Integration of Global Stability into the Simulation of a
Burning Plasma Experiment
S. C. Jardin
Princeton Plasma Physics Laboratory
Princeton, NJ 08540
Email: Jardin@pppl.gov
Burning-plasma magnetic fusion experiments necessarily operate with parameters thatlead to a wide separation of time scales. In the foreseeable future, the only possibility
for an “integrated simulation” of a burning plasma experiment is to use a number ofdifferent codes that are capable of exchanging information with one another, and thatsolve successively different sets of reduced plasma equations. The “transport timescale”
code solves a set of equations obtained by averaging over all Alfven-wave and faster
activity. It evolves a sequence of 2D equilibrium though time by alternatively integrating
the surface averaged transport equations and solving an elliptic equation that enforces 2D
force balance. These equilibrium need to be monitored against linear stability criteria,
and as one is approached, the same equilibrium needs to be passed to a non-linear MHD
code to calculate the nonlinear evolution of that instability, and it’s effect on modifyingthat equilibrium.
The need for a nonlinear global 3D MHD calculation arises from many separate but
related phenomena. These are: sawtooth oscillations, neoclassical tearing modes (NTMs),disruptions caused by short wavelength modes interacting with long wavelength modes,
pellet injection, TAE modes, edge localized modes (ELMs) and the need to calculate
vessel forces and heat loads during a major disruption and vertical displacement event.
There may also be a need to calculate the evolution of resistive wall modes (RWM) in
advanced operating scenarios. These modes are well described by extended MHD
equations utilizing either a two-fluid or a hybrid particle/fluid closure. Nonlinear 3D
MHD codes addressing these issues need to deal with the computational problems of
multiple timescales, multiple space scales, extreme anisotropy, and the modeling ofessential kinetic effects.
The Center for Extended MHD Modeling (CEMM) is a SciDAC project that has joined
together the efforts and capabilities of the M3D and NIMROD codes and codedevelopment teams, and has developed a new adaptive mesh refinement MHD code
(AMRMHD). We have made much progress in addressing many of these numericaldifficulties by using implicit methods, adaptive meshing, unstructured meshes, high-orderfinite elements, and hybrid particle/fluid models. One current focus is to perform
realistic modeling of a small tokamak, CDX-U, to demonstrate benchmarking of an
integrated model against real experimental data.
This work was supported by U.S. Department of Energy under contract number DEAC02-76CH03073. Calculations performed here have been performed at the National
Energy Research Supercomputer Center (NERSC). Web site: w3.pppl.gov/CEMM.
1

Kinetic MHD Simulation in Tokamaks
H. Naitou, J.-N. Leboeuf(1), H. Nagahara, T. Kobayashi(2), M. Yagi(3),T. Matsumoto(4), S. Tokuda(4)Electrical and Electronic Engineering, Yamaguchi University,
Ube 755-8611, Japan1)

Physics and Astronomy, University of California at Los Angeles,
CA 90095-1547, USA

2)Media and Information Technology Center, Yamaguchi University,
Ube 755-8611, Japan
3)Research Institute for Applied Mechanics, Kyushu University,
Kasuga, Kasuga 816-8580, Japan

4)

Naka Fusion Research Establishment, Japan Atomic Energy Research Institute,
Ibaraki 816-8580, Japan

Kinetic modifications of MHD modes introduce new paradigms in MHD theory.
Previous studies of the (collisionless) m=1/n=1 kinetic internal kink mode
withelectron diamagnetic effects revealed that there is a weakly unstable mode evenin the region in which theory predicts complete stabilization [1,2]. The mode pattern
has m=1 sheared poloidal flow which generates vortices due to the Kelvin-Helmholz
instability [3]. These studies have been carried out in cylindrical geometry using the
gyro-reduced-MHD(GRM) code. The relevance to toroidal geometry is quite criticalto the theory of the sawtooth crash because the mode-coupling due to toroidal effects
may dominate the nonlinear development of the instability. A modified version of the
FAR code including kinetic effects is being developed to study the effect of vortex
generation on the internal kink mode. In the cylindrical limit, the linear mode pattern
and the complex frequency obtained with the modified FAR code coincide with theresults obtained with the GRM code. Nonlinear calculations in toroidal geometry
has been started and results will be reported as available.
[1] H. Naitou, T. Kobayashi, T. Kuramoto, S. Tokuda, T. Matsumoto, J. Plasma Fusion
Res. SERIES 2 (1999) 259.
[2] H. Naitou, T. Kuramoto, T. Kobayashi, M. Yagi, S. Tokuda, T. Matsumoto, J.
Plasma Fusion Res. 76 (2000) 778.
[3] H. Naitou, T. Kobayashi, M. Yagi, T. Matsumoto, S. Tokuda, Y. Kishimoto, Book of
Abstracts, 19th IAEA Fusion Energy Conference (Lyon, France, 14-19 October2002) p.138.

2

Recent progress in simulations of kinetic-MHD instabilities
Yasushi Todo
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japane-mail: todo@nifs.ac.jp
Recent progress in simulations of kinetic-MHD instabilities, toroidicity-induced
Alfvén eigenmode (TAE) bursts, fast frequency sweeping (fast FS) mode in the JT-60U
experiments, and precessional fishbone instability, is reported.
Recurrent bursts of TAE were studied using a self-consistent simulation model [1].
Bursts of beam ion losses observed in the neutral beam injection experiment at the Tokamak
Fusion Test Reactor are reproduced using experimental parameters. Surface of section plots
demonstrate that both the resonance overlap of different eigenmodes and the dissapearance of
KAM surfaces in phase space due to overlap of higher-order islands created by a single
eigenmode lead to particle loss. Only co-injected beam ions build up to a significant stored
energy even though their distribution is flattened in the plasma center. They are not directly
lost as their orbits extend beyond the outer plasma edge when the core plasma leans on a highfield side limiter.
Particle-magnetohydrodynamic hybrid simulations of the fast FS mode in the JT-60U
experiments were carried out [2]. For a JT-60U experiment a new kind of energetic particle
mode (EPM) was found near the plasma center at frequency close to the central frequency of
the fast FS mode. The new EPM is a nonlocal mode destabilized by passing energetic ions inmonotonic magnetic shear plasma. Two types of nonlinear evolution take place depending on
the initial energetic ion pressure. When a classical distribution is taken for the initial condition,
frequency shifts only downward after saturation and large redistribution of the energetic ionsoccurs. On the other hand, when reduced distributions are considered for the initial condition,
frequency shifts both upward and downward at a rate of frequency sweeping close to that of
the fast FS mode.
For the precessional fishbone instability, linear and nonlinear evolution isinvestigated for the initial conditions with parameters similar to those of the PDX experiments[3]. It is demonstrated that the spatial profile of the fishbone mode is different from the kinkmode, and frequency shifts downward at saturation of the fishbone instability.
[1] Y. Todo, H. L. Berk, and B. N. Breizman, Phys. Plasmas 10, 2888 (2003).
[2] Y. Todo et al., J. Plasma Fusion Res. 79, 1107 (2003).
[3] Y. Shiozaki and Y. Todo, to appear in Proceedings of the 13th International Toki
Conference, JPFR SERIES 6.

