Studies of the Regenerative BBU Studies of the Regenerative BBU - - PowerPoint PPT Presentation
Studies of the Regenerative BBU Studies of the Regenerative BBU Instability at the JLab FEL Upgrade Instability at the JLab FEL Upgrade Chris Tennant and Eduard Pozdeyev Center for Advanced Studies of Accelerators Jefferson Laboratory CASA
Thomas Jefferson National Accelerator Facility
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Chris Tennant and Eduard Pozdeyev Center for Advanced Studies of Accelerators Jefferson Laboratory CASA Seminar March 4, 2005
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Phase trombone Pseudo-Reflector
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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 Mij are the elements of the recirculation transport matrix Inject at higher energy Change HOM frequency Change recirculation time Damp HOM quality factor
* recirc beam threshold
2 34 32 14 2 12 *
Alter beam optics
Change phase advance Reflect betatron planes Rotate betatron planes
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I. Reflecting Optics will Suppress BBU if… I. The transfer matrix from an unstable cavity back to itself takes the form
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ M M
32 14 34 12
M M M M = = = cos sin = α α
If α is different from 0 or 90 degrees, the effectiveness of reflecting
in BBU suppression rapidly diminishes.
α α α α
2 34 32 14 2 12
sin cos sin ) ( cos 1 M M M M Ithreshold + + + − ∝
Recall…
500 1000 1500 Threshold Current (mA) 350 300 250 200 150 100 50 HOM Orientation with Respect to the x-Axis (degrees) Theory Simulation Stable Stable
Threshold Current HOM Orientation w.r.t. the x-Axis
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α α α α
2 34 32 14 2 12
sin cos sin ) ( cos 1 M M M M 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 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − M M
32 14 34 12
M M M M − = = =
First pass The offending mode imparts an angular deflection, α, to a bunch Second pass (after rotation) The resultant displacement will be
The bunch will be unable to couple energy to the mode that caused the deflection.
α
y’ x’
'
α
x y
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electron beam in y direction
dipole HOM
First Pass
The y kick results in a y displacement
This puts the electrons in a region of longitudinal field and they can deposit energy into the HOM field
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 y z
Linac axis Transverse magnetic field of dipole HOM
x y z
Linac axis HOM axial electric field (90° out of phase with B field)
Courtesy T. Smith (HEPL)
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1.4x10
1.2 1.0 0.8 0.6 0.4 0.2 0.0 Beam Envelopes (m )
wiggler
Skew-quad reflector
interchange the x and y phase spaces (D. Douglas)
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activated, we also investigated the stability of several
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 Magnitude
Average Beam Current (mA) Inverse Qeff
5 4 3 2 1
2116 MHz in Cavity 7
QL = 6.4e+06 Ith = -14 mA
5 4 3 2 1
2106 MHz in Cavity 7
QL = 5.9e+06 Ith = 9.2 mA Average Beam Current (mA) Inverse Qeff
5 4 3 2 1
2114 MHz in Cavity 4
QL = 5.4e+06 Ith = -8 mA Average Beam Current (mA) Inverse Qeff
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back to itself
2106 MHz with Reflector ON and Phase Advance Changed Average Beam Current (mA) Inverse Qeff
2.5 2.0 1.5 1.0 0.5 QL = 5.0e+06 Ith = -17 mA
with a “local ” reflector?
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).
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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PLAY
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Recall…
) 34 ,( 12
1 M Ithreshold ∝
phase advance
Quads changed +300 G Magnitude Frequency
Stable
Ith = -7 mA
Ibeam = 0.5 mA Ibeam = 1.5 mA Ibeam = 2.5 mA Ibeam = 3.5 mA Ibeam = 6.0 mA
Quads changed +200 G Frequency
Unstable
Ith = 12 mA
Ibeam = 0.0 mA Ibeam = 3.5 mA Ibeam = 4.0 mA Ibeam = 4.5 mA Ibeam = 5.0 mA
Magnitude
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settings from -200 G to +300 G
) sin( 1 ) sin( 1
2 1
ψ β β ω ∆ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∝
r HOM threshold
T I ) sin( 1
34 r HOM threshold
T M I ω ∝
5 10 15
200 400
5 10 15 2106.5 2106.0 2105.5 2105.0
Change in Quadrupole Strength (G) Threshold Current (mA) Threshold Current (mA) HOM Frequency (MHz)
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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 dB Bandpass 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
and gain of the feedback loop
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2106 MHz mode by a factor of 5
(Above a factor of about 10, the system becomes sensitive to external disturbances)
from 2 mA to ~10 mA
HOM threshold
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 Magnitude Average Beam Current (mA) Inverse Qeff Frequency Magnitude
12 10 8 6 4 2
Ith = (7.6 - 10.6) mA
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stub tuner for each HOM port on the cavity
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 Magnitude
2.5 2.0 1.5 1.0 0.5 0.0
Average Beam Current (mA) Inverse Qeff QL = 3.8e+06 Ith = 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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Damping Circuit 3-Stub Tuner Phase Trombone Pseudo- Reflector Effect on 2106 MHz HOM Considerations for Implementation Stabilized Stabilized
beam optical methods
needed for a suitable lasing configuration? 5 x Ith 1.5 x Ith Q-Damping Beam Optics
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could stabilized (i.e. it can no longer cause BBU)
Benchmark BBU Simulation Codes
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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A special thanks to the entire JLab FEL Team for the opportunity to do these