Manchester and collimation studies
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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

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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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