3

Energetic Particles and Burning Plasma Physics

J. W. Van Dam
Institute for Fusion Studies,
University of Texas at Austin

Energetic particle physics can have an effect on stability, transport, heating andcurrent drive, edge physics, etc. Therefore it is important to develop integrated
simulation, along with theory-based modeling, for energetic particle physics in aburning plasma. This talk will describe several
capabilities, (2)Alfven cascades,(3)

convective/diffusive transport.

4

related issues: (1) predictive

nonlinear fishbone

modes,

and(4)

Nonlinear Tearing Modes in Finite-Beta Tokamaks
with Noncircular-Cross Sections
Satoshi TSURIMAKI, Satoshi HAMAGUCHI, Masahiro WAKATANI*
Graduate School of Energy Science,
Kyoto University, Uji, Kyoto 611-0011, Japan.
The numerical calculations have been performed for nonlinear interactions of tearing modes infinite-beta tokamaks and we have investigated effects of finite beta and triangularity of the plasma
poloidal cross section on them. In tokamaks it is observed that these modes are destabilized in a predisruption phase and believed to form ergodic magnetic fields that often lead to major disruptions.
Typically finite-beta effects lower the growth rate of tearing modes. However, when the beta value
increases, the shift of magnetic axis can decrease the distance between magnetic islands, which canenhance their nonlinear interactions and result in ergodic magnetic fields. In the present work, wehave evaluated these effects by varying beta values and the shape of the plasma poloidal crosssection, using a three-dimensional code to solve reduced MHD equations in toroidal geometry. The
code is based on the finite-element method (FEM) with unstructured triangular elements in thepoloidal plane and the fourier decomposition in the toroidal direction.
*deceased

0.043

0.035

n=1

0.03

n=2

0.042

growth rate

linear growth rate

0.044

0.041
0.04

0.02
0.015
0.01

0.039
0.038
0

0.025

0.005

0.2

0.4

0.6

0

0.8

0.0

1.0

1.5

2.0

beta̲axis (%)

triangularity

Fig.1
The linear growth rates for the n=1 and n=2

0.5

Fig.2
The linear
growth rate for the n=1 mode
axisβ

modes vs. triangularity.

vs.

5

.

2.5

3.0

Integrated modeling of wave-plasma interactions in fusion systems

D. B. Batchelor
Oak Ridge National Laboratories

There is great potential for electromagnetic wave techniques to provide control offusion plasmas by means of localized heating, current drive, flow drive and energetic
particle production. With support from the Scientific Discovery Through Advanced
Computation (SciDAC) program, we have established a multi-institutional
partnership between plasma physicists and computational scientists, the overarching
goal

being

to

obtain quantitatively

accuratepredictive

understandingofelectromagnetic wave processes important for heating, current drive, stability andtransport applications in fusion-relevant plasmas. Activities during the first two
years of the project have focused on massive parallelization and acceleration ofcomputer-intensive full-wave RF field solver codes, extension of all-orders methods
to two- and three-dimensional plasmas, increasing the physics detail contained in the
RF conductivity operator, inclusion of non-Maxwellian distributions, linking toFokker-Planck solvers, benchmarking and code comparison, and application to wave
propagation problems in Alcator C-Mod, NSTX and LHD.

6

Full-Wave Maxwell Simulations for ECRH
H. Hojo, T. Saito and Y. Tatematsu
Plasma Research Center, University of Tsukuba, Tsukuba 305-8577
E-mail : hojo@prc.tsukuba.ac.jp

The standard method studying electron cyclotron resonance heating (ECRH) in magneticallyconfined plasmas is ray-tracing method based on the geometrical optics.

This method describe wave

absorption due to wave-particle resonances, however, cannot take into account wave diffraction, wave
tunneling across the wave-evanescent region between cutoff and resonance, and mode conversion.
We here study full-wave Maxwell simulations for fundamental ECRH of magnetically confinedplasmas.

We solve numerically Maxwell equations for electromagnetic wave fields (E, B) and theequation of motion for induced plasma current J with the use of a finite difference and time domain(FDTD) method.

These basic equations can describe O and X (or, R and L) modes being correct under

the approximation of infinite ion mass.

We emphasize that our numerical scheme can take into

account wave diffraction, wave tunneling across the wave-evanescent region between cutoff andresonance, and also mode conversion, since it solves full Maxwell equations directly.
absorption mechanism in the present scheme can be taken into account as follows:
damping of electromagnetic waves can be introduced by adding

ν−J

The wave

The collisionalterm to the equation of motion for

induced plasma current J, on the other hand, the wave dissipations due to wave-particle resonances suchas cyclotron resonance can be introduced by adding
artificial conductivity tensor

σt

σ−⋅tE

term to the Ampere’s equation.

This

is determined so that our basic equations can reproduce the local

dispersion relation with wave-particle resonance terms in the limit of0k⊥→wavenumber perpendicular to a magnetic field, where the parallel wavenumber, where||kk⊥appeared inis theσtisapproximately determined from the local dispersion relation in the numerical calculations.
Unfortunately, the present numerical scheme cannot treat harmonic resonances such as second harmonic
ECRH, as this basically depends on the fluid theory.
We perform the full-wave Maxwell simulations for fundamental ECRH in a simple magnetic beachconfiguration, and show the numerical results on the wave absorption by ECRH and wave tunnelingacross the wave-evanescent region between cutoff and resonance.

