23P142-B
Generation dynamics of blobs and holes in reduced boundary plasma
turbulence simulation
Jiquan Li李andYasuaki Kishimoto
継全，岸本 泰明

Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan
京都大学大学院 エネルギー科学研究科 〒611-0011 京都府宇治市五ヶ庄 京都大学
The tokamak boundary turbulence is simulated in the vicinity of the last closed flux surface(LCFS) byemploying a reduced 2D model, which couples the drift-wave physics, toroidal curvature-interchange andthe sheath-interchange dynamics as well as the zonal flow effects. The focus of this work is on thegeneration dynamics of the density blobs and holes in the core-edge and the scrape-off-layer(SOL) regions,which depends on the non-adiabaticity of the electron and the sheath loss dissipation. The correlation ofedge particle transport with the solitary coherent potential dipole structures is discussed.

1. Introduction
The boundary plasma is composed by a part ofthe core—adjacent to the last closed flux surface(LCFS) (core-edge) and the scrape-off layer(SOL) in divertored fusion devices like tokamak.
It is essentially important in future burning
plasmas such as the ITER since it is all thetransport ways of plasmas particle, heat, current
and momentum to the first wall of the devices.
Maximizing the fusion power production inburning-plasma devices requires H-mode plasma
conditions, which form a “pedestal” in pressure
profile in the core-edge region. A ubiquitousfeature of the edge transport is the non-diffusive
intermittent behavior, which is characterized by aconvective blob-type dynamics. Recently, thedensity blob/hole structures have been observed
extensively in various devices with different
geometries [1]. A typical one is the emergence ofthe blobs/holes companying with a solitarypotential dipoles or multi-poles. The simulations
based on reduced 2D and 3D fluid modeling havequalitatively reproduced some main features ofthe blob/hole generation and propagation [2].
In this work, the blob/hole generation
dynamics is simulated based on a reduced 2D
edge turbulence modeling. The key parameter
dependence of the blob/hole selection by theturbulent system is investigated. Furthermore, thecorrelation of the blob/hole dynamics with thesolitary coherent potential structures is discussed.
2. Reduced 2D edge turbulence modeling
Conventionally, a 2D drift wave modeling,
namely, the so-called Hasegawa-Wakatani(HW)
turbulence, is employed to simulate the edge
turbulence, in which the parallel electron dynamics
is modeled simply through a parallel correlation

length. Here we employed an extended HW model,
which combines both the core-edge and the SOL
regions with an artificially continuous parametervariation. The nonlinear equations governing theperturbed density and potential are [3]∂ t n + [Φ, n] = ∂ x n0 ∂ y Φ + α dw (Φ − N ),(1)− α sh n + D∇ 2⊥ n + S∂ t ∇ 2⊥ Φ = −[Φ, ∇ 2⊥ Φ ] + α dw (Φ − N ) n,(2)+ α sh Φ − κ∂ y N + µ∇ 4⊥ ΦHere N = ln n , the terms with α dw = α dw0α dw ( x) andα sh = α sh 0α sh ( x) model the electron response in thecore-edge and the SOL regions, respectively. The
toroidal curvature drive is modeled by the term withκ = 2 ρ s R . The profiles α dw (x) and α sh (x) aretaken as the same as in [3]. α dw0 = 2 ρ s mi cs L2//ν ei 0 me ,α sh 0 = 2 ρ s L// with the ion-electron collision rate ν ei 0 .
The density source term S = ν ( x)[n0 ( x) − n] is active
only in the core-edge region and S = 0 in the SOL.
The normalization uses Bohm units as ωci t → t ,x ρ s → x , eΦ T → Φ and n n00 → n with ion
gyro-frequency ω ci , ion sound Larmor radius ρ sand a reference density at the core region n00 .
This reduced model may involve an unstable
drift wave, a curvature-interchange mode, a sheathinterchange mode and possibly a Kelvin-Helmholtz
mode if the flow is unstable for it. From an eigenvalue stability analysis with given initial global
profiles, it is observed that the instability spectrum
are quite wide for different radial mode numbers, as
shown in Fig.1. In addition, it is noticed that thegrowth rates tend to be the same level for different
radial mode numbers. This may have implication
for the formation of coherent blob/hole structures
since all components with the same fluctuationlevels mainly contribute to the solitary structures.

