23P083-P
Finite beta effects on alpha particle heat loads in high-beta ripple tokamak
plasmas高ベータリップルトカマクにおけるα粒子の熱損失に与える有限ベータ効果a)Michinao Bunno, a)Yuji Nakamura, b)Yasuhiro Suzuki, c)Koji Shinohara and c)Go Matsunagaa)
文野 通尚、a)中村 祐司、b)鈴木 康浩、c)篠原 孝司、c)松永 剛a)Graduate School of Energy Science, Kyoto University, Gokasho, Uji-shi, Kyoto-fu 611-0011, Japana)b)

京都大学大学院エネルギー科学研究科 〒622-0011

京都府宇治市五ヶ庄

National Institute for Fusion Science, 322-6 Oroshi-cho, Toki-shi, Gifu-ken 509-5292, Japanb)c)

核融合自然科学研究所 〒509-5292

岐阜県土岐市下石町322-6

Japan Atomic Energy Agency, 801-1 Mukoyama, Naka-shi, Ibaraki-ken 311-0193, Japanc)
原子力開発機構那珂研究所 〒311-0193 茨城県那珂市向山801-1

The energetic ion confinement is deteriorated by the ripple magnetic fields in a tokamak plasma. Not only
the finite number of external toroidal field coils but also the plasma currents change the magnetic field
configurations. The magnetic field from the plasma current was calculated from the VMEC results withbased on the Biot-Savart law. Three kinds of three-dimensional magnetic field configurations for ten beta
scenarios were prepared to analyze the finite beta effects by calculating the orbits of alpha particles.

1. Introduction
A tokamak is usually assumed as the axisymmetricsystem, however, the finite number of the toroidal
field (TF) coils creates the non-axisymmetricmagnetic field, which is call as the TF ripple. Theripple field changes the orbit of energetic ions andincreases the amount of loss particles. These losses
produce several serious problems in a tokamak,such as the deterioration of the plasma heating
efficiency and the concentration of heat loads on thefirst wall.
The accurate magnetic field structures withincluding the finite beta effects are necessary to beanalyzed for these problems because the plasma
current also changes configurations of magnetic
fields. The finite beta effects can be categorized
such as magnetic components (the todoidal orpoloidal field) or non-axisymmetric components(the axisymmetric or non-axisymmetric field). We
should estimate how the field from the plasma
current affects on the ripple induced orbit losses ofenergetic ions.
In the previous study, 2D MHD equilibrium
calculation code was usually used by assuming aplasma to be axisymmetric. Although resulting
MHD equilibrium field was axisymmetric, 3D
magnetic field can be approximately obtained bysuperimposing the ripple components of thevacuum field on it. This approximation method iscalled as the vacuum approximation. While, VMEC
is one of the 3D, free boundary MHD equilibrium
code and this code has been ordinary used in ahelical plasma [1,2]. However, VMEC was usedalso for a ripple tokamak to obtain the full 3D
MHD equilibria. The most serious problem of
VMEC was limited calculating region because ofusing the magnetic coordinates. We developed theequilibrium magnetic field calculation code withVMEC results by the Biot-Savart law. The precise
discussion was presented in the 8th APFA
2011 ”Beta value dependence on the ripple induced
losses and the heat loads”.
The research method for this study was describedin Sec.2 and these results were shown in Sec.3.
Finally, summaries and conclusions were describedin Sec.4.
2. Research method
VMEC code was used in this study to obtain theMHD equilibria and the field from the plasma
current. The calculating configurations, such as theshape of TF coils and distribution of the safety
profile q, were referred to the steady state operationof an ITER scenario 4 [3-5]. We prepared 10 beta
scenarios by changing the scale of the plasmapressure to estimate the beta value dependence on
the ripple induced losses. In addition, the magnetic
field from the plasma current was divided to 3 parts,
the axisymmetric poloidal field Bθ, axisymmetric~

toroidal field Bφ and non-axisymmetric field B. The
axisymmetric poloidal field was required to create
the closed magnetic surfaces. We made 3 kinds of
3D magnetic fields for each beta scenario,

A). Bext + BθB). Bext + Bθ + Bφ~C). Bext + Bθ + Bφ + B,
where Bext was the magnetic field from the externalcoil currents.
~The each magnetic field component Bθ , Bφ and B
in the cylindrical coordinates (R,Z,φ) was obtained
from VMEC results by the calculation code
introduced in Sec.1. The orbits of alpha particles
were calculated with these 3D fields by
F3D-OFMC code to analyze the finite beta effects
on the ripple induced losses [6].
3. Results
We calculated the orbits of 10000 alpha particles
by F3D-OFMC with each magnetic field. The loss
rate was defined as the ratio of the kinitic energy of
all loss particles at the loss point to the initialenergy of all particles and described in Fig.1, where
the green, blue and red line showed the loss rate for
A, B and C, respectively.
~This figure showed that Bθ, Bφ and B enhanced
the loss rate with increasing the volume averaged
beta <β>. The poloidal magnetic field Bθ from theplasma current produced the Schafranov-Shift andthe magnetic axis moved to the outer torus. The
increased loss rate with Bθ came from this shift
because the high ripple region was localized on theouter torus. The non-axisymmetric component also
increased the loss rate, however, this change wassmaller than other finite beta effects. While, thereason for the increasing loss rate by Bφ was notclear because this field did not affect on the shapeof magnetic flux surfaces and the ripple
components. The toloidal field worked as thediamagnetic for the high beta plasma and reduced
the strength of the magnetic field. In a result, thecontour of Bmin became to be closed at outer torus,
where Bmin was the minimum strength of themagnetic field along the toroidal angle. The orbit ofthe deeply ripple trapped particles and the tip ofbanana particles mainly followed this contour. The
detailed discussion and figures will be presented in
the poster session.
4. Summary
In this study, we used the VMEC code to analyze
the beta value dependence on the ripple inducedlosses. Three kinds of magnetic field configurations
for ten beta scenarios were prepared and the orbitsof 10000 alpha particles were followed by
F3D-OFMC code.
~All field components Bθ, Bφ and B increased the<β>Fig.1 The beta dependence on the loss rate for
scenario A (the green line), B (the blueline) and C (the red line)

ripple induced orbit losses, while the change of loss
rate from the non-axisymmetric field was small
especially in a low beta plasma. The normal <β> forthe steady state operation of ITER scenario 4 wasabout 2%, therefore, we can conclude that 3D MHD
equilibrium calculation was not required for anITER plasma.
Acknowledgments
The authors would like to thank S.P.Hirshman
and D.A.Spong for providing VMEC code andITER equilibrium data. This work is performed
with support and auspices of the NIFS
Collaborative Research Program.
References[1] S.P.Hirshman et al. Phys. Fluids 28 (1985) 1387.
[2] S.P.Hirshman et al. Comput. Phys. Comm. 43 (1986)
143.
[3] E.Strumberger et al. Nucl. Fusion 50 (2010) 025008.
[4] D.A.Spong, Physics of Plasmas 18 (2011) 056109.
[5] K.Shinohara et al. Nucl. Fusion 51 (2011) 063028.
[6] K.Tani et al. J. Phys. Soc. Japan. 50 (1981) 1726.