24E08
Nuclear plus interference scattering and energetic-ion slowing-down
distribution function in reactor-grade plasmas
炉心プラズマにおける高速イオンの核弾性散乱と減速分布関数
Hideaki Matsuura, Daisuke Sawada and Yasuyuki Nakao
松浦 秀明、澤田 大輔、中尾 安幸
Applied Quantum Physics and Nuclear Engineering, Kyushu University
744 Motooka, Fukuoka 819-0395, Japan
九州大学、エネルギー量子工学部門 〒819-0395 福岡市西区元岡744
Effect of the nuclear plus interference (NI) scattering on slowing-down distribution functions ofenergetic-ions, e.g., protons produced by 3He(d,p)4He reactions, alpha-particles produced by T(d,n)4Hereactions and deuterium beam injected into DT plasmas, are examined on the basis of theBoltzmann-Fokker-Planck (BFP) model. As a result of the acceleration of the slowing-down process ofenergetic ions due to NI scattering, the magnitude of the energetic component is relatively reduced
compared with the case when NI scattering is ignored. The degree of the reduction and its energy range arequantitatively evaluated for various plasma conditions.

1. Introduction
It is well known that fast ions slow down via
Coulomb and non-Coulombic, i.e. nuclear plus
interference (NI) [1], scattering and create
knock-on tails in fuel-ion distribution functions.
Effect of the knock-on tail formation on plasma
burning characteristics [2] and its application toplasma diagnostics [3,4] have been examined.
The NI scattering accelerates slowing-down
process of fast ions and enhances the fractionalenergy deposition from fast to bulk ions [5]. So
far, many studies concerning to the NI-scattering
effect on plasma burning characteristics havebeen made, however, the most of the previous
discussions have been focused on the effect on
distortion of the “bulk” component in fuel-ion
distribution functions and also on the transferredenergy from fast to bulk ions. When the bulk ions
are knocked up to the high-energy region, the fastions also ought to lose large fraction of theirenergy. When NI scattering is ignored, thetransferred energy per unit time from fast to bulk
ions is underestimated (slowing-down time isoverestimated) and the relative magnitude of thesuprathermal to bulk distribution components must
be overestimated compared with the case when
NI-scattering effect is considered.
Recently we examined the correlation between
the slowing-down time and the magnitude of theequilibrium slowing-down distribution functionof fast alpha-particles in deuterium-tritium (DT)plasmas [6]. It was shown that in high-density,
low-temperature range, the slowing-down time
becomes shorter and energetic component of thealpha-particle distribution function relativelydecreases, which may reduce the instability
excitation probability caused by the fast alphaparticles in the Alfvén velocity range.
The slowing-down time of the fast ions also
decreases owing to the NI scattering. In such acase the loss fraction of fast ions duringslowing-down process may also be reduced. It is
important to grasp the reduction of the fast-ion
slowing-down distribution function due to NI
scattering. In this paper, on the basis of the
Boltzmann-Fokker-Planck (BFP) simulation [7],effect of the NI scattering on fast-ion
slowing-down distribution function is evaluated.
As fast ions, alpha-particles produced by theT(d,n)4He reactions, protons by the 3He(d,p)4He
reactions or deuterium beam injected into plasma
is considered. A noticeable reduction in the fast
ion population in confined plasma is shown. The
effect of the reduction on fast-ion loss process isdiscussed.
2. Analysis Model
The Boltzmann–Fokker–Planck (BFP) equation
for fast ions, i.e., protons produced by 3He(d,p)4He
reactions, alpha-particles produced by T(d,n)4He
reactions and deuterium beam injected into DT
plasmas. As background-particle species, main fuelions and electrons, i.e., deuterons, 3He (triton), andelectrons in D3He (DT) plasma, are considered. In
this study, for simplicity, the background ions andelectrons are assumed to be Maxwellian with thesame temperature. We consider the NI scattering [8]of fast ions only by background main-fuel ions. TheNI cross sections are taken from the work ofPerkins and Cullen [8].

(4v / m p ) f p [m 3keV 1 ](4v / m p ) f p [m 3keV 1 ]

1616(a )10( b)

1015

1615

15

101610 10

1014

10

101310141013

10.0

10

100.0Ene[rgy1014101310.0

104101.0]]

2]
ke V

151013c[semec[seme3100.114Ti

Ti

4101.0103100.1
2100.0Ene[ kergyV]Fig.1 Time evolution of proton distribution functions when (a) NI scattering isconsidered and (b) ignored. In the calculations, Ti  Te  80 keV , n D  2n 3He  1020 m 3 and E  (1 / 2) p  3 s are assumed.

3. Results and Discussion
In Fig.1 (a) and (b) temporal behaviors of theproton distribution functions in a typical D3He
plasma, i.e., Ti  Te  80 keV , n D  2n 3He  1020 m 3and  E  (1 / 2) p  3 s , when (a) NI scattering is

considered and (b) ignored are shown. We
assume that proton generation by 3He(d,p)4He andD(d,p)T fusion reactions begins at t = 0. During
the simulations, the fuel-ion densities, electron
temperature and energy (particle) confinement
time are kept constant. The slowing-down
distribution is formed gradually and at 50 s after
the beginning of the simulation, it reaches a nearequilibrium state. When NI scattering is ignored,

the proton distribution function changes its shape
more slowly toward the equilibrium state. Notethat in the equilibrium state, the relative magnitudeof the bulk and suprathermal distribution
components are influenced by the NI scatteringsignificantly. In Fig.2 the equilibrium distributionfunctions when (a) NI scattering is considered and(b) ignored are shown. When the NI scattering isignored, the magnitude of the distribution function
is 50 ~ 70 % larger in the energy range from 2 to 8
MeV. The fast-ion loss fraction during theslowing-down process and Alfvén instability
excitation probability would be predicted todepend on the magnitude of the slowing-down
distribution function. By considering the NIscattering effect adequately, the fast-ion loss andinstability excitation may be reduced. Further
detailed analysis is required. At the presentation,
we also discuss the NI scattering effect on theslowing-down distribution function of alphaparticles and injected deuterium beam in DT
plasmas.
References

Fig.2 Equilibrium proton distributionfunctions when (a) NI scattering is
considered and (b) ignored.

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2405086.
[7] H.Matsuura, et al., Phys. Plasmas 13 (2006) 62507.
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20.