1. MCTF 1 Helical Solenoid Design Studies Vladimir Kashikhin (HS), Gennady Romanov (RF)

2. MCTF 2 Outline Helical Solenoid (HS) Magnetic Designs Dielectric filled RF Cavity HS Mechanical Design High Pressure Vessel Concept of HS with RF Module Design activity directions Summary

3. MCTF 3 Helical Solenoid Configurations (EPAC08) Helical Solenoids capable to generate fields required for the optimal muon cooling even at different helix periods. Large bore straight solenoids (1), helical multipole windings (2) or trapezoidal coils (3) could be used for eliminating of the misbalance between transverse and longitudinal fields. Demonstration models could use helical multipole windings for greater flexibility. The final design will be more efficient with non-circular shape coils. 1 23

4. MCTF 4 HCC Design Study (PAC09) Parameters of HCC sections. Parameter Unit Section 1st2nd3rd4th Section length m50403040 Helix period m1.000.800.600.40 Orbit radius m0.1590.1270.0950.064 Solenoidal field, B z T-6.95-8.69-11.6-17.3 Helical dipole, B t T1.622.032.714.06 Helical gradient, GT/m-0.7-1.1-2.0-4.5 High field helical solenoid Operation margin, helical dipole and gradient vs. coil thickness. HS coil optimal thickness and operation margin, and SS nominal field for different HS apertures. HS Aperture (mm) HS Optimal coil thickness (mm) HS Operation margin (%) SS Nominal field (T) 10020012.911 120150-1.48 140110-17.46

5. MCTF 5 Hybrid HS (PAC09) Hybrid HS coil characteristics. Layers thickness (mm) Normalized coil volume 1 G (T/m) Margin (%) SS field (T) HTSNb 3 SnHTSTotalHTSNb 3 Sn 20001.00 -4.6512.9-11.2 110200.390.53-4.6311.218.911.9 100300.330.54-4.5510.818.312.0 70 0.200.65-4.137.79.313.5 60900.160.75-3.925.36.814.6 501100.130.84-3.592.63.116.0 1 the HTS coil volume and the total volume of HTS and Nb 3 Sn coils normalized by the coil volume without grading The results of coil and field optimization for a hybrid HS with an external straight solenoid (SS) are summarized in Table. The first row represents the reference HS made of HTS. In all cases Bz= ‑ 17.3 T and Bt=4.06 T. The HTS-Nb3Sn hybrid HS provided practically the nominal value of field gradient G and the HTS coil volume reduction by a factor of 3 and the total coil volume reduction by a factor of 2. However, in this case the operation margin reduces by 16% and the nominal field of the straight solenoid increases by 7%. However, better performance at low fields and lower cost of Nb3Sn strands with respect to HTS materials motivates using a hybrid approach and conductor grading which allows reducing the HTS coil and the total coil volume.

6. MCTF 6 HS and Beam Matching (EPAC08) HS with helical matching sections of 3 m long at front and far ends. HS design could be used in combination with tangential muon beam injection to the helical orbit. This magnet system will be cheaper for short HS channels.

7. MCTF 7 HS Magnetic Concept for MANX (PAC07) The solenoid consists of a number of ring coils shifted in the transverse plane such that the coil centers follow the helical beam orbit. HS with RF has the same curent in each coil. The current in the coils could be chaned along the HS to obtain the longitudinal field gradients. The magnet system has a fixed relation between all components for a given set of geometrical constraints. Thus, to obtain the necessary cooling effect, the coil should be optimized together with the beam parameters. One could see that the optimum gradient for the helical solenoid is -0.8 T/m, corresponding to a period of 1.6 m.

8. MCTF 8 250 MeV Muon Beam Tracking 250 MeV muon beam could be effectively transmitted through Helical Cooling Channel. The space between HS sections is 240 mm to provide RF power input, HS current leads, LHe cooling, GH2 absorber vessel, HS cryostat walls, etc… The field drops at the HS section ends compensated by applying additional turns. Shown parallel muon beam of 100 mm diameter at front end of HS.

