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Neutrino Factory & Muon Collider Computational Challenges

FERMI NATIONAL ACCELERATOR LABORATORY US DEPARTMENT OF ENERGY. f. Neutrino Factory & Muon Collider Computational Challenges. Y.Alexahin. International Computational Accelerator Physics Conference, San Francisco, 08/31- 09/04, 2009. NF & MC Concepts. 2. Li lenses!.

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Neutrino Factory & Muon Collider Computational Challenges

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  1. FERMI NATIONAL ACCELERATOR LABORATORY US DEPARTMENT OF ENERGY f Neutrino Factory & Muon Collider Computational Challenges Y.Alexahin International Computational Accelerator Physics Conference, San Francisco, 08/31- 09/04, 2009

  2. NF & MC Concepts 2 Li lenses! NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  3. NF & MC Beam Requirements 3 The Neutrino Factory may be considered as a prelude for the Muon Collider, its requirements for muon cooling and acceleration are more modest: NF MC Beam energy, GeV 4-50 750-2000 Normalized emittances: transverse, mmrad 3 0.025 longitudinal, cm 2 7 P-driver power, MW 4 5 Since the Neutrino Factory is less demanding, I will speak mostly about the Muon Collider. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  4. Muon Collider tentative parameters 4 h z /  “Hour-glass factor” s (TeV) 1.5 3 Av. Luminosity / IP (1034/cm2/s) 0.77 3.4 Max. bending field (T) 10 14 Av. bending field in arcs (T) 6 8.4 Circumference (km) 3.1 4.5 No. of IPs 2 2 Repetition Rate (Hz) 15 12 Beam-beam parameter/IP 0.087 0.087 * (cm) 1 0.5 Bunch length (cm) 1 0.5 No. bunches / beam 1 1 No. muons/bunch (1012) 2 2 Norm. Trans. Emit. (m) 25 25 Energy spread (%) 0.1 0.1 Norm. long. Emit. (m) 0.07 0.07 Total RF voltage (MV) at 800MHz 77 886 + in collision / 8GeV proton 0.008 0.007 8 GeV proton beam power (MW) 4.8 4.3 ----------------------------------------------------------------------- P – average muon beam power (~  ) – beam-beam parameter • C – collider circumference (~  if B=const) • – muon lifetime (~ ) • * – beta-function at IP NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  5. Muon Collider Challenges 5 Proton Driver: average power ~ 5MW, Np ~ 2.51014/3ns bunch @ 8GeV – enormous space charge! Target: must withstand impact of such proton bunches (Hg jet seems a viable solution - MERIT) Muon collection and cooling: digest muon beam with N>2cm, LN~10cm, and compress it by 106 in 6D phase space Muon acceleration: fast (=2.2s) acceleration of intense bunches (N ~ 21012) – beam loading, instabilities Collider optics: correction of strong chromatic aberrations in large momentum range (~1%) beam-beam effect and its compensation Experimentation: backgrounds from decay electrons (and their X-radiation) and Bethe-Heitler muons Environmental impact: neutrino radiation! NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  6. P-Driver 6 Our estimate of the required average power ~ 5MW, this figure may decrease with better muon capture/cooling designs, FNAL Project X upgrade (2MW 8GeV p-beam) is a good candidate – see N. Solyak presentation Problem: Np ~ 2.51014/3ns bunch @ 8GeV to get 21012 muons/bunch Computational challenges:  space charge  focusing on the target  instabilities in storage/coalescing ring Additional acceleration in RCS to 20-60GeV will help (some encouragement:: our problems are not as as severe as with HIDIF - Heavy Ion Driver for Inertial Fusion - pursued by GSI and ITEP, Moscow)  NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  7. Target 7 Solenoid Jet Chamber Syringe Pump Secondary Containment Proton Beam 1 2 3 4 Hg jet @WP4 after impact of 8e12 14GeV protons in 10T field MERIT experiment at CERN (H.Kirk) Hg jet is shown to withstand up to 115kJ p-beam impact, but we may need ~3 times more. Computational challenges: MHD of jet interaction with intense proton beam  reproducibility of pion production NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  8. MHD Simulations (W.Bo, R.Samulyak) 8 FronTier Code NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  9. Muon Collection 9 dN/dp Muon distribution in decay solenoid p [MeV/c] p [MeV/c] t [ns] p [GeV/c] Varying RF phase velocity with time (D.Neuffer) Achieved with RF cavities of ~30 different frequencies (360MHz  201.5MHz) ~0.08+ / 8GeV p in 14 bunches (after initial cooling) t [ns] Adding absorbers may improve capture of high-momentum muons, but will drastically increase computation time. Challenge: optimization with up to 100 parameters (RF frequencies, gradients, phases) NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  10. Emittance Evolution (R.Palmer) 10 Final cooling (REMEX) 6D cooling NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  11. Ionization Cooling Basics 11 Principle of transverse cooling There is no longitudinal cooling in the most suitable range 2-300MeV/c. With higher momentum p > 300MeV/c it is difficult to obtain small -function which is necessary for small equilibrium emittance: NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  12. Damping Re-partition for Longitudinal Cooling 12 Dispersion and/or large positive momentum compaction  higher momentum muons make longer path in the absorber  lose more energy longitudinal cooling NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  13. 