7

ICRF heating Simulation in 3D Magnetic Field Configuration
S. Murakami, T. Seki1), M. Osakabe1), M. Sasao2), M. Isobe1), T. Ozaki1), P. Goncharov1),
J.F. Lyon3), T. Saida2), T. Mutoh1), R. Kumazawa1), K. Saito, T. Watari1), H. Yamada,
S.V. Kasilov4), A. Fukuyama and LHD Experimental Group
Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, JAPAN1)
National Institute for Fusion Science, Oroshi, Toki, Gifu 509-5292, JAPAN
2)
Graduate School of Engineering, Tohoku University, Sendai 980-8579, JAPAN3)
Oak Ridge National Laboratory, Oak Ridge, TN 37831-8072, USA
4)
Institute of Plasma Physics, National Science Center, KIPT, Kharkov, UKRAINE

Radial transport of energetic particles due to the ripple trapped particle is one of important
issues in the development of a reactor based on the helical system. The behaviors of trapped
particles are complicated and have relatively large orbit size in the radial direction in helicalsystems. These radial motions of trapped particle would enhance the radial transport ofenergetic ions. Thus, a detail study of energetic ion confinement is necessary for the helicalsystem.
In LHD, the experiment for energetic ion confinement has been successfully done. ICRF
heating experiments have shown significant performance of this heating method and up to
400keV of energetic tail ions have been observed by fast neutral analysis. Also, confinedenergetic beam ions are observed in the NBI heating experiment. These measured results
indicate a good property of energetic ion confinement in LHD. However, the measured
information is obtained as an integrated value along a line of sight and we need a reliable
theoretical model for reproducing the energetic ion distribution to discuss the confinement ofenergetic ions.
In this paper we study the complex behavior and radial transport of energetic ions during
ICRF heating using a global transport simulation code (GNET)[1,2] in LHD. This code solves
a linearized drift kinetic equation for energetic ions including complex behavior of trapped
particles in 5-D phase space. We make clear the characteristics of energetic ions distribution
in the phase space and show the confinement property of LHD configurations by comparing
the simulation and experimentally observed results.

[1] S. Murakami, et al, Nuclear Fusion 40 (2000) 693.
[2] S. Murakami, et al, in Proc. 28th EPS Conf. on Controlled Fusion and Plasma Phys. Madeira,
ECA-25A (2001) 1497-1500.

8Modeling of Neutral Beam Ion Absorption of High Harmonic
ICRF Waves in the DIII-D Tokamak
V.S. Chan*
The absorption of ion cyclotron radio frequency (ICRF) wave by
neutral beam injected ion species at high ion cyclotron harmonics(ω=nΩ, n≥2) has been observed experimentally in the DIII-D
tokamak during the 1999 experimental campaign. Anomalously
peaked pressure profile was reported in the central region of plasma
with a significant enhancement of the measured neutron rate when rf
pulses were applied to neutral beam (NB) heated discharges. Energy
spectrum from neutral particles analyzer showed a strong
enhancement of the tail energy above the NB injected energy. To
understand and quantify this phenomenon of energetic beam ion
species-wave interaction, a Monte-Carlo rf orbit code, ORBIT-RF,
has been upgraded to treat steady-state NB injection and ICRF
absorption at higher harmonics. The first ORBIT-RF results for theinteraction study of 80 keV D beam ion and 60 MHz ICRF wave at
4th harmonic resonance surface show that several experimental
observations are reproduced in the simulations within reasonableagreement using an estimated magnitude of |E+| based on a simple
model: (1) the extended tail energies of beam ions above the injectedbeam energy are found in the central region of plasma, and (2) about
20%-30% enhanced D-D reaction rate is also calculated due to theinteraction of ICRF and beam ions. Additional DIII-D experimental
results on the damping of wave on H(He3) beam ion at 2nd(3rd)harmonic resonance are being simulated and will be reported at themeeting. For quantitative comparisons and predictions, a moreaccurate wave model will be implemented to estimate the magnitude
of |E+|.
This work was supported by the U.S. Department of Energy underGrant DE-FG03-95ER54309 and DE-AC03-99ER54463.
*

In collaboration with M. Choi, J. Candy, C.C. Petty, R.I. Pinsker(General Atomics), S.C. Chiu (Sunrise Inc.), W.W. Heidbrink(UC-Irvine).

9

Recent Gyrokinetic Simulations with GYRO: Bohm
Transport in DIII-D, the Local Limit of Global
Simulations, and Transport Across a Minimum-q
Surface∗
J. Candy
General Atomics, P.O. Box 85608
San Diego, California 92186-5608 USA
Abstract
In this presentation we summarize results from three major transport studies carriedout with the global Eulerian gyrokinetic code, GYRO.1 First, and most importantly, we
discuss comprehensive simulations2 which match, within experimental error bounds, theturbulent transport levels observed in DIII-D L-mode discharges 101381 and 101391. The
experimentally-observed Bohm-like scaling of ion transport in these discharges was recovered, and the sensitive dependence of both electron and ion transport on ion temperature
gradient was also explored. These were full-physics simulations which included trapped andpassing electrons with pitch angle collisions, finite-β fluctuations, real DIII-D flux-surface
shape, linear and nonlinear E × B rotation, parallel flow shear, and radial variation of all
equilibrium quantities.
Next, we revisit the issue of gyroBohm scaling (and the breaking thereof) in the context
of a certain adiabatic-electron test case favoured by the GTC code.3 For this case, wehave shown that transport levels from local and global GYRO simulations are perfectly
matched in the limit of small ρ∗ = ρi /a. We also show that this limiting value is identicalto the local value obtained by Dimits.4 The confluence of local and global results, which weobserve repeatedly and robustly, has been previously noted5 in a more general context. For
this particular case, we show that the transition point in ρ∗ , where gyroBohm gives way toworse-than-gyroBohm scaling, is strongly dependent on the temperature-gradient profile. In
particular, use of the original “humped” GTC profile leads to the requirement ρ∗ . 1/375
for gyroBohm scaling, whereas the use of a more physical temperature-gradient profile inthe same scenario gives rise to gyroBohm scaling and recovers the local limit at the muchlarger value ρ∗ . 1/150.
Finally, we examine a conjecture regarding ion transport barrier formation in the vicinityof a minimum-q surface.6 The validity of the conjecture relies, ostensibly, on the absence of
ITG modes in the minimum-q region. Indeed, fluid transport simulations7 have shown thatwhen so-called nonresonant modes are ignored, a minimum-q region can give rise to a barrier.
However, a series of linear and nonlinear, as well as local and global, GYRO simulations
show no evidence of mode suppression or of transport reduction in the minimum-q region.
Instead, we find that transport is smoothly increasing across a minimum-q surface, and that
this region is populated by nonresonant ITG modes characteristic of the low-shear regime.
We also observe that as ρ∗ → 0, transport computed via a global simulation agrees withthat from local simulations, even at the point where s = 0.
*Work supported by the U.S. Department of Energy under Grant Nos. DE-FG03-95ER54309
and the SciDAC Plasma Microturbulence Project.
1

