J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)306–309
000–000

Reduction in 14MeV Neutron Generation Rate by ICRF Injectionin D-3He Burning Plasmas
MATSUURA Hideaki and NAKAO Yasuyuki
Kyushu University, Hakozaki 812-8581, Japan(Received: 9 December 2003 / Accepted: 20 March 2004)

Abstract
The triton distribution function during ion cyclotron range of frequency (ICRF) waves injection in D-3He plasmas
is examined by solving the 2-dimensional Fokker-Planck equation. Triton distribution function originally has a nonMaxwellian (tail) component around 1.01MeV birth energy range due to D(d,p)T fusion reaction. Owing to theextension of the original tail by ICRF injection, the high-energy resonance tritons further increase, and the velocityaveraged T(d,n)4He fusion reaction rate coefficient, i.e. 14MeV neutron generation rate, decreases from the values
when triton is assumed to be Maxwellian. It is shown that when tritons absorb ~1/200 of the fusion power from thewaves in typical D-3He plasma, i.e. T = 80keV, nD = 2×1020m-3, τE0 = 3sec and B = 6T, the 14MeV neutron generation
rate is reduced by about ~20% from the values for Maxwellian plasmas.
Keywords:
ICRF heating, triton distribution function, D-3He plasma, 14MeV neutron generation rate

1. Introduction

main fusion reactivity, e.g. 3He(d,p)4He (T(d,n)4He) reactivity
in D-3He (D-T) plasma, has been considered. In this paper
we focus our attention on the side reaction, i.e. T(d,n)4He
reaction in D-3He burning plasmas, and try to reduce theT(d,n)4He reactivity by considerably small radio-frequency(RF) heating power input. It is shown that owing to the RFpower (1/100–1/200 of the fusion power) absorption in tritons,
the 14-MeV neutron generation rate decreases by about 20%
from the values for Maxwellian plasmas. An operation modeof the D-3He fusion systems in which 14MeV neutron
generation is suppressed, is proposed.

3

The use of D- He plasma in future fusion reactor is oneof the most promising alternatives. In this plasma, the fractionof the fusion power carried by neutrons is small comparedwith the D-T plasma and highly efficient fusion is madepossible by recovery of the fusion power carried by highenergy protons. The use of this plasma in Tokamak-based
configuration, keeping radiation losses lower, is attractive andthe studies for this purpose are important for improving thesystem efficiency and for increasing public acceptability infuture fusion energy systems. So far many studies toinvestigate the characteristics of the D-3He plasmas have been
made [1]. We have especially examined the D-3He burning
characteristics considering the distortion of the fuel-ion
velocity distribution functions [2-5]. When the fraction of thenumber of fuel ions increases in the velocity range where thefusion cross section is small, velocity-averaged fusion
reactivity decreases [2]. We have previously evaluated thedegree of the reduction in T(d,n)4He reactivity (14MeV
neutron generation rate) including the effects of the Nuclear
Elastic Scattering [3,4] and magnetic field configuration [5].
In this paper, we attempt further reducing the 14MeV
neutron generation rate by ICRF injection. So far various
scenarios of plasma heating by ICRF waves using resonancesat the fundamental cyclotron frequency [6] and its harmonics[7-9] for achieving the reactivity enhancement [10] have beenmade. In most of the previous studies the enhancement in the2. Analysis model
To facilitate the analysis we focus our attention only on
the triton distribution function in burning D-3He plasmas.
Distribution functions of main fuel ions, i.e. D and 3He, andelectron are assumed to be Maxwellian at the same
temperature. The distribution functions of α-particle andproton are ignored. Steady-state triton distribution functionduring ICRF heating in D-3He plasmas is determined bysolving the following 2D Fokker-Planck equation;⎛ ∂ fT ⎞⎜⎟⎝ ∂t ⎠+Coulomb⎛ ∂f ⎞+⎜ T⎟⎝ ∂t ⎠RF1 ∂ ⎛ v3 ⎞⎟ fT + ST (v) − LT (v) = 0 ,⎜v2 ∂ v ⎝ 2τ E (v) ⎠(1)

©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchCorresponding author’s e-mail: mat@nucl.kyushu-u.ac.jp1306

Matsuura H. et al., Reduction in 14MeV Neutron Generation Rate by ICRF Injection in D-3He Burning Plasmas

where fT is total (i.e. bulk plus tail) distribution function oftriton, and is normalized so that the triton density is given bynT =∫ f (v,θ )dv .
Tζ (v) =RF=

∂f ⎞
∂ ⎛
⎜ DRF
⎟ ,∂ v⊥ ⎝∂ v⊥ ⎠σ v T(d, n) He =4fT
− ς (v) fT ,
τ P (v)(6)

