CAVITY DESIGN REPORT

1. Means CAVITY DESIGN REPORT V. Serrière, A. K. Bandyopadhyay, A. Triantafyllou, J. Jacob This work constitutes the first deliverable WP13.1 of Working Package WP13, carried out within the framework of the ESRFUP project, which has received research funding from the EU Seventh Framework Programme, FP7. All hardware and software expenses are covered by ESRF. The FP7 grant allowed hiring additional manpower to carry out this ambitious project. 1.1. Software packages Electromagnetic simulations have been performed using 3D software GdfidL [1], HFSS [] and CST microwave studio [3]. GdfidL is mainly used for wakefield computations in order to estimate the residual level of HOM impedances of the HOM damped cavity. Eigenmode and S-parameter computations are performed with HFSS and CST microwave studio. They are used for the characterisation of the fundamental mode of the cavity, the optimization of HOM dampers loaded by ferrite and RF finger studies. 1.. RF laboratory The RF laboratory is fully equipped for complete cavity characterization. In the frame work of the cavity development a new modern four port network analyses was purchased. This network analyzer is used for quality factor measurements as well as fundamental mode and HOM impedance measurements. Concerning the measurements on the cavity an extensive set of RF antennas was built in house by the RF Group s mechanical team. Impedance measurements are made using a bead pull device built up especially for this project. 1.3. Team The contribution from FP7 grant essentially allowed hiring two postdoctoral fellows (Postdocs). The kernel of the WP13 project team is composed of Dr. Jörn Jacob, RF Group leader Dr. Vincent Serrière, Engineer in charge Dr. Ayan Kumar Bandyopadhyay, Postdoc mainly working on simulations Dr. Anna Triantafyllou, Postdoc mainly working on measurements in the RF lab Bernard Ogier, Drafting Office Paul De Schynkel, Mechanics The project also benefits from occasional contributions from other members of the RF group or other groups from ESRF (vacuum, cooling ). Cavity Design Report - 1 - EU FP7 Grant

. Design of the cavity.1. Definition of the work The development of the new 35 MHz cavity for the ESRF is based on the 500 MHz European Higher Order Mode (HOM) damped normal conducting cavity with three identical circular double ridge waveguide HOM dampers loaded by UHV compatible absorbing NiZn ferrite material (C8/Countis industries) [, 5]. The cutoff frequency and the length of the dampers are adjusted for an efficient selective damping of the HOM and a minimum absorption of accelerating mode power. A proof of principle was performed in the frame of preliminary studies carried at ESRF. A first Aluminium model was numerically optimized and built with a beam pipe diameter of 76 mm. The HOM were damped by three big dampers and a first attempt to reduce the size of the dampers was performed. However, for the future ESRF cavity, a beam pipe diameter of 100 mm has been specified. The figures of merit for the future cavity are a high impedance and quality factor for the fundamental mode and low HOM impedances. Another important aspect concerns the interface between the HOM dampers and the cavity. The first units built for the Metrology Light Source near BESSY / Berlin and for ALBA / Barcelona have shown that inevitable gaps between the cavity ports and the ridges of the connected HOM dampers, as shown in figure 1, can lead to a significant impedance of the TM011 mode and to an overheating of the vacuum flanges by local surface currents [6]. Gaps Figure 1: Gaps between ridges and cavity body on ESRF aluminium model We propose a solution to avoid these gaps by splitting the HOM dampers in two parts [7]. A first coupling section will be electron-beam welded to the cavity body. The remaining part of the HOM damper including the ferrite load will be connected head on to the coupling section, at a distance where the accelerating mode power is sufficiently decayed and where RF fingers can be implemented safely to ensure a good continuity of the surface currents... Optimization of the cavity body Cavity Design Report - - EU FP7 Grant

The beam pipe diameter has been kept at 100 mm as on the existing ESRF five-cell cavities to remain compatible with the existing X-ray absorbers and to ease the installation on the storage ring. In the design process, the cavity geometry without HOM damper has first to be optimized for a high shunt impedance and a high quality factor of the fundamental mode used to accelerate the beam. As the insertion of the HOM dampers will reduce the resonant frequency of the fundamental mode, the optimization is done for a fundamental frequency of 359 MHz, i.e. the same frequency as the one of the existing aluminium model with a beam pipe diameter of 76 mm. The eigenmode solver AKS of CST microwave studio has been used to optimize the bare cavity shown in figure..1. After a first optimization of the shape and the size of the nose cone in figure.., the final optimization was achieved by varying the length and the radius of the cavity. For given values of R cav and L cav, the parameters x G and y G shown in figure.. were adjusted to keep the fundamental mode at the correct frequency. Figure..1: The bare cavity model and its cross section x G L cav / y H R cav Nose Cone Figure..: Parameters for the final optimization of the bare cavity model Five design versions of the bare cavity giving the highest fundamental mode impedances were selected for the further optimization steps. Their main geometrical parameters are summarized Cavity Design Report - 3 - EU FP7 Grant