J. Candy and R.E. Waltz, J. Comput. Phys. 186 (2003) 545.
J. Candy and R.E. Waltz, Phys. Rev. Lett. 91 (2003) 045001.
3
Z. Lin, et al., Phys. Rev. Lett. 88 (2002) 195004.
4
A.M. Dimits, et al., Phys. Plasmas 7 (2000) 969.
5
R.E. Waltz, J. Candy and M.N. Rosenbluth, Phys. Plasmas 9 (2002) 1938
6
Y. Kishimoto, et al., Nucl. Fusion 40 (2000) 667
7
X. Garbet, et al., Phys. Plasmas 8 (2001) 2793

2

10

Local and non-local Gyro-Fluid Simulation of ITG and ETG
turbulence and the statistical properties
Y. KISHIMOTO1)
J. Q. LI 1,2),

N. MIYATO 1) , and T. MATSUMOTO Taro 1) , Y. IDOMURA 1)

1) Naka Fusion Research Establishment,JAERI, Ibaraki, Japan
2) Southwestern Institute of Physics, Chengdu, P. R. Chinae-mai: kishimoy@fusion.naka.jaeri.go.jp
The turbulent-zonal flow system due to micro-scale electron and meso-scale ion
temperature gradient mode turbulence is studied based on our gyro-fluid model in order tounderstand various prominent structure formations in magnetically confinement plasma.
Here, we investigate the possible mechanism regulating the zonal flow and resultant turbulent
dynamics from various view points, i.e. secondary and higher order instabilities and saturation
mechanism, control of zonal flow instability including enhancement and diminishment,
electromagnetic effect, toroidal coupling effect due to Stringer-Winsor term and GAM, nonlocal and/or global effect, etc.

Specifically, it is found that the electromagnetic effect plays

an important role for the zonal flow and resultant transport dynamics in ETG turbulence.
The coupling between zonal mode and poloidal pressure anisotropy through Stringer-Winsor
term is found to lead to a new energy transfer channel that regulates the zonal flow level.
We also study the turbulent dynamics by introducing statistical approaches such as fractal
dimension and probability distribution function. A significant dimensionality lowing andcoherent transport characteristics are obtained for the transport dominated by zonal flows.
Reference
J. Q. Li, et al. ., The 13th International Toki Conference, December 9-12, 2003.
J.Q. Li and Y. Kishimoto, submitted to PoP (2003).
M. Miyato, et al. The 13th International Toki Conference, December 9-12, 2003.
T. Matumoto, et al., The 13th International Toki Conference, December 9-12, 2003.
Y. Idomura, et al., The 13th International Toki Conference, December 9-12, 2003.

11

Transport Model with Global Flow
M. Yagi, M. Azumi1), S.-I. Itoh, K. Itoh2) and A. Fukuyama3)
Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan
1)Japan Atomic Energy Research Institute, Naka, 311-0193 Japan2)National Institute for Fusion Science, Toki 509-5292, Japan3)Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan
Anomalous transport in high temperature plasmas is an important issue for nuclear
fusion research. This phenomenon is complicated due to the synergetic effect of thefluctuating density or temperature and the flows. To understand the transport in a systemwith flow, the conventional approaches are not enough and the more consistent
approach is necessary. In this study, a transport model with flow is proposed, taking thefluctuating electrostatic field into account. This system consists of three components:
transport, flow and turbulence. The flux-surface-averaged density and pressure evolve
according to the conventional 1D transport equation with anomalous particle and heat
fluxes. Then the neoclassical parallel flows are determined by the parallel momentum
and the heat balance equations with turbulence source[1,2]. These neoclassical flows
affect the saturation level of turbulence, hence change the anomalous particle and heat
fluxes. The radial electric field which gives rise to zonal flow is determined byturbulence. As the first step, we investigate the linear stability of ideal and/or resistive
ballooning mode with given neoclassical (global) flows solving the 2D eigenvalue
problem and estimate the quasi-linear flux. The next step is to develop a global 3D
turbulence code with equilibrium flows and evaluate the radial electric field and theanomalous fluxes. Simultaneously, impacts of spatially long-range fluctuations are also
discussed[3]. The final goal is to couple the 3D code with the transport equations.
[1] S. P. Hirshman, D. J. Sigmar, Nucl. Fusion 21 (1981) 1079.
[2] M. Kikuchi and M. Azumi, Plasma Phys. Control. Fusion 37 (1995) 1215.
[3] M. Yagi, J. Plas. Fus. Res. 79 No.5 (2003) in press (in Japanese).

12Intermittent oscillations generated by ITG-driven turbulence
Kazuo Takeda, Sadruddin Benkadda*, Satoshi Hamaguchi, and Masahiro Wakatani**
Graduate School of Energy Science, Kyoto University*CNRS URA 773, Université de Provence, France
In order to understand the mechanisms of anomalous transport due to micro-instabilities
and transport barrier formation related to generation of sheared plasma flows, we havestudied transport regimes of ion-temperature gradient (ITG)-driven turbulence using a low
degree-of-freedom model composed of 18 ODEs [1]. When the system is close to thethreshold of ITG instability, an L-H-like transition and periodic oscillations are observed in
the kinetic energy and convective flux fluctuations. As the ion temperature gradient ‘Ki’ isincreased further, the system bifurcates to turbulent regimes. In the strongly turbulent
regime, intermittent bursts (so-called avalanches) are observed, which contrasts with thereport that no such intermittency was observed in simulations of the previously proposed
low degree-of-freedom model based on 11 ODEs [2]. This intermittency is caused by thecompetition of the following 3 factors; (1) generation of sheared flows due to nonlinear
coupling among higher harmonics and suppression of ITG turbulence by the sheared flows,(2) gradual reduction of the sheared flows due to viscosity, and (3) rapid re-growth of ITG
modes due to the reduction of stabilizing effects by the sheared flows. We also obtained ascaling law between time average of the Nusselt number and the ion pressure gradient Ki.
The obtained scaling law shows that, in the case of large Ki where sheared flows become
dominant and intermittency occurs, the Nusselt number is significantly lower than its valuethat we would expect if it were not for intermittency. We have demonstrated that essential
nonlinear behaviour of the ITG turbulence can be at least qualitatively accounted for by
nonlinear interaction of several low order harmonics.
**deceased
References:[1] K. Takeda, S. Hamaguchi and M. Wakatani, Plasma Phys. Control. Fusion 44, A487
(2002)[2] G. Hu and W. Horton, Phys. Plasmas 4, 3262 (1997)[3] W. Horton, D. –I. Choi and W. Tang, Phys. Fluids 24, 1077 (1981)

