Simulations with Capone

100 keV Test Stand

0.000E+00 8.000E-024.000E-02

0.000E+00

3.500E-02

1.750E-02

FRAME: 4 29/06/04 - 16:54:00 VERSION[V4.106] OO.DRD

ELECTRIC FIELD STRENGTH IN V/M

OP-:4106

COORDINATES/MFULL RANGE / WINDOWR[ 0.0000, 0.035000] [ 0.0000, 0.035000]Z[ 0.0000, 0.080000] [ 0.0000, 0.080000]

#CONTOUR

SYMBOL: E

COMPONENT...: Z

FUNCTION MIN:-3.081E+07

FUNCTION MAX: 1.477E+04

PLOTTED MIN:-3.081E+07

PLOTTED MAX: 1.477E+04

PLOTTED STEP: 6.166E+05

INTERPOLATE.: 0

LOGSCALE....= 0

MATERIALS: 0,1,3,21,22,

Z

R

+

-3.08E+07 -2.31E+07 -1.54E+07 -7.69E+06 1.48E+04

Projected Emittance(property of one entire bunch)

Slice Emittance(depends on the location t0 of the slice within the bunch and the width σt of the slice )

P A U L S C H E R R E R I N S T I T U T

Electron Beam Dynamics Simulations for the Low Emittance GunA. E. Candel, ETH Zurich, Zurich, Switzerland

M. M. Dehler, S. C. Leemann, PSI, Villigen, Switzerland

0

1e-07

2e-07

3e-07

4e-07

5e-07

6e-07

0.325 0.33 0.335 0.34 0.345 0.35 0.3550

0.002

0.004

0.006

0.008

0.01

0.012

Norm

alize

d Tr

ansv

erse

RM

S Sl

ice E

mitt

ance

[m*ra

d]

Radi

us [m

]

z [m]

Projected Emittance: 6.2496e-7

Slice EmittanceRadius

Ai

ek dk

em dm

el dl

Aj

hi bi

Li

ej dj

G

G

Lj

jj

processingpost!

mesh

C++ POOMA II framework

solver

Capone

static field

parametersXML 3D Maxwell

field solver

measurementstake

LAM MPI parallelization

add/delete particles

push particles

scatter current

gather fields

0 0.02 0.04 0.06 0.08mean z position [m]

0

2e!07

4e!07

6e!07

[m ra

d]

normalized transverse RMS emittance

Capone 3DMAFIA 2.5D

0 0.02 0.04 0.06z / m

0

5e!08

1e!07

1.5e!07

normalized transverse slice emittance / (m rad)

Test Stand Gun Design

= e− (zi−z0)2

2β2c2σ2

wi,0 = e−(ti−t0)2

2σ2

W0 =N∑

i=1

wi,0

〈r2t0〉 =

1W0

N∑i=1

ri2 · wi,0

- Cathode Potential: -100kV

- Active Emitter Radius: ract = 100µm

- Pulse: Gaussian, cut-off at ±3σt, σt=20ps, Q≈-5.10-12C ( Î=100mA )

- Initial Energy: γ0=1.0001, initial divergence is set to zero

- Iris: riris=500µm

- Tracked Macro-Particles: N=20000

- Tracked Path: 1mm < z < 342 mm (from cathode surface to end of drift)

- Solenoid: 7A/mm2 capabale of delivering Bz=200mT on axis

Input Parameters Simulated Emittance (MAFIA)

Projected Emittance vs. Slice Emittance Sampling the Bunch Slice Emittance Calculation

ε =√〈r2〉〈pr

2〉 − 〈rpr〉2 $ γβ√〈r2〉〈r′2〉 − 〈rr′〉2

εt0 = γβ√〈r2

t0〉〈r′t0

2〉 − 〈rt0 r′t0〉2

〈r2t0〉 =

1W0

N∑i=1

ri2 · wi,0

wi,0 = e−(ti−t0)2

2σ2 = e− (zi−z0)2

2β2c2σ2 W0 =N∑

i=1

wi,0

—> Peak electric field strength below 19MV/m

—> Norm. transv. emittance at gun exit < 2.10-8 m.rad

Cathode Anode Solenoid

Electric Field Strength [V/m]1e-08

2e-08

3e-08

4e-08

5e-08

6e-08

7e-08

8e-08

9e-08

0.1 0.15 0.2 0.25 0.3 0.35

Norm

alize

d Tr

ansv

erse

RM

S Em

ittan

ce [m

*rad]

Position of Minimum Emittance z0 [m]

Solenoid VariationBz = 117 mT

Bz = 113 mT

Bz = 108 mT

Bz = 104 mT Bz = 99 mT

Bz = 95 mT

0

0.002

0.004

0.006

0.008

0.01

0.012

0.325 0.33 0.335 0.34 0.345 0.35 0.355

r [m

]

z [m]

Weight Function Evaluated at z0=0.335Macro-Particle Radius

Dynamic Field Solver Discrete Maxwell's Equations Program Structure

Simulated Gun Geometry Comparison: Capone vs. MAFIA Slice Emittance Calculations

z

y

C e = −∂b

∂t

C h =∂d

∂t+ j

S d = q

S b = 0

d = Dεe

b = Dµh

- Finite Integration Technique (FIT)

- Discretization of volume on two rectilinear grids:

- Cells with volumes , cell faces , and grid lines

- Store integrated field components

- Discrete curl operators and divergence operators

- Discrete material operators

G, G

Vi, Vi Ai, Ai Li, Li

ej =∫

Lj

!E · d!s

C, C S, S

Dε,Dµ

x

y