (  90)
We haven’t tried this (yet)
Cable 90 long
Works for narrow band
Comb filter
Gives 90 shift
More on this later…
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Slide 25
Signals from the Position Sensor - Sidebands
Path of one proton around the ring
Q = k + q = 2 + 0.19
# oscillations per revolution
Position signal: Pulses at 2.8 MHz (=fR)
Amplitude: Modulated at qfR
Betatron sidebands at (nq)fR
A deflecting field at a betatron sideband
frequency can resonantly drive the beam
…and the beam can drive such a deflecting field
 Instability
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Slide 26
Signals from the Position Sensor - Sidebands
v signals
Relatively low frequencies
Higher frequencies
Long beam bunch (80% of R)
Upper- and lower-sidebands
Orbital harmonics seen at low
frequencies
( q  0.2 )
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Slide 27
Waves on the beam
Snapshot of the beam with m=10 wave present
Wave moves around ring, but
not at proton revolution
frequency
Each proton oscillates at
betatron frequency
Amplitude of betatron oscillation
= wave amplitude
Betatron oscillations cause the
wave pattern to rotate
m
m > 0 : fast waves
upper sidebands
 Q
 1   R
 m
m < 0 : slow waves
lower sidebands
At a fixed location, one sees an
oscillation frequency of mm
Betatron sideband frequencies
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Slide 28
Instability and Lower Sidebands
Model: Beam wave drives a deflecting field in a cavity
Wave (drive) leads deflecting field (response) by 90 at resonance
Proton phase relative to deflecting field changes turn-to-turn
Deflecting field lags
proton motion by 90
 Stable
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Deflecting field leads
proton motion by 90
 Unstable
Slide 29
Comb Filters - Motivation
Beam current:
pulses at orbital frequency (fR)
If closed orbit is not centered at the BPM,
position signal pulses at fR
… in the time domain:
remove what
doesn’t change
turn-to-turn
These are not associated with the instability.
Lots of damper power can be wasted on harmonics of fR
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Slide 30
Comb Filter - Overview
IN
coax

FO
xmitter
Signal splitter
Developed by
Craig Deibele, SNS (ORNL)
Optic fiber
“Long leg”
1 or 2 turns long
(360ns or 720ns)

OUT
FO
rcver
Attenuator
matches signal
strengths
Subtract signals
(180 hybrid)
This subtracts this turn’s signal from the previous turn’s signal
Copper cable: Dispersion and attenuation in the long leg
 Use a fiber optic link
Subtract a signal from a time-delayed copy of itself
 90 phase shift
This could correct the phase shift from the BPM
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Slide 31
Comb Filter – Some Details
90 phase shift:
sin t  sin  (t   )  2 sin( ) cos[ (t   / 2)]
Signal minus
time-delayed copy
Amplitude
sincos
(90 shift)
delay
Amplitude factor changes sign across a notch
Damping at one LSB means
Driving at the next LSB
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Slide 32
Optimum Comb Filter Configuration
2180 shift between LSBs
2-turn delay in the long leg
(from the amplitude factor)
Time-domain picture:
90 overall shift is maintained
2 kicks
Of opposite polarity
2-turn delay
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Comb
Filter
90
Comb
Filter
90
90 overall shift is not maintained in
this configuration
Slide 33
Comb Filter – Some Details
Amplitudes in the two legs determine notch depth
As built:
0
200
LSB
150
100
S21 (dB)
-10
50
-15
0
-20
-50
-25
Phase(deg)
-5
-100
-30
-150
-35
-200
194
196
198
200
202
204
206
208
Frequency (MHz)
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Slide 34
Comb Filter - Results
No improvement in system performance
Closed orbit offset at the pickup had little effect on the system
Wasting power on revolution harmonics is not a major problem
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Slide 35
Instability Bandwidth – Mechanisms for Growth
Oscillations begin in narrow band …then the band grows
Why?
We’ve investigated
two mechanisms
for this growth:
1. Synchrotron motion
2. Coherent tune shift
These data courtesy of Bob Macek
Can we just damp the initial oscillation?
(Would allow a narrow-band system)
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Slide 36
Growth of Bandwidth – Synchrotron Motion Mechanism
Rotation in longitudinal phase space changes the projection of the beam onto the
phase axis
 Changes frequency content
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Slide 37
Growth of Bandwidth – Experiments with Synchrotron Motion
These data are from experiments by McCrady, Rybarcyk, Kolski
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Slide 38
Growth of Bandwidth - Non-uniform Coherent Tune Shift
Coherent tune shift depends on charge density
 changes along the beam bunch
Tune (Q) is different
here than it is here
…due to image current
“Bob Macek’s mechanism”
Constant tune:
Current-dependent tune:
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Slide 39
Growth of Bandwidth – Single-Turn Kick Experiment
Tune variation can be measured:
Growth of frequencies is observed:
These data courtesy of Bob Macek
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Slide 40
Longitudinal Noise and PSR Orbital Frequency
When PSR orbital frequency = Linac RF frequency  integer
Linac micropulses are “stacked”
This was the case till recently
High-frequency longitudinal structure is induced
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Slide 41
Longitudinal Noise and PSR Orbital Frequency
v  z  i
Longitudinal structure
shows up in v signal
Potential source of “noise”
Longitudinal structure is reduced
… but damping system
performance did not improve
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v signal is less noisy
Slide 42
Noise-Driven Beam
How does e-cloud remember
phase turn-to-turn?
Maybe head of proton beam
stores phase information
Try to destroy it with noise
Also: Does noise damp as well
as the v signal?
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Slide 43
Further Work / Wish List

Feedback in both planes

More kickers
•

Better beam from the linac
•

…with higher frequency capability
Constant energy
Coasting beam studies
•
•
Simpler system
Example: Drive beam at one frequency, then damp
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Slide 44
Summary

The damping system to control vertical oscillations associated with
the e-p instability provides 30% improvement

Improvements to the system have not enhanced performance

This work has motivated further understanding of the instability

Work continues…
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Slide 45