J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)295–298
000–000

On Potentiality of Ion Temperature and Fuel Density Ratio
Measurements in D-T Plasma Using 6Li+D and 6Li+T
Nuclear Reactions
NAKAMURA Makoto, VORONCHEV Victor T.1 and NAKAO Yasuyuki
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Hakozaki 812-8581, Japan
1
Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia(Received: 9 December 2003 / Accepted: 6 July 2004)

Abstract
Abstract The use of 6Li isotope as a low Z (which denotes atomic number) diagnostic admixture in a D-T fusion
plasma has been investigated. We show that monochromatic γ rays generated in 6Li+T and 6Li+D nuclear reactions
might be used for measurements of two important plasma parameters, bulk ion temperature Ti and the fuel density
ratio nT /nD. Results presented in the report are restricted to the case of Maxwellian plasma. A possibility of detectionof diagnostic γ rays in the presence of γ -ray background is discussed.
Keywords:
D-T plasma diagnostic, ion temperature, fuel density ratio, 6Li+T and 6Li+D nuclear reaction, γ rays

1. Introduction

spectroscopy allows controlling the variation of plasma
temperature, but it is incapable of providing reliable valuesof ion temperature Ti. The situation with fuel density ratio
measurements seems to be also intricate. In the D-T plasma,
the determination of the n T /n D ratio [2] requires asimultaneous detection of 14.06- and 2.45-MeV neutrons
produced in D(t,n)α and D(d,n)3He reactions. Unfortunately,
the strong background [3] arising from collisions of fusionneutrons with a plasma-facing wall makes it rather difficult
counting the flux of DD neutrons.
Apart from neutron measurements, nuclear-physics
activation methods have been used for plasma diagnostics.
These methods are based on seeding plasmas with lightisotopes to induce nuclear reactions most appropriate forsolving a particular problem. Convenient diagnostic reactions
are those generating γ rays which freely escape fromlaboratory plasmas. In Joint European Torus (JET), forexample, reaction-produced γ rays have already been used for
diagnosing fast particles (fusion products and ions heated byradio frequency (RF) or neutral beam injection (NBI)) [4].
Recently, a new method of ion temperature
measurements has been reported by our group [5]. The
method is based on seeding the D-T plasma with a small
amount of 6Li and detecting subsequently three narrow γ lines
associated with 6Li+D and 6Li+T nuclear reactions. It was
shown that in the Maxwellian plasma ion temperature might
be determined by comparing the respective γ -ray yields.
However, there has remained a drawback that the value of Ti

Control of burning dynamics of fusion fuels has been an
essential part of hot plasma diagnostics. An importantparameter, which determines reactivity of any plasma atthermal equilibrium, is temperature of bulk fuel ions. When amany-component plasma is considered, other essential
parameters capable of reflecting burning history also appear.
These are relative concentrations (density ratios) of fuelspecies composing the plasma.
The problem of fuel density ratio measurements iscomparatively new. At early stages of nuclear fusion researchexperimental studies were mainly focused on one-component(hydrogen or deuterium) plasmas, so density ratio diagnostics
was considered to be rather of academic interest. At present,
however, this problem has become urgent because modern hot
plasma devices can operate with deuterium-tritium mixture.
Density ratio diagnostics is of particular importance for theInternational Thermonuclear Experimental Reactor (ITER)
project, which has recently been entered in a new phaseaiming at the construction of an experimental D-T reactor.
However, the question whether the nT /nD fuel ratio can bemeasured with satisfactory accuracy has not been clear yet.
Neutron spectroscopy is the most natural way of
diagnosing fuel ions in D-T or D-D plasmas. The status of
this diagnostics for magnetic confinement fusion devices is
described in a recent review [1]. Such methods, however, do
not give an exhaustive prescription for both ion temperatureand density ratio measurements. It is known that neutron
Corresponding author’s e-mail: nakamura@nucl.kyushu-u.ac.jp1295©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchNakamura M. et al., On Potentiality of Ion Temperature and Fuel Density Ratio Measurements

derived in such a scenario depends on an unknown plasma
parameter, the ion density ratio η = nT /nD.
In this report we resolve the above drawback and discussa potentiality of absolute ion temperature and fuel density
ratio measurements. The results presented below correspondto the case of Maxwellian plasma, but an important kinetic
issue relevant to the problem is also discussed. A possibilityof counting diagnostic γ quanta in the presence of γ -raybackground is examined.