in table..1. As listed in table.., all these alternatives have the resonant frequencies around 358 MHz, quality factors in the range 0000 to 000, and an R/Q in the range of 18 to 19 Ω. The frequency of the first HOM varies from 85.5 MHz to 508 MHz. name Design1 (EPAC08) Design (rdl1) Design3 (rdl3) Design (rdr1) Design5 (rdr3) L cav R cav (mm) x G (mm) y H (mm) (mm) 0 7 1.7 5.5 00 7 1.7 50.5 19 7 1.7 100.5 0 75 1.7 50.5 0 77 1.7 100.5 Table..1: Five geometries with optimized fundamental mode impedance name Q R/Q R shunt (MOhm) Resonant Freq. (MHz) (bare cavity) Freq. of the first HOM (MHz) Design1 1189 18.65 6.13 358.089 85.56 (EPAC08) Design 15 19.139 6.15 358.091 500.85 (rdl1) Design3 0716 19.00 6.066 358.10 508.71 (rdl3) Design 1638 18.69 6.19 358.115 87. (rdr1) Design5 (rdr3) 1939 18.536 6. 358.066 91.88 Table..: Fundamental mode characteristics and frequency of the first HOM for the five selected geometries The choice of the final design for the HOM damped cavity will be explained in the next section and motivated by a large damping of the HOM resulting in a minimized longitudinal HOM impedance spectrum..3. Geometrical optimization of the HOM dampers A total of 18 such cavities will be needed to provide the required accelerating voltage of 9 MV for the ESRF storage ring and to sustain a beam power corresponding to 500 ma, including a necessary margin with respect to the planned upgrade of the ESRF from 00 ma to 300 ma. During the HOM damping optimization process, we require that all HOM impedances remain below a value giving an instability threshold at 1A for 18 identical cavities. Such a high instability threshold has been imposed to anticipate possible discrepancies between numerical simulations and the final real cavity. Cavity Design Report - - EU FP7 Grant

The ferrite absorbers used in the optimization of the HOM damping are based on the high power prototype designed by BESSY and consist of small ferrite tiles of.7 mm thickness disposed on a tapered ridge waveguide as shown in figure.3.1. Figure.3.1: Ferrite model based on BESSY design The use of standard Conflat flanges CF50 imposes a maximum inner diameter of 30 mm for the HOM dampers. For mechanical reasons the damper axes are positioned at least at 150 mm from the inner walls of the cavity end discs. As shown in figure.3., after the final precision machining of the assembly, the faces of the coupling sections will follow the inner cavity diameter. Figure.3.: Coupling section seen from inside the cavity In the design process we have first considered the design 1 in table..1. Numerical simulations with GdfidL have shown that only two dampers with a cut-off frequency of 5 MHz, separated azimuthally by 10º are required to damp the lowest HOM. They have an inner diameter of 30 mm, a gap between ridges of 69 mm, a ridge width of 60 mm and ferrite tiles over a length of 00 mm. The optimum damping is obtained for one damper at the minimum of 150 mm from the front disc and the second one at 150 mm from the back plane. A third smaller damper with a cut-off frequency at 80 MHz is needed to damp a few Cavity Design Report - 5 - EU FP7 Grant

remaining HOM at higher frequencies with impedances above the specified 1 A limit. This damper is placed azimuthally between the others and has a reduced inner diameter of 160 mm, a gap between ridges of 80 mm, a ridge width of 60 mm and ferrite absorbers over a length of 50 mm. The best results are obtained when the third damper is positioned longitudinally at 63.1 mm from the cavity equator. The longitudinal HOM impedance spectrum computed from 00 MHz to GHz is plotted on figures.3.. All the longitudinal HOM are well damped and stay far below the threshold for 1 A and 18 installed cavities. Thanks to the small inner diameter of the third damper, the quality factor of the fundamental mode will be less degraded than with three large dampers. Moreover, with its high cutoff frequency the third damper can be much shorter than the others [7]. Threshold for 1A/ 18 cavities GdfidL simulation 3 Longitudinal Impedance [kω] 1 0 0.5 1.0 1.5.0.5 3.0 3.5.0 Frequency [GHz] Figure.3.: Predicted longitudinal HOM impedances from 00 MHz to GHZ The next step was to test the HOM damping configuration for the different bare cavity configurations. Figure.3.5 shows the results obtain for the same HOM damper configuration for the five designs of the bare cavity. The longitudinal HOM impedance spectra for the designs and 3 exhibit too many strong HOM impedances to be kept as candidates in the design process. The HOM impedance spectrum for the design 5 exceeds the instability threshold only for a HOM at.6 GHz. The HOM impedance level for design is very close to the design 1. The frequencies of the most dangerous HOM are at 1.7 GHz for design1 and at.6 GHz for design 5. As the instability threshold decreases as the inverse of the frequency, we decided at this stage of the design to keep the design1 for the bare cavity. Cavity Design Report - 6 - EU FP7 Grant

