S6-5
プラズマ乱流が作り出す平行流れ場構造と密度分布構造

Structure of parallel flows and density profiles produced by plasma
turbulence
小菅佑輔 1,2Y. Kosuga1,211

九州大学高等研究院、2 九州大学応用力学研究所

Institute for Advanced Study, Kyushu Univ., 2 Research Institute for Applied Mechanics, Kyushu
Univ.
Understanding the behavior of turbulent plasmas is an important issue. Conventionally, turbulent plasmas

are thought to arise from the primary free energy source, e.g. the pressure gradient. Recent studies
have revealed the importance of the secondary structure, such as zonal flows, which are generated fromthe primary turbulence driven by the scalar gradient. Once excited, these flows become another sourcefor driving fluctuation, and the resultant fluctuation can impact the evolution of the primary structure.
As such, turbulent plasmas are characterized by the multiple free energy source, including the pressure
gradient, velocity shear, etc, and its dynamics shows strong interference among transport channels fordensity, momentum (both in the perpendicular and the parallel direction to the magnetic field). This leads
us to the notion of cross-ferroic turbulence[1], where multiple free energy source drive various turbulent
fluctuations, and its interference causes the chained reaction for the evolution of structures.
In this work, we describe a typical example of such coupled dynamics. As a specific example, we discuss
the coupled dynamics of parallel flows and density gradients. Eigenmodes in the presence of both the density
gradient and parallel velocity gradient are characterized by calculating the dispersion relation based on asimplified fluid model[2,3]. The result is√
2 + 4(1 + k 2 ρ2 )(k 2 c2 − k ρ k c ⟨v ⟩′ )
ω∗e + ω∗ey s z s zz s⊥ sω=.
2 ρ2 )
2(1 + k⊥s(1)Here ω∗e is the frequency of electron drift waves. The term with ⟨vz ⟩′ denotes the eﬀect of parallel flow
shear. The behavior is summarized in Fig.1. Here, the blue curve denotes the instability threshold in theabsence of drift waves. In this case, the mode is purely driven by parallel velocity shear. In the presence ofdrift waves, the parallel flow shear driven mode is stabilized, and its threshold is denoted by the red curve.
Above the red curve, the mode is driven by parallel flow shear, while below the curve, the mode is stableagainst the parallel flow shear, and fluctuations are mainly supported by the density gradient driven driftwaves.
The coupled dynamics is further studies by calculating the quasilinear transport fluxes:∑−ω + ω∗e eϕ̃kΓn=k y ρsn0 cs
kz2 DzTe2+∑kΠxz ∑(−ω + ω∗e )cs kz eϕ̃k=k y ρs2cs
kz2 Dz ωTekk2c2 k 2 − cs kz ρs ky ⟨vz ⟩′ eϕ̃kk y ρs s z
kz2 Dz ωTe+∑kcs kz − ρs ky ⟨vz ⟩′iky ρsω

2,2()eϕ̃kkz2 c2s.
1−i 2kz Dz ωTe(2)(3)

10w/o drift wave
w/ drift wave

|hvz i′ Ln /cs |864
2000.05|kz Ln |0.1

図 1: The instability diagram for PSFI with (red) and without (blue) drift waves for kx ρs = ky ρs = 0.8(k⊥ ρs ∼= 1.13).

Γn is the turbulent particle flux and Πxz is the turbulent flux of the parallel momentum. Dz is the parallel
electron diﬀusivity, which causes phase shift for the electron response. The physical picture becomes clearer
by investigating limiting cases. When drift waves dominate, the particle flux is mainly driven by the diagonalterm Γn ∝ ∇n, while the momentum flux can arise from the oﬀ-diagonal term (the first term, Πxz ∝ ∇n).
This oﬀ-diagonal term can generate the secondary parallel flows. On the other hand, when parallel flow
shear dominates, the momentum flux is mainly driven by the velocity shear, while the oﬀ-diagonal term in
the particle flux can drive inward contribution and competes against the outward, diﬀusive flux. This may
result in the peaked density profile, which can be viewed as a secondary structure generated in turbulence
driven by the primary parallel velocity shear. The coupled dynamics is also formulated by calculating theturbulence production rate, which is related to thermodynamic function. Ongoing work on calculating theproduction self-consistently with the dispersion relation and nonlinear dynamics with spreading eﬀect will
be reported as well.
Stimulating discussion with Prof. S.-I. Itoh, Prof. K. Itoh, Prof. Fusjisawa, Prof. Inagaki, Dr. Kobayashi,
is acknowledged. This work was partly supported by the Grants-in-Aid for Scientific Research of JSPS ofJapan (23244113, 15K17799, 15H02155), Asada Science Foundation, Kyushu University Interdisciplinary
Programs in Education and Projects in Research Development (26705).

[1] S. Inagaki, et al., submitted to Sci. Rep. (2015).
[2] Y. Kosuga, S.-I. Itoh, and K. Itoh, Plasma Fusion Res. 10 3401024 (2015).
[3] Y. Kosuga, S.-I. Itoh, and K. Itoh, submitted to Contrib. Plasma Phys. (2015).