13

JJIIFFTT W
Woorrkk sshhoopp –– kkyyooddaaii kkaaiikkaann,, KKyyoottoo,, 1155--1177,, DDeecceem
mbbeerr 22000033

Linear Stability of Electrostatic Drift Waves in Helical plasmas
Osamu YAMAGISHI, Noriyoshi NAKAJIMA, Hideo SUGAMA
National Institute for Fusion Science, Oroshi, Toki, 509-5292, JAPANYuji NAKAMURA
Graduate School of Energy Science, Kyoto University, Uji, Kyoto, 611-0011, JAPANThe linear gyrokinetic mode equation is numerically solved to investigate thestability properties of the electrostatic drift waves in helical plasmas. The mode
equation is rather exact except for the ballooning representation, and is 1D in the spaceand 2D in the velocity space, as is FULL code [1]. The circulating and trapped particles
are correctly treated, and in the electrostatic regime, ion temperature gradient mode
(ITG) and trapped electron mode (TEM) are expected to be unstable withk_perp*rho_i<~1. The electron temperature gradient mode (ETG) can also become
unstable with k_perp*rho_e<~1.0. As a model of helical plasmas, LHD [2] isconsidered, whose MHD equilibria are obtained by VMEC code [3].
The non-axisymmetric equilibrium properties of helical plasmas are expected toaffect the stability, through the curvature of field line, which is mainly determined by
the magnetic field strength B, and the perpendicular wave number k_perp, which isstrongly depending on the geometry (R, Z). These local effects on the stability can beinvestigated by the local parameter dependence of the growth rate in the ballooning
formalism, and in fact, the local growth rate was found to be sensitive to the field line
label (alpha) as well as the theta_k in the helical systems in the MHD case [4].
However it is found that in the drift wave case, their dependence is very weak. The local
parameter dependence is investigated and the destabilizing mechanism is discussed.

[1] G.Rewoldt et al., Phys.Fluids 25, 480 (1982)[2] A.Iiyoshi et al., Nucl. Fusion 39, 1245 (1999)[3] S.P.Hirshman, Phys. Fluids 26, 3553 (1983)[4] N.Nakajima, Phys. Plasmas 3, 4556 (1996): O.Yamagishi et. al., Phys Plasmas 8, 2750 (2001)

14

Control of Turbulent Transport andDynamics of Transport Barriersin Edge Tokamak Plasmas

Sadruddin Benkadda
Universite de Provence Marseilles. Frances

Control of turbulent transport in edge tokamak plasmas is an important issue forthe realization of fusion reactors. The most promising operational regime of future
reactors is characterized by the existence of a transport barrier at the plasma edge.
This barrier is not stable but relaxes quasiperiodically. It is thus important toinvestigate the physical mechanisms underlying the dynamics of such barriers inorder to use them as control tools of the turbulent transport in fusion machines.
We will review in this paper different aspects of such dynamics and show theirimplications on turbulent transport.

15

On dust dynamics in tokamak edge plasmas
S. I. Krasheninnikov1, Y. Tomita2, R. D. Smirnov3, and R. K. Janev3
1

University of California at San Diego, La Jolla, CA 92093, USA
National Institute for Fusion Science, Toki, Gifu 509-5292, Japan
3
The Graduate University for Advanced Studies, Toki, Gifu 509-5292, Japan2

It has been suggested long time ago [1] that dust particles might be a source of plasma impurities in the earlystages of a tokamak discharge. Later on the presence of significant amounts of dust has been observed in thechambers of fusion devices (see for example the review paper [2], and the references therein). The dust particle
impact on the performance of current fusion devices has still not been adequately understood [3, 4]. The
existence of dust particles in next -step fusion devices, however, may potentially pose a significant safety threat
due to the accumulation of hardly containable toxic and radioactive materials retaining tritium [2].
In this paper we consider some aspects of the dust dynamics in tokamak plasmas, and show thattransport of dust particles can be an important mechanism of core plasma contamination with impurities. We
assume that dust density in a tokamak plasma is rather small so that our consideration is based on a single dust
particle motion. Therefore, we ignore the collective phenomena associated with the dust [5].
Similarly as in the studies of dust behavior on the devices with weakly ionized plasmas (see [6], andreferences therein), a dust particle in a tokamak edge plasma can be confined in an effective potential wellformed in the sheath region by the perpendicular components of plasma friction and electrostatic forces.
However, unlike those studies, dust particles in a tokamak edge plasma are subject of acceleration by
unbalanced large parallel components of the plasma friction force, which appear due to: a) the plasma flow
along the shallow magnetic field lines and b) diamagnetic and E×B flows within the magnetized sheath.
Therefore, dust particles in tokamak divertor region can be quickly (for ~1 ms) accelerated to the speed ~3×103
cm/s, which can explain some of the puzzles in Ref. [4].
In the present study we have found that the motion of a dust particle along the wall surface, having
micro-inhomogeneities, is subject to resonance interactions with particle oscillations in the potential well. As aresult, the oscillation amplitude can grow drastically and dust particle can leave the sheath region and fly
outside it and, being pushed back by the plasma flow to the wall, bouncing time to time off the surface andfurther gaining speed by plasma flow acceleration. Finally, the amplitude of particle excursions becomes toolarge to be pushed back so that dust particle moves to another location at the wall, or flies toward the coreplasma.
Assessment of dust impact on core plasma contamination by impurities shows that: It is unlikely that
dust formation on the main chamber wall due to first wall recycling processes can strongly contribute to corecontamination. It is, however, quite likely that dust formation in the divertor region, with further dust transport
into main chamber, can play significant role in core contamination.
[1] T. Ohkawa, Kaku Yugo Kenkyu 37 (1977) 117[2] G. Federici, C. H. Skinner, J. N. Brooks, et al., Nucl. Fusion 41 (2001) 1967
[3] D. H. J. Godall, J. Nucl. Materials 111-112 (1982) 11[4] K. Narihara, K. Toi, Y. Hamada, et al., Nucl. Fusion 37 (1997) 1177
[5] P. K. Shukla, Phys. Plasma 8 (2001) 1791
[6] V. N. Tsytovich, Physics-Uspekhi 40 (1997) 53

