Studies of the Regenerative BBU Instability at the JLab...
Transcript of Studies of the Regenerative BBU Instability at the JLab...
Thomas Jefferson National Accelerator FacilityOperated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Studies of the Regenerative BBU Studies of the Regenerative BBU Instability at the JLab FEL UpgradeInstability at the JLab FEL Upgrade
Chris Tennant and Eduard Pozdeyev
Center for Advanced Studies of AcceleratorsJefferson Laboratory
CASA SeminarMarch 4, 2005
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Outline
Methods of BBU Suppression
Beam Optical Schemes• Theory• Experimental
Phase trombonePseudo-Reflector
Q-Damping Schemes• Active damping circuit• 3-Stub tuner
Summary and Future Plans
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Analytic Model for Multipass BBU• For the case of a two-pass ERL with a single cavity, containing a single HOM the
equation for the BBU threshold current is given by
where Vbeam is the beam voltage at the cavity, k is the wavenumber (ω/c) of the HOM, (R/Q)Q is the shunt impedance, Trecirc is the recirculation time and the Mijare the elements of the recirculation transport matrix
Inject at higher energy
Change HOM frequency
Change recirculation time
Damp HOM quality factor
)sin()(2
*recirc
beamthreshold TQQRkM
VIω
−=
αααα 2343214
212
* sincossin)(cos MMMMM +++≡
Alter beam opticsChange phase advanceReflect betatron planesRotate betatron planes
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Effect of Reflecting Optics
I. Reflecting Optics will Suppress BBU if…
I. The transfer matrix from an unstable cavity back to itself takes the form
II. The HOMs are oriented at either 0 or 90 degrees
⎟⎟⎠
⎞⎜⎜⎝
⎛0
0M
M
3214
3412 0MMMM
===
0cossin =αα
If α is different from 0 or 90 degrees, the effectiveness of reflecting optics in BBU suppression rapidly diminishes.
αααα 2343214
212 sincossin)(cos
1MMMM
Ithreshold +++−∝Recall…
-1500
-1000
-500
0
500
1000
1500
Thre
shol
d C
urre
nt (m
A)
350300250200150100500
HOM Orientation with Respect to the x-Axis (degrees)
Theory Simulation
Stable Stable
Thre
shol
d C
urre
nt
HOM Orientation w.r.t. the x-Axis
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Effect of Rotating Optics
αααα 2343214
212 sincossin)(cos
1MMMM
Ithreshold +++−∝Recall…
II. Rotating Optics will Suppress BBU if…
I. The transfer matrix from an unstable cavity back to itself takes the form
A rotation is effective regardless of the orientations of the HOMs
⎟⎟⎠
⎞⎜⎜⎝
⎛− 0
0M
M
3214
3412 0MM
MM−=
==
First passThe offending mode imparts an angular deflection, α, to a bunch
Second pass (after rotation)The resultant displacement will be orthogonal to the offending HOM. The bunch will be unable to couple energy to the mode that caused the deflection.
α
y’
x’
'r
(x’, y’)
αx
y
r(-y, x)
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Beam Optical Control of BBU
On-axis magnetic field kicks
electron beam in y direction
on the first pass via the
dipole HOM
First Pass Second Pass: Nominal Optics
The y kick results in a y displacement on the second pass through the cavity. This puts the electrons in a region of longitudinal field and they can deposit energy into the HOM field
Second Pass: 90° Rotated Optics
The y kick results in an x displacement on the second pass through the cavity. The bunches are in a region of zero longitudinal field and they cannot give energy to the HOM field. The feedback between the beam and HOM has been broken!
x
yz
Linac axis
Transverse magnetic field of dipole HOM
x
yz
Linac axis
HOM axial electric field
(90° out of phase with B field)
Courtesy T. Smith (HEPL)
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Skew-Quadrupole Reflector in the FEL
1.4x10-3
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Beam
Env
elop
es (m
)
wigglerSkew-quad reflector
• 5 skew-quadrupoles were installed in the backleg of the FEL to (locally) interchange the x and y phase spaces (D. Douglas)
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Local Reflector• With the reflector
activated, we also investigated the stability of several other potentially dangerous HOMs
I = 0.0 mA I = 3.5 mA I = 4.0 mA I = 4.5 mA I = 5.0 mA
BTF of 2106 MHz with Reflector ON
Frequency
Mag
nitu
de
Average Beam Current (mA)
Inve
rse
Qef
f
543210
2116 MHz in Cavity 7
QL = 6.4e+06Ith = -14 mA
543210
2106 MHz in Cavity 7
QL = 5.9e+06Ith = 9.2 mA
Average Beam Current (mA)
Inve
rse
Qef
f
543210
2114 MHz in Cavity 4
QL = 5.4e+06Ith = -8 mA
Average Beam Current (mA)
Inve
rse
Qef
f
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Local Reflector with a Change in Phase Advance• Ideally we would like to create a pure 90 degree rotation from the unstable cavity
back to itself2106 MHz with Reflector ON and
Phase Advance Changed
Average Beam Current (mA)In
vers
e Q
eff
2.52.01.51.00.5
QL = 5.0e+06Ith = -17 mA
Can you create a “global ” rotation with a “local ” reflector?Yes. By decreasing the vertical phase advance and then activating the local reflector, you can create a 90 degree rotation from the middle of Zone 3 back to itself (D. Douglas).
