MOPD027
Proceedings of IPAC’10, Kyoto, Japan
THE RF DESIGN OF THE LINAC4 RFQ
O. Piquet, O. Delferrière, M. Desmons, A.C. France, CEA Saclay, France
A. Lombardi, C. Rossi, M. Vretenar CERN, Geneva, Switzerland
Abstract
In the Linac 4 and the SPL, a 3 MeV RFQ is required
to accelerate the H- beam from the ion source to the DTL
input energy. While the 6-meter long IPHI RFQ was
initially chosen for this application, a CERN study [1]
suggested that a dedicated, shorter 3-meter RFQ might
present several advantages. The 2D cross-section is
optimized for lower power dissipation, while featuring
simple geometrical shape suitable for easy machining. RF
stability is evaluated using a 4-wire transmission model
and 3D simulations, taking electrode modulation into
account. The resulting RFQ is intrinsically stable and
does not require rod stabilizers. End circuits are tuned
with dedicated rods. RF power is fed via a ridged
waveguide and a slot iris. Vacuum port assemblies are
positioned prior to brazing to minimize RF perturbation.
The 32 tuning slugs form a set of stable sampling, able to
tune 9 modes. Tuner parameters are derived from beadpull accuracy specification and fabrication tolerances.
Signals delivered by pickup loops inserted in 16 of these
tuners will be used to reconstruct the voltage profile under
operation. Thermo-mechanical simulations are used to
design temperature control specifications.
INTRODUCTION
The Linac4 RFQ must be capable of providing the
Linac4 beam as the PS Booster injector, working at 1.1
Hz with 0.400 ms beam pulses, 70 mA beam current, or
to feed the Linac4 when working with the SPL either as
LHC injector (2 Hz, 1.2 ms, 40 mA) or as the neutrino
factory driver (50 Hz, 1.2 ms, 70 mA). The RFQ will be
of brazed-copper construction and will be built and
assembled at CERN (Figure 1).
A loaded, lossless 4-wire transmission line model is used
to relate differences between measured and desired intervane voltages (Figure 2) and to tune devices dimensions
(end plates and slugs) [2]. The location of the quadrant
bottom plane is adjusted for 345.53 MHz resonance
frequency with tuner in zero position. Electrical
parameters of 2D cross-section (without any tuner)
derived from 2D COMSOL simulations are given in
Table 1. The 346.020 MHz frequency anticipates tuner
bore detuning.
i2(z)
L2
U1
L'33
i1(z)
U2
L'12
L' 23
v 2(z)
i3(z)
L'11
Ca
v 3(z+dz)
i1(z+dz)
L3
C3
L4
v1(z)
i3(z+dz)
3
Cb
1
v 2(z+dz)
C2
C1
L1
L' 13
v 3(z)
i2(z+dz)
2
L'22
U3
C4
v 1(z+dz)
U4
4
z
z+dz
Figure 2: 4-wire line model.
Table 1: Transmission-line Parameters
Parameter
Value
Unit
parallel inductance
6.970031 10-9
H.m
parallel capacitance
30.352946 10-12
F/m
diagonal capacitance
1.954868 10-12
F/m
quadrupole eigen-frequency
346.020
MHz
dipole eigen-frequency
335.389
MHz
Table 2 reports the main electrical parameters for the
RFQ cavity, computed for the dipole and quadrupole
mode cut-off frequencies. The power dissipation is
calculated assuming 5 mΩ surface resistance for copper.
Table 2: RFQ Electrical Parameters
Figure 1: Linac4 RFQ.
RF DESIGN
Cavity design
The 2D section of the RFQ cavity has been kept
constant over the full RFQ length, in order to simplify the
mechanical fabrication.