16

Edge Plasma Modeling Using PARASOL Code
T. Takizuka
Japan Atomic Energy Research Institute, Naka Fusion Research Establishment, Naka, Ibaraki 311-0193, Japan

In magnetic confinement systems, not only open systems like a mirror but also
closed systems like a tokamak, there exist the regions of open-field plasmas. An open-fieldplasma surrounding a closed-field plasma is called a scrape-off-layer (SOL) plasma or adivertor plasma. Since the open-field plasma attaches walls of a device directly, plasma
particles and heat escape to the walls mainly along magnetic field lines. Utilizing this nature,
we expect divertor functions for the heat removal, ash exhaust, and impurity shielding infusion reactors, such as ITER. Analyses of experiments on the above functions in present
devices and predictions of their performances in future reactors have been carried out by
using comprehensive simulation codes with the fluid model. In the fluid model for
SOL/divertor plasmas, however, various physics models are introduced, i.e., boundary
conditions at the plasma-wall boundary, heat conductivity, viscosity and so on. Kinetic
approach is required to examine the validity of such physics models. One of the mostpowerful kinetic models is the particle simulation. The particle simulation, in which particle
motions and the electrostatic potential are computed self-consistently, can describe accurately
the sheath formation.
We have been developing a particle simulation code PARASOL (PARticle Advanced
simulation for SOL and divertor plasmas), and studying the edge modeling. This code treatsvarious kind of situations; one-dimensional (1D) steady state, 1D dynamic state (such as ELM
behavior), slab 2D configuration, and 2D configuration with separatrix like a tokamak
divertor configuration. The magnetic field is given. The electrostatic field inside a system iscalculated self-consistently with a usual PIC method. Coulomb collisions play very importantrole in open-field plasmas. For instance, the collisional diffusion in the velocity space is themain mechanism to supply high-energy electrons. These electrons can escape to the divertor
plate, while low energy electrons are trapped in a SOL plasma by the sheath potential. The
collisional effect is simulated by a binary collision model.

17Simple Core-SOL-Divertor Model To Investigate Plasma Operational SpaceR.Hiwataria, Y.Kuzuyamab, A.Hatayamab, K.Okanoa, Y.Asaokaa, S.Zhuc, and Y.TomitadaCentral Research Institute of Electric Power Industry(CRIEPI), Tokyo 201-8511, JAPANb

Faculty of Science and Technology, Keio University, Yokohama 223-8522,JAPANc

Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, P.R.ChinadNational Institute for Fusion Science, Toki 509-5292, JAPANTo understand operational SOL-Divertor conditions is the critical issue to realize a fusion power plant.
Those conditions should be investigated consistently with core plasma conditions. Recently, the core plasma
performance required to generate net electric power is roughly revealed [1]. According to that study, we have toincrease the ratio of greenwald density limit (fnGW) together with normalized beta value (βN), and fnGW required
to generate net electric power depends on the core plasma temperature. The core plasma temperature will be
restricted by the divertor operation of detateched plasma. Consequently, the relationship between the coreplasma temperature and the divertor operation condition has a great impact on fnGW required for a fusion power
plant. To understand such relationship between core and SOL-divertor plasma, we integrated 0D core plasma
model and two-point model into a simple Core-SOL-Divertor (C-S-D) model.
The 0D core plasma model is based on ITER physics design guideline [3] and the LH transiton condition is
installed by the same fashion as in ref. [4]. The two-point model[5,6] is basically applied to SOL-divertor
analysis. The SOL density, which is usually a given parameter, has to be calculated including the core plasma
conditions such as particle and heat flux across the separatrix. In the present study, we solve the particle balancewith a simple neutral transport model[2,6].
We compare this C-S-D model with B2-EIRENE analysis results for the attached divertor of JT-60U[9],
and

the

following

good

agreement

isobtained;

Tsol = 51.4 eV(TsolB 2 ≈ 50 eV), Tdiv = 10.1 eV(TdivB 2 ≈ 12.0 eV),

B2
B2
nsol = 0.9 ×1019 m-3(nsol≈ 1.0×1019 m-3), ndiv = 2.3×1019 m-3(nsol≈ 3.0×1019 m-3) , where those inside brackets are B2-EIRENE

results. With this C-S-D model, we also reproduce the transition phenomenon from Low to High recycling state
as reported in ref.[7,8]. We apply this C-S-D model to the HT-7U(EAST) operational space. In the first phase of
HT-7U, the plasma current will be driven with LH current driving method, where low density is preferable. In
contrast, High recycling state of divertor is required to decrease heat load on the divertor plate. We carry out the
preliminary analysis for the operation space for both core and divertor plasma. We also apply this model to ITER
LH transition phase and find the possibility of the divertor density oscillation during the LH transition, which
may makes it difficult to control divertor plasma[2]. The modelling of the detached plasma condition remains to
be done. This work is partly supported by JSPS-CAS Core-University Program on Plasma and Nuclear Fusion.
[1] R. Hiwatari, et al., J. Plasma Fusion Res. 78(2002)991, R.Hiwatari, et al., “Generation of Net Electric Power
with a Tokamak Reactor under Foreseeable Physical and Engineering conditions”, Nucl. Fusion in press.
[2] R. Hiwatari et al., in Proc. Of the 9th International Workshop on Plasma Edge Theory in Fusion Devices, San
Dieo, USA, 2003.
[3] N. Uckan and ITER Physics Group 1990 ITER Physics Design Guidelines:1989.
[4] T. Yamamoto, et al., Fusion Eng. Des. 39-40 (1998) 143.
[5] K. Borrass, Nucl. Fusion 31(1991)1035.
[6] N. Hayashi, et al., J. Nucl. Mater. 313-316(2003)1041.
[7] M.Sugihara, et al., J. Nucl. Mater. 128-129(1984)114[8] T.Takizuka,et al., JAERI-RESEARCH2003-010, 2003
[9] A.Hatayama, et al., Nucl. Fusion 40(2000)2009, J.Nucl. Mater. 290-293(2001)407

