The unique flexibility of TCV in plasma shaping has been exploited to address different aspects of tokamak physics in which the plasma shape may play a role. This paper summarizes the experiments undertaken in the TCV tokamak ("Tokamak à Configuration Variable") over the last decade in stability and transport and offers a comprehensive and integrated view of the various effects of plasma shape observed. For each of these effects, the relation between experimental results and theoretical predictions is stressed. Many of these topics are related to vital issues in ITER and to concept improvement in view of DEMO

Alberti, S.

Angelino, P.

Behn, R.

Bortolon, A.

Bottino, A.

Brunner, S.

Camenen, Y.

Coda, S.

Curchod, L.

Daouk, K.

Duval, B. P.

Fasoli, A.

Furno, I.

Goodman, T. P.

Graves, J.

Henderson, M. A.

Hofmann, F.

Karpushov, A.

Lapillonne, X.

Lister, J. B.

Marinoni, A.

Martin, Y.

Martynov, An.

Medvedev, S.

Moret, J.-M.

Paley, J. I.

Piras, F.

Pitts, R. A.

Pochelon, A.

Porte, L.

Reimerdes, H.

Ryter, F.

Sauter, O.

Scarabosio, A.

Sulmoni, L.

Sushkov, A.

Tran, M. Q.

Villard, L.

Weisen, H.

The unique flexibility of TCV in plasma shaping has been exploited to address different aspects of tokamak physics in which the plasma shape may play a role. This paper summarizes the experiments undertaken in the TCV tokamak ("Tokamak à Configuration Variable") over the last decade in stability and transport and offers a comprehensive and integrated view of the various effects of plasma shape observed. For each of these effects, the relation between experimental results and theoretical predictions is stressed. Many of these topics are related to vital issues in ITER and to concept improvement in view of DEMO.CRPPSP