3 threshold for 1A / 18 cavities GdifdL simulations for: Design1 Design Design3 Design Design5 Longitudinal Impedance [kω] 1 0 0.5 1.0 1.5.0.5 Frequency [GHz] Figure.3.5: Predicted longitudinal HOM impedances from 00 MHz to GHZ for the different cavity design 3.0 3.5.0 The next step in the design process was to include the tuner port with the movable plunger used to control the fundamental mode frequency, as well as the vacuum pumping port in the bottom of the cavity and the RF input coupler in the cavity model. The HOM impedance spectra were then computed for different tuner positions with respect to the inner cavity surface, ranging from -0 mm when the piston is fully retracted to 8 mm when the piston is fully inserted. As shown in figure.3.6, all HOM impedances still remain below the threshold for 1A/ 18 cavities, except for the HOM at 1.7 GHz. Figure.3.7 gives a zoom on this mode. For a tuner position at 8 mm inside the cavity, the impedance of the HOM significantly exceeds the instability threshold. The impedance of the HOM for a tuner at 18 mm inside the cavity is close the instability threshold. 7 Longitudinal Impedance [kω] 6 5 3 Threshold for 1A/ 18 cavities GfdidL simulations for tuner at: 0 mm 8 mm 18 mm 8 mm 38 mm 58 mm 1 0 0.5 1.0 1.5.0.5 3.0 3.5.0 Frequency [GHz] Figure.3.6: Impedance spectrum of the cavity for various tuner positions Cavity Design Report - 7 - EU FP7 Grant

7 Longitudinal Impedance [kω] 6 5 3 Threshold for 1A/ 18 cavities GfdidL simulations for tuner at: 0 mm 8 mm 18 mm 8 mm 38 mm 58 mm 1 0 1.70 1.71 1.7 1.73 1.7 Frequency [GHz] Figure.3.7: Effect of the tuner position for the HOM at 1.7 GHz 1.75 Final optimization of the cavity At this stage of the design, we received a new PC with two times four integrated cores and 16 GB of memory. This new PC allows the fundamental mode to be checked for the full structure, including the attached auxiliary equipment, which was not possible with the old biprocessor PC. To confirm the fundamental mode frequency, the JDM solver of microwave studio was used, ignoring the ferrites at the end of the HOM dampers to speed up the simulation time. The tuner was considered to be 30 mm inside the cavity. As the resonant frequency was far from the specifications, the radius of the cavity had to be increased by 1 mm. The predicted resonant frequency is 35.3 MHz, the R/Q is 17 Ohm, the quality factor 39700 and the resulting shunt impedance is 5.85 MΩ. Ignoring the ferrites has only low influence on the results for long enough dampers, as shown in later in this section. The fundamental mode frequency is sufficiently close to the nominal 35. MHz RF frequency at the ESRF to state that the so obtained geometry simulates well the future ESRF cavity (on the final copper prototype, the fine adjustment of the resonance frequency will anyhow be done by an iterative process of tuning and turning of the inner diameter). It was then decided to concentrate on the study of the damping of the 1.7 GHz HOM. The impedance spectrum is shown in figure..8 for the tuner being tangent to the radius of the cavity. The impedance spectrum doesn t exceed the instability threshold except for the impedance peak near 1.7 GHz. Simulations for different values of the tuner penetration showed that the impedance of this peak remains above the threshold for small tuner penetration while it goes below the threshold for a larger tuner penetration. Cavity Design Report - 8 - EU FP7 Grant

1 10 Threshold 1A/ 18 cavities GdifdL simulation for the tuner tangent to the cavity Longitunal Impedance [kω] 8 6 0 0.5 1.0 1.5.0.5 Frequency [GHz] Figure.3.8: Impedance spectrum for the final cavity with the tuner at 0mm A number of simulations have been carried out to find out a better position of the third damper D3 along the cavity length. But these simulations failed to indicate any better placement of D3 which would couple to the 1.7 GHz HOM more efficiently. In order to find out if this high impedance peak is due to poor absorption of HOMs in ferrites, the simulations were repeated by using perfectly matched layers (PML) at the end of the waveguide dampers. The results with ferrite absorbers and PML did not show any significant difference suggesting that the problem is linked with the coupling of this mode to the HOM dampers rather than it s absorption in the ferrite. In order to improve the coupling of the 1.7 GHz mode to the ridge waveguide dampers, the geometries of the ridges in the waveguides were varied. As the dimensions of the ridges determine the cut-off frequencies of the ridge waveguides, detailed studies of the cut-off frequencies have been done as a function of the ridge width and ridge gap. Then, simulations with different HOM waveguide ridges were carried out. From these simulations, it became clear that this mode at 1.7 GHz couples to the TM mode of the waveguide dampers even stronger than to its fundamental TE mode. It was decided to re-optimize the ridges of the smaller damper D3 in order to shift its TM cutoff below 1.7 GHz. In figure.3.9 is shown the comparison of the impedance peak at 1.7 GHz for two configurations: - with the initial HOM dampers, D1, D: TE cut-off at 5.67 MHz, TM cut-off at 1.783 GHz, and D3: TE cut-off at 8.89 MHz, TM cut-off.0 GHz, - with the same D1, D but a modified D3: TE 1.09 MHz, TM cut-off 1.51 GHz. To adjust the TM cut-off of D3, the gap between the ridges had to be increased leading also to a variation of the TE cut-off frequency. Figure.3.9 shows a significant improvement in the HOM level for the 1.7 GHz mode, yet it remains above the specified limit. It should be noted that no significant adverse effect on the other HOMs is predicted from the simulations with 3.0 3.5.0 Cavity Design Report - 9 - EU FP7 Grant

