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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

Manchester and Collimation studies

Roger Barlow


the cockcroft institute
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


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

spread the word
Spread the word…

COLSIM meeting, CERN, Dec 4 2006

  • 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

basic formalism





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

notations differ
Notations differ!

COLSIM meeting, CERN, Dec 4 2006

different levels
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

standard merlin
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

extending merlin
Extending Merlin
  • Include more modes W(m,s)
  • Include axial terms. Not just T but x and y

Ignoring axial force. assumes =’



COLSIM meeting, CERN, Dec 4 2006

implementing higher modes
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’)


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

programming note
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


Tapered collimator – diffractive regime

Wm (s)= 2(1/a2m- 1/b2m)e-ms/a(s)


double a,b;

double* coeff;


TaperedCollimatorWakePotentials(double aa, double bb, int nmax){



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);}



Wtrans(double s, int m){return s>0? coeff[m]/exp(m*s/a):0);}


COLSIM meeting, CERN, Dec 4 2006

simulation example
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

results y versus z
Results: y’ versus z

nmodes 1 2 3 4 5




1.5 mm

COLSIM meeting, CERN, Dec 4 2006

  • 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

link to existing placet
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

same beam and aperture
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



  • 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


  • 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


– next talk

COLSIM meeting, CERN, Dec 4 2006