appropriate for such diagnostics can be derived from Eqs. (3)(5):

2. Diagnostic reactions and γ -ray yields

whereC1 ≡Yγ (0.478)
Yγ (0.981)

C2 ≡We consider the following specific modes of nuclear
reactions between 6Li and fuel ions D and T:
6

Li + d → 7Be*[0.429] + n + 2.95MeV(1a)

Li + d → 7Li*[0.478] + p + 4.55MeV

(1b)

6

Li + t → 7Li*[0.478] + d + 0.15MeV(2a)

Li + t → 8Li*[0.981] + p – 0.18MeV

(2b)

66

f1 (Ti) =f3 (Ti) =6(3)6Yγ (0.478) = n Li nD〈σν〉 Li(d, p) + n Li nT 〈σν〉 Li (t,d)(4)

Yγ (0.981) = n Li nT 〈σν〉 Li (t, p) ,(5)666666Yγ (0.478)
Yγ (0.429)〈σν 〉 6 Li(d, p)〈σν 〉 6 Li(d, n)〈σν 〉 6 Li(t, d )〈σν 〉 6 Li(d, n)Yγ (0.429)
Yγ (0.981)= f 2 (Ti)(7)

= f 1 (Ti) + η f 3 (Ti) ,, f 2 (Ti) =〈σν 〉 6 Li(t, d )〈σν 〉 6 Li(t, p)

(8)

,.

where na represents the density of ion species a (a = D,T or6Li) and 〈σν〉 is the reaction rate parameter. For Maxwellianion velocity distribution functions, the rate parameter is ofthe form:
1/2⎛ 8 ⎞–E/kTi–3/2 ∞〈σν 〉 = ⎜dE ,⎟ (kTi ) ∫0 Eσ (E)e⎝ µπ ⎠(9)Equation (7) is fully independent of plasma density. The ratio
f1 of the 6Li+D rate parameters can be assumed to be constant,because cross sections of the respective reactions show similarenergy behavior in the range of thermonuclear interest. In theMaxwellian plasma f1 ≈ 0.84, while f2 is essentially dependent
on Ti. Therefore, the value of C1 is tightly interrelated with
ion temperature and, at the same time, is not affected byfluctuations of other plasma parameters. The temperature
behavior of C1(Ti) is shown in Fig. 1, which suggests that a
detection of the three γ lines would be sufficient for absolutemeasurements of bulk ion temperature, i.e. an average ion
temperature of core plasma.
Once ion temperature Ti is found (either by the above
method or from independent measurements), then the density
ratio η = nT /nD could be determined from Eq. (8). Several
curves of C2(η) corresponding to various plasma temperatures
within the 0–50 keV range are plotted in Fig. 2. At low ion

The modes lead to a formation of excited daughter nuclei
7Li*, 8Li* and 7Be* which further generate electromagnetic
radiation in their decay to ground states. The yields of these
monochromatic γ rays with energies of 0.429-, 0.478- and
0.981-MeV are given by, respectively,

Yγ (0.429) = n Li nD〈σν〉 Li(d,n)− f 1 (Ti)(6)

where µ and E are, respectively, the reduced mass and therelative energy of reacting particles, σ is cross section of
nuclear reacrion, and kTi is plasma ion temperature.

3. Scenario of ion temperature anddensity ratio measurements
In the previous work [5] we calculated cross sections of
the 6Li-induced reactions and examined the production ofdiagnostic γ rays in the Maxwellian D-T plasma. It was foundthat ion temperature might be found by comparative
measurements of any pair of 0.429-, 0.478- and 0.981-MeV γrays. This concept, however, implies that the fuel density ratioη = nT /nD should be known with sufficient accuracy.
In the present report we modify our approach andanalyze a possibility of absolute ion temperature Ti and thedensity ratio η measurements. The following relations

Fig. 1 The ion temperature dependence of C1.

