RFQ Beam Dynamics Design

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RFQ Beam Dynamics Design
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Basic RFQ vane profile with RFQ bunching

• Transverse dimensions are magnified compared with
  longitudinal.
• Beam goes from left to right.
• Four sections Radial Matching, Shaper, Gentle
  Buncher, Accelerator Section with changing cell
  geometry.
• Bunching is started in the Shaper. Adiabatic
  bunching (slow changes compared with the
  longitudinal oscillation period) is done in
  Gentle-Buncher section.
• Accelerator section typically maintains
  approximately constant synchronous phase and vane
  modulation.

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Example vane profile showing the four RFQ beam
dynamics sections- This is a 2-MeV 100-mA 80-MHz
D RFQ for neutron production.
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Radial matching of a continuous or DC beam into
the RFQ

• Matching of a continuous or DC beam into the RFQ
  presents a special problem.
• The matched ellipse parameters vary with the rf
  phase (or time) and are the same along the RFQ.
• One needs to provide a transition from a beam
  with time independent characteristics to one that
  has the proper variations with time.
• The solution is to taper unmodulated vanes at the
  RFQ input so that the radius decreases and the
  focusing strength increases from near zero to its
  full value over a distance of a few cells.
  Quadrupole symmetry is maintained throughout the
  RM section.

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Radial Matching section for matching a continuous
beam into the RFQ

• First, the matched ellipse parameters are found
  in the interior cells of the RFQ for different
  phases 90 degrees apart. These look very
  different.
• The ellipses at different phases tracked
  backwards to the input look very similar with a
  high degree of overlap. That is what we want.
• To obtain the best approximate beam match, the
  average of these ellipses is taken to be the
  matched ellipse at the input.
• Since x-x and y-y look almost identical, the
  matched input beam to the RFQ is nearly
  axisymmetric.
• If the ion source beam is axisymmetric, solenoids
  or triplets could be used for matching in the low
  energy beam transport (LEBT).
• For non-axisymmetric beams, quadrupole doublets
  can be used for beam matching into the RFQ.

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Beam envelope at phases 90 degrees apart in a
Radial Matching section. Three matched
phase-space plots (x-x and y-y) for phases 90
degrees apart are shown on the upper right. The
phase space plots at the upper left show the same
ellipses tracked backwards through the tapered RM
section. The lower plot shows the beam profiles.
Radial matching from K. Crandall using program
TRACE.
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Crandalls radial matching section

• Uses a four-term potential function
• Satisfies Laplaces equation
• Each potential term is zero at end wall
• Each potential term has physically reasonable
  s-shaped z dependence with zero at end wall and
  maximum at RFQ first cell.
• Longitudinal electric field is zero at the end
  wall and zero at first RFQ cell.
• Four equations in four unknowns are solved for
  four unknowns to get isopotential surface of RFQ
  vane profile.

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The RFQ can adiabatically bunch a continuous beam
beginning with m1, but can also be designed to
accelerate a prebunched beam.

• For a prebunched input beam the RFQ could begin
  with an mgt1 accelerator section.
• Prebunched beams have a smaller range of phases
  (maybe 60 deg or less) than for continuous
  beams.
• You can match for the average phase and have good
  matching for all phases. No need to worry about
  matching for a continuous beam.
• For a prebunched input beam, a RM section would
  not be necessary for matching.
• However, if we start abruptly with mgt1 the
  vanetip radii at the ends would not be equal and
  there would be an undesirable electric potential
  on axis. This can be corrected by adding a
  transition cell, to be discussed later.

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RFQ adiabatic bunching is important for
maintaining good beam quality in high current
beams.