this modified D3. In order to the damp the 1.7 GHz HOM even more, the position, radius and ridge shape of D3 were varied further, however, without significant improvement. 1 10 Threshold for 1A/ 18 cav impedance with initial D1, D and D3 impedance with modified D3 Longitunal Impedance [kω] 8 6 0 1.716 1.718 1.70 Frequency [GHz] 1.7 1.7 Figure.3.9: Comparison between the longitudinal impedance peak near 1.7 GHz with the previous dampers and with D3 TM cut-off at 1.51 GHz It was then decided to rework the ridges of the large dampers D1 and D to also shift their TM cut-off below 1.71 GHz. The redesigned dampers have the following cut-off frequencies: - D1, D TE cut-off at 59. MHz, TM cut-off at 1.69 GHz, D3 TE cut-off at 1.09 MHz and TM cut-off at 1.515 GHz. 1 Longitunal Impedance [kω] 10 8 6 threshold for 1 amp impedance with initial D1, D and D3 impedance with modified D3 impedace with modified D1, D and D3 0 1.716 1.718 1.70 Frequency [GHz] Figure.3.10: Comparison between the longitudinal impedance peak near 1.7 GHz with different HOM dampers. 1.7 1.7 Cavity Design Report - 10 - EU FP7 Grant

Further simulations have been done to predict the longitudinal impedance of the cavity with the redesigned dampers D1, D and D3 for different tuner penetrations. Figure.3.11 shows that for any tuner penetration the impedance spectrum remains well below the threshold limit for 1 Amp (18 cavities). Longitunal Impedance [kω] 5 3 1 Threshold 1A/ 18 cavities GdfidL simulation for tuner at -10 mm tuner at -0 mm tuner at 0 mm tuner at 10 mm tuner at 0 mm tuner at 30 mm tuner at 0 mm 0 0.5 1.0 1.5.0.5 3.0 3.5.0 Frequency [GHz] Figure.3.11: Longitudinal impedance spectrum for different tuner penetrations In the last design, the ridge width of D1 and D is only 36 mm, which is much below the 60 mm ridge width of the initial design. As a drawback, the power density will be increased significantly in the ferrite tiles on the tapered ends of the ridges and a particular attention must then be paid to the design of the cooling system for the ferrites. In order to slightly reduce this effect, further simulations have been carried out for 0 mm ridge width. The impedance level of the 1.7 GHz mode goes up again compared to that with 36 mm ridge width, but it exceeds the threshold only for a tuner position at -0mm, which does not correspond to any practical operation condition. The transverse HOM impedances still need to be evaluated. However, it is worth noting that during 16 years of operation, HOM driven transverse coupled bunch instabilities have never been observed. This is due to even lower thresholds for the transverse resistive wall instability, which is cured by a corresponding chromaticity over-compensation of the storage ring that completely screens the effect of transverse cavity HOM. Transverse cavity HOM are expected to be attenuated by our broadband HOM dampers as well, however, they do not constitute any design constraint for the new ESRF cavities. Fundamental mode absorption in the ferrite It is reminded that the ridge waveguide dampers are designed to have their cut off above the fundamental accelerating mode frequency in order to decouple it from the ferrite loads. In fact the accelerating mode of the cavity couples to evanescent ridge waveguide modes, and for Cavity Design Report - 11 - EU FP7 Grant

long enough dampers, only a little power reaches the absorbing ferrites. So, the lengths of the dampers have to be designed carefully to limit the absorption of accelerating mode power by the ferrites. To do this, the quality factor of the fundamental mode has been computed with HFSS [7] for various damper lengths. In order to limit the CPU time and the memory consumption, only one damper is included in the HFSS model at the time. The result for dampers with a cut-off at 5 MHz is shown in figure.3.1. By fitting the data with the coupling factor and the exponential decay of the fundamental ridge waveguide mode at 35 MHz, we could compute the maximum accelerating mode power dissipated in the HOM loads as a function of the damper length. 10 35x10 3 30 HFSS simulations quality factor fit extrapolated power dissipated in ferrite 6 5 3 Quality factor 5 0 15 6 5 3 10 3 10 Power dissipated in ferrite [W] 10 6 5 3 5 10 1 0 100 00 300 00 500 600 Length before ferrite [mm] 700 800 900 1000 Figure.3.1: Quality factor and accelerating mode power dissipated in the ferrites for a degraded operation at 9 MV with 1 cavities versus damper length before ferrites. Requiring less than 100 W dissipation in the ferrites for a degraded operation at 9 MV with only 1 cavities yields a design length before ferrites of 80 mm for the ridge waveguide dampers D1 and D. For the third damper D3 a similar study gives a minimum length before ferrites of 5 mm. Disposing the shorter D3 on the top of the cavities will limit their height and ease their installation in the existing storage ring tunnel. Numerical computations of the complete structure with eigenmode solvers need a large amount of memory with either HFSS or Microwave Studio if the ferrite in the damper is included in the numerical model. Even with a modern PC, to determine the impedance and quality factor of the fundamental mode, computations had therefore to be done with only one damper per simulation. The fundamental mode parameters were then extrapolated for the complete structure and are estimated to R/Q = 15 Ω, Qo = 35000, Rs = 5.075 MΩ, which is well above the required. to.5 MΩ per cavity. This gives enough room to accommodate some inevitable reductions of Qo due to imperfections in the manufacturing of such cavities. Cavity Design Report - 1 - EU FP7 Grant

