23P056-P
Effect of nuclear elastic scattering on behavior of fast α-particles
in tokamak plasmas
トカマクプラズマ中の高速α粒子挙動における核弾性散乱の影響
Daisuke Sawada, Hideaki Matsuura and Yasuyuki Nakao
澤田大輔，松浦秀明，中尾安幸
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University,
744 Motooka,Fukuoka 819-0395, Japan
九州大学院工学府エネルギー量子工学専攻 〒819-0395 福岡市西区元岡744
Assuming ITER-like plasma, the nuclear plus interference (NI) scattering is newly incorporated into thealpha-particle orbit simulation code system. The NI scattering effect on the alpha-particle orbit in themagnetic confinement device and the influences on the energetic alpha-particle confinement are examined.
It is shown that due to the NI scattering, a fraction of the energetic alpha-particle lost from the plasma tototal generation decreases to some extent.

1. Introduction
To realize the fusion reactor system, it isimportant to understand the fast alpha-particle
confinement and slowing-down process in magnetic
field configuration, and hence many numericalsimulations have been made in various reactor
systems [1-3]. In the previous alpha-particle orbit
analyses, however, the effect of nuclear plus
interference (NI) scattering [4] on the alpha-particle
behaviors has not been considered. The NI
scattering is a non-Coulombic, large-angle
scattering process, and a large fraction of thefast-ion energy is transferred in a single event. TheNI scattering may influence behavior of fast ions.
The purpose of this study is to reveal the effect ofNI scattering for confinement of alpha-particle andplasma heating process.

event ∆E can be written as∆E =E(1 − α )(1 − cos φ ) ,2(2)where E is kinetic energy of the test particle before
scattering. Here a={(mt-mb)/(mt+mb)}2, mt and mb
are mass of test particle and background ion. In thispaper, the NI scattering cross sections are takenfrom the work of Perkins and Cullen[6].

2. Analysis Model
We incorporated the NI scattering effect into theorbit analysis code, i.e. guiding center orbit code
ORBIT [5] developed at PPPL.
The probability p(v) that a test particle moving
with velocity v causes NI scattering during small
time step ∆t isp(v) = nb vσ NI ∆t ,(1)where nb is number density of background ions, andσNI is cross section of NI scattering. As a first step,
the effect of thermal motion of target particles, i.e.
deuteron and triton, was neglected. This is because
the cross section of the NI scattering is very small
in low energy region (<1MeV). Scattering angle inthe center of mass system φ was assumed to beisotropic. Transferred energy in a single scattering

Fig.1. Safety factor and current distribution assumed
this calculation [7]We assumed ITER-like plasma. Toroidal
magnetic field BT=5.3T, and radial profiles of bulk
ions and electrons densities ni=ne=1.0×1014×(1-ψpol,n2)1.5 are assumed, where ψpol,n represents
the normalized poloidal magnetic flux function ψpol.

3.5

8

3.0

7

2.5

62.05

1.5

4

1.0

1216202428
Electron (Ion) Tempareture [keV]Fig.2 The nNI parameter and the fNI parameter asfunctions of average temperature of ions

The fraction of the number of test particles thatcauses NI scattering, i.e., NNI, is increased in hightemperature range. This is because in hightemperature range, slowing down of energeticalpha-particles by Coulomb scattering is weakened
and relative magnitude of the energeticalpha-particle distribution function to bulk
component is increased. The fraction of thedeposited energy via NI scattering, i.e., fNI, issimilarly increased in high temperature range.
When electron temperature is 20 keV, fraction ofthe energy deposited to ions via NI scattering is2.45 % and the fraction of the energy deposited toions (electrons) via Coulomb scattering is estimatedas 28.9 (68.5) %. In this case the enhancement of
the fractional energy deposition to ions due to NI
scattering is evaluated as 5.8 %.
In Fig.3, (a) fraction of the energy lost from theplasma to the one initially generated, i.e., ξ, and (b)the degree of the decrement from the value when NI
scattering is ignored, i.e., η=(ξ0-ξ)/ξ0, are shown.
Here ξ0 represents the ξ value when the NI
scattering is ignored. As previously mentioned,relative magnitude of the energetic alpha-particle
component is relatively increased in hightemperature range. The energetic alpha-particles are4.07.0

3.5

6.5

3.0

6.0

2.5

5.5

2.0

5.0

1.5

4.5

1.0
0.5
0.0

consider NI scattering
ignore NI scattering
1216202428
Electron (Ion) Tempareture [keV]η [%]9fNI [%]

NNI [%]

3. Result and Discussion
In Fig.2, (a) fraction of the number of test
particles that causes NI scattering to the ones
initially generated, i.e., NNI, and (b) fraction ofenergy deposited to bulk ions via NI scattering tothe ones initially generated, i.e., fNI, are shown as afunction of electron temperature.

more difficult to trap in the magnetic fieldcompared with the low energy ones. Thus the ξvalue increases in high temperature range. When NI
scattering is ignored, slowing down of energeticalpha-particles is underestimated compared with thecase when NI scattering is considered, and relative
magnitude of the energetic alpha-particles to thebulk component is further decreased. When NI
scattering is ignored, hence the ξ value tends tohave large values over all the temperature range
compared with when NI scattering is considered.
For example at 20keV temperature, it is shown thatlost energy is decreased by about 6.5% due to NIscattering.
It is well known that as a result of NI scattering
the energetic alpha-particle changes its moving
direction significantly. In the subsequent study, theeffect on the alpha-particle confinement should also
be evaluated.

ξ [%]Radial profiles of the safety factor and current
density are shown in Fig.1 [7]. Throughout thecalculations, 30000 test particles and 100000
toroidal period calculation time are assumed.

4.0
3.5
3.0

Fig.3 Temperature dependence of rate of energy loss
and decreasing rate of energy loss by NI scattering

References[1] K. Tobita, et al., Nucl. Fusion 35 (1995) 1585.
[2] M. H. Redi. et al., Phys. Plasmas 4 (1997) 4001.
[3] V. Yavorskij, et al., Nucl. Fusion 43 (2003) 1077.
[4] J. J. Devaney and M. L. Stein, Nucle. Sci. Eng. 46(1971) 323.
[5] R.B.White, et al., Phys. Fluids 27 (1984) 2455.
[6] S. T. Perkins and D. E. Cullen, nucl. Sci. Eng. 77(1981) 20.
[7] K. Tobita, et al., Plasma Phys. Control. Fusion. 45(2003) 133.