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K.Ida, M.Yoshinuma, LHD experimental group National Institute for Fusion Science 1 April 2009

Non-diffusive terms of momentum transport as a driving force for spontaneous rotation in toroidal plasmas. K.Ida, M.Yoshinuma, LHD experimental group National Institute for Fusion Science 1 April 2009 Transport & Confinement ITPA Meeting JAEA, Naka Japan. OUTLINE. Introduction

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K.Ida, M.Yoshinuma, LHD experimental group National Institute for Fusion Science 1 April 2009

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  1. Non-diffusive terms of momentum transport as a driving force for spontaneous rotation in toroidal plasmas K.Ida, M.Yoshinuma, LHD experimental group National Institute for Fusion Science 1 April 2009 Transport & Confinement ITPA Meeting JAEA, Naka Japan

  2. OUTLINE • Introduction • Non-diffusive (off-diagonal) term, internal (spontaneous) torque and spontaneous rotation • 2 Pinch term and off-diagonal term in momentum transport • Experimental results in LHD • 3.1 radial electric field term • 3.2 ion temperature gradient term • 3.3 Causality between ∇Ti and ∇Vf • 4 What is a driving mechanism of spontaneous rotation • 5 Summary

  3. n Vq Vf T Gr Pqr Pfr qr = - M Vf = 0 even for Pfr = 0 Transport matrix Toroidal momentum transport has a diagonal and an off-diagonal term Non-diffusive (off-diagonal ) term, internal (spontaneous) torque and spontaneous rotation K.Itoh, S-I Itoh and A.Fukuyama “Transport and structural formation in plasmas” IOP publishing 1999 Pfr = - M33 Vf - M31 n -M34 T - M32 Vq Off-diagonal term (non-diffusive term) Diagonal term (diffusive term) Spontaneous rotation off-diagonal term is equivalent to intrinsic torque (Residual stress, Reynolds stress etc. O.D.Gurcan PoP 14 (2007) 042306, B.Concalves, PRL 96 (2006) 145001) (1/r) ∫r[ mini(-dVf/dt) + Text] dr = mini[- mDdvf /dr + off-diagonal term] or (1/r) ∫r[ mini(-dVf/dt) + Text+ intrinsics torque] dr = mini[- mDdvf /dr ]

  4. Momentum flux is determined by the momentum input and time derivative of Vf GM =(1/r) ∫r[ mini(-dVf/dt) + Text] dr Text : external torque Momentum flux has diffusive and non-diffusive term Diffusive and Non-diffusive terms in Momentum Flux GM = mini[- mDdvf /dr +VpinchVf +mN (vth/Ti)(eEr)+mN (vth/Ti)(dTi/dr)] pinch Er term ∇Ti /∇pi term ∇Vf driven K.Ida, PRL 86 (2001) 3040 K.Nagashima, NF 34 (1994) 449 K.Ida, PRL 74 (1995) 1990. M.Yoshida, PRL 100 (2008) 105002. Diagonal term off diagonal diffusive (shear viscosity) non-diffusive (driving terms) It is not easy to distinguish Er driven ∇Ti /∇pi driven, because they are coupled with each others. Is the pinch term really large enough to affect the rotation profile?

  5. Momentum pinch and off-diagonal term Momentum pinch m∇Vf second derivative becomes large at zero velocity (not observed in experiment!) VinwardVf m∇Vf VinwardVf momentum source at zero velocity is necessary because of the conservation of momentum Co-injection Off diagonal term m∇Vf mND∇Ti Artificial momentum source is NOT required at zero velocity Co-injection m∇Vf Since the velocity shear affects the opn transport, the causality between ∇V and ∇T is important mND∇Ti Ctr-injection

  6. Toroidal effect on momentum transport Because of the toroidal effect moment of inertia density, the conservation of the toroidal angular momentum causes an “apparent” momentum pinch in the linear momentum in the toroidal direction The pinch velocity can be evaluated as Vpinch = 2mD(-e/R+ 1/Ln) e=r/R0 dI1 < dI2 Inward outward V1 >V2 The ratio of inward pinch term to diffusive term is a order of 10-1 to 10-2 dI2 dI1 VpinchVf ~ (r/R) (LT/R0) << 1 m dVf/dr See O.D.Grucan PRL 100 135001 (2008) in details

  7. Er Non-diffusive term In LHD radial electric field can be controlled by changing the electron density slightly by taking advantage of the ion-root electro root transition As the electron density is increased the Er change its sign from positive to negative and the tnegative Er (or dEr/dr <0 ) causes toroidal rotation in co-direction (opposite to JT-60U) Flux : emimNni(vth/Ti)(Er) Torque : emimN (1/r) d[r ni(vth/Ti)Er]/dr Er non-diffusive term is driven by the torque with Er shear

  8. Transition of spontaneous rotation In TCV, a transition from ctr-rotation to co-rotation is observed as the electron density is increased. (ref : A.Bortolon, PRL 97 (2006) 235003) The sign of spontaneous rotation is same as that in LHD. But the same physics??