• For our measurements, the vertical phase advance was changed. Only after the difference orbit measure-ments have been analyzed, will we know what kind of transfer matrix was generated with this change in phase advance…
Because of the limited time setting up this configuration, the transmission was not good.
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What BBU “Looks Like”PLAY
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Phase Trombone
Recall…)34,(12
1M
Ithreshold ∝
• By all indications the 2106 MHz HOM is a vertically polarized mode• We change 4 vertically focusing quadrupoles in the recirculator to vary the vertical
phase advance
Quads changed +300 G
Mag
nitu
de
Frequency
StableIth = -7 mA
Ibeam = 0.5 mAIbeam = 1.5 mAIbeam = 2.5 mAIbeam = 3.5 mAIbeam = 6.0 mA
Quads changed +200 G
Frequency
UnstableIth = 12 mA
Ibeam = 0.0 mAIbeam = 3.5 mAIbeam = 4.0 mAIbeam = 4.5 mAIbeam = 5.0 mA
Mag
nitu
de
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Phase Trombone (cont’d…)
• We were able to easily change the quadrupole strengths from their nominal settings from -200 G to +300 G
• We observe a (1/sin) trend in the threshold current from measurements
)sin(1
)sin(1
21 ψββω ∆⎥⎦
⎤⎢⎣
⎡∝
rHOMthreshold T
I)sin(
1
34 rHOMthreshold TM
Iω
∝
-15
-10
-5
0
5
10
15
-400 -200 0 200 400
-15
-10
-5
0
5
10
15
2106.52106.02105.52105.0
Change in Quadrupole Strength (G)
Thre
shol
d C
urre
nt (m
A)
Thre
shol
d C
urre
nt (m
A)
HOM Frequency (MHz)
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Q-Damping Circuit
Concept: couple power from one of the HOM ports, shift it 180 degrees in phase, amplify the signal and feed it back through the same HOM port.
Active damping of an HOM located at 2106 MHz. The effect of the damping (right picture) is to decrease the loaded Q by a factor of ~ 10.
Directional Coupler
Network Analyzer
HOM 1
Variable Attenuator
Circulator Pre-amplifier
HOM 2
Directional Coupler
Variable Phase Shifter
10 dB
20 dBBandpass
Filter
20 dB
10 dB
BPF
Circulator
Port 2 Port 1
QL = 5.8 x 106 QL = 0.5 x 106
“Tuning Knobs”: the circuit is optimized by carefully tuning the phase and gain of the feedback loop
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Q-Damping Circuit (cont’d…)
• Damping circuit easily reduced the Q of the 2106 MHz mode by a factor of 5(Above a factor of about 10, the system becomes sensitive to external disturbances)
• The threshold is increased accordingly: from 2 mA to ~10 mA
HOMthreshold Q
I 1∝Recall… I = 0.0 mA
I = 3.3 mA I = 4.0 mA I = 4.8 mA I = 5.8 mA
Amplifier ON (Q = 1.3e06) Amplifier OFF (Q = 6.2e06)
Frequency
Mag
nitu
de
Average Beam Current (mA)
Inve
rse
Qef
f
Frequency
Mag
nitu
de
121086420
Ith = (7.6 - 10.6) mA
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3-Stub Tuner• The optimal setup requires a 3-
stub tuner for each HOM port on the cavity
• Had a difficult time and not such great data - perhaps because of broken HOM cable from Cavity 7
I = 0.5 mA I = 1.0 mA I = 1.5 mA I = 2.0 mA
Frequency
Mag
nitu
de2.52.01.51.00.50.0
Average Beam Current (mA)
Inve
rse
Qef
f
QL = 3.8e+06Ith = 2.5 mA
HOM 1
Circulator
HOM 2
10 dB
20 dB
10 dB
Circulator
Network Analyzer
Port 2 Port 1
3-stub tuner
3-stub tuner
BPF
Circulator
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Summary of Suppression Techniques
DampingCircuit
3-Stub Tuner
Phase Trombone
Pseudo-Reflector
Effect on 2106 MHz
HOMConsiderations for Implementation
Stabilized
Stabilized
• Works for only 1 mode per cavity• Not as effective at raising the threshold as
beam optical methods• Long term stability of system• Does not effect beam optics
• Can stabilize the mode against BBU• What are the effects on other HOMs?• Do they prevent reaching the requirements
needed for a suitable lasing configuration?
5 x Ith
1.5 x IthQ-D
ampi
ngB
eam
Opt
ics
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Summary and Future PlansSummary• Several methods proved to be effective at raising threshold current• It was demonstrated that using beam optical schemes, the dangerous HOM
could stabilized (i.e. it can no longer cause BBU)
Future Plans
Benchmark BBU Simulation Codes• Measure HOM polarizations• Perform BBU simulations using measured machine optics and compare with measurements
Attempt to suppress via beam-based feedback (i.e. do not effect optics and stabilize the mode) Active Damping Circuit
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AcknowledgementsA special thanks to the entire JLab FEL Team for the opportunity to do these measurements. And a particular thanks to the following individuals:
• Ivan Bazarov (Cornell)• Steve Benson• David Douglas• Georg Hoffstaetter (Cornell)• Curt Hovater• Kevin Jordan• Lia Merminga• Stefan Simrock (DESY)• Charlie Sinclair (Cornell)• Todd Smith (HEPL)• Haipeng Wang