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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

Manchester/Cockcroft

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

manchester
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

spread the word
Spread the word…

COLSIM meeting, CERN, Dec 4 2006

collimation
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

basic formalism

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

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 =’

beampipe

bunch

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’)

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

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

example
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

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

Offset

.5mm

1mm

1.5 mm

COLSIM meeting, CERN, Dec 4 2006

implications
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

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

plans
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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