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HOM Studies at the FLASH(TTF2) Linac. Nathan Eddy, Ron Rechenmacher, Luciano Piccoli, Marc Ross FNAL Josef Frisch, Stephen Molloy SLAC Nicoleta Baboi, Olaf Hensler DESY. 5 accelerating modules. bypass line. gun. undulators. FEL beam. dump. collimator section. bunch compressors. - PowerPoint PPT Presentation
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HOM Studies at the FLASH(TTF2) Linac
Nathan Eddy, Ron Rechenmacher, Luciano Piccoli, Marc Ross
FNAL
Josef Frisch, Stephen MolloySLAC
Nicoleta Baboi, Olaf HenslerDESY
FLASH Facility (formerly TTF2)
• 1.3 GHz superconducting linac– 5 current accelerating modules, with a further two planned for
installation.– Typical energy of 400 – 750 MeV.
• Bunch compressors create a ~10 fs spike in the charge profile.– This generates intense VUV light when passed through the
undulator section (SASE).• Used for ILC and XFEL studies, as well as VUV-FEL
generation for users.
dumpbunch compressors
collimator section
bypass line5 accelerating modules
gunundulators
FEL beam
Higher Order Modes in Cavities
• In addition to the fundamental accelerating mode, cavities can support a spectrum of higher order modes.
• Traditionally they are seen as “bad”.– Beam breakup (BBU), HOM heating, …
• Here we investigate their usefulness,– Beam diagnostics– Cavity alignment– Cavity diagnostics
TESLA Cavities
• Nine cell superconducting cavities.• 1.3 GHz standing wave used for acceleration.• Gradient of up to 25 MV/m.
– Addition of piezo-tuners and improvement of manufacturing technique intended to increase this to ~35 MV/m.
• HOM couplers with a tunable notch filter to reject fundamental.– One upstream and one downstream, separated by 115degrees
azimuthally.– Couple electrically and magnetically to the cavity fields.
Response of HOM modes to beam
1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
x 109
107
108
109
Raw Spectrum
TE111dipole band
TM011Monopole band
TM110dipole band
Sample HOM Spectrum
• Beam Position Monitoring– Dipole mode amplitude is a function of the bunch charge and
transverse offset.– Exist in two polarisations corresponding to two transverse
orthogonal directions.• Not necessarily coincident with horizontal and vertical directions due
to perturbations from cavity imperfections and the couplers.• Problem – polarisations not necessarily degenerate in frequency.
– Frequency splitting <1 MHz (of same size as the resonance width).
• Beam Phase Monitoring– Power leakage of the 1.3 GHz accelerating mode through the
HOM coupler is approximately the same amplitude as the HOM signals.
• i.e. Accelerating RF and beam induced monopole modes exist on same cables.
– Compare phase of 1.3 GHz and a HOM monopole mode.
HOMs as a Beam Diagnostic
Narrow-band Measurements
• ~1.7 GHz tone added for calibration purposes.
• Cal tone, LO, and digitiser clock all locked to accelerator reference.
• Dipole modes exist in two polarisations corresponding to orthogonal transverse directions.
• The polarisations may be degenerate in frequency, or may be split by the perturbing affect of the couplers, cavity imperfections, etc.
• May be difficult to determine their frequencies.
Method
• Steer beam using two correctors upstream of the accelerating module.– Try to choose a large range of values in (x,x’)
and (y,y’) phase space.
• Record the response of the mixed-down dipole mode at each steerer setting.
BPMsaccelerating module
1 8
HOM electronicssteering magnets
electron bunch
Singular Value Decomposition (SVD) to Find Modes
• Collect HOM data for series of machine pulses with varying beam orbits
• Use SVD to find an orthonormal basis set.– Select 6 largest amplitude modes– Calculate mode amplitudes
• Linear regression to find matricies to correlate beam orbit (X,X’,Y,Y’), and mode amplitudes
• Use SVD modes and amplitudes to measure position on subsequent pulses
Singular Value Decomposition
jjj
j
jjnjn
j
VV
VV
S
S
UU
UU
X
1
11111
1
111
0
0
• SVD decomposes a matrix, X, into the product of three matrices, U, S, and V.– U and V are unitary.– S is diagonal.
• It finds the “normal eigenvectors” of the dataset.– i.e. “modes” whose amplitude changes independently of each other.– These may be linear combinations of the expected modes.
• Use a large number of pulses for each cavity.– Make sure the beam was moved a significant amount in x, x’, y, and y’.
• Does not need a priori knowledge of resonance frequency, Q, etc.– Similar to a Model Independent Analysis.