6D Cooling Schemes 13 RFOFO ring (curvature  dispersion) Helical Cooling Channel “Guggenheimed” “Guggenheim” : poor transmission; problem with RF in magnetic field. HCC: no viable solution yet for RF inside coils. Both channels are selective to muon sign, it is either + or  NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  14. Helical FOFO Snake 14 N/N0 no decays! G4BL stochs. off MICCD G4BL stochs. on Transmission vs period # N [cm] 3N Dx Dy 2N 1N z alternating solenoids absorbers RF cavities G4BL simulations B [T] Bx50 Bz By50 z [cm] Normalized emittances vs period # Principle of resonant dispersion generation exploited Cooling in the first stage is ~ sufficient for a NF NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  15. Final Cooling - “Brute Force” Methods 15 (w/o longitudinal cooling) to obtain N=25m in H2 =0.7cm/ is needed High Field Solenoids: [cm]=p[MeV/c]/(1.5B[T])  = 1cm in B=50T for p=75MeV/c (=0.58) Lithium Lens B’=3000T/m (I=0.375MA, r=0.5cm)  = 1cm for p=100MeV/c Problems: The required parameters for both devices are far beyond present technology (FNAL Li lens B’<1000T/m) No complete channel design NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  16. Final Cooling - PIC 16 Sector magnets absorber PIC = Parametric resonance Ionization Cooling (first proposed by V.Balbekov in 1997) x-size shrinks due to the resonance, x’-size is kept from growing by cooling in absorbers (and re-acceleration in RF cavities) final emittance is determined by the absorber width, not by the focusing strength Two approaches are currently under study:  “Epicyclical” Helical Cooling Channel (Y.Derbenev, JLab)  Fringe Field Focusing Ring (V.Balbekov, FNAL) Problems and challenges:  no satisfactory design yet  nonlinear aberrations  space charge tuneshift Qx=Qy=1 NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  17. Optics Code for Ionization Cooling Channels 17 For design of sophisticated channels a MAD-like code is needed which include:  long-range fields of tilted and displaced off-axis magnetic elements,  fully coupled 6D optics functions calculation in presence of strong damping  analysis of higher order effects on beam dynamics (e.g. damping decrement dependence on the amplitudes of oscillations Presently there is a Mathematica prototype of such code (MICCD), a professional programmer is needed for further development x [cm] Periodic orbit in HFOFO snake: MICCD – red, G4BL v1.16 – blue z [cm] NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  18. RF Breakdown Modeling 18 Problem: High gradient RF operating in strong magnetic field (typical requirements E>30MV/m at 800MHz in B=20T) What must be modeled (Kevin Paul, Tech-X) • Field emission of electrons from conductor surfaces • Secondary emission of electrons from conductor surfaces • Sputtering • Neutral Desorption • Field-induced ionization (Tunneling ionization) • Impact ionization • X-ray production from electron impact on conductor surfaces • Surface heating due to particle impact • Surface deformation due to melting • Radiative cooling of ions Tech-X is developing a code on basis of VORPAL, allegedly ~ 1 year away NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  19. Gas Filled RF Cavities for IC (Muons Inc) 19 10% of liquid H2 High pressure H2 solves the problem with RF breakdown for any B field and at the same time serves as the lowest Z absorber, but New problem: Ionization by passing through muon beam. For complete understanding and optimization of ionization cooling channels a supercode is needed which includes:  beam dynamics with account of self-fields in plasma and stochastic processes  absorber reaction to energy deposition by the beam (bulbs in solid and liquid abs.?)  plasma evolution in strong RF field NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  20. RF for Acceleration & Collider 20 * http://www.gdfidl.de Longitudinal wake potential vs. s for the bunch length of 10mm. Calculations by V.Yakovlev, N.Solyak & A.Lunin for ILC-type 1.3GHz cavity give 2MV wake for 320 nC bunch (N=2e12)  ~10% of accelerating voltage  potential well distortion Challenge: self-consistent simulations are necessary! NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  21. Muon Collider Lattice 21 Long list of requirements:  low  ( 1cm), small circumference C (since luminosity ~ 1/C), momentum acceptance ~ 1% dynamic aperture for N~25 microns , low momentum compaction (c ~ 10-5) z with a reasonable URF detector protection from background (!) manageable sensitivity to errors  limited max no long straights (not to create "hot spots" of neutrino radiation),   … - Design of such lattice is a challenge in itself The most difficult problem: correct chromatic perturbations w/o compromising dynamic aperture. Various schemes considered, presently there are two completed designs:  K.Oide (1996): sextupoles in special CC sections (“local” correction, but the locale is out of IR). Allows to organize the sextupoles into non-interleaved pairs.  Y.A. & E.Gianfelice-Wendt:dipoles and sextupoles right in IR - saves space, less prone to errors but at the price of stronger higher-order effects NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  22. Muon Collider Lattice 22 K.Oide IR design y hor. CC ver. CC  * = 3mm, max = 901,835 m x Large beta-functions  high sensitivity to magnet errors, dynamic beta due to strong beam-beam interaction exacerbates the effect It would be beneficial to suppress beam-beam interaction at the source Computational challenges: 3D strong-strong beam-beam simulations with - magnet imperfections - self-consistent interaction with RF Simulation of beam-beam suppression by overdense plasma at IP (proposed by P.Chen & G.Stupakov in 1996)  detector backgrounds! NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  23. Where are we now? (V.Shiltsev) 23 NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

  24. 5 Years of Muon Collider R&D (V.Shiltsev) 24 A lot of state-of-the-art computing is necessary to reach this point! NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

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