# Plasma and Fusion Research

## Volume 11, 1203018 (2016)

# Rapid Communications

- 1)
- Institute for Advanced Study, Kyushu University, Fukuoka 812-8581, Japan
- 2)
- Research Institute for Applied Mechanics, Kyushu University, Fukuoka 816-8580, Japan
- 3)
- Research Center for Plasma Turbulence, Kyushu University, Fukuoka 816-8580, Japan
- 4)
- National Institute for Fusion Science, Toki 509-5202, Japan

### Abstract

The flux of parallel momentum by parallel shear flow driven instability is calculated with the self-consistent mode dispersion. The result indicates that the diffusive component has two characteristic terms: ν_{D1} ∼ v˜_{x}^{2}/γ_{(0)} and ν_{D2} ∼ v˜_{x}^{2}/(k_{∥}^{2}D_{∥}) where v˜_{x} is the fluctuation radial velocity, γ_{(0)} is the growth rate of the mode, k_{∥} is the parallel wave number, and D_{∥} is the electron diffusivity along the magnetic field. ν_{D1} results when the parallel flow shear is above the threshold, while ν_{D2} is important around the marginal state. Since typically ν_{D1} ≫ ν_{D2} ∼ D_{n}, where D_{n} is the particle diffusivity, the Prandtl number (≡ ν/D_{n}) becomes large when parallel flow shear driven instability occurs. This feature may explain the experimental observation on the difference between profiles of density and toroidal flow in edge and SOL plasmas.

### Keywords

parallel shear flow instability, dispersion relation, flux of parallel momentum

### Full Text

### References

- [1] N. D'Angelo, Phys. Fluids 8, 1748 (1965).
- [2] P.J. Catto, M.N. Rosenbluth and C.S. Liu, Phys. Fluids 16, 1719 (1973).
- [3] N. Mattor and P.H. Diamond, Phys. Fluids 31, 1180 (1988).
- [4] X. Garbet, C. Fenzi, H. Capes, P. Devynck and G. Antar, Phys. Plasmas 6, 3955 (1999).
- [5] S.-I. Itoh, Phys. Fluids B 4, 796 (1992).
- [6] S. Inagaki et al., accepted to Sci. Rep. (2016).
- [7] Y. Kosuga, S.-I. Itoh and K. Itoh, Plasma Fusion Res. 10, 3401024 (2015).
- [8] B. LaBombard et al., Nucl. Fusion 44, 1047 (2004).
- [9] Y. Kosuga, S.-I. Itoh and K. Itoh, accepted to Contrib. Plasma Phys. (2016).
- [10] P.H. Diamond, S.-I. Itoh and K. Itoh, Modern Plasma Physics Vol.1: Physical Kinetics of Turbulent Plasmas (Cambridge University Press, Cambridge, 2011).
- [11] S.-I. Itoh, K. Itoh and A. Fukuyama, J. Nucl. Mater. 220- 222, 117 (1995).