Electromagnetic Effects on the Intrinsic Rotation Generation Driven - - PowerPoint PPT Presentation

Electromagnetic Effects

• n the Intrinsic Rotation Generation

Driven by ITG Turbulence

• H. H. Kaang1, R. Singh1, Hogun Jhang1

National Fusion Research Institute, Daejeon, Korea

2014 KSTAR conference, 정선, Korea

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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 understanding on this problem is not enough. We investigate the EM effects on the intrinsic rotation generation by using fluid quasi-linear model

Intrinsic rotation observation results [Rice et al., Nucl. Fusion 2007]

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Two fluid model

To investigate EM effects :

Continuity eq. :

• Eq. of motion for ion:

Ion energy eq. : Vorticiry eq. :

• Eq. of motion for

electron:

(from electron energy eq.)

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Linear dispersion equation in slab geometry

• ni~ne , no toroidal effects ( Ln/R <<1 ), no current shear (J||’=0)
• Slab model :

ES ( classic terms ) EM ( modified ES terms )

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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

• A4 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.

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Eigenfunction of ES- Vs. EM- ITG ( no shear flow )

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.

• Getting solution for :

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Eigenfunction of ES- Vs. EM- ITG ( with flow shear )

Add the weak flow shear,

xshift=+0.011

• 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. So, asymmetry of EM-ITG mode is larger than that of ES mode even though the physical conditions are kept.

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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]

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Modification of the Reynolds stress via the EM effects

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If rewrite the Reynolds stress in the order of k|| ,

Origin

in momentum transport eq. ( There is no EM part. )

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Asymmetric eigenmode & Reynolds stress in slab model

Getting Reynolds stress for specific ky 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. SES is most dominant term

and SEM contribute about 20% of total Reynolds stress. Enhanced mode asymmetry increases Reynolds stress.

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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.