Frequency/Growth rate

0.05
l=00.04

l=1

SOL across the LCFS. The particle transport ischaracterized by non-diffusive, bursty behavior.

l=20.03
0.02

growth rates

0.01
0-0.0100.2 0.4 0.6 0.8

k1

1.2 1.4

yFig.1 Eigen-frequency (solid) and growth rate
(dashed) of linear instabilities for three low orderradial mode number l’s. α dw0 = 0.01 , α sh 0 = 0.001 ,κ = 0.002 , D = µ = 0.01 .

3. Numerical simulation of blob/hole dynamics
Nonlinear simulations are performed to study thegeneration of the blobs and holes with different
collisionality and parallel correlation length. The
former one depends on the plasma temperature anddensity, possibly also on the impurity and neutral
particle effects. The latter one is determined by theq profile at the edge roughly through L// ~ 1 qR . It
is also different for divertor or limiter plasmas. The
simulations are performed for different parameters.
Typically, the blobs/holes are simultaneously
generated around the LCFS region. The blobs
averagely propagate outwards and the holes
inwards. Meanwhile, the zonal flows are excited
mainly around the LCFS. Note an argument on therole of the zonal flow dynamics in the blob/hole
generation mechanism that the blobs/holes may
originate from the broken radially-elongatedturbulence structures like the so-called streamers by
the zonal flows. Two comparative simulations areperformed including or artificially excluding thezonal flows with the same simulation setting. It isobserved that the zonal flows may enhance theblob/hole generation with strong shearing rate along
the LCFS region, but not essential for it. The
blobs/holes are still robust without the zonal flowgeneration.
The preferred structure generation of the blobs orholes are simulated by optimizing the plasma
collisionality or the parallel correlation length,
which are represented by α dw0 and α sh 0 . It isnoticed remarkably that as α sh 0 decreases, which
may be determined by the current (or q) profile, theblob generation is dramatically enhanced and big
blobs are formed in the SOL and propagate
outwards. Meanwhile, the holes dominate the edge
turbulence with decreasing α dw0 , as shown in Fig.2.
Both the holes inwards and the blobs outwards
convert high density plasma from the core-edge to theFig.2 Enhanced density blobs (a) and holes (b) inedge turbulence. The LCFS is located around x=0.
The parameters are set as D = µ = 0.02 , κ = 2 × 10−2 ,(a) α dw0 = 10−2 , α sh 0 = 10−4 ; (b) α dw0 = 10−5 , α sh 0 = 10−3 .

Interestingly, it is observed that the density
blob/hole structures are companied closely withsolitary potential dipoles, even multi-poles. Their 
propagation directions are along the E × B drift.
The generation of the blobs and holes may originate
from the positive feedback of the convective flow
due to the local potential perturbation. As the selforganization of the edge turbulence forms thesolitary coherent potential dipole and/or multi-pole structures, the local E × B drift is enhanced aroundthe mid-plane of the dipoles so that the density
perturbation can grow to form the blobs and holes 
and propagate following the E × B flows. Theturbulent particle flux Γ = υ E × B n~
has been
calculated, showing an outward intermittency.
4. Summary
The generation dynamics of the density blobs andholes are simulated in tokamak boundary plasmas.
The enhanced blobs or holes have been observed indifferent parametric regimes. The causal relation of
the blob/hole formation with the solitary potential
dipole structure has shown the origin of theblob/hole and the intermittent particle transport.
Acknowledgments
This work was supported by the JSPS-CAS
Japan–China Core University Program on Plasmaand Nuclear Fusion and by the JSPS Asian CORE
program on Plasma and Nuclear Fusion.
References[1] D. A. D’Ippolito, et al.: Phys. Plasmas 18(2011)060501.
[2] S. I. Krasheninnikov, et al.: J. Plasma Physics 74(2008) 679.
[3] J. R.Myra, et al.: Phys. Plasmas 15 (2008) 032304.