LT (v) = −(7)

4π 2 ⎛ mT ⎞ 3 / 2dvD vD
nT ⎝ 2πT ⎠∫mexp⎛ − D vD2 ⎞ dv T
⎝ 2T ⎠∫∫⎤⎡ v +vdµv T f ⎢dvr vr2σ (vr )⎥ .
⎥⎢⎥⎦⎢⎣ v − v
DD∫T(8)T

By comparing the obtained reactivity with the one when triton, the degree ofdistribution is Maxwellian, i.e. σ v Maxwell
T(d, n) 4 He
decrement in T(d,n)4He fusion reactivity by ICRF injection isestimated. For this purpose, we introduce the following
decrement parameter;

(4)

(5)

DFor given background temperature (T ≡ TD = T3He = Te), fuelion densities (nD = 2n3He) and QRF, we numerically solve Eq.
(1). From the derived triton distribution function, we canevaluate the T(d,n)4He fusion reactivity;(3)1 2δ (v − v T )nD σ v D(d,p)TSD(d,p)T ,24π v2∫

D

where ΩT is the cyclotron frequency of the triton, and Jn–1
represents the Bessel function of the first kind of order n–1.
The perpendicular wavenumber of the ICRF wave, κ⊥, is
obtained from the cold plasma dispersion relation. Throughout
the calculation the injected wave frequency is chosen as ω =5ΩT. The coefficient CRF is determined so that the absorbed
RF power by tritons is equal to Pfusion /Q RF. Here P fusion
represents the total fusion power. The parameter QRF, which
implies the ratio of fusion power to the absorbed RF powerby tritons, is externally given in the calculations.
The third term of the left hand side of Eq. (1) represents
sink of energy due to thermal conduction. The velocitydependent energy confinement time may be written as τE (v)= cEτE0 Max[1,v/v0]γ. Here τE0 is the energy confinement time,i.e.τE0 = 3sec. The dimensionless coefficient CE is adjusted
so as to keep the velocity-integrated energy loss as (3/2)nTT/τE0. We can simulate various loss mechanism by adjusting theparameters v0 and γ.
The triton source (ST) and loss (LT) can be written

ST (v) =1dvD vDv∫where v⊥ is the velocity perpendicular to the magnetic field,i.e. v⊥ = v sin θ. The RF- induced diffusion in the velocity
parallel to the magnetic field is neglected since it only givesa small contribution [11]. The perpendicular diffusion
coefficient [6-9] due to nth harmonic ICRF waves, DRF isgiven as⎛k v ⎞DRF = CRF J n2−1 ⎜ ⊥ ⊥ ⎟ ,⎝ ΩT ⎠3/ 2⎤⎡ v+ vmexp⎛ − D vD2 ⎞ ⎢dvr vr2σ DT (vr )⎥ .
⎝ 2T ⎠ ⎢⎥⎥⎦⎢⎣ v− v

(2)

The first term in Eq. (1) represents the influence of theCoulomb collisions with background particles, i.e. D, 3He andelectron. The second term accounts for the quasi-linear
diffusion due to the ion cyclotron range of frequency (ICRF)
waves. Following Stix treatment [6], we write the distortionof the triton distribution function by ICRF injection as⎛ ∂ fT ⎞⎜⎟⎝ ∂t ⎠nD ⎛ mD ⎞2π ⎝ T ⎠⎛ σ v T(d, n) He⎞η=⎜− 1⎟ × 100 [%] .
Maxwell⎝ σ v T(d, n) He⎠4(9)43. Results and discussion
In Fig. 1 we first show the steady-state triton distributionfunction as a function of parallel and perpendicular velocity
components to the magnetic field. The distribution function
and velocities are normalized to the thermal velocity, i.e. vth,
and to the velocity vT respectively. In this calculation, plasma
temperature T = 80keV, fuel-ion and electron densities nD =2n3He = (1/2)ne = 2×1020m-3, external magnetic field B = 6Tand QRF = 160 are assumed. It has previously shown that inwhere τP (v) = cPτP0 Max[1,v/v0]γ. Here τP0 is the particle
confinement time, i.e. τP0 = 2τE0 , and vT represents thevelocity corresponding to 1.01MeV birth-triton energy. The
second term in Eq. (6) represents a triton loss by T(d,n)4He
fusion reactions, here
Fig. 12307

Triton distribution function during ICRF injection in D3
He plasmas, i.e. T = 80keV, nD = 2×1020m-3, B = 6T and
QRF = 160.