18

Non-local Transport of Strongly Coupled Plasmas
Satoshi Hamaguchi
Department of Fundamental Energy Science
Graduate School of Energy Science, Kyoto University
Collective motion of charged meso-scopic particles (i.e., particulates) immersed in aplasma (i.e., dusty plasmas) is of great interest with regard to improving ourunderstanding of the fundamental nature of strongly coupled Coulomb systems.
Observable phenomena in most laboratory dusty plasma experiments are often
macroscopic in nature, i.e., phenomena whose scale lengths are significantly larger than
the average interparticle distance and time scale much longer than the plasma frequencyof charged particulates. In order to understand the relation between the dynamics ofcharged particulates in the meso-scopic level and such observable macroscopic
phenomena, one needs a theoretical framework in which statistical properties ofparticulates are directly incorporated in the dynamical equations governing themacroscopic motion of the system. One of such models is hydrodynamic equations,where statistical properties of constituent particles are incorporated in their transport
and thermodynamical coefficients.
In the case of moderately or strongly coupled dusty plasmas, one is also often interested
in “less macroscopic” phenomena whose typical space scales are several times larger
than or almost the same as the average interparticle distance, and equally whose typicaltime scales are several larger than or almost the same as the particulate plasma
frequency. The hydrodynamics equations can also describe such phenomena
approximately if one includes memory effects in their transport coefficients.
In the present work, we model dusty plasmas by the Yukawa system, i.e., the system ofparticles interacting through Yukawa potentials, and evaluate its memory effects and therelaxation time (i.e., time scale of memory effects) in the shear viscosity, using
molecular dynamics (MD) simulations. We have found a phenomenological scaling of
the relaxation time as a function of the system parameters. These results are used toconstruct the hydrodynamics equations (i.e., generalized hydrodynamics equations)applicable to moderately or strongly coupled dusty plasmas.

19Predictive Integrated Modeling Simulations Using a
Combination of NTCC H-mode Pedestal and Core Models
Arnold H. Kritz
Department of Physics, Lehigh University
Bethlehem, PA 18015
US-Japan JIFT Workshop, Kyoto Japan
December 15-17, 2003
Predictive integrated modeling (frequently referred to as predictive transport modeling)of tokamak plasmas involves the interaction between transport, sources, sinks,
equilibrium, and large scale instabilities, to predict temperature, density, and otherprofiles. Integrated modeling simulations are used to understand the physics ofconfinement, to optimize the performance of tokamaks, and to predict the expected fusion
power production in planned burning plasma experiments. Before the development ofpredictive boundary conditions, the temperatures and densities at the edge of thesimulations were taken from experimental data. The simulations yielded core plasma
profiles that were consistent with experimental data within measurement errors. As afirst step in developing predictive boundary conditions for simulations of H-mode
discharges, static models (without the effect of periodic ELM crashes) were developed
for the height of the H-mode pedestal. These pedestal models were combined withmodels for the plasma core, such as the Multi-Mode, GLF23, and mixed-Bohm/gyroBohm anomalous transport models, to predict the temperature and density profiles in Hmode discharges. In more recent simulations, dynamic models for the pedestal and
ELMs at the edge of H-mode plasmas are used to produce time-dependent simulations ofplasma profiles from the magnetic axis to the separatrix. MHD stability codes are used tocalibrate the models that trigger ELM crashes within the integrated modeling code. A
geographically distributed collaboration developed the NTCC project, which has
explored the use of modern computer software engineering to produce Web-invocable,community-owned integrated modeling codes. The NTCC module library (which isavailable at http://w3.pppl.gov/NTCC) was established in order to facilitate thedevelopment of integrated modeling codes. A review process is in place to ensure thatmodules conform to the Module Library standards. The exchange between the author ofeach module and the reviewer often results in improvements to the module and its
documentation. Currently, there are 44 modules in the Module Library, including
modules for transport, plasma heating, equilibrium and MHD stability, H-mode pedestal,neutral gas, atomic and nuclear reaction rates, and numerical and visualization tools.

20Real-time control of internal transport barriers in JET :Experiments and simulations
D. Moreau1, 2, F. Crisanti3, L. Laborde2, X. Litaudon2, D. Mazon2, A. Murari4, T. Tala5,
P. De Vries6, R. Felton7, F. Imbeaux2, E. Joffrin2, M. Lennholm2, V. Pericoli-Ridolfini3,
M. Riva3, L. Zabeo2, K.D. Zastrow7 and contributors to the EFDA-JET workprogramme.
1

EFDA-JET Close Support Unit, Culham Science Centre, Abingdon, OX14 3DB, U. K.
2
Euratom-CEA Association, CEA-Cadarache, 13108, St Paul lez Durance, France
3
Euratom-ENEA Association, C.R. Frascati, 00044 Frascati, Italy
4
Euratom-ENEA Association, Consorzio RFX, 4-35127 Padova, Italy
5
Euratom-Tekes Association, VTT Processes, FIN-02044 VTT, Finland
6
Euratom-FOM Association, TEC Cluster, 3430 BE Nieuwegein, The Netherlands
7
Euratom-UKAEA Association, Culham Science Centre, Abingdon, U. K.

Real-time control of the plasma profiles (current, pressure and flows) is a key issue to sustain
steady state discharges with internal transport barriers (ITB) and a large bootstrap current
fraction. In order to simultaneously control the current and pressure profiles in JET ITB
discharges, a multi-variable model-based technique has been proposed. It is based on atruncated singular value decomposition (TSVD) of an integral model operator and retains the
distributed nature of the plasma parameter profiles. The related algorithms have been
implemented in the JET control system, and applied to the control of the current profile inreversed shear plasmas using three actuators (neutral beam injection, ion cyclotron heating
and lower hybrid current drive). Successful control of the q-profile has been achieved in quasi
steady state conditions with a significant fraction of bootstrap current. In these experiments
the strength of the ITB's was marginal during the control phase, due to the chosen q-profile
setpoints and to the moderate heating power which was requested by the controller. Hence,
further experiments aiming at the simultaneous control of the current profile and of thenormalized ITB temperature gradient are being pursued and first results will possibly bereported. Integrated modelling of the proposed control algorithms is also being attemptedusing transport codes (JETTO, CRONOS). Preliminary results will be shown concerninginterpretative modelling of past experiments as well as predictive modelling for future
experiments with the complete algorithms. In particular, the way the control matrix isdetermined from open loop experiments can be mocked up with simulations. The applicationof the TSVD in closed loop can then be tested in order to assess the capability of the modelbased (linear) algorithms in achieving adequate control and the effect of transport nonlinearities on the closed loop response. This can be very valuable in optimizing the proposed
method and the characteristics of the controller in parallel with the experiments.

Invited talk at the Joint Meeting of US-Japan JIFT Workshop on Theory-Based Modeling andIntegrated Simulation of Burning Plasmas, and 21COE Workshop on Plasma Theory.
Kyoto (Japan),21
15-17 Dec. 2003.

