manchester and collimation studies

Manchester and Collimation studies

Roger BarlowManchester/Cockcroft

Roger Barlow: Manchester and Collimation

COLSIM meeting, CERN, Dec 4 2006 Slide 2/19

The Cockcroft Institute

New Institute for UK Accelerator Science

Manchester-Liverpool-Lancaster joint project

Located at DaresburyWorking closely together

with CCLRC ASTeC group

ILC central (but not only) theme



Manchester• 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

Wakefields in RF cavities, HFSS, LIAR, GDFIDL

NS-FFAG (EMMA) construction

LHC through FP420



Spread the word…



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



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)

r’

s

r

s

Dimensions of PotentialMaxwell’s EquationsW 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)]



Notations differ!Quantity Our notation Stupakov Wilson Chao Zotter & Kheifets

The field wake field Wakefield Wakefield wake field wake field

Impulse produced by leading particle

Wake potential wz(r,r’,s),

Wake or Wake function, wt(,’,s)

wake potential Wz(r,r’,s),

W(r,r’,s)

Wake potential F||, F

Wake function G(rb,r’e,s)

Impulse from all leading particles in the bunch

Bunch potential W(r,s)

No explicit symbol

Wake potential or bunch potential Vz(s), V(s)

Wake potential

Wake Potential W() with =s/c

Function of which Wake potential is derivative

Invariant wake V

Wake Potential W

Not used ‘a quantity’ V

Not used

Panofsky-Wenzel Theorem

wt /s =wl

W /s =Wz

ds F||

= /z ds F

G /s=G||

Modal decomposition

Wake FunctionWm(s)

Fm(s) F(s)(no index)

Wake function Wm(s)

G||(m)(s) G(m)( s)



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 12 gives massive computation gain for almost no loss of detail



Standard Merlin Divide ~100,000 particle bunch into ~100 slicesTransverse wakefield*. Dipole (m=1)term onlyIgnores 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 calculationsW(s) function cunningly attached to beamline

component * MERLIN also does longitudinal wakefields, but they’re

not very important for collimators



Extending Merlin

1) Include more modes W(m,s)2) Include axial terms. Not just T

but x and y Ignoring axial force. assumes =’

beampipe

bunch



Implementing higher modes

wT = m Wm(s) r’ m rm-1 [cos(m(- ’)) r- sin(m(- ’))]r and unit vectors resolved into x,yLeading 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 isWX = 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



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)



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);}}



Simulation example

• Charge 2 1010

x=3 my=10 m x=36 10-9 mm y=1 10-9 mm• E=1.19 GeVZ=0.65 mm• Collimator Aperture 1.9 mm length 40

cm



Results: y’ versus z nmodes 1 2 3 4

5

Offset.5mm

1mm

1.5 mm



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



Link to existing PLACET

Formulae given – CLIC note 671y’=(2Nre/a2) exp(z2/2z

2) y

(diffractive regime)Clearly has shape folded in – need to

unfoldCannot trace in Stupakov(1995)Positive exponential is puzzlingStill, can implement as MERLIN class…



Same beam and aperture

1.5 mm offset

.5 mm offset1.0 mm offset

Effect increases with offset

Scale is crazy – probably simple units problem

Behaviour at large z incomprehensible



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

manchester and collimation studies

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