  9. Physics model of Er non-diffusive term The Er non-diffusive term is nearly equivalent to the spontaneous torque due to Er shear if the derivative radial electric field much rather than that of non-diffusivity coefficient and temperature. emimN (1/r) d[r ni(vth/Ti)Er]/dr ~ emi mN ni(vth/Ti)(dEr/dr) The symmetry breaking of turbulence and existence of radial electric field shear can produce the internal toroidal torque and results in the spontaneous velocity gradient). See O.D.Gurcan Phys. Plasmas 14 (2007) 042306 in details Spontaneous velocity gradient Internal toroidal torque Spontaneous rotation V = 0 at the plasma edge

  10. Torque scan experiment in LHD 1 co/ctr-NBI 2 balanced NBIs 2 balanced and 1 co/ctr-NBI Near center (R < 4.1m)  NBI driven toroidal rotation dominant Off center (R > 4.1m)  spontaneous toroidal rotation dominant The asymmetry of toroidal rotation is quite significant at higher ion temperature. This asymmetry is due to the Non-diffusive term in momentum transport.

  11. Spontaneous part of toroidal rotation velocity Asymmetry part of the rotation (average of Vf between co and ctr-NBI plasma) increases as the ∇Ti is increased. Near edge (R ~ 4.6m )  spontaneous toroidal rotation due to Er (> 0). Core  spontaneous toroidal rotation due to ∇Ti is dominant

  12. ∇Ti Non-diffusive term There is a clear relation between the ion temperature gradient and change in toroidal rotation in the power scan experiment in LHD. • Ion temperature gradient causes spontaneous toroidal rotation in co-direction • opposite to that observed in JT-60U [Y.Koide, et. al., PRL 72 (1994) 3662, Y.Sakamoto, NF 41 (2001) 865] • same as that observed in JET [G.Eriksson PPCF 34 (1992) 863] and Alcator C-mod [J.Rice et al., NF38 (1998) 75].

  13. ∇Ti and ∇Vf causality Since the toroidal rotation velocity shear affect the ion transport, it is important to study the causality between ∇Ti and ∇Vf at the transient phase) Early phase (t = 2.09s)  counter rotation is driven : direct effect of NBI Later phase (t = 2.29s)  co-rotation is driven : secondary effect of increase of ∇Ti Increase of velocity shear (in co-direction) appears after the ∇Ti is increased

  14. What is physics mechanism of spontaneous rotation? What we know 1 There is an non-diffusive term in momentum transport 2 The non-diffusive terms are relating to Er and ∇Ti (or ∇pi) 3 The direction of spontaneous rotation observed is different (even among tokamak experimets) What we do not know 1 How the direction of spontaneous rotation is determined? 2 How the magnitude of the non-diffusive term (or magnitude of spontaneous torque) is determined? 3 Does the multi non-diffusive terms suggests multi physics mechanism in the plasma or just expansion of complicated term, which include to Er and∇Ti, ∇pi, etc……

  15. Summary • Two Non-diffusive terms (off-diagonal term) of toroial momentum transport are observed separately in LHD : one is Er terms and the other is ∇Ti term. (Their coupling is too strong in tokamk) • 2. Er term is dominant near the plasma edge and positeive Er causes a spontaneous rotation in the counter-direction. • 3. ∇Ti term is dominant at the half of plasma minor radius and causes a spontaneous rotation in the co-direction. (The causality is investigated (∇Ti ∇Vf)

  16. Evidence of turbulence driven parallel Reynolds stress Cross correlation between parallel and radial fluctuating velocities Radial-parallel contribution to the production of turbulent kinetic energy In TJ-II stellarator, significant radial-parallel component of the Reynolds stress, which drives spontaneous parallel flow is observed See B.Concalves, Phys. Rev. Lett. 96 (2006) 145001 in details

  17. Problem of concept of momentum pinch Momentum pinch Co-injection second derivative (curvature) predicted contradicts to that measured in experiment. m∇Vf m∇Vf VinwardVf VinwardVf m∇Vf m∇Vf VinwardVf VinwardVf Ctr-injection

  18. Velocity pinch due to turbulent equipartition (TEP) Velocity pinch is possible under the condition of conservation of angular momentum during the transition phase when density profile changes from flat to peaked ones bur not in the steady-state. Density profile rotation profile Skater makes a spin by reducing an angular momentum inertia density, but he/she can not keep the spin forever! Particle pinch velocity pinch dI1 < dI2 V1 >V2 decay due to viscosity sustained dI2 dI1 See O.D.Grucan PRL 100 135001 (2008) in details

  19. 1980’ Toroidal rotation of Ohmic plasma CTR rotation of Ohmic plasma in PLT [NF 21 (1981) 1301] PDX [NF 23 (1983) 1643] and Alcator C-mod [NF 37 (1997) 421] Early 90’ Toroidal rotation of ICRF plasmas CTR rotation in JIPP-TIIU [NF 31 (1991) 943] Co rotation in JET [PPCF 34 (1992) 863] in Alcator C-mod [NF 38 (1998) 75] Mid 90’ Non-Diffusive term of momentum transport in NBI heated Plasmas CTR rotation in JT-60U [NF 34 (1994) 449] in JFT-2M [PRL 74 (1995 ) 1990] CTR Spontaneous toroidal flow in helical plasma in LHD [2005] Spontaneous toroidal flow in the plasma with ITB CTR rotation in JT-60U [PRL 72 (1994) 3662, PoP 3 (1996) 1943, NF 41 (2001) 865] CTR rotation in TFTR [PoP 5 (1998) 665] CTR rotation in Alcator C-mod [ NF 41 (2001) 277] Early 2000’ Spontaneous toroidal flow driven by ECH CTR rotation in CHS (anti-parallel to <ErxBq>) [PRL 86 (2001 ) 3040] CTR rotation driven by ECH plasma in D-IIID [PoP 11 (2004) 4323] History of toroidal momentum transport studies

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