
スタッフリスト
Name 
: Nobuyuki AIBA 
Title 
: Principal Researcher, Concurrent Staff of BA Project Coordination Group and Advanced Plasma Modeling Group 
Address 
: 8011 Mukoyama, Nakashi, Ibaraki, 3110193, JAPAN 
Research Title
Effects of a Toroidal Rotation on the Stability Boundary of the MHD Modes in the Tokamak Edge Pedestal

Abstract 

Effects of a toroidal rotation are investigated numerically
on the stability of the MHD modes in the edge pedestal,
which relate to the typeI edgelocalized mode (ELM). A new
linear MHD stability code MINERVA is developed for solving
the FriemanRotenberg equation, which is the linear ideal
MHD equation with flow. As the result of the stability
analysis, it is revealed that the sheared toroidal rotation
destabilizes the edge localized MHD modes. The change of
the safety factor profile affects this destabilizing effect.
This is because the rotation effect on the edge MHD
stability becomes stronger as the toroidal mode number of
the unstable MHD mode increases, and this toroidal mode
number strongly depends on the safety factor profile. 

(a) Stability diagram on the (j_{ped}, α_{96}) plane, where j_{ped} is the normalized current density near the pedestal, α is the normalized
pressure gradient, the subscript 96 means the value at ψ=0.96,
where the pressure gradient is steepest. The numbers in this
figure shows the toroidal mode number of the MHD modes that
determine the stability boundary. (b) Mode structure of the n=500
core ballooning mode in the sheared rotating equilibrium. This is
obtained by MINERVA as the benchmarking test. 

Reference 

[1] N. Aiba, S. Tokuda, M. Furukawa, N. Oyama and T. Ozeki, 22^{nd}
IAEA Fusion Energy Conference, Geneva, Swiss 2008 TH/P912.

Effect of equilibrium properties on the structure of the edge MHD modes in tokamaks

Abstract 

Effects of the pressure profile and the current density
profile inside the top of the pedestal and that of the plasma
shape on the expansion of the structure of the unstable
edge MHD mode are investigated numerically. The structure
of the edge MHD mode is expanded by spreading the
envelope of the edge ballooning mode structure due to the
increase of the pressure gradient inside the top of the
pedestal, and by decreasing the toroidal mode number of
the most unstable mode due to the increase of the current
density inside the top of the pedestal. In strongly shaped
plasmas, the pressure gradient inside the top of the
pedestal can approach to the ballooning mode stability
boundary and the current density increases enough to
reduce the toroidal mode number of the most unstable
mode. These increases of the pressure gradient and the
current density destabilize the edge MHD mode and expand
the structure of this mode. 

(a) Pressure profiles of the marginally unstable equilibria with
different pressure gradient inside the top of the pedestal. (b)
Mode structures of the most unstable modes in the different
pressure profile equilibria. 

Reference 

[1] N. Aiba, N. Hayashi, T. Takizuka, S. Tokuda and T. Ozeki, J. Phys.: Conf. Ser. 123, 012008 (2008).

Numerical Method for the Stability Analysis of Ideal MHD Modes with a Wide Range of Toroidal Mode Number in Tokamaks

Abstract 

Numerical method for the stability analysis of ideal MHD
modes is invented by using the physical model based on
the twodimensional Newcomb equation in combination
with the conventional ideal MHD model. The MARG2D code
built on this numerical method realizes to analyze the
stability of ideal MHD modes with a wide range of the
toroidal mode number. The validity of MARG2D has been
confirmed by benchmarking tests with the DCON code by
identifying the stability boundary of low toroidal mode
number MHD modes, and the ELITE code by comparing the
growth rates of intermediate to high toroidal mode number
MHD modes. With the MARG2D code, the MHD stability
property of JT60SA, the complemental experiment of ITER,
is investigated with a focus on the effect of the plasma shape. 

Benchmarking results between MARG2D and ELITE[2].
(a) Dependence of the growth rate on the toroidal mode
number n. (b) and (c) Mode structures of the eigenfunction of
n=10 edge localized MHD mode obtained by MARG2D and
ELITE, respectively. 

Reference 

[1] N. Aiba, S. Tokuda, T. Fujita, T. Ozeki, M.S. Chu, P.B. Snyder
and H.R. Wilson, Plasma and Fusion Res. 2, 10 (2007).
[2] P. B. Snyder et al., Phys. Plasmas 9, 2037 (2002).

Effects of 'Sharpness' of the Plasma CrossSection on the MHD Stability of Tokamak Edge Plasmas

Abstract 

Stability of a peeling, a ballooning, and a peelingballooning
modes, which relate to edgelocalized modes (ELMs), are
investigated numerically with the linear ideal
magnetohydrodynamic (MHD) stability code MARG2D.
Effects of 'sharpness' on the stability of the peelingballooning
mode are examined, where the sharpness is
defined in terms of the curvature at the top or bottom of the
outermost flux surface. It is found that the stability limit of
the pressure gradient significantly improves as the
sharpness increases even when the ellipticity and the
triangularity are unchanged. The sharpness is an important
parameter for high performance Hmode operations with
high pedestal pressure. 

