G. Wu, H. Wang, R. A. Rimmer, C. E. Reece Abstract: Three different tip geometries in a HOM coupler on a CEBAF Upgrade Low Loss cavity have been evaluated by HFSS simulation to understand the tip surface heating problem under various situations. The surface heat loss was calculated for modified tip designs and for the standard tip design under different notch tuning conditions. The result shows that detuning the notch frequency reduces surface heating insignificantly. Different tips differ not so much in surface losses. The nail shaped tip with wider tip-to-coupler distance is the best option among three tip geometries if one wants to reduce surface heating while not compromising HOM damping. 09/11/2004
Evaluation of HOM Coupler Probe Heating by HFSS Simulation 1. Introduction The probe tip of DESY type High Order Mode (HOM) coupler is located right in the electric field minimum for the cavity fundamental mode to reduce the power transmission through the HOM coupler. This electric filed minimum is also a magnetic field maximum in this transmission line type HOM coupler. The current on the coupler tip surface causes the heating problem. To maximize the HOM damping of CEBAF Upgrade cavities both on Low Loss and High Gradient shapes, the HOM coupler position was moved closer to the end cell. This increased the magnetic field ratio between the coupler tip to the cavity equator and produced extra heat on the coupler tip. If the heat is not sufficiently conducted away through the probe feedthrough, it can lower the cavity quality factor (Q) or cause the tip to become normal conductor. This note describes the simulation results on the local magnetic field around the tip calculated by HFSS code. 2. Computer Model A 3D computer model was constructed as shown in Figure 1. A Low Loss shape, single cell cavity is used as the resonator. A coaxial line was inserted in the left side beam pipe to act as an input probe to transmit RF power. The output is a 50Ω coaxial line connected to the HOM probe tip. The fillet geometries on the notch rod and the two inductive stubs inside of the HOM coupler are eliminated to avoid dense meshes on those corners in the 3D meshing. Fig. 1 3D RF model used in the HFSS simulation. The HOM coupler and the right side beam pipe was cut away by 135-degree to show the inside geometry. The model accuracy was checked through different mesh densities. Three mesh regions were chosen. These are the cavity beam pipe, HOM can and notch cap. To ensure the 1
consistency of mesh densities, the HOM can and the notch cap regions were manually seeded as shown in Figure 2. Fig. 2 Manual seeding of the 3D RF model. Meshes for HOM can and notch cap are shown. When the mesh densities of the HOM can and the notch cap were increased, the S 21 transmission curve remained the same for the notch frequency region as shown in Figure 3. This implies that this model is accurate at least for the frequencies between the cavity frequency and the notch frequency. Fig. 3 The transmission coefficient vs. frequency. To calculate the local magnetic field around the tip, the notch frequency has to be tuned into the cavity resonance. This is the most time consuming part of the simulation. Figure 4 shows the tuning process. 2
Fig. 4 The frequency tuning of the notch filter. The current HOM coupler tuning procedure to tune the notch gap is to set the notch minimum very close to the cavity resonance. The external Q is around 10 12 or higher. 3. Local field (a) (b) Fig. 5 The electric field magnitude (a) and magnetic field vector (b) in the HOM can. Figure 5 shows the tip locates in the electric field minimum in the HOM can and corresponding maximum magnetic field wrapped around the center conductor of the HOM coupler. 3
For different geometries, the code gives slightly different cavity stored energies. Typically, the cavity equator field and the tip magnetic field are identified as shown in Figure 6. Then the ratio of to the two is calculated. (a) (b) Fig. 6 The magnetic fields at the cavity equator (a) and the tip (b). (a) (b) (c) Fig 7. Three tip geometries: (a) Tip1, standard shape, (b) Tip 2, rod shape, (c) Tip 3, nail shape. Three tip geometries have been modeled as shown in Figure 7. The dimension of Tip 1 is the standard design. Tip 2 is a simple rod with a 0.059-in round fillet. Tip 3 dimensions are shown in Appendix A. Their local magnetic field is shown in Figure 8. All the tips have a 30-mil gap between the tip and the coupler center conductor (hook). All Q ext s were tuned to around 10 13. 4
(a) (b) (c) Fig. 8 The local magnetic field around probe Tip 1 (a), Tip 2(b) and Tip 3 (c) 5
