5.1 Cavity and Coupling Coil Module
5.1.1 Introduction
Eight 201.25-MHz RF cavities, in two 4-cavity assemblies, are needed in the cooling channel
for the MICE experiment. The cavity design is based on that for the Study-II cooling channel,
a 2.75-m lattice with four cavities per cell. Due to the (financial) limitation of having only 8
MW of RF power available, the MICE cavities will be operating at a gradient of about 8
MV/m (compared with the 16 MV/m specification for the Study-II cooling channel), and thus
will provide a maximum accelerating RF voltage of 21 MV. As the cavities must operate in a
strong magnetic field, normal conducting technology must be utilized. In addition, to
accommodate the large transverse size of the muon beam, a large beam aperture is needed.
These somewhat conflicting requirements make it very inefficient to use a conventional openiris cavity geometry, as the cavity shunt impedance decreases significantly with increasing
beam iris size. The cavity shape chosen is based on a slightly re-entrant rounded pillbox
profile with a very large beam aperture and a small nose cone. To achieve high shunt
impedance, the beam aperture is terminated electromagnetically using thin, curved beryllium
foils (“windows”) or possibly thin-walled Al tubes (“grids”). These Be windows or grids can
be almost transparent to the muons, while presenting a good conducting boundary for the RF
fields.
A module containing a 4-cavity assembly and a coupling coil, referred to as the “RFCC
module” is shown in Figure 5.1-1. Here, we describe the electrical, mechanical, and thermal
requirements of the cavities and possible iris structures.
201 MHz Cavity
Curved Be window
SC coupling coil
Figure 5.1-1. Four 201 MHz cavities are shown installed in the MICE cooling channel. This
drawing shows the RFCC module
5.1.2 The cavity profile
The MICE cavity has a shape similar to that for the Study-II design, that is, a slightly
reentrant, rounded pillbox profile with a large beam aperture, as shown in Figure 5.1-2. The
cavity geometry is optimized in terms of minimizing peak surface field and in terms of
accommodating either Be windows or grids to close the beam iris. The cavity length is chosen
to give the maximum shunt impedance for a given space. In the Study-II design, the central
cavities in each cooling cell had 21-cm radius beam irises, while the end cavity irises were
reduced to 18 cm radius to take advantage of the lower beta function close to the absorbers.
By design, the irises are thick enough to accommodate either a pair of foils or a grid of tubes.
For MICE, all cavities will have the same beam iris dimension, 21-cm radius, and they are
terminated by thin pre-curved Be foils. Foils are curved in the same direction to minimize
cavity frequency shifts due to foil deformation under RF heating. Compared with the Study-II
design, where pre-stressed or stepped windows were proposed, the pre-curved window has
higher mechanical strength with a predictable deformation direction under RF heating. The
cavity frequency shifts induced by the window deformation are smaller and well within the
tuner’s tuning range.
Figure 5.1-2. The 201 MHz MICE cavity profile
There are four 4-inch ports at the cavity equator for RF couplers, vacuum, and diagnostics.
The four ports are evenly distributed around the cavity equator, which means that they must
penetrate the equator’s e-beam weld joint. These ports will be pulled directly through the
cavity equator weld. To simplify port fabrication, we employ a 6.5º spherical section from
the cavity center line, as indicated in Figure5.1-3, to permit simple circular cuts at the equator.
A 2º angle is used on the cavity side walls to avoid creating a parallel-plane geometry, since
such a geometry, in general, enhances multipactoring. Of course, with strong external
magnetic fields in the cooling channel, it remains to be seen whether this small tilt angle
helps.
This cavity profile, in combination with the pre-curved Be windows, allows more space
between the cavities for the tuner mechanism and for mounting the windows themselves. Any
practical assembly of foils (or grids) requires some space for installation and access. The
selected configuration, with each pair of cavities having curved windows oriented in opposite
directions, provides more space for the superconducting (SC) coupling coil and tuner
structure, as indicated in Figure 5.1-1.
Table5.1-1. Main calculated cavity parameters for the 201-MHz cavity.
Parameter
Radius (mm)
Length (mm)
RT2 (M/m)
Quality factor, Q0
Value
610
430
22
54,000
5.1.3 Terminations of the beam iris
Due to the short lifetime of muons, the cooling channel length must be kept to a minimum.
