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

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

3. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 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: NFMC Beam energy, GeV4-50750-2000 Normalized emittances: transverse,  mm  rad30.025 longitudinal, cm27 P-driver power, MW45 Since the Neutrino Factory is less demanding, I will speak mostly about the Muon Collider.

4. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Muon Collider tentative parameters 4  s (TeV)1.53 Av. Luminosity / IP (10 34 /cm 2 /s) 0.773.4 Max. bending field (T)1014 Av. bending field in arcs (T)68.4 Circumference (km)3.14.5 No. of IPs22 Repetition Rate (Hz)1512 Beam-beam parameter/IP0.0870.087  * (cm)10.5 Bunch length (cm)10.5 No. bunches / beam11 No. muons/bunch (10 12 )22 Norm. Trans. Emit. (  m)2525 Energy spread (%)0.10.1 Norm. long. Emit. (m)0.070.07 Total RF voltage (MV) at 800MHz77 886  + in collision / 8GeV proton0.0080.007 8 GeV proton beam power (MW)4.84.3 ----------------------------------------------------------------------- P  – average muon beam power (~  ) C – collider circumference (~  if B=const)  – muon lifetime (~  )  * – beta-function at IP – beam-beam parameter h  z /   “Hour-glass factor”

5. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Muon Collider Challenges 5 Proton Driver: average power ~ 5MW, Np ~ 2.5  10 14 /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 10 6 in 6D phase space Muon acceleration: fast (  =2.2  s  ) acceleration of intense bunches (N  ~ 2  10 12 ) – 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!

6. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 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  10 14 /3ns bunch @ 8GeV to get 2  10 12 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) 

7. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Target 7 1 2 3 4 Syringe Pump Secondary Containment Jet Chamber Proton Beam Solenoid 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

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

9. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Muon Collection 9 Muon distribution in decay solenoid 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) Achieved with RF cavities of ~30 different frequencies (360MHz  201.5MHz) ~0.08  + / 8GeV p in 14 bunches (after initial cooling) p [MeV/c] t [ns] dN/dp p [GeV/c] t [ns] p [MeV/c] Varying RF phase velocity with time (D.Neuffer)

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

11. Ionization Cooling Basics 11 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: Principle of transverse cooling NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009

12. Damping Re-partition for Longitudinal Cooling 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 12

13. 6D Cooling Schemes “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  “Guggenheimed” Helical Cooling Channel RFOFO ring (curvature  dispersion) NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 13

14. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Helical FOFO Snake 14 absorbersRF cavitiesalternating solenoids z [cm] B x  50 B [T] BzBz B y  50 DxDy z Cooling in the first stage is ~ sufficient for a NF  2N  N [cm]  1N  3N G4BL stochs. on MICCD N/N 0 G4BL stochs. off no decays! Transmission vs period # Normalized emittances vs period # Principle of resonant dispersion generation exploited G4BL simulations

15. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Final Cooling - “Brute Force” Methods 15 (w/o longitudinal cooling) to obtain   N =25  m in H 2   =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

16. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Final Cooling - PIC 16 PIC = Parametric resonance Ionization Cooling (first proposed by V.Balbekov in 1997) 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 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 Sector magnets absorber Qx=Qy=1

17. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 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] z [cm] Periodic orbit in HFOFO snake: MICCD – red, G4BL v1.16 – blue

18. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 RF Breakdown Modeling 18 –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 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) Tech-X is developing a code on basis of VORPAL, allegedly ~ 1 year away

19. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Gas Filled RF Cavities for IC (Muons Inc) 19 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. 10% of liquid H 2 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

20. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 RF for Acceleration & Collider 20 * http://www.gdfidl.de 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! Longitudinal wake potential vs. s for the bunch length of 10mm.

21. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 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 U RF  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

22. NF & MC challenges - Y.Alexahin ICAP09, San Francisco, August 31 2009 Muon Collider Lattice 22  y  x  * = 3mm,  max = 901,835 m hor. CC ver. CC 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! K.Oide IR design

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

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