Linac4 RFQ electrical
parameters
quadrupole
dipole
Units
Vane voltage
78.27
78.27
kV
Quality factor
10269
9936
Stored energy
0.372
0.395
J/m
Dissipated power
78.738
83.848
kW/m
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Proceedings of IPAC’10, Kyoto, Japan
Electric fieeld (max)
30.860
35.312
M
MV/m
Kilpatrick
1.675
1.917
Magnetic field
fi (max)
5444
5595
A
A/m
Magnetic fiield (in J6)
5397
5550
A
A/m
MOPD027
vanees, the rod and the endd plate, for thermal andd
mech
hanical simulaations (Figuree 5).
The study for thee tuning of thee end cells haas shown thatt
dipole rods are not requiredd because th
he frequencyy
sepaaration betweeen the acceleraating quadrupole mode andd
the adjacent
a
dipolle modes is abbout 5 MHz, which shouldd
guarrantee sufficiennt stability duuring operation
n.
Vane Moduulation Effect
Electrical parameters
p
(pparallel and diaagonal capaciitance
variations vs. abscissa along
a
RFQ, assuming
a
connstant
parallel induuctance) of V22TERM moduulated structurre are
estimated byy COMSOL 3D simulation of each RFQ
Q cell.
Quadrupole and dipole frequency shhifts (respecttively
-0.208Mhz and
a -3.871MH
Hz with respeect to their values
v
for un-moduulated structurre) are used to
t estimate EigenE
frequencies and
a voltage prrofile of moduulated cells (F
Figure
3). Q-mode frequency
f
shift and voltagee difference shhould
be easily canncelled by tuneers.
F
Figure
4: Vacuuum port.
Figure 3: Relative Q-modee voltage diffeerence vs. Abscissa.
Figgure 5: End ceell with rod.
VACUU
UM PORTS
p
are arraanged in arraays of diaphrragms
Vacuum ports
designed to attenuate thhe RF transsmission intoo the
vacuum systtem, but theese openings lead an appparent
increase of resonating volume.
v
This increase caan be
compensatedd by carefullyy adjusting thhe position off port
assembly in its RFQ openning. SOPRAN
NO 3D simulaations
have been peerformed to esstimate the opptimum positiion of
a port design (Figure 4). Furthermoree, the port wiill be
experimentallly adjusted before second brazing in ordder to
reduce mechhanical defaults due to machining
m
andd first
brazing.
END CEL
LLS TUNIN
NG
The tuninng of the end region, wiith respect too the
quadrupole mode,
m
is madde by adjustinng the length of 4
rods. 3D caalculations with
w
SOPRAN
NO software have
been perform
med (1) to opttimize the diam
meter and position
of the rod inn order to minnimize the electric field bettween
rod and vane, (2) to optiimize the tuniing range of these
rods and (3) to obtain thee power deposition on bothh, the
TU
UNING STR
RATEGY
Th
he tuning of thhe RFQ cavityy will be assurred by a set off
32 identical 80m
mm-diameter ppiston tuners plus the RF
F
inpu
ut coupler andd the three RF
F dummy porrts. (Figure 1))
Tuneer 2D inducctance slopee required by
b the RFQ
Q
transsmission line model are deerived from COMSOL
C
3D
D
simu
ulations. Diffferent slug tuuner position
ns have beenn
exam
mined, from -440 mm to +355 mm. The reesulting linearr
frequ
uency shift in
i [0, +35] sshows that Slater's
S
smalll
pertu
urbation theorry may be aapplied safely
y in this casee
(Figu
ure 6).
Tu
uner spacing is
i directly relaated to RFQ voltage
v
tuningg
process [3]. Beadd-pull measurrements are used
u
to sensee
longitudinal magnnetic field Hz(x0,y0,z) vs. abscissa z att
somee transverse loocation {x0,y0} in RFQ quaadrants, and a
conv
version factorr κ(z) = V(z)/Hz(x0,y0,z) is
i applied too
recov
ver the value of inter-vane voltage V(z).
CO
OMSOL 3D simulations hhas also show
wn that tunerr
spacing larger than 240 mm
m would yield
y
relativee
variaations of κ(z) less than a few
w 10-3.