• Bunching of high-current DC using rf cavities
  upstream of the linac increases the injected beam
  density causing space-charge-induced emittance
  blowup at high currents.
• K-T proposed adiabatic bunching with minimal
  compression of the beam density, avoiding the
  emittance blowup from space charge.
• But adiabatic bunching was not practical before
  the RFQ was invented, since it requires many
  longitudinal oscillation periods to gradually
  change the parameters, which requires a lot of
  real estate.
• Length of the adiabatic bunching section b3. So
  you need small b to shorten it.
• The RFQ allows adiabatic bunching within a
  practical length, by providing strong-focusing at
  low-velocities, which lowers the injection energy.

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Adiabatic bunching description

• The objective is to produce acceleration and high
  capture efficiency of the incident DC beam
  without longitudinal beam compression.
• Inject beam at low energy, typically 30 to 100
  keV for protons.
• Initial accelerating field is zero (no initial
  vane modulation).
• Initial synchronous phase -90 degrees, where
  the bucket has 360 deg phase acceptance. This
  allows beam capture at all input phases.
• Gradually increase the vane modulation to
  increase the accelerating field.
• Gradually increase the cell-to-cell spacings to
  move the synchronous phase towards the crest of
  the accelerating field.

In linac convention the crest of the
accelerating wave is at 0 deg, and phases for
acceleration and longitudinal stability range
from -90 to 0 deg.
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K-T approach to adiabatic bunching for
high-currents

• As the beam is accelerated, the bunch phase
  length shrinks, but the bunch spatial length in
  centimeters can remain nearly constant.
• Constant spatial bunch length avoids the large
  space-charge force from longitudinal compression
  that is associated with conventional bunching.

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Adiabatic bunching determines A and fs as
function of bs.

• In linear region, the product of longitudinal
  oscillation frequency times the squared bunch
  length is an adiabatic invariant. This implies
• Product of separatrix phase length Y times
  synchronous velocity is held constant. Controls
  bunch size in nonlinear region.

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Example vane profile with adiabatic bunching in
the gentle-buncher section. The shaper is a
prebuncher that linearly ramps phase and vane
modulation.
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RFQ beam-current limit formulas are the basis of
high current RFQ design

• For RFQ designs of high-current beams one needs
  to provide an adequate beam-current limit in the
  design process.The Physics
• RFQ beam current is limited by the strength of
  the electric focusing
• Focusing must compensate for space charge and
  must confine beam to within the available
  aperture.
• Both transverse and longitudinal current limits
  can be calculated from the RFQ parameters, based
  on 3D ellipsoid model for the space-charge
  field.
• Current Limit ReferencesT.P.Wangler, RF
  Linear Accelerators, John WileySons 2nd Ed.
  (2008) pp.301-302.T.P.Wangler, Space Charge
  Limits in Linear Accelerators, Los Alamos Report
  LA-8338 (1980).

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RFQ Beam Dynamics Movie

• This shows beam dynamics of the RFQ.
• Horizontal scale is exaggerated.
• Viewed from rest frame of a bunch. The vanes are
  moving.
• Notice that after bunch is formed the bunch
  physical length remains approximately constant,
  consistent with the design objective.

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RFQ input and output
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Special sections for input and output of the RFQ

• Radial matching section is typically 4 to 6
  cells long, has a flared vane profile, and can be
  used at either input or output of the RFQ.
• Dm transition cell can be used at either input
  or output to smoothly transition from m1 to mgt1
  or from mgt1 to m1.
• m1 section has pure quadrupole symmetry, and
  arbitrary length. Its Iength can be chosen to
  adjust the output transverse phase space ellipses
  

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Input radial matching section

• Input Radial Matching section provides transverse
  matching for a continuous (DC) input beam between
  the space-periodic low-energy transport line and
  the time-periodic RFQ.
• Crandall showed that radial matching works by
  gradually increasing the quadrupole focusing
  strength, done by reducing the aperture over a
  distance of about 4 to 6 RFQ cells. A converging
  input beam is required.
• A converging vanetip profile with pure quadrupole
  symmetry is also required.

