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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
A. Gallo: The DAFNE 3rd Harmonic Cavity
SUMMARY:
A) Introduction
B) 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
A. Gallo: The DAFNE 3rd Harmonic Cavity
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
A. Gallo: The DAFNE 3rd Harmonic Cavity
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
Main RF voltage
Main cavity shunt
impedance
Main cavity Q-factor
Main cavity input
coupling factor
RF harmonic frequency
RF harmonic voltage
Harmonic cavity shunt
impedance
Harmonic cavity Q-factor
Natural bunch length
Bunch length
(lengthening regime)
RF acceptance
Typical lifetime (colliding
beams)
VRF [kV]
KLOE Run 2002
110
2004 Run
200
Rs=V2/2PRF [M]
1.9
1.9
Q0
31500
31500

 4.6
 4.6
fH [MHz]
VH [kV]
-----
1104.87=3 fRF
56
RH=V2/2PH [M]
---
0.48
Q 0H
z0 [cm]
--1.6 (@Ib  0 mA)
18500
2.5 (@Ib  0 mA)
z [cm]
2.5 (@Ib  20 mA)
3.1 (@Ib  35 mA)
RF/E
 0.5 %
 0.7 %
 3600 (@Ib  17 mA)
 2500 (@Ib  34 mA)
T [s]
 1300 (@Ib  17 mA)
A. Gallo: The DAFNE 3rd Harmonic Cavity
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).
A. Gallo: The DAFNE 3rd Harmonic Cavity
Beam Dynamics Issues:
A) Shift of the coherent synchrotron frequencies of the coupled
bunch modes
B) Spread of the bunch synchronous phases generated by a gap
in the bunch filling pattern
C) Bunch lengthening process in the double RF voltage regime
D) Touschek lifetime expected improvements
E) Beam dynamics in the cavity parking option
A. Gallo: The DAFNE 3rd Harmonic Cavity
Shift of the coherent synchrotron frequencies of the
coupled bunch modes
The interaction between the beam and
impedance of the two cavities perturbs
coupled bunch coherent motion (mainly
mode “0”, “1” and “Nb-1”) shifting
synchrotron frequency accordingly to:
2
 c   1  2 I c
 
i n

i2 2h E e
2
i2   RF
c

the
the
for
the
pZ i ( p r )e   p r  t  ; i  any integer
2
p  iN b  n  c
VRF sin  s  3VH sin  H
2h E e
(R/Q)H=25 
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.
A. Gallo: The DAFNE 3rd Harmonic Cavity
Spread of the bunch synchronous phases generated by
a gap in the bunch filling pattern
A 15÷25 % 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 selfgenerated 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.
A. Gallo: The DAFNE 3rd Harmonic Cavity
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.
A. Gallo: The DAFNE 3rd Harmonic Cavity
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 -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.
LFB ON
LFB OFF
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 simulated 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.
A. Gallo: The DAFNE 3rd Harmonic Cavity
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 (VRF=110
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
VRF=200 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.
A. Gallo: The DAFNE 3rd Harmonic Cavity
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.
Dn=2.5
A. Gallo: The DAFNE 3rd Harmonic Cavity
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
A. Gallo: The DAFNE 3rd Harmonic Cavity
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
A. Gallo: The DAFNE 3rd Harmonic Cavity
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
A. Gallo: The DAFNE 3rd Harmonic Cavity
DAFNE 3rd Harmonic Cavity: longitudinal impedance
measurements
MAFIA Simulations
Measurements
M4 monopole
M4 monopole
no wire
wire meas.
M1
M2
M3
M4
M5
M6
M7
M8
M9
f [GHz]
1.105
1.335
1.600
1.650
1.899
2.094
2.270
2.495
2.524
Q
R/Q []
23000
26
10
16
30
6
50
2
50
4
110
7
120
9
170
3
230
10
f [GHz]
1.105
Q
R/Q []
16500
21.4
not measurable (n.m.)
n.m.
n.m.
n.m.
n.m.
n.m.
1.65
168
16.8
n.m.
n.m.
n.m.
2.100
2289
2.466
2.507
224
60
140
278
n.m.
n.m.
n.m.
n.m.
The impedance of the cavity longitudinal modes have
been evaluated by measuring the Q-factors from portto-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.
A. Gallo: The DAFNE 3rd Harmonic Cavity
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.
D1
D2
D3
D4
D5
D6
f [GHz]
1.089
1.244
1.445
1.618
1.797
1.886
Simulations
Q
R/Q [/m]
438
66
35
26
158
22
158
29
266
37
283
24
Measurements
f [GHz]
Q
R/Q [/m]
1.070
450
146
not measurable (n.m.)
n.m.
n.m.
1.400
1.560
1.725
1.865
139
175
163
190
29
n.m.
n.m.
74
A. Gallo: The DAFNE 3rd Harmonic Cavity
DAFNE 3rd Harmonic Cavity:
Tuning and Parking
MAFIA model of
the cavity tuner
Port-to-port measurements of
the parked cavity (Dn=+2.5)
DAFNE 3rd harmonic cavity measured tuning range
A. Gallo: The DAFNE 3rd Harmonic Cavity
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);
A. Gallo: The DAFNE 3rd Harmonic Cavity
CONCLUSIONS (cnt’d):
• 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.
A. Gallo: The DAFNE 3rd Harmonic Cavity
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.