Emission Modeling for PITZ · 04. Dec. 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie...

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Emission Modeling for PITZ

Erion GjonajTU Darmstadt, TEMF

TEMF-DESY Collaboration Meeting

December 19th, 2013

Introduction

SPCH simulations in the gun

- Lienard-Wiechert PP simulations

- DG-PIC simulation

- CST PS PIC simulations

- Comparison

Emittance results at the EMSY1

Transverse spot inhomogeneities

Space charge limits

Conclusions

Contents

Large differences are found between measurement and simulation -optimum emittance vs. spot size, spch limit, …

Find source of discrepancy on simulation side

Introduction

M. Krasilnikov, FEL 2013

Hypothesis 1: problems originate at the cathode / gun

Hypothesis 2: beam dynamics at emission time not properly modeled

Introduction

z / (cm)

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 20

1Mean velocityDivergence

Particle velocities at emission time

Bunch emission completed

Inertial frame codes (Astra,Parmela, …)

Relative particle motion neglected

Retardation effects (partially) omitted

No acceleration radiation

Full EM simulations

Particle-Particle (PP) codes

Particle-In-Cell (PIC) codes

Lienard-Wiechert PP

Introduction

now +ct-ctr

r0(tr)

tn tn+1

cathode

image charges

R·nmacroparticles

( )( )( )

( )( )

4 1 1rt t

R Rπε=

− − × − × = + − ⋅ − ⋅

n β β n n β βE

β n β n

Store full history of trajectories

Search retarded interaction point for every particle-particle pair

Scaling: N2 x ∆t2

acceleration radiation

Lorentz contraction retardation

Dicontinuous Galerkin (DG) PIC

Introduction

1ix − ix 1ix +

( , )iE x t

1( , )iE x t−

1iI −( ) ( )3 2 3 0

d d dt

ε ϕ ϕ ϕ∂

∂ − × + ∇ × =∂∫ ∫ ∫

Er r n F r H

1( , ) ( , ) ,

2E t t− + × = × + n F n E r E r

1( , ) ( , )

2H t t− + × = × + n F n H r H r

FEM-like field approximation on gridwith high order basis functions

Weak form of Ampere’s law

Numerical interface fluxes

Dicontinuous Galerkin (DG) PIC

Introduction

( , ) ( ) ( )p p p pp

t Q t W t = − ∑j r v r r

11( , ) ( )n

te n n ei it

t t dt t++ = ∫J j

( )p pW −r r

( )q qW −r r

epΩ( )3

( ) ( ) , ( )ep

e ei p p p i

t Q t d W t ϕΩ

=∑ ∫j v r r r

Current density approximation

Grid projection

Total grid current / time step

Beam dynamics over short distance (up to 2cm behind cathode)

- Sufficient to observe possible issues at emission time

- Analyze numerical convergence

- Identify numerical parameters for full-scale simulations

- Perform comparison between different approaches

- Estimate space charge limits

- 3D-simulations throughout the following (except for Astra)

- Nom. parameters/ PITZ-1.8: Q = 1nC, FWHM: 20/2 ps, XY_rms = 0.4mm, …

SPCH Simulations in the Gun

LW-PP convergence

wrt. time step wrt. number of particles

DG-PIC convergence

wrt. approximation order wrt. number of particles

CST PS (PIC) convergence

0 2 4 6 8 10 12 14 160

εε εε x /( ππ ππ

0 2 4 6 8 10 12 14 160

CST-5, ∆∆∆∆x=∆∆∆∆y=0.50mm, ∆∆∆∆z=0.01mm CST-4, ∆∆∆∆x=∆∆∆∆y=0.10mm, ∆∆∆∆z=0.01mm CST-3, ∆∆∆∆x=∆∆∆∆y=0.05mm, ∆∆∆∆z=0.01mm CST-2, ∆∆∆∆x=∆∆∆∆y=0.02mm, ∆∆∆∆z=0.01mm CST-1, ∆∆∆∆x=∆∆∆∆y=0.01mm, ∆∆∆∆z=0.01mm Relative error for CST-1 & CST-2 on right axis

finest mesh resolution

relative error for the best two mesh resolutions

CST PS (PIC) performance

CPU time

CST PS (PIC) performance

Comparison

full EM vs. inertial frame

Comparison

slice emittance (@ 2cm) slice energy spread (@ 2cm)

Comparison for other bunches (Q = 1nC)

XY_rms = 0.5mm XY_rms = 0.6mm

Origin of discrepancy

single particle fields

Hierarchy of approximations retardation contraction radiation relative motion

0 E-statics (ES)

≪1 E-statics / B-statics (ES-MS)

const.bunch in uniform motion /average frame (UMAF)

∓ ∓

individual particles in uniformmotion / local frame (UMLF)

∓ ∓

( )( )( )

( )( )

4 1 1r

cR Rπε ==

− − × − × = + = × − ⋅ − ⋅

n β β n n β βE B n E

β n β n

Origin of discrepancy

Emittance at EMSY1

XY_rms = 0.4mmAstra DG

Emittance at EMSY1

XY_rms=0.4mm

XY_rms=0.5mm

XY_rms=0.6mm

Emittance at EMSY1

1nC0.1nC

spch limit @ > 0.25mm

spch limit @ > 0.4mm

same “optimal” XY_rms

Emittance at EMSY1

DG-PIC1nC

XY_rms = 0.4mm

Astra1nC

XY_rms = 0.4mm

Emittance at EMSY1

DG-PIC1nC

XY_rms = 0.3mm

DG-PIC1nC

XY_rms = 0.35mm

Transverse Spot Inhomogeneities

Cath_11.3XY_rms = 0.3mm

Laser QE map Charge density

Cath_110.2XY_rms = 0.3mm

Transverse Spot Inhomogeneities

Emittances up to 7cm

Particles go lost at the cathode

Space Charge Limits

Charge extraction – Q_bunch = 1nC

XY_rms=0.3mm

~0.9nC

~0.75nC

Space Charge Limits

XY_rms=0.25mm

~0.9nC

~0.75nC

numerical convergence?

Space Charge Limits

DG convergenceXY_rms = 0.3 mm

Space Charge Limits

DG (non-) convergenceXY_rms = 0.25 mm

Space Charge Limits

CST PS (non-) convergence

Space Charge LimitsCharge extraction vs Q_bunch

Used assumption on source limited emission is

probably wrong (?)

Modeling errors exist in Astra simulations

- charge expansion effects at the cathode are neglected

- projected emittance is overestimated: ~20% off at 1nC / 0.4mm

- Predicted SPCH limits are lower than should be if source limited emission is assumed

But, systematic shift in the optimal parameters (spot size) cannot be explained by these “numerical problems”

The emission regime is yet unclear

- If spch limitation occurs (partially)completely different beam dynamics isto be expected

Conclusions

Thank you for your attention

Emission Modeling for PITZ · 04. Dec. 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie...

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