Recent Pr ogr ess in Numer ical Modeling of Relaxation Phenomena in - - PowerPoint PPT Presentation

Recent Pr ogr ess in Numer ical Modeling

• f Relaxation Phenomena in ST

MIZUGUCHI Naoki, Riaz KHAN and HAYASHI Takaya

National Institute for Fusion Science

• 1. I

Intr oduction

• 2. E

ELM in MAST

• 3. ST with cur r ent hole
• 4. S

Summar y Contents

STW2004 Sept.29-Oct.1, Kyoto Univ.

Sokendai

Intr oduction

• bjective

"r elaxation" spontaneous collapse & r eor der mechanism, constr aint,... under standing and pr ediction of non- linear r elaxation phenomena topics : ELM cur r ent hole

ELM in MAST

http://www.fusion.org.uk/mast/news/dec03.html A.Kirk et al., PRL 92, 245002

• filament- like str uctur e

along field lines

• time scale ~100µsec
• er upt fr om outboar d
• > back into the plasma
• ballooning

Example of nonlinear simulation

initial condition

• exper imental data fr om NSTX

linear mode str uctur e

• n=12 ballooning mode

nonlinear development

(movie)

For mation of cur r ent filament

plasma vacuum flow cur r ent

• appear on the r idge
• nonunifor m
• par tial r econnection

cur r ent (j- j0) pr essur e

bulge n=1 component n=2 component positive pileup of multiple modes nonunifor m gr owth due to the phase r esonance (low- n case)

Mechanism of filament for mation

Spontaneous phase alignment

time

Filament for mation and par tial r econnection

cur r ent filament field line plasma flow

ELM in MAST ~ summar y and futur e wor k

• nonlinear development of

ballooning mode

• nonunifor m for mation of

cur r ent filament

• par tial loss of plasma

thr ough r econnection

• r elaxed

FLR cor r ection - - ongoing r apid and steep natur e

ST with cur r ent hole?

Experimental observation of current hole in JT-60U (T. Fujita et al. PRL 87,245001(2001) ) Current hole accompanying MHD oscillations observed in JET

"cur r ent hole"

• obser ved in auxiliar y heated lar ge tokamak
• sometimes accompanied by MHD activities
• good confinement and high beta

in ST ? availability/ stability/ NL dynamics

MHD equilibr ium with stationar y flow

(axisymmetr ic 2D, tor oidal flow)

• * = r2 pr

r F F r3 f 2 r

• * = r2 pz

z F F

• * = r

r 1 r

• r + 2

z2

• : modified Gr ad- Shafr anov eqs.

rB

= F = F

( )

v r = f = f

( )

p + j B v

( )v = 0

: EOM for steady state p = p

( )

Numer ical solution

scheme

• * =

r2

• 2 pzz + prr

( ) F

F r 3r

• 2 f 2

pr = r r2

* + F

F

( ) rf 2

pz = z r2

* + F

F

( )

• p =

div solve two( ) Poisson's eqs. simultaneously by iter ations xample of solution

• Z
• R
• p

poloidal flux & pr essur e

R Z

tor oidal flow

R R R

q P j r adial pr ofiles

Numer ical solution

Nonlinear simulation r esult

(V=0 case) low- n components ar e emphasized

• disor der ed
• less r estor ing for ce

(movie) (movie)

stabilized destabilized

(another pr ofile is used for initial condition)

Effect of tor oidal flow

• linear ized MHD eqs.
• time development

for each tor oidal mode w/ o flow with flow

Summar y

Recent topics on our nonlinear simulation r esear ch ar e r eviewed.

• ELM in MAST

* nonunifor m filament- like str uctur e * loss thr ough r econnection

• ST with cur r ent hole

* less r estor ing for ce * (de)stabilization by shear flow

Futur e wor k

• extend beyond r esistive MHD model

FLR, fast par ticle,...

• compar ison with exper iments