(a) Crosssections of the equilibria with different sharpness
parameters at the top. (b) Stability diagram of the edge localized
MHD modes on the (j_{edge}, alpha) diagram, where j_{edge} is the
normalized plasma current density at the plasma surface, alpha
is the normalized pressure gradient at the pedestal. 

Reference 

[1] N. Aiba, S. Tokuda, T. Takizuka, G. Kurita and T. Ozeki, Nucl.
Fusion 47, 364 (2007).

Analysis of an aspect ratio effect on the stability of external MHD modes in tokamaks with Newcomb equation

Abstract 

Stability analysis of the external magnetohydrodynamic
(MHD) modes is carried out by solving the twodimensional
Newcomb equation. Emphasis is put on an effect of the
aspect ratio on the achievable plasma pressure. The
decrement of the aspect ratio improves the achievable
plasma pressure and increases the toroidal mode number
of the external mode restricting the pressure. 

Dependence of the β_{N} limits on the wall position determined
by the stability of 1≤n≤10 MHD modes in (a) A=2.44, (b)
3.26, and (c) 6.00 equilibria. 

Reference 

[1] N. Aiba, S. Tokuda, T. Ishizawa, J. Plasma Phys. 72, 1127 (2006).

Extension of the Newcomb equation into the vacuum for the stability analysis of tokamak edge plasmas

Abstract 

The formulation for solving numerically the twodimensional
Newcomb equation has been extended to
calculate the vacuum energy integral by using a vector
potential method. According to this extension, a stability
code MARG2D has been adapted, and coded for parallel
computing in order to reduce substantially the CPU time.
The MARG2D code enables a fast stability analysis of ideal
external MHD modes from low to high toroidal mode
numbers on the basis of the single physical model,
and then the code works as a powerful tool in an integrated
simulation where it is combined with transport codes,
and also in the analysis of tokamak edge plasma experiments. 

Mode structure of the n=40 edge localized MHD mode obtained by MARG2D in (a) the radial direction and
(b) the (R,Z) plane. 

Reference 

[1] N. Aiba, S. Tokuda, T. Ishizawa and M. Okamoto, Comput. Phys. Commun. 175, 269 (2006).

Application of the 2dimensional Newcomb problem in a tokamak

Abstract 

The theory of the Newcomb equation has been applied to
lown external modes in a tokamak and a method has been
developed to compute the stability matrix that gives the
change of plasma potential energy due to external modes
in terms of the surface values of the perturbations. By
using this method, the spectral properties of the ideal
external modes has been elucidated, such as coupling
between external modes and internal modes, and the
difference of the stability properties between a normal
shear tokamak and a reversed shear tokamak. These
results will be also useful in the stability analysis of
resistive wall modes. 

Reference 

[1] N. Aiba, S. Tokuda, T. Ishizawa and M. Okamoto, Plasma Phys. Control. Fusion 46, 1699 (2004).

The Effect of the Aspect Ratio on the External KinkBallooning Instability in HighBeta Tokamaks

Abstract 

A theory for the stability analysis of ideal external modes is
developed with the property of the Newcomb equation.
This theory is also useful for stabilizing resistive wall
modes by feedback controls. As an application of this
theory, the effect of the aspect ratio on the ideal
magnetohydrodynamic (MHD) stability limits of tokamak
plasmas are examined numerically. The toroidal mode
number n=1 external modes are stabilized by making the
aspect ratio smaller. 

Reference 

[1] N. Aiba, S. Tokuda, T. Ishizawa and M. Okamoto, J. Plasma Fusion Res. SERIES Vol. 6, 241244 (2004).

Simulation Study on the Motion of the Pressure Perturbation in an Axisymmetric Toroidal System [1]

Abstract 

In tokamaks, it is observed that an ablated and ionized
pellet moves toward the low field side of the torus. This
phenomenon can be considered as the Magneto
HydroDynamic (MHD) wave propagation in the 1/R varying
toroidal field because the pressure perturbation is induced
by injecting a pellet, where R is the major radius of
tokamaks. The dominant mechanism which causes this
displacement is revealed, by solving nonlinear MHD
equations numerically, as the multidimensional nonlinear
fast magnetosonic wave propagation in a toroidal
magnetic field. Linear wave propagation does not work for
this displacement. The nonlinearity is clarified by
successive approximation. 

Reference 

[1] N. Aiba, S. Tokuda, T. Hayashi and M. Wakatani, J. Phys. Soc. Jpn. 73, 364373 (2004).