Predict position at one cavity from positions at adjacent cavities
X resolution ~ 6.1µm Y resolution ~ 3.3 µm
Cavity Alignment ACC5
• X: 240 micron misalignment, 9 micron reproducibility• Y: 200 micron misalignment, 5 micron reproducibility
Multi-Bunch Processing
Multi-Bunch Processing
Multi-Bunch Initial Results
HOM as BPM in DOOCs
VMEHOM
Front-End
DOOCsMatlab Vectors
Calibration Constants
DataBase
DisplayX, X’Y, Y’
HOM BPM Details
knk
n
jnj
n
kjk
j
AA
AA
XX
XX
VV
VV
1
111
1
111
1
111
n
n
n
n
knk
n
k
k
yy
yy
xx
xx
AA
AA
MM
MM
1
1
1
1
1
111
1,441
1,111
11111
Mode VectorsRaw Data
Amplitudes
Calibration Matrix
4D Position
k ~ 6, j ~ 100 to 4k
DESY System
• Need to read out raw data for mod*cav*coupler channels at 4k to 10k data points per for multibunch then perform dot products to determine mode amplitudes
• This requires a lot of I/O in the front-end (slow) and then a bunch multiply accumulates which must be done sequentially on the front-end processor
• The current system is unable to report a position for every pulse at 5Hz for single bunch even with only a few cavities per module enabled
Custom FPGA Based Board• Extreme flexibility inherent in
FPGA– Algorithms and functionality can
be changed and updated as needed
– Code base which can be used for multiple projects
– Intellectual Property (IP) cores provide off the shelf solutions for many interfaces and DSP applications
• The speed of parallel processing– Can perform up to 512
multiplies using dedicated blocks
• The Pipeline nature of FPGA logic is able to satisfy rigorous and well defined timing requirements
Dot Product FPGA Implementation
• Store mode vectors in FPGA RAM• Perform dot product (multiply accumulate) in FPGA for
digitized data as it arrives from ADC• Simply read out mode amplitudes which are available as
soon as data has arrived• Can perform calculation on all channels in parallel• Also able to store raw data in internal RAM
ADC
FPGA
xn*vn,jCoupler Data
Dedicated HOM BPM Digitizer
• Dedicated HOM Digitizer– Provide amplitudes in real time– Reduce front-end processor I/O and load by orders 3-
4 orders of magnitude• Maximum rate still limited by front-end I/O
– Provide bunch by bunch data for every pulse
• Design dedicated 8 channel digitizer– Modify existing design ~ 6 months– Commissioning time (have prototype already)– Conservative estimate of $200 per channel
Broadband System
• Broadband (scope-based) system– Monitor HOM modes up to 2.5GHz – Several simultaneous channels (4 or 8)– Limited dynamic range (8 bit scope)– Use for Phase measurement
Monopole Spectrum• Data taken with fast scope. Both couplers
for 1 cavity shown
Note that different lines have different couplings to the 2 couplers: More on this later
Monopole lines due to beam, and phase is related to beam time of arrival
Fundamental 1.3GHz line also couples out – provides RF phase
Analysis of Monopole Data
• Lines are singlets – frequencies are easy to find• Find real and imaginary amplitudes of the
waveform at the line frequency• Find phase angle for each HOM mode• Convert phases to times• Weight the times by the average power in each
line• Correct the scope trigger time using this
weighted average of the times• Calculate the phase of the 1.3GHz fundimental
relative to this new time
Beam Phase vs. RF Measurement During 5 Degree Phase Shift
Measure 5 degree phase shift commanded by control system
See about 0.1 degrees of rms
Summary• HOMs are useful for diagnostic purposes.
– Beamline hardware already exists.– Large proportion of linac occupied with structures.
• Beam diagnostics.– Accelerating RF and beam induced monopole HOM
exist on same cable.• No effect from thermal expansion of cables.• Can find beam phase with respect to machine RF.
– Dipole modes respond strongly to beam position.• Can use these to measure transverse beam position.
• Cavity/Structure diagnostics.– Alignment of cavities within supercooled structure.– Possibility of exploring inner cavity geometry by
examining HOM output and comparing to simulation.
Backup Slides
Intuitive modes?• This calibration matrix, M, shows how much of each SVD mode
contributes to the modes corresponding to x, y, (x’, y’).• Therefore, can sum the SVD modes to find the intuitive modes.
– Lack of calibration tone in the reconstructed modes, as expected.– Beating indicates presence of two frequencies, i.e. actual cavity modes
are rotated with respect to x and y.– Could rotate these modes to find orientation of polarisation vectors in the
cavity…
• Using SVD on the (n x j) cavity output matrix, X, produces three matrices.– U (n x j), S (j x j, diagonal), and V (j x j)
• V contains j modes.– These are the orthonormal eigenvectors.– “Intuitive” modes will be linear combinations of these.
• The diagonal elements of S are the eigenvalues of the eigenvectors.– i.e. the amount with which the associated eigenvector contributes to the
average coupler output.– It can be shown that the largest k eigenvalues found by SVD are the largest
possible eigenvalues.
• U gives the amplitude of each eigenvector for each beam pulse.
Using SVD
jjj
j
jjnjn
j
VV
VV
S
S
UU
UU
X
1
11111
1
111
0
0
Theoretical Resolution
• Corresponds to a limit of ~65 nm– Included 10 dB cable losses, 6.5 dB noise figure, and 10 dB
attenuator in electronics.• Need good charge measurement to perform
normalisation.– 0.1% stability of toroids, to achieve 1 um at 1 mm offset.– Not the case with the FLASH toroids.
• LO has a measured phase noise of ~1 degree RMS.– This will mix angle and position, and will degrade resolution.– LO and calibration tone have a similar circuit, and cal. tone has
much better phase noise.• Therefore, should be simple to improve.
2
2q
Q
RU
TkU bth 2
1Energy in mode – Thermal noise –
HOM Calibration Overview
DOOCs
VMEHOM
Front-EndMatlabControlCode
MatlabAnalysis
Code
TTF2CorrectorsBPMs, Etc
Display
Display
Matlab Data
Structure
Matlab Vectors
Steering Plots
Apply calibration to a different dataset
Practical system
• Can use 2 LO frequencies to mix both the 1.3GHz, and the 2.4GHz Homs to a convienent IF (~25MHz).
• Digitize with same system used for dipole HOM measurements.
• Filters will greatly improve signal to noise– Dual bandpass for 1.3GHz, and 2.4GHz– Risk introducing phase shifts from filters
• System low cost – couplers already exist, electronics is inexpensive.
HOM Downmix Board
Input and sample out
Bandpass filters
Pre-amplifier
Mixer
IF outputamplifier