9. MCTF 9 Helical Solenoid Combined with RF Cavity The optimal helix period should be less or equal RF wave length (K.Yonehara, V. Balbekov PAC09). At 200 MHz - 800 MHz frequency range, the wave length and the helix period are in range of 1.5 m – 0.375 m. The 200 MHz cavity has 1.2 m diameter and it is too large to be placed inside HS. Possible solution is to use a dielectric loaded cavity (M.Popovic, et. al., PAC09) to reduce the RF cavity ID. The GH 2 absorber at high pressure could be used for cavity cooling. Cavities powered through HS cryostat penetrations.

10. MCTF 10 Dielectric Filled 200 MHz RF Cavity Cell Inner HS diameter is 590 mm. 200 MHz pillbox type cavity with beam bore diameter of 150 mm is investigated. The cavity is filled with ceramic to reduce its overall diameter. Cavity inner diameter 2R Total cavity length L including 2.5 mm walls Beam bore diameter 2r Ceramic AL-995 with ε=9.6 and tan δ=0.0002 ( Popovic et al., RF Cavities Loaded with Dielectric for Muon Facilities, PAC09 ). Ceramic has inner radius ≥ r, outer radius = R and length = L-walls. Vacuum The walls of cavity are copper. Cavity beam apertures are closed with foils (or grids). In simulations the foil is made of copper as well. Foil

11. MCTF 11 Dielectric Filled 200 MHz Cavity Cell Required frequency of 200 MHz, beam aperture of 15 cm diameter and given ceramic with ε=9.6 define transverse dimensions of the cavity. The minimal cavity diameter that can be achieved is 44 cm, while ceramic has inner radius 15 cm. The cavity is completely filled with ceramic material except beam bore. Therefore all transverse parameters are fixed. So, only cavity length and surface fields are available for optimization. L=10 cm E-field H-field Field amplitudes correspond to 1 J of stored energy

12. MCTF 12 Since the cavity is closed, electric field on axis E is almost constant at any cavity length L as long as surface field E surf is kept constant. Energy gain per cavity of length L according to the expression will be as shown: Energy Gain per Cavity β = 0.9 φ = 0 ω = 2 πf Transit time factor is maximal at L=0.67m. But the helix design requires the cavities as short as possible. Let’s see what would be a result of segmentation of the accelerating channel into sequence of much shorter cavities.

13. MCTF 13 Cavity Shunt Impedance and Q-factor In an accelerating cavity we are really more interested in maximizing the particle energy gain per unit power dissipation. We define an effective shunt impedance of a cavity as where q is a particle charge, P – dissipated power, V eff – effective voltage that takes into account field phase and transit time factor. The simulations shows that the cavity is very non-effective for shorter lengths. This is mostly because of high velocity of the muons ( β≈ 0.9) and related transit time factor.

14. MCTF 14 Increasing of cavity length also has its downsides. Approximately at 30 cm a saturation of E eff starts, while power losses are still linearly increasing. Secondarily, in longer cavity the losses in ceramic dominate, making heat removal more problematic. Cavity Parameters vs. Length

15. MCTF 15 Freq, MHz200L, cm2 Q1900Rs eff, MOhm/m0.6 Power total, MW11.45Emax, MV/m18 Power wall, MW7.33Energy gain, MeV0.36 RF Cavity Total Power 400 MHz dielectric loaded cavity M.Popovic et al, PAC09 200 MHz dielectric loaded cavity

16. MCTF 16 Independent phasing is very flexible. But 11 MW per cavity and 200 MHz operating frequency require extremely big transmission lines and couplers. Coupled cell structure 80 cm long and operating at 0-mode may help to reduce number of transmission lines and couplers to two units. Coupled Cavity Cell Structure Helical Solenoid Coupled cell structure Power coupler Conductive outer wall Ceramic filling Conductive grid, supported by ceramic disks Cell length 2 cm No conductive walls between ceramic disks

