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THE DAFNE 3RD HARMONIC CAVITY
A. Gallo , with D. Alesini, R. Boni, S. Guiducci,
F.Marcellini, M. Migliorati, L. Palumbo, M. Zobov
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SUMMARY

• Introduction
• DAFNE Beam Dynamics with the harmonic cavity
• Shift of the coupled bunch mode coherent
  synchrotron frequencies
• Spread of the bunch synchronous phases generated
  by a gap in the bunch filling pattern
• Bunch lengthening process in the double RF
  voltage regime
• Touschek lifetime expected improvements
• C) Harmonic Cavity Design, Construction and
  Measurements
• Cavity profile design
• Integration of the KEK-B SC cavity HOM damper in
  the design
• Cavity construction and bench measurements

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INTRODUCTION Motivations for Installing a
Harmonic Cavity at DAFNE

• Improving the Touschek lifetime by lengthening
  the bunch ()
• Improving the Landau damping coming from the
  non-linearity of the voltage along the bunch
• Adding one degree of freedom to the ring
  longitudinal focusing, that allows setting more
  independently the bunch length and the RF
  acceptance. In this way a whole class of beam
  experiments becomes available.
• () not only also by increasing the ring dynamic
  aperture and the RF acceptance

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If the harmonic voltage is phased to reduce the
total RF slope, the bunch natural length
increases. The further lengthening produced by
the ring wakes can be estimated by a
multiparticle tracking simulation
 
Working point of the main and harmonic RF systems
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The required harmonic voltage is very moderate
(56 kV), while the stored multibunch current is
quite large (typically 1A). The harmonic voltage
can be easily generated from the passive beam
excitation of one cavity per ring. The passive
option is far less complicated and expensive
compared to the active one. In this case the
cavity efficiency is not the first priority and
the cavity design can be mainly addressed to the
HOM suppression
 
In the passive mode the cavity has to be
progressively detuned from the 3rd harmonic line
as the current increases to keep the harmonic
voltage constant. The harmonic voltage can be
switched off by tuning the cavity far from the
3rd harmonic line of the beam spectrum and in
between two revolution harmonics (parking option).
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Beam Dynamics Issues

• Shift of the coherent synchrotron frequencies of
  the coupled bunch modes
• Spread of the bunch synchronous phases generated
  by a gap in the bunch filling pattern
• Bunch lengthening process in the double RF
  voltage regime
• Touschek lifetime expected improvements
• Beam dynamics in the cavity parking option

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Shift of the coherent synchrotron frequencies of
the coupled bunch modes
The interaction between the beam and the
impedance of the two cavities perturbs the
coupled bunch coherent motion (mainly for mode
0, 1 and Nb-1) shifting the synchrotron
frequency accordingly to
The reduction of the mode 0 coherent frequency
is not dangerous since the motion is heavily
Robinson damped. A weak excitation of mode 1 is
expected to be damped by the Longitudinal
Feedback System.
(R/Q)H25 ?
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Spread of the bunch synchronous phases generated
by a gap in the bunch filling pattern
A 1525 gap in the bunch filling pattern is
required in DAFNE operation to avoid ion trapping
in the e- ring. Macro-particle tracking
simulations predict the behaviour of non-uniform
beams in the ring. Different bunches along the
train experience different kicks from the
self-generated long range wakes. A spread of the
bunch parasitic losses results.
47 out of 60 bunches
The parasitic loss spread is converted in a
synchronous phase spread by the RF voltage curve.
Being the local RF slope reduced by the harmonic
voltage contribution, the synchronous phase
spread is much enlarged compared to the no
harmonic cavity case.
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Lengthening process of the bunches along the
train in the double RF voltage regime
The bunch centroids occupy different positions
along the total RF voltage (which is largely
non-linear). Then each bunch seats at a
different RF slope and have its own synchrotron
frequency and charge distribution. So, each bunch
has its own "natural" length, its equilibrium
profile (in the lengthening regime) and, in the
end, its own Touschek lifetime.
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Spread of the bunch synchronous phases effects
on the Longitudinal Feedback System performances
A large spread of the synchronous phases can
change the position of the interaction point (IP)
from bunch to bunch affecting the luminosity if
some bunches collide out of the vertical
b-function waist. If the synchronous phase spread
is equal in the two beams, the IP positions
remain fixed and only the collision times vary
with respect to the RF clock.
A large synchronous phase spread can also affect
the LFB performances if the front-end and/or the
back-end hardware lose its synchronization over
some bunches. The tracked oscillations of bunches
1, 24 and 47 simu-lated for a 1.6 A, 47 bunches
beam are shown. Under these conditions the LFB
seems still effective, while also a Landau
contribution to the beam stability is visible.
LFB ON
LFB OFF
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Touschek lifetime expected improvements
Lifetime evaluations have been made by a
dedicated code that takes into account the
limited physical aperture of the vacuum chamber
but not the limitations in the momentum
acceptance coming from the ring dynamic aperture.
Bunch currents of 17 and 34 mA have been
considered.
The blue plots are normalized to the KLOE 2002
run case (VRF110 kV) and the average lifetime
improvement over the bunch train is expected to
be ?80. The red plots are normalized to the the
case of a single voltage VRF200 kV and the
average lifetime improvement over the train,
coming only by the bunch lengthening in this
case, is ?35. These computed factors are now
more realistic since recently the DAFNE dynamic
aperture has been considerably increased.
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The cavity parking option
The harmonic voltage can be almost completely
switched off by tuning the cavity away from the
3rd harmonic of the RF and in-between two beam
revolution harmonics. The coupled bunch modes
having their unstable sidebands near the adjacent
harmonics are only weakly excited, while the
synchronous phase spread much less emphasized.
Dn2.5
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DAFNE 3rd Harmonic Cavity Main Features

