S5-3
Ion Temperature Gradient Driven Turbulence with Strong Precession
Resonance
強い捕捉イオン共鳴を伴うイオン温度勾配乱流	 
Yusuke Kosuga
小菅佑輔
Institute for Advanced Study, Kyushu University
6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
Research Institute for Applied Mechanics, Kyushu University
6-1 Kasuga Koen, Kasuga, Fukuoka, 816-8580, Japan
九州大学高等研究院	  〒812-8581	  福岡市東区箱崎6-10-1
九州大学応用力学研究所	  〒816-8580	  春日市春日公園6-1
As a typical example of plasmas in non-equilibrium and extreme state, turbulent plasmas with strong
resonance are introduced. Two examples are discussed. The first one is current carrying 1d plasmas. The
role of phase space structures in driving nonlinear ion acoustic turbulence is illustrated by rigorous
numerical investigation. The second example is ion temperature gradient driven turbulence with strong
precession resonance. The role of clusters of resonant trapped ions, called trapped ion granulations isemphasized throughout. Impact of trapped ion granulations on transport and frequency broadening is
discussed.

1. Introduction
Turbulent plasma is an example of a system in
non-equilibrium and extreme state. Sinceturbulent plasmas of interest, such as spaceplasmas, fusion plasmas, etc. are often incollisionless regime, the dynamics of turbulent
plasma involves the degree of freedom in phasespace (velocity + real space). This is very uniquefeature of turbulent plasmas. As a consequence,
waves are Landau-damped even in collisionlessplasmas, where wave-particle resonance allows
energy exchange between them. When resonancebecomes strong enough to trap resonant particles
in waves, phase space vortex (BGK modes) canform. Once formed, phase space vortex can drive
turbulent transport by exerting dynamical friction,
as first predicted by Dupree.[1]In this work, we discuss recent developmentsin the research of turbulent plasmas with strongwave-particle resonance. In the first part of thework, we discuss recent numerical study ofcurrent carrying plasmas.[2] The role of phasespace vortex in driving nonlinear current driven
ion acoustic turbulence is emphasized. In thesecond part, we discuss application to fusion
plasmas. As a specific example, we focus on ion
temperature gradient driven turbulence withstrong precession resonance.[3,4] We discuss thatclusters of resonant trapped ions, called trapped
ion granulations, can form and impact turbulence
characteristics and transport.

2. Current Carrying Plasma
Here we consider a current carrying 1d plasma.
The system is linearly unstable, when electron drift
velocity exceeds ion acoustic speed. This is a wellknown current driven ion acoustic (CDIA)
instability and is a typical example of plasma
instability with velocity space origin.
When resonance becomes strong enough, phasespace density holes can form. For example,
formation of ion holes and its impact on subcriticalinstability was studied theoretically and numerically.
More recently, rigorous numerical simulation wasused to illustrate structures in phase space and toidentify the role of phase space structures innonlinear instability. In contrast to previous study,
the recent work unambiguously identifies nonlinear
instability in barely unstable regime.[2]Fig.1. Illustration of phase space vortex in electron
distribution function. Abscissa space, ordinate
velocity.[2]Fig. 2. A cartoon of trapped ion granulations andtransport via dynamical friction.[4]3. Magnetically confined plasma	  Strongly resonant turbulence can arise in fusion
plasmas as well. In tokamaks, magnetically trapped
particles are characterized by 1D precession motion.
Thus precession resonance between trapped
particles and modes has 1D structure and can havestrong resonance. As a result, in trapped ion
turbulence, formation of clusters of resonating
trapped ions (trapped ion granulations) is quite
likely.[3] Once formed, trapped ion granulations
release free energy, by exerting dynamical friction
on electrons. Dissipative electrons are required totrigger free energy release from this channel.	  Another macroscopic consequence due to theformation of trapped ion granulations is broadened
spectrum.[4] Of course in turbulent plasmas
frequency spectrum is broadened. However, inaddition to conventional broadening due tomode-mode coupling, granulations can broadens
the frequency spectrum via Cerenkov emission.
While trapped ion granulations move throughplasmas, they emit waves via Cerenkov emission.
Since the Cerenkov emitted waves do not have tosatisfy dispersion relation, spectrum is broadened.
The line width is calculated in [4] and shows
sensitivity to electron dissipation. This is sincetrapped ion granulations release free energy via
dynamical friction.	  As on-going work, we are working on numerical
identification of trapped ion granulations. In thisdirection, we are trying to calculate microscopic
property of trapped ion granulations, i.e. strong
correlation at small scales. 2 point phase spacedensity correlation of trapped ion granulations show
logarithmic divergence in the limit of 1→2. For
typical parameters, required resolution is very
severe. For example, required resolution to resolve
the distance of one resonance to another at typicalwave number is ΔE / Ti ~ 0.04 for q = 2 andρ* = 1 / 200 . It is very demanding to resolve thisFig. 3. Schematics for steady state balance.[4]scale while resolving spatial turbulence scales. For
this reason, reduced model would be more
appropriate for this study, than complete fullgyrokinetic models.
4. Summary and discussion
In summary, we discussed strongly resonant
turbulence as a typical example of non-equilibrium
and far-extreme state. In 1d current carrying
plasmas, phase space density holes due toelectrostatic trapping can drive nonlinear instability.
In toroidal plasmas, trapped ions can resonate withwaves and can form clusters of resonating trapped
ions, granulations. Once formed, trapped ion
granulations drive transport by exerting dynmiacal
friction on electrons and broadens frequency
spectrum by Cerenkov emitting attached wake.
Numerical investigation is on-going to identify
trapped ion granulations.
Acknowledgments
Stimulating discussion with and encouragementfrom Prof. S.-I. Itoh, Prof. P.H. Diamond, Prof. K.
Itoh, Dr. M. Lesur, Prof. T.S. Hahm, Dr. O.D.
Gurcan, Dr. G. Dif-Pradalier, Prof. K. Ida, Prof. A.
Fujisawa, Prof. S. Inagaki are acknowledged. This
work was supported by Grants-in-Aid for Scientific
Research of JSPF of Japan (23244113 and25887041), Asada Science Foundation, Kyushu
University Interdisciplinary Programs in Education
and Projects in Research Development.
References[1] T.H. Dupree: Phys. Rev. Lett. 25 789 (1970)[2] M. Lesur, P.H. Diamond, and Y. Kosuga: Plasma
Phys. Control. Fusion 56 075005 (2014).
[3] H. Biglari, P.H. Diamond and P.W. Terry: Phys.
Fluids 31 2644 (1988)[4] Y. Kosuga, et al.: Phys. Plasmas 21 102303 (2014)