Measurements versus simulations In the preparatory phase for this project, a first aluminium model had been built and characterized in the lab for a version with three identical big dampers. They have a TE cut-off frequency of 30 MHz and a length before ferrite of 1. m is required to avoid over-heating by the fundamental mode. The dampers are positioned as follows: two dampers are tangent to the front disk of the cavity and the third one is tangent to the back disk. A first attempt to reduce the damper size was performed using two dampers with a TE cut-off frequency at 60 MHz and a length before ferrite of 70 mm and a third damper with a TE cut-off of 750 MHz. In order to validate the principle of the new cavity design, a characterization of the existing aluminium model has been performed using only the two dampers with a TE cut-off frequency of 60 MHz. A first series of measurements was carried out with both dampers in the front plane of the cavity as shown in figure.3.13. Figure.3.13: Cut view of the aluminium model with two damper in the front plane The measured characteristics of the fundamental mode are: f res = 35.6 MHz, R/Q = 150 Ω, Q = 19100 (the used aluminium alloy has a lower conductivity than copper). The impedance measurements for the HOM from 60 MHz up to GHz are summarized in the figure.3.1 and compared to GdfidL simulations. The agreement between measurements and simulations is globally satisfactory for the HOM spectrum, but discrepancies appear on three individual HOMs at 875 MHz, 137 MHz and 758 MHz. For the HOM at 875 MHz, the measurements give a value seven times smaller than the 5.5 kω predicted by simulation. For the HOM at 1.37 GHz the measured impedance is a factor two higher than the numerical prediction, however, it remains well below the instability thresholds for 1A and 18 cavities. A much more dramatic discrepancy concerns the HOM at 758 MHz, for which the simulation predicts a small impedance, well below the tolerated threshold, but as much as 11 kω with a Q of 900 is measured on the lab model. The measured impedance is clearly above the design limit. Cavity Design Report - 13 - EU FP7 Grant

1.0 11.0 10.0 Threshold 1A/ 18 cavities GdfidL simulations measurements 9.0 Longitunal Impedance [kω] 8.0 7.0 6.0 5.0.0 3.0.0 1.0 0.0 0.0 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.0 1.30 Frequency [GHz] 1.0 1.50 1.60 1.70 1.80 1.90.00 Figure.3.1: Simulation and measurements of the first aluminium model The characterization of the HOM at 758 MHz has been repeated for the configuration in figure.3.15, with one damper in the front plane and the other damper in the back plane. Figure.3.15: Cut view of the aluminium model with one damper in the front plane and one damper in the back plane In this configuration the Q value of this mode reduces to 1300 and the impedance R/Q is no longer measurable, i.e. it is in the noise of the measurement method. For the final ESRF design, the larger HOM dampers D1 and D will also be disposed in opposite locations with respect to the cavity equator, i.e. as in figure.3.15, which gave a low HOM impedance at 758 MHz on the existing aluminium model. Cavity Design Report - 1 - EU FP7 Grant

Eigenmode computations with microwave studio and HFSS have been performed to try and understand the physics of this HOM at 758 MHz, but results are not conclusive. Microwave eigenmode solvers don t converge and HFSS gives a quality factor of only 100. These discrepancies observed between simulation and measurement also fully justify a posteriori the margin taken in the design by specifying the maximum tolerated HOM impedances for an instability threshold above 1 A. Moreover, these discrepancies between numerical simulations and measurements have limited our confidence in numerical simulations to some extent. Prior to launching the fabrication of the power prototype, the absence of high HOM impedances at 758 MHz but also at other frequencies will be checked. It will also be used to compare the impedances obtained with a 0 mm and a 60 mm width of the dampers D1 and D, in particular to check if the HOM at 1.7 GHz really has the strong impedance predicted by GdfidL. This will condition the final decision for the D1 and D ridge width... Test of the RF fingers Figure..1 shows surface currents computed with the Microwave Studio eigenmode solver JDM for only one damper connected to the cavity and a maximum accelerating voltage of 815 kv, i.e. well above the nominal 500 kv per cavity. High surface currents are predicted in the whole cross section of the coupling section. In figure..1, surface currents start from 800 A/m close to the cavity and decay exponentially along the damper. Figure..1: Surface current density on the HOM damper In the flange that will connect the ferrite loaded damper to the coupling section, the copper gasket will guarantee the electrical continuity on the outer cylinder. In the ridge zones, the electrical continuity will be established by means of RF fingers inserted between the head on connected ridges, as sketched in figure... Cavity Design Report - 15 - EU FP7 Grant