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Beam envelope at phases 90 degrees apart in a
Radial Matching section. Three matched
phase-space plots (x-x or y-y) for phases 90
degrees apart are shown on the upper right. The
phase space plots at the upper left show the same
ellipses tracked backwards through the tapered RM
section. The lower plot shows the beam profiles.
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Output radial matching section

• Output radial matching section has a flared-out
  vane profile and can be used at the end of the
  RFQ vanes, where it eliminates an axial on-axis
  output potential.
• Also, output phase space ellipses for both x-x
  and
• y-y can be made identical (same Courant-Snyder
  parameters) after beam expansion in the output
  radial matching section. This is good for
  matching into an output solenoid channel.
• An output radial matching section allows matching
  to a periodic transport channel after the RFQ for
  both H and H- beams.

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RFQ transition cell (K. Crandall) is very useful
for either the entrance and exit of the RFQ.
First we discuss the RFQ exit.

• For an RFQ where the vanes end abruptly at the
  end of the last accelerating cell, the unequal
  spacing of the vanetips causes a time-varying
  on-axis potential at the end and undesirable
  output beam-energy variation.
• Consequently, Crandall introduced a new type of
  cell called the transition cell which makes a
  smooth transition from a full modulation (mgt1) to
  pure quadrupole symmetry (m1).

K.R.Crandall, Ending RFQ Vane Tips With
Quadrupole Symmetry, Proc. 1994 Linac Conf.,
Tsukuba, Japan, (Aug 21-26, 1994)pp.227-229.
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Vane-tip profiles from the RFQ two term potential
function for constant mgt1. The RFQ acceleration
cells with unequal aperture spacing and nonzero
on-axis potential and field.
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Now add Crandalls transition cell for ending RFQ
vanes with pure quadrupole symmetry. This avoids
unwanted energy change at the RFQ exit
Vane-tip profiles in final accelerating cell
(left) with mgt1 Is followed by a Dm transition
cell (right) which ends RFQ vanes in pure
quadrupole symmetry with m1
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Transition cell (continued)

• The transition cell is described by a special
  three-term potential solution to Laplaces
  equation.
• Crandall matches the potential and first two
  derivatives at the interface between the two cell
  types.
• The length of the transition cell is slightly
  less than bl/2 length of the last accelerating
  cell

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Transition cell can also be used at the RFQ
entrance for acceleration of a prebunched beam

• The RFQ can be designed to accelerate a
  prebunched beam which has a limited phase length.
  The beam doesnt need to be adiabatically bunched
  in the RFQ.
• You can use a transition cell going from m1 to
  mgt1 to avoid an on-axis potential at the
  entrance.

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RFQ transition cell at the entrance

• If you start RFQ with an mgt1 accelerator section,
  the lack of quadrupole symmetry means there is a
  time-varying on-axis potential at the input,
  which produces an undesirable time-dependent
  energy change at the input.
• The on-axis potential at the input is eliminated
  by beginning the RFQ with an entrance transition
  cell which starts the RFQ with pure quadrupole
  symmetry (m1) and transitions smoothly in one
  transition cell to the desired mgt1.
• The entrance transition cell is then followed by
  the first mgt1 accelerating cell.

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m1 section

• The m1 section is an optional section with
  unmodulated vanes (quadrupole symmetry) that can
  follow a exit transition cell.
• The length of the m1 cell may be chosen to
  provide the desired RFQ output transverse ellipse
  orientation.
• The ability to vary the phase of the output
  provides flexibility to facilitate matching at
  the RFQ exit. Examples are shown for different
  output phases on the right.

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MSU reaccelerator RFQ
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MSU Re-accelerator 4-Rod RFQ is being designed
and built. Beam dynamics by MSU, construction by
U. of Frankfurt.