17. MCTF 17 Electric field Azimuthal magnetic field (no losses on grids) Cavity 0-mode of Operation Q = 4420; R sh_eff = 3.84 MOhm;

18. MCTF 18 For L=80 cm shunt impedance is not maximal, but still high enough. For 80 cm long cavity 77% of total power dissipations occurs in ceramic 80 cm long Cavity Parameters

19. MCTF 19 RF Cavity Filling Time and Losses Time constant τ = Q loaded /πf = 4420/(2 π 200[MHz]) = 3.52 μs Filling time (99%) T 99 = 4.6 τ = 16.2 μs For rectangular RF pulse length of T 99 : T 99 RF cavity effective filling time 16.2 μs. Pulses Repetition rate 15 Hz. Total RF power 100 MW for 80 cm. Average power losses 24.3 kW

20. MCTF 20 High Pressure Vessel for H 2 Gas Absorber 1.6m long helical tube (1) mounted inside cylindrical shell (2) and supported at ends by flanges (3). Tube thickness 58 mm. Gas pressure 100 atm. Peak Von Mises stress is 130 MPa for SS 316 (In agreement with ASME, II, part D code). Maximum displacement is 0.55 mm. 123123

21. MCTF 21 Hoop Lorentz forces intercepted by stainless steel rings around the coils Transverse Lorentz forces intercepted by support flanges Outer LHe vessel shell provide mechanical rigidity to the structure The peak stress is ~60 MPa HS Mechanical Concept The first model built and successfully tested

22. MCTF 22 Helical Cooling Channel Helical Cooling Channel (HCC) is a Superconducting Helical Muon Beam Transport Solenoid (HS) integrated with RF acceleration system. The following steps should be performed during design studies and R&D before final systems integration and prototyping: - Define RF outer dimensions, space for power wave guides, external power losses and cryoloads, system weight, etc… ; - Define the High Pressure gas (absorber) vessel parameters; - HS magnetic and mechanical design; - HS manufacturing technology; - HS models tests; - HS unit design with space for RF system; - HS prototype unit fabrication and tests w/o RF; - HS fabrication and tests with RF.

23. MCTF 23 HS+RF Cooling Channel

24. MCTF 24 Future Directions of Activity Design 200 MHz RF cavity integrated with Helical Solenoid. Design Helical Solenoid integrated with RF cavity. Continue HS short model fabrication and tests. Design a section of HCC. Fabricate and test section of HS. Fabricate and test section of RF. Assemble and test HCC (HS+RF) without absorber. Test HCC with absorber. Test HCC with a beam.

25. MCTF 25 Model of HCC (Half Period) The HCC model goals: Test RF helical structure parameters and performance in the helical magnetic field. Test Helical Solenoid performance. Test RF cavity power source. Test High Pressure GH 2 system as absorber and cooler. On the base of these tests verify the HCC system design and integration with sub-systems.

26. MCTF 26 Summary Proposed and investigated various versions of Helical Solenoids capable generate needed for muon ionization cooling fields. Proposed configuration of gas and dielectric filled helical RF system (HRF) integrated with Helical Solenoid. Shown a good transmission through sections of Helical Solenoid for 250MeV muon beam of 100 mm diameter. Estimated needed RF power, cavity parameters and average energy losses. Proposed concept of integration of RF cavity with Helical Solenoid in Helical Cooling Channel. Proposed the directions of activity in FY2010.

27. MCTF 27 HS Design Studies Contributors N. Andreev, V. Balbekov, E. Barzi, V. Derbenev, A. Didenko, S. Kahn, V.V. Kashikhin, M.Lamm, M. Lopes, A.Makarov, D. Orris, M. Tartaglia, R. Johnson, K. Yonehara, M. Yu, G. Velev, A. Zlobin