Neutron Wall Loading Profile Neutron Wall Loading Profile Using CAD/MCNP InterfaceUsing CAD/MCNP Interface

Mengkuo WangMengkuo Wang

ARIES MeetingARIES MeetingSep 16, 2004Sep 16, 2004

University of Wisconsin - MadisonUniversity of Wisconsin - Madison

(Last time) First step: torus(Last time) First step: torus

First Wall divided poloidally First Wall divided poloidally into 15 degree binsinto 15 degree bins

First WallFirst WallPlasma SurfacePlasma Surface

(last time) Result Differ by (last time) Result Differ by ~3% for 5cm SOL~3% for 5cm SOL

0 20 40 60 80 100 120 140 160 1801.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

OutboardInboard

Wall loading at First Wall Wall loading at Plasma surface

Neu

tron

Wal

l Loa

ding

[MW

/m2 ]

Poloidal Angle (Degree)

(last time)Wall subtract Plasma S(last time)Wall subtract Plasma Surfaceurface

Second step: Cross Section Second step: Cross Section Sweep ObjectSweep Object

ΦΦ=0°=0°andandΦΦ=30°=30°

Cross Section Sweep Object Cross Section Sweep Object (cont)(cont)

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

Actual Source:

av

=2.1 MW/m2

peak

=2.9 MW/m2

min

=0.34 MW/m2

=00

Ave=2.1

Line source at Magnetic Axis Actual Source Uniform Source Average

NW

L a

t Pla

sma

Sur

face

(M

W/m

2 )

Surface Number 0 2 4 6 8 10 12 14 16 18 20 22 24 260

1

2

3

4

5

6

Actual Source:

av

=2.09 MW/m2

peak

=3.04 MW/m2

min

=0.74 MW/m2

=300 Line Source at Magnetic Axis

Actual Source Uniform Source Average

Ave=2.09

NW

L at

Pla

sma

Sur

face

(M

W/m

2 )

Surface Number

Third step: Computation model of stThird step: Computation model of stelleratorellerator

Horizon and toroidal Horizon and toroidal subdivision, each patsubdivision, each patch as tally surfacech as tally surface 7.5 degree toroidal 7.5 degree toroidal

subdivisionsubdivision 0.5 m horizontal su0.5 m horizontal su

bdivisionbdivision Combine the symmeCombine the symme

try patch to reduce rtry patch to reduce relative errorelative error

5 days on a 2.4GHz li5 days on a 2.4GHz linux stationnux station

9% ~ 10% relative err9% ~ 10% relative erroror

Computation model of stelleratoComputation model of stelleratorr

60

0

By the symmetry, By the symmetry, select portion from select portion from 0 to 60 degree0 to 60 degree

9 cross sections9 cross sections 8 neutron wall load 8 neutron wall load

profilesprofiles

9 Cross Section of Plasma Boundary (red) and WP 9 Cross Section of Plasma Boundary (red) and WP Center (green)Center (green)

Computation resultComputation result

0 5 10 15 20 25

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Outbound InboundInboundInbound

150 - 22.5

0

NW

L at

pla

sma

surfa

ce (M

W/m

2 )

Surface Number

0 5 10 15 20 25

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Outbound InboundInboundInbound

22.50 - 30

0

NW

L at

pla

sma

surfa

ce (M

W/m

2 )

Surface Number

0 5 10 15 20

0.5

1.0

1.5

2.0

2.5

3.0

Outbound InboundInbound

300 - 37.5

0

NWL

at p

lasm

a su

rface

(MW

/m2 )

Surface Number

0 5 10 15 20

1.0

1.5

2.0

2.5

3.0

3.5

Outbound InboundInbound

37.50 - 45

0

NW

L at

pla

sma

surfa

ce (M

W/m

2 )

Surface Number

0 5 10 15

1.0

1.5

2.0

2.5

3.0

3.5

Outbound InboundInbound

450 - 52.5

0

NW

L at

pla

sma

surfa

ce (M

W/m

2 )

Surface Number

0 5 10

1.5

2.0

2.5

3.0

Outbound InboundInbound

52.50 - 60

0

NWL

at p

lasm

a su

rface

(MW

/m2 )

Surface Number

0 5 10 15 20 25 300.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Outbound InboundInbound

00 - 7.5

0

NW

L at

pla

sma

surf

ace

(MW

/m2 )

Surface Number0 5 10 15 20 25 30

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Outbound InboundInbound

7.50 - 15

0

NW

L at

pla

sma

surf

ace

(MW

/m2 )

Surface Number

Peak is at OutboundPeak is at Outbound

ΓΓpeak=3.24MW/m²peak=3.24MW/m²PSarea=800.6m²PSarea=800.6m²ΓΓave=1.985MW/m²ave=1.985MW/m²

0 10 20 30 40 50 601.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

Toroidal Angle Bin: 7.50

PF=2000 MW

Pn=1600 MW

OBup OBdown OBup2 OBdown2

NW

L at

pla

sma

surf

ace

(MW

/m2 )

Toroidal position (Degree)

Problem of CAD based Problem of CAD based MCNPMCNP

Performance of CGM/MCNPPerformance of CGM/MCNP CAD based MCNP is about 10 – 30 times CAD based MCNP is about 10 – 30 times

slower than standard MCNPslower than standard MCNP ReasonReason

CAD function is not optimized for a CAD function is not optimized for a single functionsingle function

Ray-object intersection function is Ray-object intersection function is compatible with all type of geometrycompatible with all type of geometry

Ray-object intersection function also test Ray-object intersection function also test for vertex and edgefor vertex and edge

Future PlanFuture Plan

Speed up calculationsSpeed up calculations Bounding boxBounding box Spatial subdivisionSpatial subdivision Direction techniquesDirection techniques

Neutron Source ProfileNeutron Source Profile the neutron production rate (in )the neutron production rate (in )13 scm

8.12220 ])/(1[])/(2.01[)/( ararSarSn

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Sn/

S0

r/a

Plasma Cross SectionPlasma Cross Section

Magnetic center

‘‘a’ is calculated ba’ is calculated by CAD ray-fire functiy CAD ray-fire functionon Start from magnetic Start from magnetic

centercenter Direction is determiDirection is determi

ned by sampling torned by sampling toroidal and poloidal dioidal and poloidal directionrection

Neutron Source ProfileNeutron Source Profile ‘‘r’ is from magnetic centerr’ is from magnetic center

Center position is computed by a constant table and two formula.Center position is computed by a constant table and two formula. Constant TableConstant Table n rmag zmag n rmag zmag 0 8.5672E+00 0.0000E+000 8.5672E+00 0.0000E+00 1 6.0678E-01 -2.9852E-011 6.0678E-01 -2.9852E-01 2 4.1392E-02 -1.8349E-022 4.1392E-02 -1.8349E-02 3 -2.2776E-03 1.2718E-033 -2.2776E-03 1.2718E-03 4 -1.1638E-03 7.3849E-044 -1.1638E-03 7.3849E-04 5 -9.5859E-04 -9.9194E-065 -9.5859E-04 -9.9194E-06 6 -6.2693E-05 6.6409E-05 6 -6.2693E-05 6.6409E-05 in the following formula;in the following formula; R=sum{ rmag(n)*cos(np*n*phi)}R=sum{ rmag(n)*cos(np*n*phi)} Z=sum{ zmag(n)*sin(np*n*phi)}Z=sum{ zmag(n)*sin(np*n*phi)}

‘‘a’ is from magnetic center to plasma surfacea’ is from magnetic center to plasma surface Use a CAD ray-fire function obtain ‘a’.Use a CAD ray-fire function obtain ‘a’.