• Input energy 12 keV/u
• Output energy 600 keV/u
• Trans. Emitt 0.6 p-mm-mrad
• Long. Emitt 0.3 p ns-keV/u
• Frequency 80.5 MHz
• Length 3.5 m
• Transmission 82
• Room temperature structure
• On order from U. of Frankfurt(Alwin Schempp)
• Delivery Fall 2009

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The ISIS Four-Rod RFQ at Rutherford Appleton
Laboratory35 keV to 665 keV H- beam, 202.5 MHz,
V90 kV showsa four-rod internal structure
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The MSU reaccelerator RFQ will look similar to
this CW 4-rod for SARAF (Soreq applied research
accelerator facility in Israel).4 mA D, CW,
3MeV, 176 MHz, 3.8 M , 220 kW, 39 cells.
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SARAF 4-ROD RFQ 4-mA D to 3 MeV, 176 MHz, 3.8
m long, 250 kW power 39 cells Tuning plates,
shown between the stems, are for flattening the
voltage distribution.
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Rough Details on 4-Rod RFQ for MSU (Some of this
may need to be updated.)

• Copper-plated steel for rods (short vanes) and
  stems, and an aluminum tank and Copper plating
  done at GSI.
• 20 to 30 of power losses are on the rods. Outer
  tank has about 5 of losses. Stems and tuning
  plates between the stems have the rest.
• 90 kV maximum intervane voltage.
• Stems are bolted to tank.
• Q4000.
• L3.5m
• RF power 150 kW for 90 kV on vanes and 3.5 m
  rod length. One power coupler in the middle of
  RFQ.
• Uses shims to align rods. Rods aligned to 100
  microns.
• Rods, stems, and outer tank are all water cooled.
  
• Rods are water cooled separately from stems since
  because they determine the capacitance, they have
  a big effect on resonant frequency.
• Water-cooled tuning plates between stems are
  independently positioned for achieving flat
  voltage profile. Intervane voltage profile
  uniform to 2.5 .
• Uses square tank instead of cylindrical tank
  because of better delivery time, 10 mo.
• Vacuum will require about two 500 liter/sec
  turbopumps provided by MSU.

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RFQ Beam Dynamics Features of MSU four rod RFQ

• The input beam is prebunched with a multiharmonic
  buncher (3 frequencies to approximate a sawtooth)
  instead of using adiabatic bunching within the
  RFQ. Prebunching shortens the RFQ.
• Transition cells at entrance and exit are used to
  provide proper transition from non-quadrupole
  symmetry at ends of a normal RFQ accelerating
  cell with m2 to quadrupole symmetry with m1.
  Transition cells reduce undesirable axial fields
  at entrance and exit gaps.
• Input end consists of a radial matching section
  followed by a transition cell. Output end
  consists of a transition cell followed by a
  radial matching section. These radial matching
  sections provide x-y symmetric phase space
  ellipses needed for matching to the external
  solenoid lenses.

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Beam Dynamics Features of MSU RFQ design

• A question still under study is whether the
  nonzero potential on axis caused by the
  nonsymmetric stem configuration at the ends of
  4-rod RFQ causes any problems. Schempp believes
  this is a small effect.

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Peak surface fields and RF electric breakdown are
important topics for the RFQ
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Kilpatrick Criterion on RF Breakdown
About 40 years ago, W. D. Kilpatrick analyzed
the data on rf breakdown, and proposed the
conditions that would avoid rf breakdown. The
results were expressed by T.J.Boyd in a
convenient formula
where f is the frequency, and EK is called the
Kilpatrick limit. The equation must be solved
iteratively for EK. The criterion is based on
experimental results that were obtained in an
era before clean vacuum systems were prevalent.
The criterion is conservative by today's
standards.
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Bravery Factor Modification
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RFQ Commissioning
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MSU Re-accelerator 4-Rod RFQ is being designed
and built. Beam dynamics by MSU, construction by
U. of Frankfurt.

• Input energy 12 keV/u
• Output energy 600 keV/u
• Trans. Emitt 0.6 p-mm-mrad
• Long. Emitt 0.3 p ns-keV/u
• Frequency 80.5 MHz
• Length 3.5 m
• Transmission 82
• Room temperature structure
• On order from U. of Frankfurt(Alwin Schempp)
• Delivery Fall 2009

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Rough Details on 4-Rod RFQ for MSU (Some of this
may need to be updated.)