This calls for use of the highest possible gradient RF accelerating structure in the channel. As
already noted, given the large transverse size of a muon beam, it is obvious that
accommodating it using conventional open-iris RF structures would be very inefficient for
acceleration. However, a great improvement in shunt impedance of the cavity can be made if
we close the beam iris electromagnetically by using either a thin metal foil or thin-walled
tubes. To minimize scattering of the muons by the cavity terminations, we choose a low-Z,
thin with good electrical and thermal conductivity material. In our baseline design, we adopt a
pre-curved thin beryllium window to cover the iris. The requirement on thickness is that the
windows must be sufficiently thick to conduct away the heat generated by the RF currents,
keeping the thermal stress within the window well below the Be yield-strength limit.
Be windows
The Be window is made from a thin pre-formed high-purity beryllium sheet that is bonded (or
brazed) to a copper annular ring. Figure5.1-3 shows a picture of a pre-curved Be window for
an 805 MHz cavity. This window is approximately one-third scale version of the window
needed for the 201 MHz cavity.
Figure5.1-3. An 8-cm-radius curved Be window made by Brush-Wellman for 805-MHz RF cavity
tests. An equivalent 21-cm-radius window will be used for the MICE 201-MHz cavity.
Thermal performance
When the foil is heated by RF power, the only cooling mechanism for the window is thermal
conduction within the foil from center to edge. In such a case, the temperature distribution
assumes an approximately fourth-power profile versus window radius. Figure 5.1-4 shows a
calculated temperature distribution in a 0.38-mm-thick Be foil assuming an ideal 201 MHz
pillbox cavity with 21-cm-radius Be windows.
Figure 5.1-4. Temperature distribution of a 21-cm-radius, and 0.38-mm thick Be window calculated
assuming an ideal 201 MHz pillbox cavity with 8.4 kW total average power dissipation on the cavity.
In Study-II, we adopted pre-stressed and stepped window designs where the window
thickness is determined by the maximum allowable temperature gradient (caused by RF
heating) within the window that will keep the window flat. For a pre-stressed window, the
window remains flat until the thermal expansion exceeds the tensile pre-stress. At this point
compressive stress is generated in the foil, and it starts to deflect by buckling into a gently
bowed shape. The maximum allowed temperature difference is about 35C and it is
approximately independent of the radius and thickness. Of course, a thicker foil takes more
power before reaching the buckling temperature. For larger windows, such as the 21-cm
radius needed for the 201-MHz cavity, the foils become quite thick and the scattering of the
muons would become significant. Another way to reduce the scattering is to use stepped
windows, which take advantage of the power density profile ( r2, with r the window radius),
and make the windows thinner in the middle, where the core of the beam passes, and thicker
towards the outside, where there are fewer particles. It is thus possible to reduce the scattering
while maintaining the same temperature rise in the foil. The pre-curved window design takes
advantage of the pillbox-like cavity profile by allowing the two windows to deflect in the
same direction, thus keeping the cavity frequency shift to a minimum and well within the
tuner’s range. The window profile and its thickness are determined by allowable thermal
stress induced by RF heating within the foil. Table5.1-2 lists the foil thickness of the stepped
foils used in Study II, the equivalent flat-foil thickness that would keep the temperature below
the critical temperature, and the corresponding thickness needed for a pre-curved foil. Given
its more favourable thickness requirement, we have adopted the pre-curved foil approach.
Table5.1-2. Be foil dimensions for 201 MHz RF cavities for Study-II.
Middle foil radius (inner/outer) [cm]
Middle foil thickness (inner/outer) mm]
Equivalent flat foil thickness [mm]
Pre-curved foil thickness [mm]
14/21
0.7/1.4
1.152
0.38
5.1.4 RF and thermal analysis
Preliminary RF design of the cavity was performed using the URMEL and MAFIA codes
running in the frequency domain. The cavity fields and frequency are recalculated using a
finite-element analysis (FEA) code, ANSYS. Good agreement was achieved among these
codes. Nevertheless, the ANSYS simulations give a more accurate RF power density
distribution on the cavity surfaces, as is necessary for a proper thermal analysis. For MICE,
the anticipated peak power per cavity (limited by available RF power) is 1 MW at a duty
factor of about 0.1% (i.e., 1-ms at a 1-Hz repetition rate). The average power is then only 1
kW, quite modest for a 201 MHz copper cavity and well below the 10 kW assumed for the
Study-II cavity. Nevertheless, the cavity body needs direct cooling to handle the 1 kW
average power losses and thus stabilize the cavity frequency. A simple scheme using external
cooling tubes gives sufficient cooling for the MICE cavity. The cooling design is based upon
room-temperature operation, although the option of operating at lower temperature (e.g., LN2
temperature) has been kept open. This option would reduce the cavity surface resistance and
offers a higher acceleration gradient for the same peak RF power, at the cost of additional
refrigeration and tuner complexity.
