FAR-TECH, Inc., 3550 General Atomics Court, MS 15-148, San Diego, CA 92121Tel: (858) 455-6655, Fax (858) 450-9741 www.far-tech.com

Modeling ECRIS Plasma Using 2D GEM

(Generalized ECRIS Model)

Liangji Zhao, Jin-Soo Kim, Brian Cluggish

2

Abstract

• The GEM (General ECRIS Model) code is developed by FAR-TECH,Inc. to model plasmas in ECRIS devices using experimental knobssuch as magnetic field, rf and the geometry of the device.

• The code models ECRIS plasma electrons by the bounce-averagedFokker-Planck equation, ions as fluid and neutrals by particlebalancing.

• It has been extended to include 2D (axial and radial) spatial featuressuch as 2D ECR heating and ion radial diffusion. The convergenceand consistency of the code have been studied. It is parallelizedusing the MPI technique to boost the calculation speed.

• Example results of simulated 2D profiles of ECRIS plasma and theradial dependence of CSD (charge state distribution) will bepresented.

3

Extension of GEM 1D(z) to 2D(r,z)

• GEM 1D simulates ECRIS plasma along the axis.

– Use only experimental knobs as inputs.– Advance hybrid model: bounce-averaged Fokker-Planck

EDF modeling, ion fluid modeling, and neutral particlebalancing modeling.

– Has produced consistent results with the experiments.

• GEM 2D simulates ECRIS plasma in both radial and axialdirections.

– The importance of radial dependence of ECR ion sourcesis recognized experimentally.

– GEM 2D can model the football shape ECR resonancesurface more accurately.

4

GEM 2D can simulate ECRIS device

Vextract

Grounded tube

ECR Plasma

Plasma sheath

Groundedelectrode

1+ ion beamn+ ion beam

Microwaves

Magnetic field lines

Modeled by GEM

Simulation parameters for ANLECR-I device:RF: 323 W @ 10 GHz

Vessel: 3.8 cm radius,29 cm length

Gas pressure: 10-6 – 10-7 Torr, Oxygenne ~ 1018 m-3

Te ~ 10-100eV (edge)1 – 10’s keV (core)

Ti ~ 1eV

5

ECRIS plasmas are confined in minimum-B magnetic

mirror configuration – 3D geometry

Magnetic confinement is a simple magnetic mirror with a multicusphexapole field for min-B stability.

Experimental B magnetic field configuration on ANL ECR-I

Mirror: 0.3-0.5 T on axis at midplane,Mirror ratio= 4.5 & 3Hexapole: 0.8 T at chamber wall

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Magnetic field lines

Z

0.00 0.05 0.10 0.15 0.20 0.25 0.30

R

-0.04

-0.02

0.00

0.02

0.04

Radial grids are azimuthally averaged 2D magnetic field flux

surfaces. GEM 2D models volume heating.

Contour of 3Dfield

2D filed lines

7

2D ECR resonance surface

2,

0 1/2,

res

res

B z r B

Brf rf res

res

BD z r D e

B

2

2

1

1c

2D modeling of rf diffusion term:

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GEM models ion, electron, and neutral dynamics

IONS:Cold and highly collisional,Fluid ion model

ELECTRONS:bounce time << collision timeNon-Maxwellian electron distribution function (EDF)1D bounce-averagedFokker-Planck electron code fe(v,)

NEUTRALS:Unimpeded by magnetic fields:Density profile determined by particlebalance

Bz

z

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Bounce-averaged Fokker-Planck code modeling 2D EDF

• Mirror trapped electrons in ECRISare almost collisionless.

• EDF is non-Maxwellian.• 0D bounce-averaged Fokker

Planck code, FPPAK94 , is used tocalculate EDF.

• Bounce averaging greatly reducesrun time.

• Model includes– ECR heating– Velocity space diffusion– Loss cones– Plasma sheath

GEM 2D calculated EDF

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EDF mapping: EDF f(v) at mid-plane to f(v,z) in space

zvfe ,,

00dvvvdv

000 coscos dv

vd

•EDF at any axial location is related with the EDF on midplane

through energy and magnetic momentum conservation:

•In GEM 2D, EDF on each radial cell is calculated independentlywith the assumption that radial transport of electrons is negligible.

•Sheath potential at both ends defines the lose cone of theelectrons in Fokker Planck code.

•Electron temperature is defined as the average electron energy.

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• Assume neutral density distribution has no radial dependence and neutraltemperature is room temperature everywhere in space.

• Neutral losses inside the plasma due to ionization and charge-exchangeare balanced by neutral gas input from outside of the plasma:

Neutrals: volume averaged modeling

cxzcxionizationz

zzzzzgpz

VRnRRVn

nnAnnAnnAv

,1,0

01,0101,01,00

)(

))()()(5.0

Z

A z A z+1A pz

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GEM 2D Ion fluid modeling radial and axial transport

• The 2D ion continuity equation is solved using upwind method:

qrjqjqjqjz

z

outqj

inqj

qjvrn

rrunA

zASS

t

n,,,,,,

, 11

• Ions are cold, Ti~1 eV, and highly collisional– Mean free path < 1 mm– Ions all have same axial speed– Radial and azimuthal speed are different for each ion.

• Full 2d2v EDF used to calculate ionization rates:– A+n + e- A+n+1 + 2e-

• Ion loss rate is limited by electron confinement in magnetic mirror.

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Equations of 2D fluid modeling

The ion continuity equation:

qrjqjqjqjz

z

outqj

inqj

qj vrnrr

unAzA

SSt

n,,,,,,

, 11

The radial and azimuthal velocities are calculated from ionmomentum equations:

j

qcj

pkpkqjpkqjpkjkqj

jk

jqj

jk

qj

in

qj

qj

inqj

qcj

qrj

pkprkqrjpkqjpkjkqj

jkr

jqj

jkr

qrj

in

qrj

qj

inqjqj

jqj

qjB

qcj

rqj

m

qeB

vvKnnF

mn

Fvv

n

Sv

vvKnnF

mn

Fvv

n

S

r

n

mn

Tk

B

Ev

,

,,,,,,,

,

,,

,

,

,

,

,,,,,,,

,

,,

,

,,

,

,

,

,

)(

1

)(

1

The axial ion momentum equation is z

j

qj

ininqj

qj

qj

qjj

qjBqj

qj

qj

qrj

qj

Em

qeuuS

n

z

n

nm

Tk

z

uu

r

uv

t

u

,,

,

,

,

,,

,

,

,

,

1

1

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GEM 2D predicts hollow electron density profiles in device

Density peaks wheremost ECR power isabsorbed

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GEM 2D predicts hollow electron temperature profiles of

plasma

Peak in temperaturecoincides with resonantsurface

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GEM 2D predicts hollow CSD of extracted ion sources

Extracted Charge State Distribution (CSD)

GEM 2D

ANL ECR-I data

Radially integrated CSD andexperimental data

CSD at different radial positions

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Experimental evidence of the hollow profile of ECRIS plasma*

* S. Biri, ICIS03, Dubna, Russia

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Summary

• GEM 1D is successfully extended to 2D:

– 3D ECRIS magnetic field modeling and 2D azimuthally averaged field.

– 2D ion fluid modeling.

– 2D ECR heating modeling.

– GEM 2D is parallelized using MPI.

– Improved stability by using upwind method.

• GEM 2D results are cross-checked with GEM 1D.

• The radial dependence of plasma profiles and CSD are consistent withthe experimental observations.