• Round Shape Aluminium Cell
• Low R/Q (?25 ?)
• Wide  Tunability     (-1.5 frev? 3.5 frev)
• KEK-B SBP Ferrite Damper
• Cavity to Damper Tapered Connection
• No direct Ferrite exposure to the Beam

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DAFNE 3rd Harmonic Cavity HFSS Simulations
s21 monopole port to port transmission by HFSS
simulations
Fundamental M1 mode confined in the cell
High Order M4 monopole damped in the ferrite load
s21 dipole port to port transmission by HFSS
simulations
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DAFNE 3rd Harmonic Cavity bench measurements
DAFNE 3rd harmonic cavity (with no ferrite damper
and tuner) on bench
DAFNE 3rd harmonic cavity port-to-port
measurements and mode identification
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DAFNE 3rd Harmonic Cavity longitudinal impedance
measurements
M4 monopole
no wire
wire meas.
M4 monopole
The impedance of the cavity longitudinal modes
have been evaluated by measuring the Q-factors
from port-to-port measurements and the R/Q
factors with the wire excitation method. The wire
measurements have given no clear results, with
the exception of the fundamental mode M1, because
the resonant impedances were not distinguishable.
In the case of the M4 monopole, the wire changed
so much the field configuration that the mode
resulted undamped and its impedance value
unrealistic.
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DAFNE 3rd Harmonic Cavity transverse impedance
measurements
In the wire measurements of the transverse
impedance of the cavity dipoles the D1, D3 and D6
modes were recognizable. Their estimated
impedance is reported in the table below, and
their contribution to the machine transverse
impedance is substantially smaller than that
given by the less damped dipole modes of the main
RF cavity.
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DAFNE 3rd Harmonic Cavity Tuning and Parking
MAFIA model of the cavity tuner
Port-to-port measurements of the parked cavity
(Dn2.5)
DAFNE 3rd harmonic cavity measured tuning range
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CONCLUSIONS

• One harmonic cavity per ring passively powered by
  the beam will be installed in DAFNE in the near
  future (middle 2004?) to lengthen the bunches.
  The expected Touschek lifetime increase, due also
  to improvements of the dynamic aperture and RF
  acceptance, is ? 80
• Positive effects on the beam dynamics due to
  larger Landau damping and larger natural bunch
  length are also expected
• The shift of the coupled bunch coherent
  synchrotron frequencies are under control, since
  the R/Q of the passive cavity is not too high
• The presence of a gap in the bunch filling
  pattern will produce a large spread of the
  synchronous phases. Different bunches will
  collide at slightly different IPs and the
  synchronization of the bunch-by-bunch feedback
  systems may be affected
• The actual tolerability of such effects can not
  be exactly predicted since it depends on the
  operating conditions (such as the gap width)

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CONCLUSIONS (cntd)

• The bunch charge distribution changes for
  different bunches along the train and the
  Touschek lifetime gain is not uniform over the
  train
• The parking option, which virtually switch-off
  the harmonic voltage, can be considered as a
  reliable back-up procedure in case the effects of
  the gap in the filling pattern will result
  unmanageable
• Two cavities have been designed, built and tested
  on bench. A very good suppression of the HOMs has
  been obtained by incorporating in the design the
  SBP ferrite damper of the KEK-B SC cavities
• The bench measurements are in substantial
  agreement with computer simulations based on the
  MAFIA and HFSS codes
• The cavity can be tuned over a wide range (5
  revolution harmonics around the RF 3rd harmonic)
  with a tuning plunger with a long stroke.

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Thanks to Dr. Furuja and to the KEK-B staff for
providing us 3 SBP ferrite dampers, together with
their expertise to make them work.