Integrated Simulation Based on TASK Code
A. Fukuyama, M. Honda and T. Akutsu
Department of Nuclear Engineering, Kyoto University,
Yoshida-Hommachi, Sakyo-Ku, Kyoto 606-8501, Japan
In order to predict the behavior of burning plasmas and to develop a scheme tocontrol them, a simulation code system which integrates various theory-basedmodels and large-scale simulations is strongly desired.

For this purpose, we havestarted the activity of "Burning Plasma Simulation Initiative" which stimulates thecollaboration among universities, NIFS and JAERI.

One of the first targets of thisactivity is to propose a common data-interface between the existing and coming
simulation codes and to develop a reference core code based on the TASK code
which has been developed in Kyoto University and will be available as an open
source code.
The TASK code is composed of several modules for equilibrium (EQ), transport(TR), Fokker-Planck (FP), ray-tracing (WR), full wave (WM), wave dispersion (DP),data interface (PL), and common libraries. Each module works now, but the datainterface is under reconstruction.

Some of recent results of the TASK code, such as

dependence of the internal transport barrier formation on the bootstrap current
models, evaluation of electron cyclotron current drive for neoclassical tearing modestabilization, and analysis of Alfven eigenmodes in a reversed configuration.
We are planning several extensions of the modules. One is a new transportmodule, TX, which solves the flux averaged fluid equation and describes the toroidal
and poloidal plasma rotation and the radial electric field.

The analysis of edgetransport barrier formation is also in the scope of this module.
wave analysis of global stability, WA.

Preliminary results will be presented.

Extension to the analysis of helical system will be also discussed.

22

Another is the full

1-D Transport Simulation for a 3-D MHD Equilibrium
Yuji Nakamura, Yasuhiro Suzuki
Graduate School of Energy Science, Kyoto University, Gokasho,Uji, Kyoto 606-0011, JAPANSeveral 1-D transport code simulation studies have been done for non-axisymmetric toroidal
plasmas such as stellarators (or helical systems). Many of these studies adopted the cylindricalapproximation similar to the circular tokamak cases. Transport simulations for non-circular
tokamak plasmas can be done by a combination of the 1-D transport code and the 2-D MHD
equilibrium code, so called 1.5-D transport code. In the same sense, several 1D transport
simulations combined with a 3-D MHD equilibrium()Vr¢code have been performed in helical systems.
Most of these studies use the specific volume
and neoclassical ripple transport coefficients
calculated from the data obtained by the VMEC 3-D MHD equilibrium code, which is a 3-D
inverse solver based on the variational principle.
In this talk, we will briefly review 3-D MHD equilibrium calculations and 1-D transport
simulations for helical systems, and will discuss some difficulties and problems to be resolved. As
an example, Fig.1 shows an MHD equilibrium of an L=1 helical-axis heliotron, Heliotron J (H-J)
calculated by the PIES code, which can calculate a 3-D MHD equilibrium without assuming theexistence of nested flux surfaces. It is shown in Fig. 1 that magnetic islands can exist in 3-D MHD
equilibria of stellarator plasmas and they will affect transport like NTMs in tokamaks.
Not only for the helical systems, ripple loss or diffusion of alpha particles is one of theimportant issues on tokamak fusion reactors. It has been pointed out from the 3-D MHD
equilibrium calculation for the rippled tokamak that ripple structure can be changed in the finite
beta plasmas. Finite beta effects on the alpha ripple loss will also discussed.

Fig.1 Top view and puncture plots of an MHD equilibriumin the Heliotron J calculated by the PIES code23Remote Collaboration Environment on the Grid
Koji KOYAMADA1)
2)

3)

Teruo Matsuzawa , Motoi Okuda

1) Kyoto University, Kyoto, Japan, 2) JAIST, Ishikawa, Japan 3) Fujitsu Limited, Japane-mai: koyamada@kudpc.kyoto-u.ac.jp
In the visualization group of the VizGrid project, we plan to develop a tele-immersive
environment using volume communication technologies, which mean a suite of technologies
for communicating using volume datasets. The volume communication make the best of
volume graphics technologies, where a volume data is represented as a three-dimensional
array of voxels. The term voxel is used to characterize a volume element. It is a generalizationof the notion of pixel that stands for a picture element. Today, widely used 3D computer
graphics first extracts geometry data from volume data, and then uses polygonal meshes torepresent an object by its surface.
Volume rendering-based graphics, that is, volume
graphics uses voxels - 3D or volumetric pixels - as basic element to represent not only thesurface but also the entire inner part of an object. The volume graphics visualization issuperior to polygon based 3D graphics in means of image quality and performance when wevisualize highly complex objects that our project has to handle with finest details. In thisproject, we will develop a volume communication suite, that is an infrastructure that makes aremote collaborative environment, and it is composed of a series of techniques that are
applied on a volume dataset generated from real scenes and computer simulations.
These
techniques include volume creation, volume compression/decompression, volumetransmission, volume display, and volume search., We will describe three accomplishments,
which were completed in 2002, a streaming-based and a CPG-based visualization techniques,
and an ongoing development of a portable tele-immersive system which uses multi-viewpoint
display system and a 3D pointing device with a perspective of the finalized system.
Reference
1) Y. Watashiba, J. Nonaka, N. Sakamoto, Y. Ebara, K. Koyamada and M. Kanazawa, "A Streaming-based
Technique for Volume Rendering of Large Datasets," Proceedings of the IASTED CGIM2003, pp. 187192, 2003
2) R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin and H. Fuchs., "The Office of the Future : A Unified
Approach to Image-Based Modeling and Spatially Immersive Displays Proc. SIGGRAPH 98, pp. 179-188,
1998
3) J.L. Helman and L. Hesselink, “Visualization of Vector Field Topology in Fluid Flows”, IEEE Computer
Graphics and Applications, vol.11, No.3, pp.36-44, 1991
4) C. L. Bajaj, V. Pascucci, and D. R. Schikore, “Visualization of Scalar Topology for Structural Enhancement”,
Proceeding of the IEEE Visualization, pp.51-58, October 1998
5) K. Sakai., K. Koyamada, K. Kamisawa, A. Doi, "Classifying Scalar Field by using Critical Point Graph,”the 10th International Symposium on Flow Visualization, F326, 20026)T. Itoh, K. Koyamada,“Automatic Isosurface Propagation by Using an Extrema Graph and Sorted Boundary
Cell Lists,”IEEE Transactions on Visualization and Computer Graphics Vo.1, No.4, pp. 319-327, 1995
7)S. M. Seitz and C. R. Dyer, “View Morphing,” Proc. SIGGRAPH 96, pp. 21-30, 1996

24