Figure..: HOM damper with RF fingers and a copper gasket for head on connection to the coupling section The minimum required length of the coupling section is determined by the position at which the evanescent modes are sufficiently decayed and the surface currents remain below the level, which the RF fingers can withstand without arcing or over-heating. In order to specify this current level, a power test was carried out with tapered ridges built into a section of WR300 waveguides as shown in figures..3 and... The distance between the flat tops of the ridges was 8 mm and the tapered sections allowed a matching to -8 db. Microwave Studio simulations showed that for 1 MW of RF passing through this device, surface currents of 600 A/m are induced on the flat top of the ridges. Figure..3: Tapered double ridge WR300 waveguide with head on connected ridges, for power test of RF fingers Cavity Design Report - 16 - EU FP7 Grant

Figure..: Insertion of RF fingers on the ridges faces The top and bottom ridges of this device are built in two parts, which are connected head on. The faces of the front ridges have been machined to receive RF fingers at mm from the edges, as shown in figure... The power tests were carried out on the RF system of the ESRF booster. The device was placed after the circulator between an H-bend and the dummy load. An already installed arc detector was placed on the H-bend to interlock the RF power in case of RF finger arcing. Thermal sensors (PT100) were inserted in the top ridges to follow up their temperature. The RF power was increased slowly up to 1.05 MW without arcing of the RF fingers. After 3 hours of test the device had heated up to 80º C on the flat top of the ridges, compared to a 0º C heating of the bare waveguides around the device. After this first test, the device was dismounted and no trace of over-heating or arcing was observed. No problem was observed after three further run tests. Comparing numerical results and the RF power passing through the device during the tests, we could determine a minimum length of 80 mm for the coupling sections of the 5 MHz cutoff dampers D1 and D. With this length, we are even safer for the smaller 1.057 GHz cutoff damper D3. 3. Final design The geometry of the future HOM damped single cell cavity for the ESRF has been determined through the design process described in section. Except for a pending decision on the width of the ridges for the larger HOM dampers D1 and D, all the important dimensions are now frozen. In order to finalize the dimensioning of these ridges, an aluminium model has been ordered and will be delivered at the beginning of November 008. Figure 3.1.1 shows the assembly of the aluminium model. It is configured as the future high power prototype that will be developed during the coming two years. This includes all the Cavity Design Report - 17 - EU FP7 Grant

ports for the vacuum pumps, the tuners, the RF input couplers as well as for the RF pickups and vacuum gauges. Figure 3.1.1: Assembly of the aluminium model The damper assemblies are fabricated in such a way that the ridges can easily be dismounted and replaced for a comparison of 0 mm and 60 mm ridge width in the dampers D1 and D. Shorter pieces of ridge waveguides are being manufactured to vary the HOM damper lengths and verify experimentally according to figure.3.1 the length before ferrite needed for a low absorption of the fundamental mode. The next major phase of the project will start as initially scheduled in the second part of October 008 with the writing of the specification for the copper power prototype and the preparation of the corresponding technical drawings. It is planned to issue a call for tender for the power prototype early in 009. The final check of the design with the new aluminium model in the RF lab will be carried out in parallel and will not delay the preparation of the power prototype. This includes the final choice of the ridge width for the larger dampers D1 and D, which will depend on the characterization of the aluminium model. The delivery of the high power copper prototype constitutes the next milestone WP13. of this working package and it is expected to take place as scheduled within the coming two years. Cavity Design Report - 18 - EU FP7 Grant

. References [1] www.gdfidl.de [] www.ansoft.com [3] www.cst.com [] E. Weihreter, Status of the European HOM Damped Normal Conducting Cavity, Proceedings of the EPAC 08, Genoa, 008. [5] www.countis.com [6] M. Langlois, P. Sanchez, M. Cornelis, Measurements of the RF cavity for the ALBA storage ring, Proceedings of the EPAC 08, Genoa, 008. [7] V. Serrière, J. Jacob, A.K. Bandyopadhyay, D. Jalas, A. Triantafyllou, L. Goirand, B. Ogier, N. Guillotin, Status of HOM damped cavities for the ESRF storage ring, Proceedings of the EPAC 08, Genoa, 008. Cavity Design Report - 19 - EU FP7 Grant

