B eam screen cooling: scaling from LHC to FHC

1. Beam screen cooling: scaling from LHC to FHC Philippe Lebrun FHC meeting on beam pipe design, CERN 20 December 2013

2. The beam screen concept Magnet cold bore (1.9 K) Beam screen (>> 1.9 K) G. Claudet, F. Disdier, Ph. Lebrun, M. Morpurgo, P. Weymuth, Preliminary Study of a superfluid helium cryogenic system for the Large Hadron Collider, LHC Note 26 (1985)

3. Rationale for beamscreentemperature1) Thermodynamics • ExergyloadDE = measure of (ideal) refrigerationduty DE = DEcm + DEbs DE = Qcm . (Ta/Tcm – 1) + (Qbs – Qcm) . (Ta/Tbs – 1) • WithQbs = heatload to beamscreen Tbs = beamscreen (average) temperature Qcm = residualheatload to cold mass Tcm = cold mass temperature (1.9 K for LHC) Ta = ambienttemperature (290 K) • Minimize total exergyload • Estimate Qcm = f (Tbs) • Calculation: radiation + conduction along supports with contact resistance • Measurements on full-scale thermal models

4. Measuredresidualheatloadfrombeamscreen to cold mass

5. Residual heat load modelfrom beam screen to cold mass Conduction dominates up to ~100 K

6. Total exergyloss vs beamscreentemperatureParameter: beamscreenheatload

7. LHC beam vacuum requirements • Beam vacuum lifetimedominated by nuclearscattering of protons on residualgas • Beam vacuum lifetime of ~100 h required to • Limitdecay of beamintensity • Reduceenergydeposited by scattered protons to ~ 30 mW/m • residualgasdensity in the 1014 m-3 range • residual pressure in the 10-9 to 10-8 Pa range • Cryopumping on cold bore at 1.9 K meetstheserequirements • This wouldbesufficient in absence of beam-induceddesorption

8. Cryopumping of beam vacuum at 1.9 K 100 h lifetime for hydrogen Saturation pressure of all gasesexceptheliumvanishat 1.9 K M. Jimenez

9. Rationale for beamscreentemperature2) Dynamic vacuum • Beam-induceddesorption of cryopumpedgasmoleculesdegrades vacuum • beamscreenshelters 1.9 K cryopumping surface from proton/ion/photon induceddesorption • pumpingholes for desorbedmolecules (4%) • Avoidbeamscreentemperatureswherevapor pressure of condensedspecies (H2, H2O, CH4, CO, CO2) are in the 10-7 to 10-4 Pa range: insufficientpumping speed to the cold bore at 1.9 K • allowed ranges 5 – 20 K, 40 – 60 K, 100 – 120 K, > 190 K V. Baglin

10. Rationale for beamscreentemperature3) Transverse wallimpedance • Beamstabilityrequireslow transverse impedance • Transverse impedance ZT(w) ~ rR /w b3 r wall electrical resistivity R average machine radius b half-aperture of beam pipe • Transverse resistive-wallinstability • dominant in large machines withsmall aperture • must becompensated by beam feedback, providedgrowth of instabilityis slow enough (~ 100 turns) • maximizegrowth time t~ 1/ZT(w) i.e. reduce ZT(w)  for a large machine with small aperture, low transverse impedance is achieved through low r, i.e. low-temperature wall coated with >50 mm copper (typically < 50 K for RRR=100)

11. 0.17 W/m per aperture Heatloads to beamscreen1) Synchrotron radiation frombendingmagnets • Charged particle beams bent in a magnetic field undergo centripetal acceleration and emit electromagnetic radiation • Whenbeams are relativistic, radiation isemitted in a narrowcone • Median of spectrumEc ~ g3/R • Power radiated per m Psyn ~ g4/R2 withg = relativistic factor of beam, R = radius of curvature UV, easy to screen

