Emission Modeling for PITZ · 04. Dec. 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | PD Dr.rer.nat. habil. Erion Gjonaj | 10 DG-PIC convergence

04. Dec. 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | PD Dr.rer.nat. habil. Erion Gjonaj | 1

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)

v / c

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

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

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

tr

r(t)

r0(tr)

tn tn+1

t

cathode

image charges

R·nmacroparticles

( )( )( )

( )( )

2

3 320

1

4 1 1rt t

q

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 +

x

E

( , )iE x t

iI

1( , )iE x t−

1iI −( ) ( )3 2 3 0

i i i

H

I I I

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

n

te n n ei it

t t dt t++ = ∫J j

eΩ

pvpr

( )p pW −r r

qv

qr

( )q qW −r r

epΩ( )3

( )

( ) ( ) , ( )ep

e ei p p p i

p t

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

0.5

1

1.5

2

2.5

3

εε εε x /( ππ ππ

*mra

d*m

m)

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

z /mm

Rel

avtiv

e E

rror

/%

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


RAM


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)

∓ ∓

0

individual particles in uniformmotion / local frame (UMLF)

∓ ∓

( )( )( )

( )( )

2

3 320

1 1,

4 1 1r

r

t t

t t

q

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

2nC

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

X =

X =

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

@5pC


Thank you for your attention

Documents

Emission Modeling for PITZ · 04. Dec. 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | PD Dr.rer.nat. habil. Erion Gjonaj | 10 DG-PIC convergence