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The General Particle Tracer (GPT) code
B van der Bas d Geer G Marieke de Loos P l Pulsar Ph Physics i The Netherlands www.pulsar.nl
There are two kinds of simulation codes: - Codes that everyone always complains about - Codes that nobody ever uses
FEI: Electron microscopes
Eindhoven: 210,000 inhabitants 25% jobs in technology and ICT
Technological regions in Europe: 1) Stockholm 2) Helsinki 3) Eindhoven / München
ASML: Wafer steppers 2010: 4,508 M€ In ‘nerd city’ Eindhoven the number of autistic children is twice as high as in the rest of the country
University of technology: 3000 employed 7000 students 600 PhD students
Eindhoven Pulsar Physics: Bas & Marieke
Philips research: Consumer electronics Medical devices Etc. etc. etc.
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History of GPT development 1992 Initial development FELIX FOM FELIX, FOM-Rijnhuizen Rij h i 1994 First commercial user: Stanford University, University USA 1996 Founded our company: Pulsar Physics Physics, www.pulsar.nl www pulsar nl Continuous development Collaborations with Rijnhuizen, TU/e, Rossendorf, Strathclyde, DESY Daresbury, DESY, Daresbury Rostock, Rostock …
Launching project: FELIX, FOM-Rijnhuizen
2006 GPT has become a well-established simulation tool for the study of charged particle dynamics.
GPT Users Worldwide www.pulsar.nl/gpt
48 Research institutes Andrzej Soltan Institute for Nuclear Studies Advanced Industrial Science and Technology (AIST) Akita National College of Technology Argonne National Laboratory (ANL) Bhabha Atomic Research Centre Brookhaven National Laboratory Cells Centre for Advanced Technology Consorcio ESS BILBAO Daresbury Laboratory Deutsches Electronen-Synchrotron (DESY) European Synchrotron Radiation Facility (ESRF) Fermi National Accelerator Laboratory (FNAL) FOM-Rijnhuizen Forschungszentrum Jülich GmbH Forschungszentrum Rossendorf (FZR) Helmholtz-Zentrum Berlin High Energy Accelerator Research Org. (KEK) Institute of Applied Electronics (IAE) Institute of Modern Physics (IMPCAS) Interfacultair Reactor Instituut Japan Atomic Energy Agency (JAEA) Jefferson Laboratory Korea Atomic Energy Research Institute (KAERI) Lawrence Berkeley National Laboratory Los Alamos National Laboratory (LANL) Marshall Space Flight Center (NASA) M B Max Born IInstitute tit t Max-Planck-Institut für Quantenoptik (MPQ) Moscow Engineering Physics Institute (MEPHI) National Synchrotron Radiation Research Center Naval Postgraduate School Netvision Paul Scherrer Institute (PSI) P h Pohang A Accelerator l t L Laboratory b t (POSTECH) Rafael Laboratories Rutherford Appleton Laboratory (RAL) Sincrotrone Trieste S.C.p.A. Soltan Institute for Nuclear Studies Stanford Linear Accelerator Center (SLAC) Sameer R&D of Govt. of India Sh Shanghai h i IInstitute tit t off A Applied li d Ph Physics i Sincrotrone Trieste S.C.p.A. Soreq Research Center Stanford Linear Accelerator Center (SLAC) Tekniker Tokyo Institute of Technology TRIUMF
Poland Japan Japan USA India USA Spain India Spain UK Germany France USA Netherlands Germany Germany Germany Japan Japan China Netherlands Japan USA South Korea USA USA USA G Germany Germany Russia Taiwan USA Israel Switzerland S th Korea South K Israel UK Italy Poland USA India Chi China Italy Israel USA Spain Japan Canada
9 Commercial companies Bharat Electronics Ltd. Biosterile Technologies FEI Company Hitachi Ishikawajima-Harima Heavy Industries Kobe Steel, Ltd. Océ Printing Systems Positronics Research Sumitomo Heavy Industries
India Russia Netherlands Japan Japan Japan Germany USA Japan