Infoscience - École polytechnique fédérale de Lausanne

 22nd IAEA Fusion Energy Conference, Geneva, Switzerland, 12-18 October 2008 Physics Insight & Performance Benefit in MHD & Energy Transport...  0 1 2 3 40123456δ=0.46δ=0.23δ=0.00τ saw [ms]triangularity scan (κ≈1.51)PEC /V1 [MW/m3]  κTCV triangularity scanSawtooth Period [ms]δ=1.5 (a)  numerical (KINX) Ideal Stability of m=1,n=1analyticalδWδ(b)  1.52.02.53.00.2 0.4 0.6 0.8 1 1.2 1.400.20.40.60.81.00.52 0.53 0.54 0.55 0.56 0.570.70.8Time [s]Soft x-ray [a.u.]#17683Elongation κSoft x-ray [a.u.] Inversion radius ρinv(a)(b)(c) WHY STUDY also SHAPES different from ITER? • Test of MHD and transport theory• Negative triangularity improves confinement • Confinement scales with  I p  ( τ E ,  n e ,  β , fast ions...),and   I p max  can be increased by plasma cross-sec-tion shaping at constant magnetic field  • Many parameters depend on plasma shaping andreciprocally, active plasma shaping offers a meanto control these parameters• Optim. of devices beyond ITER, innovative shapes SHAPING VARIABLES • elongation  κ,  triangularity  δ , including negative,squareness • aspect ratio R/a• limited / diverter shape    SHAPE INFLUENCES ... • MHD  stability (sawteeth, modes, disruptions,ELMs, TAE damping & gaps)• Confinement , edge transport barrier, performance• Transport  (electron heat, rotation) • Integrated approach  of plasma shaping  needed :several phenomena  with crucial impact on plasmacontainement  are influenced by shape, e.g. :•e.g. ELMs( shape ) can destroy ITBs (e.g. JET)•Sawteeth( shape ) can trigger NTMs • Some effects of plasma shaping can differ withplama scenario, e.g.: • τ E ( δ ) increases towards  neg  δ  in L-mode (core)increases towards  posit  δ  in H-mode (pedestal)  A. Pochelon, Y. Camenen 1 , A. Marinoni, S. Brunner, S. Coda, J. Graves, F. Hofmann, An. Martynov, S. Medvedev 2 , F. Piras, H. Reimerdes 3 , O. Sauter, A. Scarabosio  4 , L.Villard, S. Alberti, C. Angelino  5 , R. Behn, A. Bortolon, A. Bottino  4 , L. Curchod, K. Daouk, B.P. Duval, A. Fasoli, I. Furno, T.P. Goodman,  M.A. Henderson,  A. Karpushov, X. Lapillonne, J.B. Lister, Y. Martin, J.-M. Moret, J.I. Paley, R.A. Pitts, L. Porte, F. Ryter  4 , L. Sulmoni, A. Sushkov  6 , G. Tonetti, M.Q.Tran, H. Weisen and the TCV Team 1 Ecole Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherches en Physique des PlasmasAssociation EURATOM-Confédération Suisse, CH-1015 Lausanne EPFL, Switzerland 1. Motivations 4. MHD & stability: modes & disruptions0 5 1000.20.4Ne19*R/Bphi1/q9500.20.41/q9500.20.41/q950 5 10Ne19*R/Bphi0 5 10Ne19*R/Bphi1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.200.20.40.61 1.461.562.3 -0.440.220.340.62TriangularityElongationTCV disruptivity in Hugill diagram (all disruption types)0.001/s 100/s0.1/s 10/sDisruptivity ext.-mode with  m / n =3/1~ q a —> coupling to int. mode 2/1  q =3 disruptivity reduced by shaping Disruptivity (disr./s) in Hugill diagram vs  δ  and  κ  low disr.=blue, high disr.=red q =3 high density disr. notch stabilized by ( κ , δ )-shaping MHD modes leading to disruption q =3-events: 3 shape ranges:low, medium, high shapingdisrupt, modes, no modes κ =1.3,  δ =0.2 (weak shaping) - 2/1: dominant mode leading to disrupt.- Locking of 3/1 to 2/1 correlates with the 2/1 becoming disruptive -  Shaping reduces the 3/1 external mode • 2/1- Δ ’-stability does not improve, even deteriorates  towards high  κ ! • Essential role of mode coupling (from exp. and th.)