HOM Studies at the FLASH(TTF2) Linac

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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

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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.

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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

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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.

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Response of HOM modes to beam
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Sample HOM Spectrum
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HOMs as a Beam Diagnostic

• 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 lt1 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.

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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.

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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.

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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

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Singular Value Decomposition

• 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.

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Predict position at one cavity from positions at
adjacent cavities
X resolution 6.1µm
Y resolution 3.3 µm
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Cavity Alignment ACC5

• X 240 micron misalignment, 9 micron
  reproducibility
• Y 200 micron misalignment, 5 micron
  reproducibility

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Multi-Bunch Processing
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Multi-Bunch Processing
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Multi-Bunch Initial Results
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HOM as BPM in DOOCs
VME HOM Front-End
Display X, X Y, Y
DOOCs
DataBase
Matlab Vectors Calibration Constants
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HOM BPM Details
Raw Data
Mode Vectors
Amplitudes
k 6, j 100 to 4k
Calibration Matrix
4D Position
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DESY System

• Need to read out raw data for modcavcoupler
  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

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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

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Dot Product FPGA Implementation
FPGA
ADC
S
xnvn,j
Coupler Data

• 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

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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

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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

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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
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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

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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
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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.

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Backup Slides
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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

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Using SVD

• 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.

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Theoretical Resolution
Energy in mode
Thermal noise

• 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.

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HOM Calibration Overview
VME HOM Front-End
TTF2 Correctors BPMs, Etc
Matlab Control Code
Display
Matlab Data Structure
DOOCs
Matlab Analysis Code
Display
Matlab Vectors
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Steering Plots
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Apply calibration to a different dataset
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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.

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HOM Downmix Board
IF output amplifier
Mixer
Pre-amplifier
Bandpass filters
Input and sample out
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