12. Heatloads to beamscreen2) Beam image currents in the resistivewall • Beam of chargedparticles = electricalcurrent • « Image currents » are induced in the (resistive) wall of the vacuum chamber, producingohmic dissipation • Power per m Prw ~ N2r1/2 with N = particlebunch charge r = electricalresistivity of wall • Low-resistivity • Copper vs stainlesssteel • Lowtemperature • Magneto-resistance • Eddy currentsatmagnetresistive transition => 75 mm Cu (RRR = 100) on 1 mm austeniticsteel

13. Heatloads to beamscreen3) Electron cloud • Photo-electronsextractedfrom the wall by synchrotron radiation, canberesonantlyaccelerated by the successive particlebunches => multipacting => buildup of electroncloud • Energydeposition by electonshitting the wall • Intensity of electroncloudgoverned by • photon irradiation of the wall ⇒low reflectivity surface • bunch repetition rate ⇒ increase bunch spacing • secondary electron yield ⇒ low-SEY surface and beam “scrubbing”

14. Functional design map of beamscreen FUNCTION PROCESS DESIGN FEATURE Low-conduction supports Limitresidualheatload to cold mass Reducebeam-inducedcryogenicloads High-conductivitycopperplating Intercept synchrotron radiation Increasedevelopment time of transverse resistive-wallinstability Coolingatlowtemperature Limitresistivewallimpedance Austeniticstainlesssteel structure Resisteddy-current forces atmagnetquench Structural materialwithhighresistivity Pumping slots Preservefieldquality in magnet aperture Low-permeabilitymaterials Avoidtemperaturesfavoringdesorption of commongasspecies Maintain good beam vacuum Providepumpingfromshielded cold surface Sawtooth absorber Limitreflectivity and SEY of beamscreen surface Limitdevelopment of electroncloud Beamscrubbing

15. Design space for LHC beamscreenParameter: beamscreenheatload

16. Beam screen heat loads[W/m per aperture] V. Baglin, Ph. Lebrun, L. Tavian, R. van Weelderen, Cryogenic beam screens for high-energy particle accelerators, Proc. ICEC24 Fukuoka, Cryogenics and Superconductivity Society of Japan (2013) 629-634

17. Compared parameters of hadron colliders

18. LHC-type beam screen for FHCAssumption Tcm = 1.9 K

19. LHC-type beam screen for FHCAssumption Tcm = 1.9 K

20. Fromexergy to power consumption • Real electrical power to refrigeratorPref Pref= DE/h(T) withh(T) = efficiencyw.r. to Carnot = COPCarnot/COPReal Pref = Qcm . (Ta/Tcm – 1)/h(Tcm) + (Qbs – Qcm) . (Ta/Tbs – 1)/h(Tbs) • WithQbs = heatload to beamscreen Tbs = beamscreen (average) temperature Qcm = residualheatload to cold mass Tcm = cold mass temperature (1.9 K for LHC) Ta = ambienttemperature (290 K) • Minimizetotal electrical power to refrigerator

21. h(T) = COPCarnot/COPReal measured fit measured

22. LHC-type beam screen for FHCAssumption Tcm = 1.9 K

23. Coolingpotential of cryogens for beamscreen Operating the beam screen at higher temperature would allow other cooling fluids

24. Summary • Original motivation for LHC beamscreen: thermodynamics • Reduceexergyload to the cryogenic system, and therefore power to refrigerator • Also essential for • Ensuring good (dynamic) vacuum for circulatingbeams • Limitdevelopment of beam collective effects and instabilities • Beamscreen design spaceconstrained by multi-physics • Thermodynamics • Electromagnetism • Materialproperties • Vacuum • Thermohydraulics • Assume FHC has same cold mass temperature and similarbeamscreen as LHC • FHC higherlinearheatloadspush thermodynamic optimum towardshigherbeamscreentemperatures (~ 80-100 K for 80 km ring): isthis acceptable? • Power to refrigeratorneeded to compensate for synchrotron radiation load of ~ 40 W/m per aperture for 80 km ring wouldbe ~ 600 W/m per aperture withthermodynamicallyoptimizedbeamscreen, i.e. ~ 100 MW for complete FHC • In absence of beamscreen, itwouldbe > 5 GW!