23P034-P
Effect of nonlinear collisions on the α-particle confinement
in helical plasmas
ヘリカルプラズマにおける非線形衝突の α 粒子閉じ込めへの影響
Yoshitada Masaoka, Sadayoshi Murakami
政岡義唯, 村上定義
Department of Nuclear Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, JAPAN京都大学工学研究科原子核工学専攻 〒 606-8501 京都市左京区吉田本町
Confinement of α-particles is investigated including the collisions with various plasma species suchas electron, deuterium, tritium, and high-energy α-particle itself in a heliotron fusion reactor basedon the LHD configurations. GNET code (Global NEoclassical Transport) is improved to take into
account the nonlinear collision effect on the α-particle confinement. The real and velocity space
distributions are analyzed and the energy and particle loss rate changing the background plasma
parameters are evaluated.

1

Introduction

Confinement of energetic particles is one of theimportant issues in the fusion reactor research.
Energetic α-particles are produced by D-T fusion
reactions and the energy of α-particle is indispensable to sustain a high temperature fusion plasma.
Also the lost energetic α-particles might damage
the first wall. Therefore, it is important to confine
the energetic particles until the energy slow-down
to thermal energy. Particularly, in helical systems,
energetic particle trajectory is complicated in athree dimensional magnetic configuration. Thus
the confinement of energetic particles is one of
the critical issues in designing a helical reactor.
Additionally, collisions between the energetic particles could enhance the pitch angle scattering[1]and would deteriorate the confinement. Thus theanalysis including the both complicated orbit andnonlinear collision effects are necessary to makeclear the energetic particle confinement in LHDplasmas.

2Simulation ModelIn this study, we assumed a heriotron type fusion reactor extending the LHD magnetic configuration [2]. This reactor is based on the NeoClassical transport optimized (NC) configuration
which is the inward shifted magnetic configuration optimized the neoclassical transport based on
Rax = 3.53m in LHD [3]. Rax is the magnetic axis
position in the major radius. This reactor config-uration has the plasma volume of 1000m3 and themagnetic strength of 5T at the plasma center.
In order to analyze a stationary distribution ofα particles including the nonlinear collision effects,
we solve the drift kinetic equation for α particles
in five dimension phase space using the GNET
(Global NEoclassical Transport) code [4]. This
code uses a Monte Carlo technique to calculate
the distribution function following test particles.
The drift kinetic equation is described as follow ;∂fα+ (#v! + #vD ) · ∇fα + #̇v · ∇V fα∂t= C(fα ) + L(fα ) + Sα(1)where fα is the distribution function of α particles,#v! and #vD are the velocity parallel to magneticline and the drift velocity respectively. L is theloss term form the last closed flux surface and Sα
is the source term of the α particles generated byfusion reaction.The source term Sα is evaluatedby using fusion reaction rate.
C is the Coulomb collision operator including
the linear collision effects C linear and the nonlinear collision effect C nl . C linear includes the operator of the pitch angle scattering and the energy scattering with background ions and electrons. These operators have been evaluated by
Boozer and Kou-Petravic [5] and are described asfollow ;and tritium (0.5), Case 3 : electrons, deuterium(0.45), tritium (0.45), and α particles (using lin!"#$1/2
λn = λn−1 (1 − νd τ ) ± 1 − λ2n−1 νd τ(2) ear collision operator) (0.1), Case 4 :, deuterium%&'((0.45), tritium (0.45), α particles (using nonlin3 En−1 dν
En = En−1 − (2ντ ) En−1+ear collision operator) (0.1), where the number of2
ν dEn−1parentheses are the ratio of ion charge density.
1/2±2 {ET En−1 (ντ )}(3)
We found that an increase of mass density ofwhere λ = v! /v. v and v! are the particle velocity background plasma leads to degradation of theand the velocity parallel to magnetic line. νd is confinement efficiency of the α particle because
the deflection collision frequency. τ is length of a of enhancement of the pitch angle effect. Assumtime step. n and n − 1 are numbers of time step, ing the Maxwellian background plasma is distriand The symbol ± means the sign is to be chosen bution, for each collision operator, we can not seerandomly. En , ET are the energy at time step n a clear difference the α particle confinement are
and thermal energy respectively. The subscript almost same. This indicate the validity of our nonlinear collision operator.
k, l are the components of Einstein convention.
We can write the nonlinear collision operator
C nl with Rosenbluth potentials [6] as)*∂ 2 φ(#v ) ∂φ(#v ) ∂nl
C! = Λ c+f (#v ) (4)∂v! ∂v!
∂v!2+ 2∂ φ(#v ) ∂ψ(#v ) ∂nlC⊥ = 2Λ+2∂v⊥ ∂v⊥∂v⊥,22∂ ψ(#v ) ∂−f (#v ),(5)2 ∂v 2∂v⊥⊥where Λc = ln Λ(eα eb /mα )0 )2 . Λ is the theCoulomb logarithm. eα and eb are charges oftest α-particles and of background ions and electrons, especially. mα is the mass of test α-particlesand )0 is permittivity of free space. φ and ψ are
Rosenbluth potentials. v! and v⊥ are the velocities parallel and perpendicular to magnetic filedlines. In this paper, we assumed that the background plasma consists of electrons, deuterium,tritium, and α particles. Electron temperature Teand density ne profiles are taken to beTe (ρ)[keV] = 9.5(1 − ρ ) + 0.5,2ne (ρ)[10 m20−3] = 1.9(1 − ρ ) + 0.1,8(6)(7)

where ρ is normalized minor radius.

3Benchmark

We run the GNET code until the test α particles
are thermalized varying the background plasma
parameters and applying the linear and/or nonlinear collision operator. We estimate α particle confinement with four cases of the backgroundplasma conditions : Case 1 : electrons and deuterium (1.0), Case 2 : electrons , deuterium (0.5),

4Summary

We have investigated α particle confinement in ahelical type fusion reactor with varying the background plasma parameter and the collision operator, keeping the charge neutrality. The validityof our nonlinear collision operator is verifyed. We
will use this collision operator in order to estimate
α-α particle collision effect with non-maxwelliandistribution.

Acknowledgments
The authors were grateful for the support of theMinistry of Education, Culture, Sports, Scienceand Technology of Japan via “Energy Science in
the Age of Global Warming” of Global Center ofExcellence (G-COE) program (J-051).

References[1] K. Okano, et al., Nucl. Fusion 31 (1991) 1349.
[2] A. Iiyoshi, et al., Nucl. Fusion 39 (1999) 1245.
[3] S. Murakami, et al., Nucl. Fusion 42 (2002) L19.
[4] S. Murakami, et al., Nucl. Fusion 46 (2006) S425.
[5] A. Boozer, et al., Phys. Fluids 24(5) (1981)851.
[6] N. Rosenbluth, et al., Phys. Rev. 107 (1957) 1.