New HCC RF Cavity Concept F. Marhauser, MuPlus, Inc

F. Marhauser, 11/2013, p.2 Gas-Filled Pressurized RF Cavities The high-pressure gas-filled cavities fulfill multiple functions, which may make the concept superior to vacuum cavities 1)Provides continuous, homogeneous ionization cooling 2)Elevates RF breakdown limit, particularly important in presence of external multi-Tesla magnetic fields 3)Dramatically reduces multipacting and dark current 4)Serves as thermal coolant of the cavity walls and beryllium windows K. Yonehara et al., Proc. PAC09, Vancouver, Canada, TU5PFP MHz test cell

F. Marhauser, 11/2013, p.3 Original Idea: Pillbox with ceramic aim: cavities follow helical path of magnetic channel combining cooling and rf acceleration most efficiently use of multiple short cavities (here: 24 cavities) per helical period main challenge: cavity radial size needs to be reduced to fit into magnetic channel  insert ceramic IPAC 2010, M. Popovic et al., THPEA047 IPAC 2010, S.A. Kahn et. al., WEPE072 IPAC 2010, K. Yonehara et al., MOPD076 Muon Collider Design Workshop 2009, V. Kashikin, G. Romanov

F. Marhauser, 11/2013, p.4 Original Idea: Pillbox with ceramic with ceramic: R = 78 mm (leaving ~46mm bore radius) w/o ceramic: e.g. R = 142 mm for f = 805 MHz Reduction in radial size: ~factor 2 with readily available technical alumina (e.g. Wesgo 995,  = 9.3 at r.t.) This is not a practical design yet

F. Marhauser, 11/2013, p.5 Pillbox w/o ceramic - Power Considerations Helical channel requires short cavities (~few cm) to reduce power levels to reasonable values Power to feed each cavity can only be reduced by shorten cavity further while P peak /L increases Optimum length ~ 10 cm for P peak /L E.g. at E acc (  ) = 16 MV/m (on axis)  P peak ~ 0.5 MW per cavity, P peak /L ~ 5 MW/m Example: f = 805 MHz (OFHC, r.t.) r = 142.5mm  = (p  =225 MeV/c)

F. Marhauser, 11/2013, p.6 Pillbox with ceramic - Power Considerations Major drawback: smaller radial size  much larger wall losses, i.e. peak power required Optimum length with Alumina ceramic shifted to L act ~ 8 cm E.g. E acc (  ) = 16 MV/m  P peak ~ 2 MW per cavity, P peak /L ~ 25 MW/m Factor 5 higher compared to pillbox w/o ceramic AND still tan  = 0 We need shorter units (few cm) to reduce P peak and to follow helical path smoothly, but P peak further increases P peak /L Example: f = 805 MHz (OFHC, r.t.) r = 142.5mm  = (p  =225 MeV/c) tan  = 0, eps = 9.3

F. Marhauser, 11/2013, p.7 How to improve situation ? Sacrifice size of cavity to reduce losses and optimize shape of ceramic Example: f = 650 MHz (OFHC, r.t.) r =  = 9.3  = (p  =200 MeV/c) ceramic: Al 2 O 3 L act = 27.3 mm (HCC segment 5) ceramic placed insiderecess to hold ceramic (~1mm) antenna hole

F. Marhauser, 11/2013, p.8 More Previous Layout Fewer cavities (factor 2) to increase cavity length, thereby reducing P peak and P peak /L to some extent

F. Marhauser, 11/2013, p MHz Helical Cooling Channels Example: f = 650 MHz (OFHC, Be r.t.) r =  = 9.3  = (p  =200 MeV/c) 160 atm GH 2 ceramic: Al 2 O 3 P thermal = 220 E acc =16MV/m L act = 20.8 mm P peak ~ MW required in 650 MHz segments if low loss ceramic found (e.g. AL995)

F. Marhauser, 11/2013, p MHz Helical Cooling Channels Example: f = 650 MHz (OFHC, Be r.t.) r =  = 9.3  = (p  =200 MeV/c) 160 atm GH 2 ceramic: Al 2 O 3 P thermal = 220 E acc =16MV/m L act = 20.8 mm P peak ~ MW required in 650 MHz segments if low loss ceramic found (e.g. AL995) P peak /L ~ 17 – 43 MV/m

F. Marhauser, 11/2013, p.11 Constraints with Ceramic-filled Cavities Dielectric strength limits performance, not RF-breakdown at metal surface in high-pressure cavity We may loose the benefits of gas elevating RF breakdown There are also many other practical/fabrication concerns with regard how to implement ceramic into cavity L.M. Nash et al., Proc. IPAC2013, Shanghai, China, TUPFI068

F. Marhauser, 11/2013, p.12 Constraints with ceramic-filled Cavities Dielectric strength limits performance, not RF-breakdown at metal surface in high-pressure cavity We may loose the benefits of gas elevating RF breakdown There are also many other practical/fabrication concerns with regard how to implement ceramic into cavity L.M. Nash et al., Proc. IPAC2013, Shanghai, China, TUPFI068

F. Marhauser, 11/2013, p.13 New Idea - Reentrant Cavities Can we eliminate the ceramics completely without sacrificing size of cavity? Be window

