Billion Particle Linac Simulations for Next Generation Light Sources g

Billion Particle Linac Simulations for Next Generation g Sources Light

Ji Qiang Lawrence Berkeley National Laboratory LINAC08, Sep. 29 – Oct. 3, Victoria, Canada, 2008

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In Collaboration With

—R. D. Ryne —M. Venturini —A. A. Zholents

Work supported by the Office of Science, U. S. Department of Energy, under Contract No. DE-AC02-05CH11231 using computing resources National Energy Research Scientific Computing Center

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Next Generation Light Sources Present Great Opportunities for Scientific Discovery —Biology —Material M t i l science i —Condense matter physics —Chemistry Chemistry Interface-mediated Functionality

Functional Interfaces

orbital

lattice

spin

charge

LaTiO3 (d1)

Mott

Mott

FM

metal

Band

Band

FE

ME

SrTiO3 (d0)

Attosecond capabilities allow direct probing of atomic electron correlation (Hu and Collins, Phys. Rev. Lett. 96, 073004 (2006))

Ultrafast x-ray spectroscopy offers new insight by providing elemental and interfacial sensitivity, quantification of electronics structure and bonding, dichroism to separate spin and orbital components of magnetic moments, atomic structural dynamics, and a capability for separating correlated 3 LBNLphenomena directly in the time domain (figure courtesy R. Ramesh, MSD).

Fundamental Parameters Driving FEL Cost and Performance • Electron beam emittance ε • High brightness gun, minimize emittance growth in accelerator • High gradient accelerator as low energy as possible • Manipulate and condition beam for the FEL process

εn λx−ray ≈ γ 4π

• Peak current Ipeak • Bunch compression, minimize distortion from longitudinal wakefields

⎛ ⎞ εn ~ f ⎜ I peak , ,σ E ⎟ γ ⎝ ⎠

Power/ undulator length

• Energy spread σE • High brightness gun, minimize distortion from longitudinal wakefield and microbunching instability • El Electron t beam b energy γ • High gradient accelerator • Short period undulators

Courtesy of A. Zholents

λx−ray x ray

λundulator = 2γ 2

⎛ K2 ⎞ ⎜1+ ⎟ 2 ⎠ ⎝ 4

Challenges for Electron Beam Delivery System

—Generation of low emittance, low energy spread, high peak current, t i.e. i hi high hb brightness i ht electron l t b beam —Acceleration, transport, and compression of high brightness electron beam —Preservation of beam quality in the presence space-charge effects, wake fields, and coherent synchrotron radiation —Lower machine cost

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Need for Large Scale Simulations Final Longitudinal Phase Space Distribution w/o SC and CSR (Using 10M and 1B particles)

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Microbunching Instability • Initial density modulation induces energy modulation through long. impedance Z(k), converted to more density modulation b a chicane by hi Î growth th off slice li energy spread d / emittance! itt ! R56 peak current ~50 A bi

Energy

Ζ(k) linac

λ

C Current modulation d l i

1%

peak current ~1000 A ΔΕ bf >> bi or G= bf/ bi >> 1 magnetic chicane

λ

t

Gain=10 10% t

Courtesy of Z. Huang, SLAC

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Predicting Uncorrelated Energy Spread in Future Light Sources: Convergence Studies up to 5 Billion Particles IMPACT-Z Uncorrelated Energy Spread versus # of Macroparticles: 10M, 100M, 1B, 5B

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Current Features of the IMPACT Code •

•

• • • •

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External Beam Line Elements: • Quadrupole, Dipole, Solenoid + RF gap, 3D constant g channel,, Sextupole, p , Octupole, p , Decapole p focusing • DTL, CCDTL, CCL, SC, User-defined element Two Numerical Integraors: • Linear Map • Nonlinear Lorentz Force Integrator 3D Space Charge with 6 Types of Boundary Conditions Transverse, longitudinal short range wakefields and CSR wakefields M l i l Charge Multiple Ch States S Two types of parallel implementations: • Domain decomposition with dynamic load balance • Particle-field Particle field decomposition Pre and post-processing codes

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Particle--In Particle In--Cell Simulation with SplitSplit-Operator Method Initialize particles Advance positions & momenta a half step using Hext

Setup and solve Poisson equation

œCharge deposition on grid

Advance positions & momenta a half step using Hext

Field solution on grid žField interpolation at particle positions (optional) diagnostics Advance momenta using Hspace charge Courtesy of R. Ryne

