Relaxation events & self-organization in tokamak plasmas
Yanick Sarazin CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
Acknowledgements: G. Dif-Pradalier, V. Grandgirard, Ph. Ghendrih, X. Garbet Guy Pelletier Teacher in plasma physics 1993-94 Former PhD Director 1994-97 President of jury of HDR 2008
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 Thermonuclear fusion energy principles D + T → He + n D: hydrogen stable isotope He : helium (stable ϕ & χ) T: hydrogen unstable isotope n: neutron
impact on device must be produced must be used to produce T not key for ITER not key for ITER
Threshold condition for thermonuclear fusion (interaction distance 10 -13 m) ≥ → Eth 10 keV Plasma state
20 keV D+T plasma 14 MeV neutron → external heat source + T generation 3.5 MeV Helium ashes ( α particles) → plasma heat source
Plasma energy balance:
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 Energy confinement time CEA | Y. Sarazin | Page 2 Outline
A historical perspective on Controlled Fusion
The ITER project: objectives & present status
Plasma confinement in tokamaks: Basic principles Gyrokinetic description of plasma turbulence
Plasma self-organization & turbulence control
Sawteeth: core reconnection due to internal kink modes
ELMs: edge violent relaxations
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 3 A brief history of controlled Fusion & ITER
1950's Tokamak concept: Igor Tamm, Andrei Sakharov First tokamak experiments: Lev Artsimovich (Kurchatov Institute, Moscow)
1968 IAEA conf. at Novosibirsk: Russians announce 1keV achieved in a Tokamak
1985 USSR proposal to build an international Tokamak → ITER
1988 –1990 Conceptual Design Activities under IAEA
1992 Engineering Design Activities
1998 USA leave the project – Reduction of cost / Downgrade of objectives
2003 China & Korea join the project, USA back again
2005 (June 28) Cadarache is chosen as the ITER site
2016 Tore Supra → WEST
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 4 Constant progress since tokamak discovery
Ignition (self-heating): → ∞ Q = P fus /P add
Break Even: Q = 1
Condition for ignition Performance (Lawson): τ 20 −3 ni E ~ 3.10 m .s
Ti ~ 20keV
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 5 ITER characteristics & objectives
Courtesy D. Campbell "Demonstrate scientific & technical feasibility of fusion energy for peaceful purposes"
Performance: ° Stationary Q>5 – Inductive Q>10
° Typical Pfusion ~500 MW ° Nb of pulses: ~10 4 of 300-500s duration ° Average neutron flux > 0,5 MW/m 2
Operation: ° Studying burning plasmas ° Testing breeding blankets ° Showing readiness of critical technolgies: ITER superconductor magnets, remote handling , JET high power flux plasma facing components TS R (m) ° Demonstrating safe operation & low impact 0 12345678910 on environnement
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 6 ITER construction status
… First plasma expected in 2020 in expected plasma First
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 7 Main scientific challenges for ITER
Plasma confinement : Limitating thermal losses = controlling turbulence saturation Stable MHD equilibrium = preventing dramatic relaxation events (ELMs , sawteeth , disruptions)
Plasma-wall interaction : Plasma physics issues: Heat exhaust (10-20 MW/m2) Preventing dilution by impurities Technological constraints: "Resistant" plasma facing materials ( neutrons + thermal flux) Safety (T trapping)
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 8 Outline
A historical perspective on Controlled Fusion
The ITER project: objectives & present status
Plasma confinement in tokamaks: Basic principles Gyrokinetic description of plasma turbulence
Plasma self-organization & turbulence control
ELMs in H-mode: edge violent relaxations
Sawteeth: core reconnection due to internal kink modes
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 9 Plasma confinement in tokamaks
MHD equilibrium: Lorentz force balances pressure gradient Helicity of magnetic field lines is essential ( q = nb poloidal turns / toroidal one ) >1 → Tokamak = nested toroidal magnetic surfaces ↔ χ <<χ Transport strongly anisotropic ( confinement): ⊥ || ⇒ Pressure, temperature, current ~constant on magnetic surfaces
R a
Turbulence degrades the confinement
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 10 Gyrokinetic description of turbulence
Low collisionality of tokamak plasmas → 6D kinetic description (wave-particle resonances, trapped particles, etc. )
ω 5 -1 ω 8 -1 Turb. freq. turb ~10 s << cyclotron freq. ci ~10 s 2 ⇒ phase space reduction: 4D + 1 invariant ( µ=mv ⊥ /2B) → gyrokinetic approach (fast cyclotron motion "averaged out")
particle guiding-center
ρ ≥ -3 c 10 m
Vlasov → Gyrokinetic eq. involving guiding-center distrib. Function µ with F( x,v || , ,t) [Brizard & Hahm, System closed by quasi-neutrality: RMP 2006] δ δ + nGCe = Z i ( nGCi npol ) with n pol = polarization density
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 11 Turbulence regulates cross-field transport
Tokamak plasmas are unstable w.r.t. thermo-convection → ∇ Radial velocity field in the Sun (ASH instability driving terms: ⊥T & inhomogeneity of B field code [Brun et al., 2010])
Fluctuations of electric potential
Characteristics of turbulence: ρ k⊥ i ~1
k|| qR ~1 ω 1/2 turb ~ v th /(RL T) δφ ∼ρ ∼ -3 e /T i/a 10 Velocity field is turbulent :
vE×B fluctuations → ⊥ transport (heat, particles, …) GYSELA
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 12 Outline
A historical perspective on Controlled Fusion
The ITER project: objectives & present status
Plasma confinement in tokamaks: Basic principles Gyrokinetic description of plasma turbulence
Plasma self-organization & turbulence control
ELMs in H-mode: edge violent relaxations