MOPP108 Proceedings of EPAC08, Genoa, Italy STATUS OF HOM DAMPED ROOM-TEMPERATURE CAVITIES FOR THE ESRF STORAGE RING* V. Serrière, J. Jacob, A.K. Bandyopadhyay, D. Jalas, A. Triantafyllou, L. Goirand, B. Ogier, ESRF, Grenoble, France N. Guillotin, SOLEIL, Gif-sur-Yvette, France. Abstract At the ESRF, longitudinal coupled bunch instabilities driven by cavity HOM are currently avoided up to the nominal current of 00 ma by precisely controlling the temperatures of the six five-cell cavities on the storage ring. A longitudinal bunch by bunch feedback has recently allowed overcoming the remaining HOM and thereby increasing the current in the storage ring to 300 ma. In parallel, HOM damped room-temperature cavities are being developed for highly reliable passive operation at 300mA. They are designed for a possible later upgrade to higher currents. INTRODUCTION The development of the new 35 MHz cavity for the ESRF is based on the 500 MHz European HOM damped normal conducting cavity with three circular double ridge waveguide HOM dampers loaded by UHV compatible absorbing NiZn ferrite material (C8/Countis industries) [1, ]. The cutoff frequency and the length of the dampers are adjusted for an efficient selective damping of the HOM and a minimum absorption of accelerating mode power. The first units built for the MLS near BESSY and for ALBA have shown that an inevitable gap between the cavity ports and the ridges of the connected HOM dampers can lead to a significant impedance of the TM011 mode and to an overheating of the vacuum flanges by local surface currents [3]. We propose a solution to avoid the gap by splitting the HOM dampers in two parts. A first coupling section will be e-beam welded to the cavity body. The remaining part of the HOM damper including the ferrite load will be connected head on to the coupling section, at a distance where the accelerating mode power is sufficiently decayed and where RF fingers can be implemented safely to ensure a good continuity of the surface currents. To achieve 300 ma safely, design margins have been taken corresponding to a maximum of 500 ma of stored beam in terms of power, i.e..5 MW of transferred beam power, and to 1 A in terms of HOM damping. In order to provide the nominal accelerating voltage of 9 MV with some operational margin and to limit the copper losses it is foreseen to install 18 new cavities in the ESRF storage ring. The next section summarizes the numerical optimization of the cavity body and the HOM dampers. We then report on power tests of RF contact fingers for the head on connection of ridge waveguides, using a special WR300 tapered ridge waveguide fed with 1 MW of RF power. *This work, carried out within the framework of the ESRFUP project, has received research funding from the EU Seventh Framework Program (FP7). 07 Accelerator Technology Main Systems 808 HOM DAMPING To anticipate possible discrepancies between numerical simulations and impedance measurements, we require that all HOM impedances remain below a value giving an instability threshold at 1A for 18 identical installed cavities. The use of standard Conflat flanges CF50 imposes a maximum inner diameter of 30 mm for the HOM dampers. For mechanical reasons the damper axes are positioned at least at 150mm from the inner walls of the end discs. As shown in figure 1, after the final precision machining of the assembly, the faces of the coupling sections will follow the inner cavity diameter. Figure 1: Coupling section seen from inside the cavity. The beam pipe diameter has been kept at 100 mm as on the existing five-cell cavities to remain compatible with the existing X-ray absorbers and to ease the installation. In the design process, first a single cell cavity without HOM dampers has been optimized to obtain a maximum shunt impedance of 6.1 MΩ. (R/Q = 18.5 Ω, Qo = 1100). Then the HOM dampers have been optimized for a wide frequency span from 00 MHz to GHz. Numerical simulations with GdfidL [5] have shown that only two dampers with a cut-off frequency of 5 MHz, separated azimuthally by 10º are required to damp the lowest HOM. They have an inner diameter of 30 mm, a gap between ridges of 69 mm and a ridge width of 60 mm. The ferrite model used in these computations is based on the high power prototype designed at BESSY. It consists of an assembly of small ferrite tiles with a thickness of.7 mm over a length of 00 mm []. The optimum damping is obtained for one damper at the minimum of 150 mm from the front disc and the second one at 150 mm from the back plane. A third smaller damper with a cut-off frequency at 80 MHz is needed to damp a few remaining HOM at higher frequencies with T06 Room Temperature RF