• Thus other mechanisms acting like wall stab. of external mode 3/1,  - and coupling with higher  q  integer vacuum flux surfaces  q = 4, 5, ...• Δ ’-stab predicts 2/1  stable in  I p -ramp • Thus wall stabil. of the 3/1 mode isessential to avoid destab. of 2/1 by 2/1 MHD modes: 3/1 -> 2/1 MHD stability (PEST-3)3.2 3.4 3.6 3.8 4-35-30-25-20-151050510qar s’'<0  STABLEm=2 free b.m=3 free b.m=3 fixed b.'>0  UNSTABLE# 21400-- Scarabosio NF07 3. MHD and stability:  q =1 sawteeth q =1 radius scaling:  studied over a large  κ -range  • the limiting    pressure inside  q =1 ( β Bussac )is determined by shape • τ ST   follows ideal internal kink  stability• parallel to Mercier ideal stability over thisshape range Sawtooth period/stability central ECH (1.1< κ <2.1   and -0.2< δ <+0.5)Sawtooth period/stability for -0.6< δ <+0.3, OH Sawtooth disappearance at high  κ  >2.3 - 2.6, in OH ... ρ inv  = < j > / ( q 0  j 0 )   inversion radius ρ inv   ≈  2 ( q eng   ( κ 0 +1/ κ 0 )) -1 , with   q eng =5 abB /   RI p OH ... and at lower  κ    with off-axis ECH • both triangularity signs are stabilizing(shorter sawteeth)• δ W ideal int kink  and  τ ST  show the samebehaviour with  δ  (min. close to  δ  ~ -0.3) sawtooth period  τ ST ( δ ) δ W ideal int kink ( δ ) 123456789 10 11 121314151617181920212223242526272829303132333435363738#18128 @ t=0.65s   0 0.5 1020040060080010001200ρpolTe [eV]t=0.534s0 0.5 1020040060080010001200ρpolTe [eV]t=0.567sTHOMSON - #17683a) b) κ =2.45 κ =2.53t=0.5st=1.4s κ At very high  κ  &  l i <0.7,sawteeth disappear  ( γ ideal int kink  > ω *i /2 ),  replaced by  m / n =1 multi-harmonic modes on  q =1 keeping a flat central pressure profile with  ρ 1  unchanged  (infernal, in-terchange modes?)   multi-harmonics  m =1,2,3 on  q =1 with off-axis ECH current profile broadening, as in  high  I N  OH discharges   ρ 1   ≠  const, decreasing with off-axis ECH 1/1          2/2          3/3 —>   ideal internal kink  Weisen NF02, PPCF98Reimerdes PPCF00Martynov PPCF05Reimerdes PPCF06 Scarabosio thesis06 T e τ ST [ms]75 80 85 90 95 100 10500.050.1amplitude PSD [a.u.] R [cm]75 80 85 90 95 100 105−4−2024phase [rad]R [cm]Am=3 multiplied by 5 m=2 m=1 m=3  2. TCV facility & Shaping achievements Flexible plasma shaping • X2, 2 nd  harm., 82.7GHz, 3MW, 6 LFS launchers, steerable during dis-charge• X3, 3 rd  harm., 118GHz, 1.5MW• Cut-off densities:X2 : 4.2 10 19  m -3 X3: 11.1 10 19  m -3 R =0.88m,  a =0.25m,  R/a ~3.5 B <1.54T,  I p <1MA    0.9 <  κ   < 2.8 - 0.7 <  δ   < +1 ... matched by a flexible heating system, entirely based on ECRH 16 independent shaping coilsoperational diagram limited by : n=0 vertical instabilityn=1 external kink (IN & β-limit)current limit at high κβ-limit at high κβN~2 reached with 1.5MW X3 at κ95~1.6 in H-mode  More power needed to test the β-limit at high κ!Ideal MHD pre-dicts the current limitκ=2.5 at low IN, with off-axis ECHvertical stability requires broad current profilest=0.5st=1.4sHofmann PPCF01Pochelon NF01Camenen NF07Paley PPCF07Hofmann PRL97Porte NF07, Alberti JoPh05, Pochelon SMP05INκX3 system (118GHz, 1.5MW)X2 system (82.7GHz, 3MW)Upper Lateral Launchers (4)Equatorial Launchers (2)At fixed q(a) , ρinv and <j> increase with shaping, κEC• τST depends strongly on plasma shapeat const ρ1disruptivity [s-1]1 University of Warwick, UK      2 Keldysh Institute, Moscow, RF     3 General Atomics, San Diego, CA, US      4 IPP Garching, Germany      5 CEA-Cadarache, France      6 