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MOPD027
Proceedings of IPAC’10, Kyoto, Japan
Table 3: Calculated Tuuner Position Range
m position
min
p
max position
Tuner
T
(mm)
(mm
m)
slugs
s
-4.0
+3
30.5
freq-freq2
2D vs tuner penetration
Dborre = Dtuner + 2mm
35
3 Tuners / me
eter
30
Dtuner=80m
mm
freq-freq2D ( MHz )
25
Freq flush
f
= 345.525626 MHz
Freq
q 2D = 346.020509 MHz
20
RF
R port
0
+9.0
+
15
RF POWER
P
C
COUPLING
G
10
5
0
-5
-10
-50
-40
-30
-20
-10
0
10
20
30
40
penetration ( mm )
Figure 6: 3D frequenncy shift vs. tuuner position.
TU
UNER POS
SITION RA
ANGE
Errors inn the mechaanical consttruction havee an
important im
mpact on the electromagnet
e
tic behavior of
o the
RFQ cavity. Once the connstruction of the
t RFQ moduule is
achieved, theese errors cann be compenssated by meaans of
the slug tuuners. Tunerr position liimits requireed to
compensate for given connstruction erroors may be deerived
from inter-vvane capacitance errors. Tolerancess on
electrodes tipps are definedd by the two nuumbers t and δ:
δ
- center off curvature of each electrodee tip is locatedd in a
square with side
s 2t, centerred at its theorretical locationn;
- electrodee tip radius errror is boundedd by ±δ.
Present evaluation
e
usses t = 30 µm
m and δ= 100 µm.
Tuner positiions are alsoo used to com
mpensate forr CQQ
errors resultting from vane modulatioons. The resuulting
capacitance relative
r
error volume
v
is dispplayed in Figuure 7.
It is inscribeed in a parallelepiped bounnded by ±2.2293 %
along the QQ
Q axis, and ±3.516 % along SQ and TQ axes.
a
RF
F input port follows the same design
n as in IPHII
projeect. Coupling is tuned by addjusting the diiameter of thee
coup
pling hole. RF
F simulationss are used to estimate RF
F
lossees in RFQ crooss section, eend cells, vaccuum ports…..
The power dissippated by the ttuner assemblly is stronglyy
depeendent of tunner position rrange required for tuning..
Beam
m loading is
i 210 kW aat 70 mA beeam current..
Therrefore, the tottal power proovided to the RFQ may bee
estim
mated betweeen 480 kW and 620 kW.
W. HFSS andd
COM
MSOL softwaares are usedd to estimate coupling forr
diffeerent hole raddii (Figure 8). A radius beetween 6 mm
m
and 7 mm has beeen defined annd will be ad
djusted duringg
the setting
s
of the RFQ
R
accordinng to tuner possition.
Figuure 8: RF pow
wer coupling.
CONCLU
USION
A complete annalysis of thhe Linac4 RF
FQ has beenn
perfo
ormed using RF simulatting codes 3D
3 (Comsol,,
Soprrano and HFS
SS) and a RFQ
Q 4-wire tran
nsmission linee
mod
del. These toolls are used to calculate diffferent systemss
(as end
e cells or tuuner) requiredd to compensaate errors duee
to th
he mechanical construction.
Figure 7:: Capacitance relative error volume, in thhe
{QQ,SQ
Q,TQ} basis.
Tuner possition range required for compensatioon of
these capacitance errorss, and tuningg at 352.2 MHz
operating freequency, is evvaluated usingg method desccribed
in [3]. Resullting values (without
(
any safety marginn) are
shown in tabble 3.
[1] A. Lombardi,, C. Rossi, M
M. Vretenar, Design
D
of ann
RFQ Accelerrator optimizzed for Linacc4 and SPL,,
CERN-AB-20007-027-RF.
[2] O. Piquet, M.. Desmons, A
A. France Tuniing proceduree
of the 6 meterrs IPHI RFQ, PAC07.
[3] A. France, O.
O Delferrière,, M. Desmon
ns, O. Piquett
Design of slug tuners for thhe SPIRAL2 RFQ,
R
PAC07.
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A08 Linear Accelerators