F. Marhauser, 11/2013, p.14 Reentrant Cavities Example: f = 650 MHz (OFHC, Be r.t.) r = mm  = (p  =200 MeV/c) 160 atm GH 2 gap = 37 mm (segment 5) L act = gap * Sqrt(2) = mm Same cavity radius as before P peak ~ 500 kW (factor ~2 reduced) P peak /L ~ 4.4 MW/m (up to factor ~10 reduced) At the same time: number of cavities reduced by factor 6 (24  4) Design allows ideal helical path to traverse always center of Be windows (optimum clearance)

F. Marhauser, 11/2013, p.15 Reentrant Cavities Example: f = 650 MHz (OFHC, Be r.t.) r = mm  = (p  =200 MeV/c) 160 atm GH 2 gap = 37 mm (segment 5) L act = gap * Sqrt(2) = mm Same cavity radius as before P peak ~ 500 kW (factor ~2 reduced) P peak /L ~ 4.4 MW/m (up to factor ~10 reduced) at the same time: number of cavities reduced by factor 6 (24  4) design allows ideal helical path to traverse always center of Be windows (optimum clearance) much more space for coupler and pickup probe (can be positioned on one side) RF isolation (cross-talk) between cavities improved

F. Marhauser, 11/2013, p.16 Pressure Vessel R.P. Johnson et al., COOL’13, MOAM2HAO3, here for ceramic-filled cavities pressure vessel

F. Marhauser, 11/2013, p.17 Pressure Vessel Space constraints (implementation into magnet bore) remains an issue

F. Marhauser, 11/2013, p.18 Pressure Vessel Space constraints (implementation into magnet bore) remains an issue Have to look into reducing size with reasonable tradeoff concerning power requirements

F. Marhauser, 11/2013, p.19 Pressure Vessel Space constraints (implementation into magnet bore) remains an issue Have to look into reducing size with reasonable tradeoff concerning power requirements E.g. slightly increasing number of cavities can reduce P peak further decrease

F. Marhauser, 11/2013, p.20 Pressure Vessel Space constraints (implementation into magnet bore) remains an issue Have to look into reducing size with reasonable tradeoff concerning power requirements E.g. slightly increasing number of cavities can reduce P peak further decrease Yet, we are already in the peak power capability range of cheap magnetron RF sources Work in progress!

F. Marhauser, 11/2013, p.21 RF Parameters e.g. segment 5 (650 MHz, 0.4m period), design easy scalable to any frequency ParameterSymbolUnitReentrant cavity FrequencyfMHz650 Cavity radiusRmm140.1 Helical radiusacm6.4 Helical periodλm04 Muon momentumpMeV/c200 Normalized velocityβ=v/c Operating temperature (nominal)T op K298 GH 2 pressureP GH2 atm160 GH 2 relative permittivityε r,GH GH2 ionization 200 MeV/cdE/dxMeV/cm0.058 Be ionization 200 MeV/cdE/dxMeV/cm3.23 Window thickness (each)L Be µm60 Active cavity length (in z)L gap mm37 (iris gap) Largest inner wall distanceL max mm93.0 (dome) Active length c  2·L gap mm52.3 Shunt impedance c R(β)MΩ3.48 Unloaded Quality factorQ0Q Characteristic shunt impedance c R/Q(β) 169 Total ionization losses (GH 2 + Be)E loss MeV0.82 Synchronous phaseφsφs degrees140 Effective voltageU eff kV801 Required accelerating field (on equilibrium orbit) E acc= U eff /(  2·L z )MV/m24.4 Required accelerating field d  2·E acc MV/m34.6 Effective electrical field c E eff (β) 15.3 Stored energyWsWs J2.36 Peak powerP peak kW470 Peak power per L wall P peak /L max MW/m5.1 Fill time (99% of energy) e t fill µs10.2 Average powerP avg W310 Generator power e PgPg kW600 a at room temperature, b Wesgo Al 995, c R/Q(β) = U eff 2 /(2π·f·W s ), c on equilibrium path, d equivalent on-axis field definition e based on beam loading (e.g. rep. rate of 64 Hz, muons per bunch)

F. Marhauser, 11/2013, p.22 Benefits 1)No ceramics a)not limited by dielectric breakdown (typically around 15 MV/m) b)no charge pile up (risk of arc damage) c)lower RF losses d)no triple junction e)no local field enhancement at dielectric (includes ceramic edges) f)no brazing, no metallization losses 2)Significantly reduced peak power requirements (P peak and P peak /L) a)Larger quality factor b)Larger shunt impedance 3) Largely reduced capital costs for cavities a) significantly reduced number of cavities b) simpler design c) easier fabrication d) significantly reduced number of RF sources with more relaxed peak power specification 4) Required generator peak power in capability range of cheap magnetrons (few 100 kW) 5) More space available for coupler and diagnostic probes 6) Full RF isolation between adjacent cavities (no crosstalk through gridded windows)

F. Marhauser, 11/2013, p.23 Fabrication Conceive manufacturing as for SRF cavities, i.e. using deep-drawing to produce half cells Leave half cell oversized Tune half cell by trimming equator Join half cells by EBW Final design of Be windows and implementation still to be done