As shown in Figure 5.1-5, the water-cooling lines are welded to the cavity body. These lines
are 10-mm diameter copper tubing. The cooling water will be provided by a closed-loop
system, with the facility LCW system providing circulation. ANSYS simulations show that
the proposed water-cooling system provides adequate cooling of the cavity body. The
maximum temperature rise in the cavity walls is about 10 °C.
Figure 5.1-4 shows the temperature profile of the cavity calculated by ANSYS code assuming
8.4 kW average power dissipation over the cavity. The maximum temperature rise is 10 °C on
cavity walls, and the temperature rise across the foil (pre-curved 0.38-mm thick Be) is about
60 °C, which is safely below the temperature gradient that results in thermal stress within the
foil.
Figure 5.1-5. Cavity model showing external cooling tubes.
Figure 5.1-6. ANSYS temperature calculation for 201 MHz cavity with 21-cm curved Be windows
assuming 8.4 kW total average power dissipation on the cavity.
5.1.5 Vacuum requirements
A single vacuum system will be used to pump the volume within the high-gradient RF
cavities as well as the volume within the module’s vacuum vessel that encompasses the
cavities. The system will provide for a vacuum level within the cavities in the 10–9 Torr range,
while the module vacuum vessel will operate in the 10–7 Torr range and provide a guard
vacuum for the RF cavities. Each pair of cavities will have a dedicated manifold and vacuum
pump with accompanying gate valve. The same manifold will have a low-conductance path to
the vacuum vessel volume to provide pumping and to prevent the possibility of a differential
pressure from developing across the cavity windows that could cause permanent damage. Due
to the presence of strong solenoidal magnetic fields, cryo-pumps will be used to provide the
pumping. The pumps will be located close to the cavities to minimize the conduction path. A
mechanical scroll type pump will be used to provide rough vacuum prior to introducing the
cryo-pumps to the system. The proposed vacuum system arrangement is shown in Figure
5.1-7.
Figure 5.1-7. Cavity vacuum system.
A thorough bake out of the cavity interiors will be carried out using a dry nitrogen purge at an
elevated temperature prior to installation within the vacuum vessel. It is not anticipated that a
bake out of the vacuum vessel, cavity exteriors and other components within the vessel will
be needed due to the less stringent vacuum requirements in these areas.
5.1.6 RF coupler
RF power is fed into the cavity using a conventional coaxial type loop coupler. A disk type
RF window will be integrated into the coupler. Although we are specifying the input power
level to be 4 MW, as for Study II, normal MICE operation requires only that the coupler
provide critical coupling and transmit 1 MW peak RF power at 1 kW average power. The
MICE coupler is based on the coaxial coupler designed for the Spallation Neutron Source
(SNS) project, although slight modifications are needed to make it work at 201 MHz. The
MICE cavity has two ports for the RF couplers. Each coupler is designed to handle up to 2.5
MW peak power. This configuration will be the case when more RF power becomes available
in the future, or that of feeding the available 8-MW of power to two cavities for high gradient
tests, and studies of dark currents and x-ray. For nominal MICE operation, one coupler per
cavity should be adequate to transmit 1 MW peak power. Both peak and average RF power
requirements for the MICE experiment are modest under normal operating conditions, so we
do not expect any technical challenges in this regard. However, operating the coupler in a
strong magnetic field poses some concerns about multipactoring, gas discharge, etc. Coating
the couplers with a thin TiN layer should prevent multipactoring. The coupler will be tested
and conditioned separately. We are in the process of acquiring some SNS-type couplers from
Jefferson Laboratory for tests in the MTA at Fermilab.