• Copper-plated steel for rods (short vanes) and
  stems, and an aluminum tank and Copper plating
  done at GSI.
• 20 to 30 of power losses are on the rods. Outer
  tank has about 5 of losses. Stems and tuning
  plates between the stems have the rest.
• 90 kV maximum intervane voltage.
• Stems are bolted to tank.
• Q4000.
• L3.5m
• RF power 150 kW for 90 kV on vanes and 3.5 m
  rod length. One power coupler in the middle of
  RFQ.
• Uses shims to align rods. Rods aligned to 100
  microns.
• Rods, stems, and outer tank are all water cooled.
  
• Rods are water cooled separately from stems since
  because they determine the capacitance, they have
  a big effect on resonant frequency.
• Water-cooled tuning plates between stems are
  independently positioned for achieving flat
  voltage profile. Intervane voltage profile
  uniform to 2.5 .
• Uses square tank instead of cylindrical tank
  because of better delivery time, 10 mo.
• Vacuum will require about two 500 liter/sec
  turbopumps provided by MSU.

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SARAF four-rod RFQ is the first four rod RFQ
designed for CW (100) duty operation. MSU four
rod RFQ will be the second one.
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The MSU reaccelerator RFQ will look similar to
this CW 4-rod for SARAF (Soreq applied research
accelerator facility in Israel).4 mA D, CW,
3MeV, 176 MHz, 3.8 M , 260 kW, 39 cells.
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SARAF 4-ROD RFQ 4-mA D to 3 MeV, 176 MHz, 3.8
m long, 260 kW power 39 cells Tuning plates,
shown between the stems, are for flattening the
voltage distribution.
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Beam commissioning

• Operating in pulsed mode for beam commissioning
  with average power lt 200W, limited by beam
  diagnostics.
• Beam current measured in LEBT before the RFQ
  (Faraday cup) and also in MEBT after the RFQ
  (modular parametric current transformer).
• Output ion energy measured with time of flight
  with two MEBT BPMs used as phase pickups. Also
  Rutherford scattering monitor from thin gold foil
  target for beam energy measurement.
• Longitudinal bunch width measured with two Fast
  Faraday cups located downstream of RFQ.

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High RF power commissioning for SARAF four-rod RFQ

• The main challenge is removing 250 kW from the
  3.8-m rods, an unprecedented heat density. A
  high-flow water-cooling system including flow
  inside the rods is incorporated.
• A common RF conditioning procedure is to
  gradually raise the RF power at low duty factor,
  keeping the vacuum pressure below about 10-6
  torr.
• Then gradually increase duty factor. This allows
  RF conditioning while limiting risk of arcing
  damage on rods.

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High RF power performance status

• What performance has the SARAF RFQ achieved?
• -Design power for deuterons is 260 kW
• RF conditioning for about two months after
  opening up for the first time last year. Since
  then
• -Achieved 280 kW at 15 duty factor-Achieved
  240 kW CW for 30 min-Achieved 210 kW CW for 2
  hr
• -Achieved 190 kW CW for 12 hours.
• But recent field-emission problems and melting of
  a tuning plate forced them to open up for a
  second time.

I. Mardor et al. Status of the SARAF CW 40 MeV
Proton/Deuteron Accelerator , PAC2009,
Vancouver, to be published.
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Special actions to improve the RF conditioning
for the SARAF four-rod RFQ

• Needed to round sharp edges on bottom of rods
  especially where rods are in close proximity to
  stems, to reduce field-emission problems
• Cleaning the rods.
• Bake at 75 deg C for a week.
• Add a third cryopump to the two existing turbo
  pumps.
• A tuning plate melted due to extremely high
  current density for reasons not yet clear. It is
  being replaced.