RRC Kurchatov Institute, Moscow, RF22nd IAEA Fusion Energy Conference, Geneva, Switzerland, 12-18 October 2008δ=−0.4HFSδ=−0.2 δ=+0.2 δ=+0.4LFS... from plasma Shaping Experiments in the TCV tokamak6. Electron heat transport versus shape and collisionality7. Innovative ideas, prospects, e.g.Presence of suprathermals−0.6 −0.4 −0.2  0.0  0.2  0.4 0 51015δ1.50.90.3PtotMW[ms]Eeτ(1.8 10  /ne_av)0.46260p I   [kA]260400260&OHEC19•• MHD: Sawtooth period/internal kink stability: stabilized by ±δ, destabilized byhigh κ• Supression of q~3 ramp-up disruptions by plasma shaping: role of mode coupling (3/1 —> 2/1) and wall stabilization (of q~3, 4, 5...) • Heat transport: Dominant role of geometrical factor (SEF) at high νeff, impor-tant for κ-changes• Transport improves by a factor 2 in L-mode from δ =+0.4 to δ =-0.4 at low νeff• Central role of collisions, modifying χe with shape (here triangularity)• Negative triangularity physical effect: 1) role of shear (increasing k⊥) and 2) trapped e- toroidal precession versus TEM mode frequency (decrea-sing γ  of the mode)• Thus, shape effects on confinement & transport depend on collisionality, which determines the dominant micro-instablity type and transport associated• exploration of - heat, momentum, particle transport - with shape• TCV plasma shaping acts as a stringent test bench for theories, validation of models, by gradually changing parameters and extending their covered range .5. Confinement and geometry  Ohmic confinement at medium densities (νeff ~ 2.5-10)• Negative triangularity 1) modifies the resonance between the toroidal precessional drift frequency of trapped electrons and the mode frequency, reducing the growthrate γ of the mode 2) enhances the local shear, increasing k⊥ of the mode.Collisionality νeff • Strong τEe(δ) dep. found,asymmetrical in δ, unlike SEF• No more explained by SEF only: χe must vary with δ.• Strong τEe increase with κ, (κ<~2.3) • Mild decrease with δ  (δ>0)0 0.2 0.4 0.6 0.8 105101520253035ρ<|∇ρ|2 >  [m−2]κ=2.8, δ=+0.4κ=1.1, δ=+0.4κ=1.6, δ=−0.7κ=1.6, δ=+0.71 1.5 200.511.522.5κτ Ee/τ EecircIp=Cteρ1=CteSEF          −0.5 0 0.500.511.52δτ Ee/τ EecircIp=CteSEF       The SEF (Shape enhancement factor) evaluates the part of τEe-variation  due to the geometrical shape factor, keeping same diffusivity χe(ρ)  (and ∇Te(ρ))SEF=τEe shape / τEe circ with same χe  (ASTRA)keeping sawtooth inv. radius ρ1~const (for similar profiles)local flux surface averagedgradient geometrical factor EC confinement at low densities (νeff ~ 0.2-1)SEF adequately accounts for τEe-variations with shape in OH medium density discharges (νeff ~ 2.5-10)Central ECH and covering a large δ-range:  - 0.6 < δ < +0.5 Triangularity scan (νeff ~ 0.1-1)Te, gradTe-variation expts• χe-depends  on collisionality νeff, rather than on e.g.: Te, ne, or R/LTe,with νeff= 0.1R ne Zeff / Te2 = νei/ωDe, where ωDe = curvature drift frequency.• and χe decreases with colisionality νeff diff. Thom.CXRSTEM dominated regime (no ETG in 0.2<ρ<0.7 range,due to high Zeff & high Te/Ti ) Triangularity and collisionality dep. (in TCV L-mode, TEM-dominated)2 2.5 3 3.5 4 4.5 5 5.5−1001020ne,av (1019 m−3)Central toroidal rotation uφ0 (km/s) a)TCV 30500TCV 321270 0.2 0.4 0.6 0.8 1−20−1001020before inv.after inv.