5.1.7 Cavity tuning requirements
As beam loading is negligible, the active tuning system will be designed to bring the cavities
on frequency initially and to compensate for Lorentz detuning forces and for temperature
variations due to water supply changes and RF heating. Since two cavities will be fed by a
single RF source, it is necessary to be able to independently tune the cavities to the correct
frequency. Due to the high quality factor of the cavity (Q  54,000), the unloaded cavity
bandwidth is only 3.7 kHz and the loaded bandwidth is 7.4 kHz at critical coupling. Tuning
will be accomplished using mechanisms mounted externally on the cavities and having a
relatively slow response time. The tuning scheme will be similar to that used for
superconducting cavities (e.g., those at CEBAF at Jefferson Laboratory) in which the cavity is
mechanically stretched or compressed along the beam direction within the elastic limits of the
material. There will be six such mechanisms mounted on each cavity. Finite-element analysis
of the deformed cavity shape subject to external tuning loads, in conjunction with an RF
analysis, has been used to determine the frequency sensitivity of the tuning system. As the
cavity is compressed or contracted axially by tuning loads applied to a ring just outside the
perimeter of the windows, the frequency will shift by about 229 kHz/mm (the displacement is
per cavity side). For the MICE cavities, the tuner will be designed to deform the cavity over a
range of ±1500 µm (±345 kHz) with approximately 1 µm precision. Given the cavity’s Q
value, 229 Hz of detuning corresponds to approximately 3 of RF phase shift, or 1 part in 103
in accelerating gradient, which is the level of stability required for a 10–3 emittance
measurement. Experience from CEBAF operations and examination of the literature indicate
that mechanical schemes using micro-drive stepping motors can easily achieve this range of
motion with the required accuracy. This tuner scheme will easily accommodate any small
changes in the cooling water temperature that may occur. Bulk water temperature fluctuations
of the order of 1ºC or less have been assumed. The thermal expansion coefficient of copper is
1710–6 K–1 at room temperature, so the frequency variation would be about 3.4 kHz for a 1ºC
temperature change of the cavity.
5.1.8 Cavity integration
Integration of the cavities into the cooling channel will be a multi-step process. As each
cavity assembly with installed tuner mechanisms is inserted into the vacuum vessel, the tuners
will be joined to the vessel interior wall at specific mounting points. The RF coupler and
vacuum connections will be made up at this time as well. Since the cavities are separately
installed and are not interconnected, the tuning for each cavity is completely independent of
the others. After the four cavities are installed in the vacuum vessel, the cooling lines will be
torch brazed to a series of vacuum feed-throughs to allow the passage of water through the
vacuum vessel walls. Additionally, another set of feed-throughs will allow connections to be
made to the tuner mechanisms. After capping the vessel ends, a final leak check will be
performed to check all feed-through and flange connections. Leak checking of the individual
cavities will not be required since the cavities are contained within the module vacuum vessel.
A 4-cavity assembly with the associated coupling coil is shown in Figure 5.1-8. The MICE
cooling channel contains two such units as previously described and shown in Figure 5.1-9.
The assemblies are connected to the Absorber and Focusing Coil (AFC) modules by means of
bellows and vacuum-tight flanges at the ends of the vessels.
Figure 5.1-10. MICE cooling channel layout
For possible LN2 (77 K) operation, the primary concern is heat leakage through the cavity
mounts. To mitigate this issue, materials with very low thermal conductivity will be used to
make the cavity connections to the vacuum vessel wall. The RF couplers will incorporate
bellows to allow for thermal contraction of the cavities. Since the RF power supply frequency
can be tuned to the resonant frequency of the cavity at LN2 temperature, the effective range of
the tuners will remain unchanged.
5.1.9 Cavity performance
Table5.1-3 summarizes the MICE cavity requirements compared with the Study-II
parameters. Because the MICE cavity gradient is limited by the available RF power of 8-MW,
we expect to get a total of about 21-MV acceleration (on crest) from eight MICE cavities.
Peak surface field is only 12 MV/m, compared with the Kilpatrick value at 201-MHz of 15
MV/m. In terms of RF gradient, peak surface field and power dissipation on the Be widows,
the overall technical risk of the MICE RF system is low. Nevertheless, the cavities have to
operate in a strong magnetic field, so cavity and coupler conditioning, dark currents, and xray production need further investigation. The new MUCOOL Test Area now under
construction, will provide an excellent facility for these studies. The pre-curved Be windows
for the 805 MHz cavity will be tested in the MTA at Fermilab this year. They will provide
valuable information on the above issues that will help optimize our designs for both the
cavity and the MICE detectors.
Table5.1-3. MICE cavity requirements compared with the Study-II parameters.
Parameters
Veff on crest (MV)
E0 equivalent (MV/m)
Epeak on surface (MV/m)
Peak power per cavitya (MW)
Peak forward power at 3 filling (MW)
Average power (kW)
a
MICE
2.67
7.5
12.3
0.9
1.0
1.0
Actual cavity Q0 assumed 85% of theoretical value.
Study-II
5.76
16.2
26.5
4.18
4.63
8.36