2014 KSTAR conference, 정선 , Korea P-6 Electromagnetic Effects on the Intrinsic Rotation Generation Driven by ITG Turbulence H. H. Kaang 1 , R. Singh 1 , Hogun Jhang 1 National Fusion Research Institute, Daejeon, Korea
Introduction ● The intrinsic rotation observed in the magnetic confinement devices suppresses the instabilities. ● The intrinsic rotation generation without external momentum input is important problem for the future devices in which the NBI may not deliver the sufficient strong momentum. ● The electromagnetic effects are expected to give influence on the intrinsic rotation generation when the equilibrium profile is steep. However, the Intrinsic rotation observation results understanding on this problem is not enough. [Rice et al., Nucl. Fusion 2007] We investigate the EM effects on the intrinsic rotation generation by using fluid quasi-linear model 2
Two fluid model Continuity eq. : Vorticiry eq. : Ion energy eq. : Eq. of motion for ion: Eq. of motion for electron: To investigate EM effects : (from electron energy eq.) 3 3
Linear dispersion equation in slab geometry • n i ~n e , no toroidal effects ( L n /R <<1 ), no current shear (J || ’=0) • Slab model : ES ( classic terms ) EM ( modified ES terms ) 4 4
Convergence of eigenfunction at a rational surface • If there is no shear flow, the equation is even for x. The EM effects can not bring asymmetry of eigenfunction by themselves • A 4 is usually large because Ls/Ln >1. This term plays the infinite potential in Schrödinger eq. So, the eigenfunction should be zero at rational surface (x=0) We solve this dispersion equation numerically by using shooting method. 5 5
Eigenfunction of ES- Vs. EM- ITG ( no shear flow ) • Getting solution for : Where, analytic solution for ES-ITG mode : The eigenvalues are not much different between ES and ES modes. • • The EM eigenmode is incoherent with the analytic solution of ES case; amplitude of real part and the shape of imaginary part are different. But the mode width is not changed. 6
Eigenfunction of ES- Vs. EM- ITG ( with flow shear ) Add the weak flow shear, The eigenvalues for ES and ES are not changed although the • flow shear is applied. The ES-ITG mode is simply shifted with flow shear. • • The EM ITG mode with flow shear is not simple shifted because of the mode convergence at rational surface. x shift =+0.011 So, asymmetry of EM-ITG mode is larger than that of ES mode even though the physical conditions are kept. 7
Fluid quasi-linear theory for the momentum transport • From the equation of ion motion, Similar form (radial grad. of averaged value ). So, we combined these terms as a modified Reynolds stress. Another mechanism investigated by [Wang & Diamond, PRL 2013] 8 8
Modification of the Reynolds stress via the EM effects If rewrite the Reynolds stress in the order of k || , Origin in momentum transport eq. ( There is no EM part. ) 9 9
Asymmetric eigenmode & Reynolds stress in slab model Getting Reynolds stress for specific k y with driven eigenfunction : take average for k || ES EM • S reduces the Reynolds stress with the opposite sign with the diffusive term. • S increase the Reynolds stress with same sign with the diffusive term. S ES is most dominant term and S EM contribute about 20% of total Reynolds stress. Enhanced mode asymmetry increases Reynolds stress. 10 10
Conclusions • We investigate the electromagnetic ITG mode and the intrinsic rotation generation driven by that. • The electromagnetic effects enhanced asymmetry of the eigenmode because the mode converge into zero at the rational surface. However, the electromagnetic effects do not break the symmetry of the mode by themselves and need other symmetry breaking condition, such as flow shear. • The Reynolds stress becomes stronger as the mode asymmetry is enhanced. • We are working on to figure out when the electromagnetic effects becomes larger and how much they contribute on the compare to the generation of the intrinsic rotation. 11
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