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Green Function Solution of Poisson’s Equation (with 3D Open Boundary Conditions)

φ(r) = ∫ G(r, r' )ρ(r' )dr' N φ (ri) = h ∑ G(ri − ri' )ρ (ri' ) i '=1

G ( x, y , z ) = 1 / ( x + y + z ) 2

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Direct summation of the convolution scales as N6 !!!! N – grid number in each dimension Hockney’s Algorithm:- scales as (2N)3log(2N) - Ref: Hockney and Easwood, Computer Simulation using Particles, McGraw-Hill Book Company, New York, 1985. 2N

φc(ri) = h ∑ Gc(ri − ri' )ρc(ri' ) i '=1

φ (r ( i) = φc (r ( i)

f i = 1, N for 11

Space--Charge Driven Energy Modulation vs. Distance in a Drift Space Space

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Calculation Longitudinal and Transverse Wakefield Using FFT +∞

Fx ( s ) = q ∫ WT ( s − s ' ) x( s ' )λ ( s ' )ds ' s

+ +∞

Fz ( s ) = ∫ WL ( s − s ' )λ ( s ' )ds ' s

+∞

F ( s ) = ∫ G ( s − s ' ) ρ ( s ' )ds ' −∞

⎧W ( s ) for s ≥ 0 G(s) = ⎨ ⎩ 0 for s < 0 2N

Fc ( si ) = h∑ Gc ( si − si ' ) ρ c ( si ' ) i '=1

F ( si ) = Fc ( si )

for i = 1,...N 13

Computing Operation Comparison between the Direct Summation and the FFT Based Method

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1D CSR Wake Field Including Transient Effects

Ref: 1) E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, Nucl. Instrum. Methods Phys. Res., Sect. A398, 373 (1997). 2) M M. Borland Borland, Phys Phys. Rev Rev. Sepecial Topics - Accel. Accel Beams 4, 4 070701 (2001). (2001) 3) G. Stupakov and P. Emma, ``CSR Wake for a Short Magnet in Ultrarelativistic Limit,'' SLAC-PUB-9242, 2002.

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Test of the CSR Wake Implementation for a Short Bend

R = 1.5 m, Arc=10 cm From G. Stupakov and P. Emma

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Up Sampling of Initial Particle Distribution —Maintain global properties of the original distribution •emittances •current profile, •energy-position correlation —Reduce shot noise of the original particle distribution by using more macroparticles —A A 6D box centered at the original is used to generate new macroparticles —Uniform sampling in transverse 4D —Linear sampling in longitudinal position following original current profile —Cubic C bic spline to obtain the energ energy-position position correlation 17

A Comparison of Direct Sampling and Up Sampling Initial current profile from direct sampling and up sampling

Final longitudinal phase space from direct sampling and d up sampling li

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Vision for a Future Light Source Facility at LBNL A HIGH REP-RATE, SEEDED, VUV — SOFT X-RAY FEL ARRAY Courtesy of J. Corlett, LBL

Beam manipulation and conditioning

Array of configurable FELs Independent control of wavelength, pulse duration, polarization Configured g with an optical p manipulation p technique; seeded, attosecond, ESASE Beam distribution and individual beamline tuning g ~2 GeV CW superconducting linac

W. Wan, et. al. TUP101

Low-emittance, high rep-rate electron gun

A Zholents A. Zholents, et et. al al. TUP046

Laser systems, timing & J. Staples, et. al. THP118 synchronization

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Choice of Numerical Grid Point power spectrum of density fluctuation with different grid points

linear uBI gain function vs. wave length

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Final Uncorrelated Energy Spread with Different Number of Grid

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Effects of Initial Current Profiles final energy spread with different initial current profiles

four types of initial current profiles

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Final Energy Spread vs. Initial Uncorrelated Energy Spread

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Final Longitudinal Phase Space Distribution (5 billion Particle Simulation) A. Zholents, et. al. TUP046

40 MeV 70 A

250 MeV 1 kA

2.4 GeV

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Final Transverse Slice Emittance and Peak Current Profile

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Summary and Future Plans —Large number of macroparticles are needed for accurately simulation of electron beam transport through linac subject to microbunching instability —Current linac design satisfy the performance requirements for an array of soft X-ray FELs. —Integration of large scale linac simulation together injector simulation —Benchmark Benchmark simulations with experimental measurements

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