ρψToroidal rotation uφ (km/s) b)δ=0.48 δ=0.00Shaping, by changing  χe, Te, Ti , Te/Ti, Zeff, wall-contact, etc... ,   gives an opportunity for untangling the un-derlying physic, in par-ticular the change of dominant TEM turbu-lence with νeff.Non-linear gyrokinetic local collisional (GS2)larger k⊥ at δ<0, reducing the mixing lengthtransportγ/k⊥2 at low n8. Conclusionslow νeffhigh νeffheat flux versus pitch angleHeat transp Qe (shape geom., flux surf. averaged Te-gradients) To sustain the same pressure profile at δ =-0.4than at δ =+0.4 demands only half the power,due to the reduction of χe toward negative δ.Triangularity and many parameters varied• As good as H-mode...Transport simulations reflect exp. χe in TEM regime:• decrease of  χe towards high νeff and negative δ• triangularity effect on χe smaller at high νeff, see also vs. pitch-angle• but disagree for the radial dependence: possibly a global effect.Rotation inversion vs. ne is shape dependentH-mode at negative triangularity• 2 EC deposition locations• Varying Ptot = P1 + P2and   P1 / P2 Linear and non-linear GK simulations of heat transport0 0.2 0.40.20.40.60.8δ=−0.3,  n=100 0.2 0.40.20.40.60.8δ=+0.5,  n=10mixing length transport0102030γ   [104 s−1]δ=+0.5δ=+0.2δ=−0.30.20.40.6k ⊥ρ s5 10 15 20 2501530γ/k⊥2   [m2 /s]δ=+0.5δ = - 0.3δ=0.48δ = 0.00=  reducing triangularity• Systematic exploration of plasma shape effects on H-mode properties(also at negative triangularities: test of models over broader range of shapes)• improved eITB properties at negative triangularity with lower transport?• impurity, particles transport with elongation and triangularity• divertor with low shear to reduce heat load and study transport• Further shape studies:Moret PRL97, Weisen NF97varying δvarying κCamenen thesis06Coda 98, Pochelon NF99, Weisen NF98Pochelon EPS99Camenen PPCF05Camenen PPCF05, Thesis06, NF07Camenen NF07Camenen PPCF05Bortolon PRL06 Duval PPCF07 PP08This work was supported in part by the Swiss National FoundationAngioni PoP03Moret PRL97Is geometry sufficient to explain?Gyrokinetic simulationslinear, global (LORB) Doublet Snowflake (hexapole) divertorRuytov PP 07 08Piras 2008Hofmann EPS 96TCV Hofmann EPS960.6 0.8 1 1.2−1−0.500.510.6 0.8 1 1.2−1−0.500.510.6 0.8 1 1.2−1−0.500.51Medvedev EPS 08To study the ef-fect of shape on:- confinement,- transport, - ELM/quiescent regime, - pedestal, - β-limit & RWM at low power with ECH X3GS2 linearδκCamenen PPCF05Marinoni subPPCF 08Camenen NF07χe ml -variation with κ,δMarinoni subPPCF 08Marinoni subPPCF 08• Shapes effects on χe and τEe depend on collisionality • Collisionality unifies the description of OH & EC transport (different νeff) 0 0.2 0.4 0.6 0.8 1012345ρT e [keV]Camenen NF070 1 2 3 4 5 602468101/νeff∝ Te 2/(neZeff)χ e   [m2 /s]ρ=0.55δ=+0.4δ=+0.2δ=−0.2δ=−0.4δ=+0.4δ=−0.40 1 2 3 42468101214161/νeffχ e [m2 /s]δLCFS=+0.4δLCFS=−0.4ρ = 0.70δ=−0.4δ=+0.40 0.2 0.4 0.6 0.8 1 1.210−210−1100101102Heat flux [a.u.]1/νeff=0.25μB0/EHFpass/HFtot~5%HFpass/HFtot~10%0 0.2 0.4 0.6 0.8 1 1.210−210−1100101102Heat flux [a.u.]1/νeff=2.5μB0/EHFpass/HFtot~5%Untrapped TrappedB0/Bmax B0/BminδLCFS=−0.4δLCFS=+0.4GS2 non-lineareITB at negative triangularity: better?• Shape is related to vital issues in ITER and to concept improvement in view of DEMOTransport with κ, will depend on νeff and instability ...

Physics Insight and Performance Benefit from Plasma Shaping Experiments in MHD and Energy Transport in the TCV Tokamak

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Physics Insight and Performance Benefit from Plasma Shaping Experiments in MHD and Energy Transport in the TCV Tokamak

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