Table 1. The Tip magnetic field and their associated surface heat loss. (see following notes for details) Tip1 Detuning effect Notch Gap(mm) Freq(Hz) Stored Energy (J) S12 S12 (db) Tip field Qext_HOM Qext_FPC Cap Ring or Back Taper or Rod coax Total loss 6.37873836 1.51150E+09 1.2520E-07 3.018E-06-110.4 10.83% 1.31E+14 1.19E+03 5.86E-05 2.72E-05 6.42E-05 1.75E-07 5.72E-05 6.38 1.51150E+09 1.2540E-07 3.192E-05-89.9 10.17% 1.17E+12 1.19E+03 5.08E-05 2.38E-05 5.52E-05 1.27E-07 4.95E-05 6.386 1.51150E+09 1.2400E-07 6.789E-05-83.4 10.08% 2.56E+11 1.18E+03 5.04E-05 2.34E-05 5.53E-05 1.25E-07 4.92E-05 6.394 1.51150E+09 1.2620E-07 1.389E-04-77.1 10.07% 6.22E+10 1.20E+03 5.02E-05 2.35E-05 5.45E-05 1.29E-07 4.89E-05 6.45 1.51150E+09 1.2534E-07 5.324E-04-65.5 9.75% 4.20E+09 1.19E+03 4.66E-05 2.19E-05 5.10E-05 1.36E-07 4.56E-05 6.5 1.51150E+09 1.2578E-07 8.658E-04-61.3 9.33% 1.59E+09 1.19E+03 4.30E-05 2.00E-05 4.79E-05 1.55E-07 4.23E-05 7 1.51090E+09 1.2396E-07 3.330E-03-49.6 8.25% 1.06E+08 1.18E+03 3.37E-05 1.53E-05 3.59E-05 6.42E-07 3.26E-05 Different Tip Configurations Tip 1 30mil sharp 6.357183218 1.51150E+09 1.2594E-07 1.877E-04-74.5 11.58% 3.40E+10 1.20E+03 5.97E-05 5.09E-05 7.54E-05 1.77E-07 7.09E-05 Tip 1 50mil 6.400347444 1.51090E+09 1.2524E-07 3.627E-06-108.8 9.25% 9.04E+13 1.19E+03 4.35E-05 2.07E-05 4.95E-05 9.13E-08 4.34E-05 Tip 1 30mil 6.37873836 1.51150E+09 1.2520E-07 3.018E-06-110.4 10.83% 1.31E+14 1.19E+03 5.86E-05 2.72E-05 6.42E-05 1.75E-07 5.72E-05 Tip 2 30mil 6.490982026 1.51120E+09 1.2335E-07 1.13E-05-99.0 12.25% 9.21E+12 1.17E+03 2.51E-05 0 5.59E-05 0 3.09E-05 Tip 3 30mil 6.460581814 1.51150E+09 1.2523E-07 1.08E-05-99.4 9.33% 1.03E+13 1.19E+03 4.24E-05 3.06E-05 2.75E-05 1.07E-06 Note: The table is an editable spreadsheet object. 3.87E-05 Tip 1 Detuning effect lists the parameters for different notch tuning. Tip 1 30 mil sharp is for standard shape Tip 1 with sharper tip corner, tip-coupler gap is 30 mil. Tip 1 50 mil is standard shape tip with tip-to-coupler gap at 50 mil. Tip 2 30 mil is rod shape tip with tip-to-coupler gap at 30 mil. Tip 3 30 mil is nail shape tip with tip-to-coupler gap at 30 mil. Stored energy is for Low Loss shape end-cell between iris to iris. S12 is the transmission S-parameter from input coax to HOM coax output. Tip field is the magnetic field at the middle of the tip surface facing coupler as a percentage of the equator magnetic field. Qext_HOM, Qext_FPC is calculated through single cell stored energy and the corresponding S-parameter for the ports. 2 Cap, Ring/Back, Taper/Rod, coax denotes the value of total H ds for different sections of the probe as shown in the picture below. Total loss is the total probe heat (watt) per (MV/m) 2 assuming 12µΩ surface resistance (R s ) and 3.8mT/(MV/m) equator magnetic field. The total loss in the last column in the spreadsheet is obtained by: 2 3.8mT 2 W loss = ½R s ( H ds)( ), 12.0A/m is the equator magnetic field when total 12.0A/ m H 2 ds is calculated. 6
Fig. 9 The transmission coefficient vs. frequency Table 1 lists the actual tip field ratio and the corresponding Q ext. The transmission S 12 is shown in Figure 9. One can see that tip 2 has lower transmission coefficient, which is due to the small tip area. The 10dB loss implies the potential 10 times higher Q ext for HOM damping. When the tip 1 is pulled out 20mil more, the surface magnetic field drops a little, while the transmission coefficient becomes 5dB lower. From Figure 9, the HOM s 1.82GHz peak shows higher Q ext. Fig. 10 The TM010 mode Q ext decreases when notch gap increases for Tip 1. 7
Fig. 11 The HOM Q ext vs. the tip magnetic field for Tip 1. For standard tip 1, when the notch gap was increased to detune the notch frequency as shown in Figure 10, the tip surface magnetic field did drop, but not low enough (Figure 11). The HOM external Q listed in Figure 10 and 11 is for a single cell cavity. For a 7- cell cavity, a factor of 7 should be applied to the TM010 mode Q ext. (a) (b) Fig. 12 The heat loss versus temperature: Tip 1 under different HOM tuning condition (a), Tip 1,2,3 with 30 mil probe gap and Tip 1 with 50 mil probe gap (b). 8
From the numbers listed in table 1, the overall heat losses on the tip for a 20 MV/m cavity field under different temperatures were plotted in Figure 12. Here the surface resistance for niobium is calculated as the function of the surface temperature by the BCS theory. It shows that the proper thermal optimization may be more efficient compared to the geometric optimization. 4. Conclusion The simulations results show that the notch detuning has only weak effect. The Tip 2 and the Tip 1 in a larger gap sacrifice the HOM damping, but the decrease of the surface magnetic field was not significant. The Tip 3 that maintains the same HOM damping by the same tip head size did not show an elevated tip magnetic field. The relative small surface area on the probe tip makes it the best option, yet not with dramatic improvement. Because the tip heat loss increases exponentially when tip temperature increases, the thermal properties of the probe and feedthrough are most important. 5. Acknowledgment The three tip geometries were proposed by C. Reece and Co. during the HOM meeting in August 12, 2004. We would like to thank the team of G. Ciovati, E. Daly, T. Elliott, W. Funk, P. Kneisel J. Mammosse, B. Manus, J. Ozelis, L. Phillips, J. Preble and T. Rothgeb for their assistance. 9
6. Appendix A The dimensions of Tip 3 used in HFSS computation. 10