Sawteeth: core reconnection due to internal kink modes
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 13 Turbulent transport exhibits avalanches
Transport dynamics ≠ diffusion + convection ∆ Intermittent (1/freq.) large scale avalanches (length >> corr ) ± ρ ± 3 -1 Propagation velocity ~ * vth (~ 10 m.s in ITER)
[Sarazin et al., NF 2010]
) 16 1 GYSELA − c
ω ρ 14 ( *=1/512) 4
12
10 GYSELA [Sarazin NF '10] time (10 time
8
6
Heat flux 4 [gBohm units] 2 0.3 0.5ρ=r/a 0.7
From Black Holes to Cosmic Rays:Heating when plasmas source go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 14 Turbulence self-regulates via Zonal Flows
Sheared poloidal flow can efficiently reduce turbulence level via vortex shearing Turbulence itself can generate such flows: Zonal Flows (meso-scale, low freq.) Reynolds stress component – analogous to hydrodynamics (e.g. Jupiter)
Radially elongated convection cells when ZF artificially suppressed (streamers)
GYSELA ρ ν T 8 ( *=1/256, *=0.05)
6 ZF radially localized ("staircase") 4 4.10 5 Limit extension of avalanches ExB shearing rate t Gradient R/L Gradient 2 c → Micro transport barriers ω
5 [Dif-Pradalier et al., PRL 2009, PRE 2010] 0 2.10 80 100 120 140 160 ρ From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | =r/aPage 15 Complex transport barrier dynamics
Transport Barrier triggered by prescribed E ×B sheared flow (vorticity source) in Gyrokinetic simulation* *[HPC simulation: ~2 millions CPU hours – 34 billions grid points] The barrier experiences quasi-periodic relaxation events
[Strugarek et al., PPCF 2012, PRL 2013] Snapshots of non-axisymmetric electric potential fluctuations During Relaxation Event
t=9.22ms During Transport Barrier
t=8.59ms SDvision
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 16 Outline
A historical perspective on Controlled Fusion
The ITER project: objectives & present status
Plasma confinement in tokamaks: Basic principles Gyrokinetic description of plasma turbulence
Plasma self-organization & turbulence control
ELMs in H-mode: edge violent relaxations
Sawteeth: core reconnection due to internal kink modes
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 17 Transition from Low to High confinement regime
Plasma spontaneously bifurcates from L- to H-mode when P heating > P threshold H-mode = reference scenario for ITER (may not be avoidable anyway) No theoretical prediction of the threshold so far Current understanding: triggered by Zonal Flows , then sustained by Mean Flow
H-mode : Solar Tachocline : Transport Barrier for Transport Barrier for heat & particles Turbulence imagingangular momentum
H-mode = Tachocline Edge transport barrier Radiation at separatrix interior Quasi-periodic relaxation events (ELMs)
Convection zone From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 18 ELMs could damage ITER divertor
ELMs in JET tokamak
Edge Localized Modes = quasi- periodic relaxations of H-mode barrier
Huge particle & energy losses (~1 MJ in JET) - short time scale (~200 µs)
ELMs can be detrimental to plasma facing components (P>20MW.m-2)
JET magnetic geometry
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 19 Analogy with solar flares
Solar flares: relaxation of the NASA magnetic field on the sun surface
Ejection of energetic particles
Impact on satellite communications
ELM-crash simulation with JOREK code [Huysmans et al., 2012]
CEA-IRFM / Iter Organization
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 20 Outline
A historical perspective on Controlled Fusion
The ITER project: objectives & present status
Plasma confinement in tokamaks: Basic principles Gyrokinetic description of plasma turbulence
Plasma self-organization & turbulence control
ELMs in H-mode: edge violent relaxations
Sawteeth: core reconnection due to internal kink modes
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 21 Sawteeth redistribute energy & particles
Sawteeth internal kink modes at q~1 complete/partial reconnection time scales: period ~ few 10 2ms – crash < 1ms
Time (s) Main issues: Degrade the confinement Can generate seed islands for Neoclassical Tearing Modes (→ possible loss of α particles) Question: can they wash out impurities from the core plasma?
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 22 Complex structures after the crash
Fast reflectometry measurements → tomographic reconstruction of density Crescent-like structures observed after the crash Before crash After crash ) -3 Tore Supra m
19 Shot #44634 [R. Sabot et al. 2010] Density Density (x10
[T. Nicolas et al., Sawtooth cycle & asymmetric structures PoP 2012] well captured by 2-fluid full-MHD 3D [H. Lütjens et al., nonlinear code XTOR-2F NF 2008, 2009, 2010] Density advected by fast flows in vorticies
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 23 Structures do not prevent impurity exhaust
Overall particle redistribution analogous to Kadomtsev's predictions (although ≠ mechanism) Impurities accumulate close to mixing layer Crescent structures remain small → little effect on particle redistribution
[T. Nicolas et al. 2013]
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 24 Concluding remarks
International "Controlled Fusion community" in support to ITER Controlled Fusion much active in Asia (energy needs) → machines are built τ Constant progress in performance (nT E) & technology since 1951
Understanding-Predicting-Controlling capabilities increase rapidly: Improved diagnostics (many are 2D) High Performance Computing (towards Exascale: 10 18 flops)
Critical plasma issues for ITER : Understanding & predicting H-mode power threshold Avoiding / mitigating ELMs Avoid disruptions (including radiative collapse) & runaway electrons
From Black Holes to Cosmic Rays: when plasmas go wild, Les Houches, 14-18.10.2013 CEA | Y. Sarazin | Page 25