1 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference presented by Ph. Ghendrih S. Benkadda, P. Beyer M. Bécoulet, G. Falchetto, X. Garbet, V. Grangirard, G. Huysmans, P. Kaw,M. Ottaviani, Y. Sarazin University of Provence & Association Euratom-CEA Institute for Plasma Reasearch, India, DIII-D team, USA These contributions have benefitted from the Festival de Théorie held in Aix-en Provence July 2001 & 2003 Next Festival July 2005 presented by Ph. Ghendrih S. Benkadda, P. Beyer M. Bécoulet, G. Falchetto, X. Garbet, V. Grangirard, G. Huysmans, P. Kaw,M. Ottaviani, Y. Sarazin University of Provence & Association Euratom-CEA Institute for Plasma Reasearch, India, DIII-D team, USA These contributions have benefitted from the Festival de Théorie held in Aix-en Provence July 2001 & 2003 Next Festival July 2005 Relaxation & Transport in Fusion Plasmas Global, flux driven, 2D & 3D fluid, non-linear simulations of plasma transport Large scale flows, fronts & zonal Relaxation dynamics Scaling parameters & control

2 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Relaxation & Transport in Fusion Plasmas Collision Frequency Effect on Turbulent Transport Gloria Falchetto et al. poster TH/1-3Rd Dynamics of Barrier Relaxation Sadri Benkadda et al. poster TH/1-3Rb ELM control with stochastic transport Marina Bécoulet et al. poster TH/1-3Rc SOL scaling with density front propagation Philippe Ghendrih et al. poster TH/1-3Ra

3 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Zonal Flow Enhancement at low ii ii damped zonal flows  radial transport ii damped zonal flows  radial transport weak damping of zonal flows  shearing = upshift of threshold  T i  reduced transport weak damping of zonal flows  shearing = upshift of threshold  T i  reduced transport *= 3.5 Electrostatic potential *= 0.7 Poloidal section Global, fluid, non-linear 3D ITG turbulence // Landau damping flux driven F inj Global, fluid, non-linear 3D ITG turbulence // Landau damping flux driven F inj G. FalchettoTH/1-3Rd Control parameters F inj & * Control parameters F inj & *

4 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Lower collisionality * = reduced turbulent transport G. FalchettoTH/1-3Rd Similar * effect in SOL turbulent transport Zonal flows versus front propagation Similar * effect in SOL turbulent transport Zonal flows versus front propagation Steady state simulation :  trend with F inj / * Mean shearing rate  T i gradient increase

5 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Front transport in SOL Ballistic motion M  ~ 0.04  ~ 4 % L // ? ( ~ 2.4 m !) Ballistic motion M  ~ 0.04  ~ 4 % L // ? ( ~ 2.4 m !) r   x =  s  t = 600 /  i  x =  s  t = 600 /  i Ph. Ghendrih TH/1-3Ra 2D SOL interchange n / n(r) n(r) Defining a Density Front

6 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference SOL width scaling = balance of diffusive and ballistic région stable  diffusif 2048  s Source Intermittency : Ballistic over-density transport Intermittency : Ballistic over-density transport ballistic Diffusive Ph. Ghendrih TH/1-3Ra Analytical scaling L // 5/8 e-folding length :

7 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference 3D turbulence Resistive ballooning barriers = shear ExB flow driven without zonal flows  prey / predator Transport Barrier & Relaxations S.Benkadda TH/1-3Rb r q = 2.5p (a.u.) r q = 2.5p (a.u.) Relaxation events pressure flux potential fluctuations

8 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Electrostatic Mode at Barrier Location potential fluctuations S.Benkadda TH/1-3Rb  (5,2) mode q / p Pressure gradient r t Barrier extent multiple structures multiple structures Radial ballistic propagation inward & outward Radial ballistic propagation inward & outward

9 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference linear growth + shearing out à la Dupree Transitory growth & stabilization by shear flow Transitory growth & stabilization by shear flow shear  E  ' E x collisional diffusion D coll shear  E  ' E x collisional diffusion D coll  p 0 exp(  t  t 3 /  D 3 ) ~ ~ ~ ~ t 3 shearing out : Dupree time  D   / (D coll  ' E 2 ) 1/3 t 3 shearing out : Dupree time  D   / (D coll  ' E 2 ) 1/3 pp Flux p  p 0 exp(  t  i   t) ~ ~ ~ ~ Doppler effect Linear growth S.Benkadda TH/1-3Rb p 0 effect collisional effect p 0 effect collisional effect ~ ~

10 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Modelling ELM activity DIII-D:# T/1.13MA q 95 =3.8 Ballooning linear growth + 2D transport : SOL = sink Ballooning linear growth + 2D transport : SOL = sink pp t ELM :  B r / B ~10 -2 (n=-10) M. Bécoulet TH/1-3Rc ELM cycle p  

11 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Controlled confinement degradation M. Bécoulet TH/1-3Rc I-coil = 4 kA p   ELM cycle I-coil = 4 kA no ELM pp t p*p* External ~  B r / B ~10 -4 (n=-3)     erg barrier  well  (m 2 s -1 ) Confinement loss  erg controlled Confinement loss  erg controlled

12 / 12 Association EURATOM-CEA IAEA 20th Fusion Energy Conference Large scale flows and Front propagation Zonal Flows : lower *  larger  T i Fronts : SOL width  R 0.63 Dynamics of Barrier Relaxation = time delay growth rate  -1 and velocity shearing-out ELM control by external magnetic perturbation can be made robust confinement penalty is controlled More on Zonal flows : gyrokinetics Large scale flows and Front propagation Zonal Flows : lower *  larger  T i Fronts : SOL width  R 0.63 Dynamics of Barrier Relaxation = time delay growth rate  -1 and velocity shearing-out ELM control by external magnetic perturbation can be made robust confinement penalty is controlled More on Zonal flows : gyrokinetics ELMs, Zonal Flows, Fronts Control of Large Scale Structures TH/P6-7 TH/1-3Rc TH/1-3Rb TH/1-3Rd TH/1-3Ra Posters P3/P4 Posters P3/P4