43 Universities Abertay Dundee Ankara University Australian National University Cornell University Delft University of Technology Technische Universität Darmstadt Eindhoven University of Technology (TUE) Florida State University G i Groningen U i University i Hiroshima University Imperial College Johannes Gutenberg-Universität Mainz Kyoto University Kyungpook National University University of California at Los Angeles (UCLA) L d U London University i it C College ll Manchester University Melbourne University McGill University München University Nagoya University Nebraska – Lincoln University Nij Nijmegen U University i it Osaka University Oxford University Paris – sud University Sichuan University Stanford University Strathclyde T h i h Universität Technische U i ität Darmstadt D t dt Tel Aviv University Tohoku University Tokyo University Toronto University Tsukuba University Tsinghua University T Twente t University U i it University of Abertay Dundee University of Strathclyde Utrecht University Vanderbilt University Wisconsin University Yale University
UK Turkey Australia USA Netherlands Germany Netherlands USA N h l d Netherlands Japan UK Germany Japan South Korea USA UK UK Australia Canada Germany Japan USA N th l d Netherlands Japan UK France China USA UK G Germany Israel Japan Japan Canada Japan China N th l d Netherlands UK UK Netherlands USA USA USA
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GPT simulation approach
Study phase-space evolution of charge particle bunches • 106 sample particles • In external fields • Including g space-charge p g forces • In 3D Applications: • Charged particle accelerators and beamlines • Electrons, protons, muons, …
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Equations of motion
GPT tracks sample particles in time-domain • Equations of motion
dr dp = q ⋅E + × B dt dt dr cp = dt m 2c 2 + p ⋅ p include all non-linear effects • •
Solved with 5th order embedded Runge Kutta, adaptive stepsize GPT can track ~106 particles on a PC with 1 GB memory
•
Challenge: E(r,t), B(r,t), flexibility without compromising accuracy
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Analytical fields
Solenoid with rectangular cross section r2z + a
Bz ( z, r = 0) = ∫
∫ 2(r
r1 1z−a
IBz ( z , r = 0) =
µ0 I r 2
µ0 I
2
+z ) 2
3
2
dzdr
(
z logg r + r 2 + z 2
4a (r2 − r1 ) Bz ( z , r = 0) = IBz ( z + a, r2 ) − IBz ( z + a, r1 )
)
− IBz ( z − a, r2 ) + IBz ( z − a, r1 )
rectcoil(ECS,r1,r2,L,I) 1 1 B z ( z , r ) ≈ B ( z ) − B '' ( z ) r 2 + B ( 4 ) ( z ) r 4 − K 4 64 1 1 Br ( z , r ) ≈ − B ' ( z )r + B ''' ( z )r 3 − K 2 16
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Magnet
1D, 2D, 3D Rely on external solvers Fields are summed 3D positioning, 3D orientation
200
150
R [mm m]
• • • •
Field-maps
100
Example: Strathclyde rf-photo gun 0 -50
0
50
100
150
200
z [mm]
GPT
C it Cavity 40
R [m mm]
Marieke e de Loos Pulsar P Physics
50
30 20 10 0
0
20
40
60
80
100
120
140
Only this part is fed into GPT
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Coulomb interactions
Macroscopic: • Space-charge • Average repulsion force • Bunch expands p • Deformations in phase-space • Governed by Poisson’s equation Microscopic: • Disorder induced heating • Neighbouring particles ‘see’ each other • Potential energy → momentum spread • Stochastic effect • Governed by point-to-point interactions
GPT simulations PRL 93, 094802 O.J. Luiten et. al. JAP 102,, 093501 T. van Oudheusden et. al. PRST-AB 9, 044203 S B van der Geer et S.B. et. al al. PRL 102, 034802 M. P. Reijnders et. al.
JAP 102, 094312 S.B. van der Geer et. al.
