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

STW2004 Sept.29-Oct.1, Kyoto Univ. Recent Pr ogr ess in Numer ical Modeling of Relaxation Phenomena in ST MIZUGUCHI Naoki, Riaz KHAN and HAYASHI Takaya National Institute for Fusion Science Sokendai Contents 1. I Intr oduction 2. E ELM in MAST 3. ST with cur r ent hole 4. S Summar y

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

ELM in MAST - filament- like str uctur e along field lines - time scale ~100 µ sec - er upt fr om outboar d http://www.fusion.org.uk/mast/news/dec03.html - > back into the plasma - ballooning A.Kirk et al., PRL 92 , 245002

Example of nonlinear simulation nonlinear development linear mode str uctur e - n=12 ballooning mode (movie) initial condition - exper imental data fr om NSTX

For mation of cur r ent filament plasma vacuum flow cur r ent pr essur e (j � - j � 0 ) cur r ent - appear on the r idge - nonunifor m - par tial r econnection

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

Spontaneous phase alignment time

Filament for mation and par tial r econnection plasma flow field line cur r ent filament

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

ST with cur r ent hole? "cur r ent hole" - obser ved in auxiliar y heated lar ge tokamak - sometimes accompanied by MHD activities - good confinement and high beta Current hole accompanying Experimental observation of current hole in JT-60U MHD oscillations observed (T. Fujita et al. PRL 87 ,245001(2001) ) in JET in ST ? availability/ stability/ NL dynamics

MHD equilibr ium with stationar y flow (axisymmetr ic 2D, tor oidal flow) ( ) v = 0 �� p + j � B � � v � � : EOM for steady state � F � r 3 f 2 * � = � r 2 p r � F � � � � � r � r � : modified Gr ad- Shafr anov eqs. � * � = � r 2 p z � F � � F � � � * = r � � r + � 2 � 1 � � z � � � � � z 2 � r r � v � ( ) ( ) ( ) � = F = F � p = p � r = f = f � rB

Numer ical solution � r 2 F � r 3 � r ( ) � F � * � = � 2 p z � z + p r � r � 2 f 2 � scheme � � � � � � ( ) � rf 2 p r = � � r � * � + F � r 2 � F div � p = � � � � ( ) p z = � � z * � + F � r 2 � F � solve two( ) Poisson's eqs. � simultaneously by iter ations � xample of solution Z � � �� p �� �� �� � R

Numer ical solution r adial pr ofiles j � q P Z R R R R poloidal flux & pr essur e tor oidal flow

Nonlinear simulation r esult (V=0 case) - disor der ed - less r estor ing for ce (movie) low- n components ar e emphasized (movie)

Effect of tor oidal flow - linear ized MHD eqs. - time development for each tor oidal mode w/ o flow with flow stabilized destabilized (another pr ofile is used for initial condition)

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