H.Y. Lee

K. Nishioka

S. "Nishimura

S." Kobayashi

Y. Nakamura

National Institute for Fusion Science (NIFS-Repository)

    Numerical and experimental analyses of neoclassical flows are one of the important issues in fusion plasma studies. Experiments for investigating a configuration dependence of the neoclassical flows are now actively performed in Heliotron-J [1]. In a previous report [2], a comparison of theoretical calculations of the NB- (neutral beam) driven ion flows and the CXRS measurement is shown.  However, spontaneous flows driven by the radial gradient force ∂pa/∂r, ∂Ta/∂r, ∂Φ/∂r were not discussed in detail. When applying the theory in Refs.[3], an important issue in this radial gradient force effect is the non-diagonal coupling between parallel flows and radial transport included in the full Onsager symmetric transport matrix  !abn i"sqabni"s / Ta#$%%&'(( =L11abL12abL21abL22ab#$%%&'((Xb1Xb2#$%&'(b)       +L1EaL2Ea#$%%&'((BiE(A)B2 1/2+L1FaL2Fa#$%%&'((BiFf1B2 1/2 When the NB-driven flows of ions and electrons are generated, they change the radial particle and heat fluxes and thus there will be a minor correction on the ambipolar radial electric field. In the present analyses on the Heliotron-J experiments, this determination mechanism of the radial electric field is consistently included in the parallel flow calculations. Figure 1 shows the calculated parallel velocities of the target plasma ions in co- and counter- NB(E=30keV, H+) injection shots. Here, used target plasma parameters are ne(r)=1.5×1019[1−(r/a)2]m−3, Te(r)=300[1−(r/a)2]eV, Ti(r)=175[1−(r/a)1.57]1.11eV, and the target particles’ density ratio is e−:D+:C6+=1:0.82:0.03 (Zeff=1.9). The total external momentum input is calculated by applying the HFREYA and MCNBI included in the FIT3D code[4]. Various energy components of the beam (E,E/2,E/3) generated in the positive ion source injector are taken into account. The Laguerre expansion coefficients  v!Lj(3/2)(xa2 )Caf faM , ff( )d3v" of the RMJ operator for collisions between thermalized particles’ Maxwellian faM and the tangentially injected fast ions’ velocity distribution ff are added to the simultaneous parallel force balance equations, which are previously generalized to cases with multiple ion species [5]. It can be seen that the NB-driven flow component is dominant at core region in the Heliotron-J experimental condition. Figure 2 shows calculated ambipolar potential in these shots. This direction of the correction by the NB-driven radial particle fluxes is consistent with a qualitative prediction by the well-known mechanism of so-called Ware pinch.    A next step improvement of the numerical code is to implement the eigen function method [6] for taking account the fast ion trapping effect in the friction collision term Caf faM , ff( ) . A poloidal CXRS measurement to investigate this radial electric field experimentally is also planed in near future. !"#!"$!#$#"$"#%$%#$ $&% $&' $&( $&) "<u||CB>/<B2>(1/2) , V|| [km/s]*+,Co-NBICtr-NBICXRS(a)!"#!"$!#$#"$"#%$%#$ $&% $&' $&( $&) "<u||D,CB>/<B2>(1/2)  [km/s]*+,Co-NBICtr-NBIwithout NBI(b) Fig.1 (a) Measured and calculated flow velocities  Bu!a /B  [km/s] of C6+ ions. (b) calculated flow velocities of D+ (dashed lines) and C6+ (solid lines) ions. The co- and counter-injection shots and a case without the external momentum input are compared. !"##!$%#!$##!&%#!&##!%### #'$ #'( #') #'* &!+,-./01Co-NBICtr-NBI Fig.2  Calculated ambipolar potentials for co- and counter-injection shots.    [1] Lee,H.Y., Kobayashi,S., et al. Plasma Phys. Control. Fusion 55, 035012 (2013) [2] Nishioka,K., et al., NIFS Ann.Rep.2013, 19th ISHW (2013) [3] Sugama,H., Nishimura,S., Phys.Plasmas 9, 4637 (2002) [4] Murakami,S., et al., Trans.Fusion Technol., 27,259 (1995) [5] Nishimura,S., Sugama,H., et al., Phys.Plasmas 17, 082510 (2010), 18, 069901 (2011) [6] Hsu,C.T., Catto,P.J., and Sigmar,D.J., Phys. Fluids B 2 280 (1990) 537§38. Comparison of Neoclassical Flow Calculations by the Moment Method with CXRS Measurement on Heliotron JNishimura, S.,  Nishioka, K., Nakamura, Y., Lee, H.Y., Kobayashi, S. (Kyoto Univ.)

Comparison of Neoclassical Flow Calculations by the Moment Method with CXRS Measurement on Heliotron J

Abstract

Similar works

Full text

Available Versions

National Institute for Fusion Science (NIFS-Repository)