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Geometry of RFQ rods and stems that had
field-emission
Back side of RFQ vanes have been machined to
avoid field emission near the opposite vane stem
(You can see the indentation . Max field there
is 13 MV/m.)
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Rods were remachined near where stems with
opposite voltage caused arcing damage
Rods showed signs of extensive field emission
between bottom of rods and stems of opposite
voltage. Rods were remachined and sharp edges
were removed.
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SNS four-vane RFQ

• Ratti et al., Proc. Of LINAC2002, Gyeongju,
  Korea, pp 329-331.
• 402.5 MHz RFQ accelerates 50 mA H- from 65 keV to
  2.5 MeV, 1-msec pulses at 60 Hz.
• Transmission measurement versus RF power agrees
  well with Toutatis code. (See the figure)
• Slit-and wire/harp collector to measure
  transverse emittance. Agreement of measured
  emittances with simulations is very good.

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SNS H- RFQ designed and built by LBNL65 keV to
2.5 MeV, 402.5 MHz

• 4-vane RFQ with p-mode stabilizers for dipole
  mode supression
• 4 modules with 3.72-m total length
• 402.5 MHz resonant frequency
• 640 kW pulsed power needed to achieve nominal
  gradientwithout beam
• 8 power couplers
• 80 fixed tuners
• Dynamic tuning implemented by adjusting cooling
  water
• 2.5 min. needed to reach stable operation from
  cold start

SNS RFQ seen from the LEBT (Low-Energy Beam
Transport) side.
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SNS transmitted beam current versus RF power. The
abcissa is the RF power which is proportional to
square of intervane voltage.
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SNS RFQ issues

• SNS had two operational events that are believed
  to have caused some problems with the RFQ
  frequency.
• One was with very low temperature of the cooling
  water which may have taken the RFQ out of design
  range.
• The other event resulted in an excess pressure in
  the cooling water.

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SNS RFQ issues (continued)

• Consequence appears to have been an irreversable
  resonant frequency shift that was out of range of
  feedback citcuit.
• The frequency shift was fixed by adjusting the
  fixed tuners which has since provided stable
  operation.

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ISIS 4-rod RFQ
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ISIS (Rutherford Appleton Lab) four-rod RFQ

• Letchford et al., Proc of 2005 Particle Accel.
  Conf. Knoxville, Tennessee
• X-ray end-point measurement confirms the vane
  voltage calibration by monitoring the
  bremsstrahlung from the cavity.
• As design field level was approached during
  commissioning, sparking and vacuum pressure
  increased. Eventually full field level was
  achieved.
• But after 2000 hours of operation the spark rate
  began to increase until operation at design field
  level was no longer possible.

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ISIS four-rod RFQ (cont)

• Visual inspection through window on the cavity
  showed considerable arcing damage on vanes.
• RFQ was dismantled to clean and polish the rods
  (easy to do with the removable insert).
• After reassembly the RFQ was baked using 200 W of
  CW RF power with cooling water shut off.
• Since then the RFQ has operated with no
  degradation of performance. The X-ray dose rate
  fell by two orders of magnitude.

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An explanation for the ISIS RFQ problems

• Due to miscommunication during assembly, some
  parts may not have been cleaned after machining
  and assembly.
• The resulting arcing got worse and worse until
  they couldnt maintain the design field level.
• They had to open up to clean and polish to repair
  the arcing damage.

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ISIS RFQ commissioning results

• An electrostatic energy separator was used to
  distinguish accelerated beam from non-accelerated
  beam at the output.
• Observed transmission of accelerated beam 95
  agreed well with simulations.
• Output beam energy and energy spread was measured
  with a gas scattering energy analyser. Good
  agreement with simulations.
• Bunch length at RFQ output was measured using a
  moveable fast Faraday cup. Good agreement as
  function of vane voltage with simulations.
• Transverse beam emittances were measured at RFQ
  output. For matched beam at input, there was no
  observable emittance growth at output, in
  agreement with simulations.