Nature Photonics Vol 2 2, May 2008 M. Centurion et. al. And many others…
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Space-charge models in GPT
Considerations: • Relative contribution of granularity/microscopic effects • Accuracy requirements ↔ amount of patience ↔ hardware 3D Particle in Cell (PIC)
Space-charge (Macroscopic)
Poisson solver Gisela Pöplau Rostock Universityy
Tree code
Correlation heating (Microscopic)
Barnes&Hut
Particle-in-Cell
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Bunch in laboratory frame
•
Mesh-based electrostatic solver in rest-frame
Bunch in rest frame
• •
Bunch is tracked in laboratory frame Calculations in rest-frame z ' ≈ γ z , γ = 1
•
Mesh – Density follows beam density – Trilinear interpolation to obtain charge density
Poisson equation
•
Solve Poisson equation
Interpolation
•
2nd order interpolation for the electrostatic field E’
•
Transform E’ to E and B in laboratory frame
Meshlines
ρ' − ∇2 V ' = ρ ' / ε 0
E' = −∇V ' B' = 0 {E, B} = L(E' )
1− v2 / c2
Charge density
Lorentz transformation to laboratory frame
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Multi-grid Poisson solver
•
Key feature: – Anisotropic meshing to reduce number of empty nodes
•
Main challenge g – Stability
•
Multi-grid Multi grid solver – Developed by Dr. G. Pöplau Rostock University, Germany – Scales ~O(N1) in CPU time – Select stability vs. speed
DESY TTF gun at z=0.25 m, 200k particles.
Gisela Pöplau, Ursula van Rienen, Bas van der Geer, and Marieke de Loos, Multigrid algorithms for the fast calculation of space-charge effects in accelerator design, IEEE Transactions on magnetics, Vol 40, No. 2, (2004), p. 714.
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3D Space-charge simulations
Simulations codes seem to be up-to-the-job: • GPT http://www.pulsar.nl/gpt • Parmela3D LANL Benchmarking of 3D space charge codes using direct phase space measurements from photoemission high voltage dc gun Ivan V. V Bazarov, Bazarov et et.al. al PRST-AB 11, 100703 (2008).
EMMA
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Work in progress: • 3D field-maps for all magnets • No rf acceleration, no problems foreseen • GPT solver → Closed-orbit • 3D PIC space-charge model
Closed orbit
Phase-space after one turn
Granularity effects
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Disorder induced heating g
px
Space charge
velocity [km /s]
100
t=0
50 0 -50 -100 100
velocity [km m/s]
100
x
50 0 -50 -100
6
100
T [K]
velocity [[km/s]
4
2
50
t=20 ps
0 -50 -100
0 0 GPT
t=10 ps
10
20
30
40
50
time [ps]
60
70
80
90
100
-10 GPT
-8
-6
-4
-2
0
2
4
6
x [micron]
GPT simulations: n=1018 m–3
8
10
Barnes-Hut
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Hierarchical tree algorithm: • Includes all Coulomb interactions in 3D • O(N log N) in CPU time • User-selectable accuracyy Division of space
J. Barnes and P. Hut, Nature 324, (1986) p. 446.
Tree data structure
Laser-cooled ion source
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Ionization
MOT parameters Temperature: 200 µK vth 0.22 m/s n 1018 m–3
σL
Excitation
R
Ultra-cold ion beam a d
V
Coulomb interactions
Typical current: R σL
10 pA 13 µm 1.4 µm
Geometry V d a
2 kV 20 mm 1 mm
Simple theory predicts total collapse of brightness But that is without acceleration…
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Experimental results
M. P. Reijnders, N. Debernardi, S. B. van der Geer, P.H.A. Mutsaers, E. J. D. Vredenbregt, and O. J. Luiten, Phase-Space Manipulation of Ultracold Ion Bunches with Time-Dependent Fields PRL 105, 034802 (2010).
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Ultrafast electron diffraction (UED)
Bunch length
~100 fs
Timescales of chemical processes
Charge
~100 fC
Single shot
Coherence length
few nm
Few times unit cell size
50 fs
100 kV
3 GHz RF cavity longitudinal E E-field field
Electron source concept for single-shot sub-100 fs electron diffraction in the 100 keV range JAP 102, 093501 (2007). T. van Oudheusden, E. F. de Jong, S. B. van der Geer, W. P. E. M. Op ’t Root, and O. J. Luiten, and B. J. Siwick.
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UED: Beamline design
Four variables: • Solenoid 1 strength • Solenoid 2 strength • Cavityy p phase • Cavity field
100 kV
S1
30 fs
S2
120 W ~
TM010 sample
400 mm Four constraints: • No average energy gain in cavity • Longitudinal waist at sample • Transverse waist at sample • Specified spot size
maximum compression CSalphaz=0 CSalphaxy=0 sigma=250 µm
Plug into GPT, and wait… (typically about 10 runs, depending on starting conditions)
sample
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GPT transverse movie
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GPT longitudinal movie
UED results (10 fC)
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At sample: p • >10 nm coherence length •