Matsuura H. et al., Reduction in 14MeV Neutron Generation Rate by ICRF Injection in D-3He Burning Plasmas

typical D-3He plasmas, high-energy tail is formed in triton
distribution due to continuous triton generation by D(d,p)T
reaction around 1.01-MeV triton birth energy range. It isfound that the triton tail is extended by ICRF injection in
high-energy (high perpendicular velocity) range. This is owing
to the wave energy is transferred to the tritons, who haveresonant velocity, through the cyclotron motion. The numberof the high-energy resonant tritons hence increases comparedwith Maxwellian.
In Fig. 2 the T(d,n)4He fusion cross sections [12] arepresented as a function of triton energy (and also as a functionof normalized triton velocity) in the laboratory systems. As iswell known, the T(d,n)4He cross section has a peak around~100keV triton energy, and high-energy tritons more thanseveral hundreds-keV energy hardly make the T(d,n)4Hefusion reaction. As a result of increment in the fraction of thehigh-energy component to the total (bulk plus tail) tritons,
the velocity-averaged T(d,n) 4 He fusion reaction rate
coefficient decreases from the values for Maxwellian. By
using the Eq. (8), we can evaluate the T(d,n) 4He fusion
reaction rate coefficient for the triton distribution function
shown in Fig. 1 as 6.8×10-22m3sec-1. (If we assume both
deuteron and triton distribution functions are Maxwellian, theT(d,n)4He fusion reaction rate coefficient is 8.9×10-22m3
sec-1). In this case, the decrement in the T(d,n)4He fusion
reaction rate coefficient by ICRF injection is estimated as η= –23.5%.
In Fig. 3 the decrement parameter η is presented as afunction of temperature for several Q RF values. The
background deuteron density is fixed as nD = 2×1020m-3. The
degree of the decrement parameter has a maximum value
around ~90keV plasma temperature. This is because the nonMaxwellian component, i.e. high-energy tail, is trapped into
the bulk component in high temperature range, whereas thefraction of the tail becomes small in low-temperature range.
It should also be noted that the degree of the decrement
becomes small with increasing QRF values. This is because
the extension of the high-energy tail in triton distributionfunction by ICRF waves is weakened for small RF power
absorption.
We next show the decrement parameters as a function ofdeuteron density in Fig. 4. The plasma temperature is fixed
as 80keV. The degree of the decrement has a peak around nD= 1.5×1020m-3. This is explained, in high-density range, thecollisional slowing-down via Coulomb collisions withbackground ion is enhanced, and the number of tritons who
belong in the tail-component decreases. In low density range
the fusion power output decreases, and the RF power
absorption is relatively small.
Throughout the calculation it has been shown that in a
typical reactor-grade D-3He plasma, the 14-MeV neutron
generation rate can be decreased more than 20% by extending
the original triton tail using the ICRF injection. We haveshown an idea of the operation mode in which 14MeV
neutron generation rate is suppressed by small ICRF injection,
through a simple 2D Fokker-Planck simulation. In this paper
3308

Fig. 2T(d,n)4He fusion cross sections as a function of triton
energy (velocity) in the laboratory systems.

Fig. 3The decrement parameters η as a function of plasma
temperature.

Fig. 4The decrement parameters η as a function of deuterondensity.

Matsuura H. et al., Reduction in 14MeV Neutron Generation Rate by ICRF Injection in D-3He Burning Plasmas

we have not examined how much fractions of the injected RF
power is actually absorbed by tritons. To make this point
clear, more detailed analysis including the space profiles ofplasma temperature and density would be necessary.

[5]
[6]
[7]
[8]
[9]

H. Matsuura et al., Nucl. Fusion 40, 1611 (2000).
T.H. Stix, Nucl. Fusion 15, 737 (1975).
J. Kensner, Nucl. Fusion 18, 781 (1978).
D.T. Blackfield et al., Nucl. Fusion 22, 255 (1982).
A.V. Longinov et al., Plasma Phys. Control. Fusion 34,119 (1992).
[10] J.M. Dawson et al., Phys. Rev. Lett. 26, 1156 (1971).
[11] D. Anderson et al., Nucl. Fusion 25, 1751 (1985).
[12] Duane, B.H., BNWL-1685, Battelle Pacific NorthwestLab. (1972).

References[1] W.R. Fundamenski et al., Fusion Technol. 29, 313(1996).
[2] H. Matsuura et al., Fusion Technol. 22, 329 (1992).
[3] Y. Nakao et al., Fusion Technol. 27, 555 (1995).
[4] H. Matsuura et al., Nucl. Fusion 39, 145 (1999).

4309