Eindhoven. FEI: Electron microscopes. University of technology: 3000 employed 7000 students 600 PhD students

www pulsar nl www.pulsar.nl The General Particle Tracer (GPT) code B van der Bas d Geer G Marieke de Loos P l Pulsar Ph Physics i The Netherlands ww...
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www pulsar nl www.pulsar.nl

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 •

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