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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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 3/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 4/19
Spread the word…
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 5/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 6/19
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)]
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 7/19
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)
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 8/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 9/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 10/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 11/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 12/19
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)
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 13/19
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);}}
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 14/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 15/19
Results: y’ versus z nmodes 1 2 3 4
5
Offset.5mm
1mm
1.5 mm
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 16/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 17/19
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…
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 18/19
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
Roger Barlow: Manchester and Collimation
COLSIM meeting, CERN, Dec 4 2006 Slide 19/19
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