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Manchester and Collimation studies

Manchester and Collimation studies. Roger Barlow Manchester/Cockcroft. The Cockcroft Institute. New Institute for UK Accelerator Science Manchester-Liverpool-Lancaster joint project Located at Daresbury Working closely together with CCLRC ASTeC group ILC central (but not only) theme.

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Manchester and Collimation studies

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  1. Manchester and Collimation studies Roger Barlow Manchester/Cockcroft

  2. The Cockcroft Institute New Institute for UK Accelerator Science Manchester-Liverpool-Lancaster joint project Located at Daresbury Working closely together with CCLRC ASTeC group ILC central (but not only) theme COLSIM meeting, CERN, Dec 4 2006

  3. Manchester NS-FFAG (EMMA) construction • Roger Barlow • Adriana Bungau • Adina Toader • Rob Appleby • Dragan Toprek • Federico Roncarlo • Anthony Scarfe • Roger Jones • Ian Shinton • Chris Glasman • Ben Spencer • Narong Chanlek • Keith Potter (Hon. Prof.) • New lecturer being advertised Collimation and Wakefields for EuroTev and LC-ABD ILC Beam Dump 2mrad optics LHC through FP420 Wakefields in RF cavities, HFSS, LIAR, GDFIDL COLSIM meeting, CERN, Dec 4 2006

  4. Spread the word… COLSIM meeting, CERN, Dec 4 2006

  5. Collimation • Damage studies. GEANT4 simulation compared with FLUKA (Adriana) • Effect of collimation on beam (Adriana) • SLAC ESA beam tests (Adriana) • Halo: Production and behaviour. Long talked about but never started. Adina now learning PLACET to do this • Wakefields: Implementation of short-range (intra-bunch) wakefields in Merlin (and other programs?): rest of talk COLSIM meeting, CERN, Dec 4 2006

  6. r’ s s r Basic formalism Effect of leading particle on trailing particle, integrated over path through aperture and ignoring transverse motion during passage, is Impulse W(r,r’,s) Dimensions of Potential Maxwell’s EquationsW is the derivative of some function which is a solution of the 2D Laplacian Fourier Expansion in angle gives (=  -’) for devices with axial symmetry wT = m Wm(s) r’m rm-1 [cos(m) r- sin(m)] COLSIM meeting, CERN, Dec 4 2006

  7. Notations differ! COLSIM meeting, CERN, Dec 4 2006

  8. Different levels Less calculation means losing detail • Impulse on trailing particle of single particle leading by distance s . ‘wake potential’. • Impulse on trailing particle of slice of particles leading by distance s: Merlin • Impulse on trailing particle from all leading particles:(s’) W(s’-s) ds’.‘bunch potential’: PLACET • Average Impulse. (s’) (s) W(s’-s) ds ds’Most literature But going from 12 gives massive computation gain for almost no loss of detail COLSIM meeting, CERN, Dec 4 2006

  9. Standard Merlin Divide ~100,000 particle bunch into ~100 slices Transverse wakefield*. Dipole (m=1)term only Ignores axial component y’= Wcomponent(s) Qslice (Q is slice charge x offset) W(s) evaluated only ~100 times Takes ~100,000 x 100 /2 rather than ~100,000 x 100,000/2 calculations W(s) function cunningly attached to beamline component * MERLIN also does longitudinal wakefields, but they’re not very important for collimators COLSIM meeting, CERN, Dec 4 2006

  10. Extending Merlin • Include more modes W(m,s) • Include axial terms. Not just T but x and y Ignoring axial force. assumes =’ beampipe   bunch COLSIM meeting, CERN, Dec 4 2006

  11. Implementing higher modes wT = m Wm(s) r’m rm-1 [cos(m(- ’)) r- sin(m(- ’))] rand  unit vectors resolved into x,y Leading and trailing particle quantities all mixed up, but… Putting it all together and applying trig formulae the effect o a particle due to a slice is WX =  m W m (s) rm-1{ C m cos[(m-1) ] + S m sin[(m-1)]} WY =  m W m (s) rm-1 { S m cos[(m-1)] - C m sin[(m-1) ]} where C m= r’m cos(m’) S m= r’m sin(m’) Factorisation!! Simple sum over <trailing particle>x<aperture>x<leading slice> terms and can be calculated almost as easily as standard Merlin COLSIM meeting, CERN, Dec 4 2006

  12. Programming note • Couple of changes needed to Merlin (functions made virtual) • New SpoilerWakeProcess class that does the summations. Inherits from WakeProcess • New SpoilerWakePotentials class that provides prototypes for W(m,s) functions. Inherits from WakePotentials. Pure virtual. • Particular collimator types implemented by providing a class that inherits from SpoilerWakePotentials and provides actual W(m,s) COLSIM meeting, CERN, Dec 4 2006

  13. Example: Tapered collimator – diffractive regime Wm (s)= 2(1/a2m- 1/b2m)e-ms/a(s) TaperedCollimatorWakePotentials:SpoilerWakepotentials{ double a,b; double* coeff; public: TaperedCollimatorWakePotentials(double aa, double bb, int nmax){ a=aa; b=bb; nmodes=nmax; // nmodes is a data member of SpoilerWakePotentials coeff=new double[nmodes]; for (int i=0;i<nmodes;i++) {coeff[i]=2*(pow(a,-2*i)-pow(b,-2*i);} } ~TaperedCollimatorWakePotentials(){delete[]coeff;} Wtrans(double s, int m){return s>0? coeff[m]/exp(m*s/a):0);} } COLSIM meeting, CERN, Dec 4 2006

  14. Simulation example • Charge 2 1010 • x=3 m • y=10 m • x=36 10-9 mm • y=1 10-9 mm • E=1.19 GeV • Z=0.65 mm • Collimator Aperture 1.9 mm length 40 cm COLSIM meeting, CERN, Dec 4 2006

  15. Results: y’ versus z nmodes 1 2 3 4 5 Offset .5mm 1mm 1.5 mm COLSIM meeting, CERN, Dec 4 2006

  16. Implications • For small offsets, dipole mode is good enough • For large offsets, dipole mode is not good enough • Kick factors (<y’/y>) are not enough. There is a big variation in the kick (which increases ) and it is systematic so shape is non-Gaussian. After the first collimator anyway • For detailed studies we need to know particle-by-particle wake. Not integrated over Gaussian – the code does that COLSIM meeting, CERN, Dec 4 2006

  17. Link to existing PLACET Formulae given – CLIC note 671 y’=(2Nre/a2) exp(z2/2z2) y (diffractive regime) Clearly has shape folded in – need to unfold Cannot trace in Stupakov(1995) Positive exponential is puzzling Still, can implement as MERLIN class… COLSIM meeting, CERN, Dec 4 2006

  18. Same beam and aperture 1.0 mm offset .5 mm offset Effect increases with offset Scale is crazy – probably simple units problem Behaviour at large z incomprehensible 1.5 mm offset COLSIM meeting, CERN, Dec 4 2006

  19. Plans Roger: • Talk tomorrow to experts here and understand formulae and how to implement them • Implement other standard aperture formulae • Extend to non-axial apertures.. (Chao ‘considerably more complicated’. Yokoya + Stupakov for Gaussian bunch?) Possible at the expense of another summation? • Implement in other codes? BDSIM unsuitable(?) . PLACET looks possible Adina • Retrain as accelerator physicist • become familiar with using PLACET – use for halo simulations • Visit CERN for ~2 weeks in New Year to gain experience • Numerical wakefield simulation and adaptation to MERLIN-style approach Adriana – next talk COLSIM meeting, CERN, Dec 4 2006

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