Proceedings of EPAC08, Genoa, Italy MOPP108 impedances above the specified 1 A limit. This damper is placed azimuthally between the others and has a reduced inner diameter of 160 mm, a gap between ridges of 80 mm and a ridge width of 60 mm. The absorber also uses small ferrite tiles, now over a length of 50 mm. The best results are obtained when the third damper is positioned longitudinally at 63.1 mm from the cavity equator. The longitudinal HOM impedance spectra computed from 00 MHz to GHz and from GHZ to GHz are plotted on figures and 3, respectively. Longitudinal Impedance [kw].0 3.5 3.0.5.0 1.5 1.0 0.5 0.0 0. 0.6 Threshold for 1A/ 18 cavities GdfidL Simulation 0.8 1.0 1. 1. Frequency [GHz] Figure : Predicted longitudinal HOM impedances from 00 MHz to GHz. Longitudinal Impedance [kw].0 3.5 3.0.5.0 1.5 1.0 0.5 0.0.0. Threshold for 1A/ 18 cavities GdfidL Simulation..6.8 3.0 3. Frequency [GHz] Figure 3: Predicted longitudinal HOM impedances from GHz to GHz. All the longitudinal HOM are well damped and stay far below the threshold for 1 A and 18 installed cavities. Thanks to the small inner diameter of the third damper, the quality factor of the fundamental mode will be less degraded than with three identical dampers. Moreover, with its high cutoff frequency the third damper can be much shorter than the others. The transverse HOM impedances still need to be evaluated. However, it is worth noting that during 15 years of operation, HOM driven transverse coupled bunch instabilities have never been observed thanks to the high chromaticity of the storage ring needed to suppress the resistive wall instability. Transverse HOM are therefore not a design constraint for the new ESRF cavities. The lengths of the dampers have to be designed carefully to limit the absorption of accelerating mode power by the ferrites. To do this, the quality factor of the 3. 1.6 3.6 1.8 3.8.0.0 fundamental mode has been computed with HFSS [6] for various damper lengths. In order to limit the CPU time and the memory consumption, only one damper is included in the HFSS model at the time. The result for dampers with a cutoff at 5 MHz is shown in figure. By fitting the data with the coupling factor and the exponential decay at 35 MHz, we could compute the maximum accelerating mode power dissipated in the HOM loads as a function of the damper length. 35x10 3 Quality factor 30 5 0 15 10 5 0 HFSS simulations quality factor fit extrapolated power dissipated in ferrite 00 00 600 800 Length before ferrite [mm] 10 6 10 3 6 10 6 10 1 1000 Figure : Quality factor and accelerating mode power dissipated in the ferrites for a degraded operation at 9 MV with 1 cavities versus damper length before ferrites. Requiring less than 100 W dissipation in the ferrites for a degraded operation with only 1 cavities, yields the design length before ferrites of 80 mm. For the third damper a similar study gives a minimum length before the ferrites of 5 mm. This is compatible with the installation of the cavities in the storage ring tunnel, if the third damper is placed on the top of the cavity. Numerical computations of the complete structure with eigenmode solvers need a large amount of memory with both HFSS or Microwave Studio [7]. To determine the impedance and quality factor of the fundamental mode, computations had therefore to be done with only one damper per simulation. The fundamental mode parameters were then extrapolated for the complete structure and are estimated to R/Q = 15 Ω, Qo = 35000. RF POWER TESTS OF RF FINGERS FOR THE HEAD ON CONNECTION OF RIDGE WAVEGUIDES Figure 5 shows surface currents computed with the Microwave Studio eigenmode solver for only one damper connected to the cavity and a maximum accelerating voltage of 815 kv. High surface currents are predicted in the whole cross section of the coupling section. In the flange that will connect the ferrite loaded damper to the coupling section, the copper gasket will guarantee the electrical continuity on the outer cylinder. In the ridge zones, the electrical continuity will be established by means of RF fingers inserted between the head on connected ridges. In figure 5, surface currents start from 800 A/m close to the cavity and decay exponentially Power dissipated in ferrite [W] 07 Accelerator Technology Main Systems T06 Room Temperature RF 809

MOPP108 Proceedings of EPAC08, Genoa, Italy along the damper. The minimum required length of the coupling section is determined by the position at which the surface currents remain below the level, which the RF fingers can withstand without arcing or over-heating. In order to specify this current level, tapered ridges were built into a section of WR300 waveguides as shown in figures 6 and 7. The top and bottom ridges of this device are built in two parts, which are connected head on. The faces of the front ridges have been machined to receive RF fingers at mm from the edges, as shown in figure 7. The power tests were carried out on the RF system of the ESRF booster. The device was placed after the circulator between an H-bend and the dummy load. An already installed arc detector was placed on the H-bend to interlock the RF power in case of RF finger arcing. Thermal sensors (PT100) were inserted in the top ridges to follow up their temperature. The RF power was increased slowly up to 1.05 MW without arcing of the RF fingers. After 3 hours of test the device heated up to 80º C on the flat top of the ridges, compared to a 0º C heating of the waveguide network around the device. After the first test, the device was dismounted and no trace of overheating or arcing was observed. No problem was observed after three further tests. Figure 7: Insertion of RF fingers on the ridge faces Figure 5: Surface current density on the HOM damper The distance between the flat tops of the ridges was 8 mm and the tapered sections allowed a matching to -8 db. Microwave Studio simulations showed that for 1 MW of RF passing through this device, surface currents of 600 A/m are induced on the flat top of the ridges. Figure 6: Tapered double ridge WR300 waveguide with head on connected ridges, for power tests of RF fingers Comparing numerical results and the RF power passing through the device during the tests, we could determine a minimum length of 80 mm for the coupling sections of the 5 MHz cutoff dampers. With this length, we are even safer for the 80 MHz cutoff damper. CONCLUSION AND OUTLOOK The design of a strongly HOM damped cavity was optimized numerically. Effective HOM damping is predicted with two HOM dampers having a cut-off frequency of 5 MHz and one with a cut-off frequency of 80 MHz. The smaller damper brings less degradation of the quality factor of the fundamental mode than a design with three identical large aperture dampers. The numerical results will be compared with measurements on an aluminum prototype in the coming months. Power tests have demonstrated that RF fingers can be used for the head on connection of a ridge waveguide damper on a coupling section of reasonable length, which will be welded on the cavity. This will allow avoiding the gap between the ridges and the cavity port and the associated impedance and heating problems. Tests with different types of RF fingers are planned in order to further optimize the mechanical and electrical interface. Studies of the vacuum system configuration and the thermal behavior are under way. The goal is to launch the fabrication of a high power copper prototype by the end of the year. REFERENCES [1] E. Weihreter, Status of the European HOM Damped Normal Conducting Cavity, this conference. [] www.countis.com [3] M. Langlois et al., Measurement of the RF cavity for the ALBA storage ring, this conference. [] E. Weihreter et al., A Ridge Circular Ferrite Load for Cavity HOM Damping, EPAC06 [5] www.gdfidl.de [6] www.ansoft.com [7] www.cst.com 07 Accelerator Technology Main Systems 810 T06 Room Temperature RF