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Nakamura M. et al., On Potentiality of Ion Temperature and Fuel Density Ratio Measurements

Fig. 2temperature diagnostics. It is important, however, that thenon-Maxwellian deviation is unlikely to affectsignificantly yields of other exothermic reactions in Eq.
(8). Therefore, the 0.429- and 0.478-MeV γ -ray signals
could be used for nT /nD ratio measurements, even if some
distortion of ion distributions exists.
2. The γ lines can be resolved experimentally. Doppler
broadening is estimated to be less than 15 keV, so it does
not cause γ -line overlapping. A more serious problem is
detection of the diagnostic signals in the presence of γ ray background. In the present report we analyze apossibility of counting the 0.429- and 0.478-MeV γ raysin the Compact Ignition Tokamak (CIT) and theTokamak Fusion Test Reactor (TFTR). In the both cases
the concentration of 6Li is assumed to be 1% of plasma
density. In CIT, the flux of background quanta [10] withenergy around 0.5 MeV within the 10-keV spectral range(corresponding to widths of the diagnostic γ rays) isestimated to be ~ 1012 cm-2 s-1. Yields of the 0.429- and0.478-MeV signals in CIT plasma (Ti = 40 keV, nT = nD= 1015 cm-3) is estimated by us to be at the level of (2–4) × 109 cm-3 s-1. These values are very similar to thoseused in a previous analysis [11] of γ -ray detection inCIT. By analogy with results of Ref. [11] we find thatthe signal to noise ratio R is close to unity, i.e., marginalfor the measurements. However, even when the signal tonoise ratio is less than 1 (R < 1), measurement is possibleusing the long exposure time of the detector. The
exposure time tc required for counting a signal with afractional error f equals (B + S)/(Sf )2 where B and S are,respectively, background and signal count rates [12]. For
TFTR plasma (Ti = 20 keV, nT = nD = 1014 cm-3) with B= 3,900 counts s-1 and a detector adjustment adopted inRef. [12] we find:

The dependence of C2 on the ion density ratio η = nT /nD.
The values of ion temperature (in keV) are given on theright.

temperature (below the D-T ignition point) the dependenceof C2 on η is rather weak, so the density ratio could not bemeasured with satisfactory accuracy. However, in the 10–50
keV temperature range, which corresponds to the important
phase of plasma burning, the measurements of the nT /nD ratio
might become possible.
The above conclusions have been derived under twomodel assumptions. First, velocity distributions of plasma ionswere taken to be Maxwellian and, second, it was assumed
that the γ rays could be resolved and distinguished from γ ray background. These points are worth discussing below:
1. It is known that in the D-T plasma ion distributions
are not described by the purely Maxwellian form. Apossible source of the distortion results from nuclear
elastic scattering of 3.5-MeV α-particles by fuel ions.
This scattering is accompanied by large momentum
transfer and produces fast (knock-on) deuterons andtritons that perturb high-energy tails of the distributions.
Such fast ions of MeV energies were both predicted
theoretically [6-8] and recently observed in JET
experiments [9]. Apparently, the distortion of distributionfunctions can affect rate parameters of the diagnostic
reactions, especially, the endothermic mode (2b). The
latter is suppressed in the deep sub-barrier range andproceeds with sizable probability at energies only well
above the reaction threshold. This means that the yieldof 0.981-MeV γ rays should be sensitive to the shape oftriton distribution at high energy and then a small
deviation from the Maxwellian form might change
significantly the γ -ray flux. Therefore, the model
temperature profile of C1 in Fig. 1 might be changed
crucially for realistic distributions, so the above method
would not be able of providing high accuracy ofS(0.478) = 1,645 counts s-1 tc (0.478) = 33 ms
S(0.429) = 929 counts s-1tc (0.429) = 89 ms
The values of tc correspond to measuring the signals withaccuracy of 25% by a single NaI detector. When a 10 ×
10 array of detectors is used, the exposure time tc can befurther reduced by two orders of magnitude [12].
Moreover, since the diagnostic γ rays are monochromatic, the background B and the exposure time tc
could be also reduced by counting the signals within anarrow spectral range not exceeding ~ 10 keV. Suchmeasurements could be performed using Ge(Li)detectors, which have high resolution of only few keV.
The above estimations are very likely to be also valid
for ITER plasma.

4. Conclusions
In the present report we have investigated the use of 6Li
isotope as a low-Z diagnostic admixture in the D-T fusion
plasma. Our main goal was to understand whether γ rays
generated in 6Li+T and 6Li+D nuclear reactions could beemployed for measuring two important plasma parameters ion temperature Ti and the fuel density ratio η = nT /nD.
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Nakamura M. et al., On Potentiality of Ion Temperature and Fuel Density Ratio Measurements

References

In the Maxwellian plasma, Ti could be determined bymeasuring comparative yields of three reaction-produced γrays. The method, however, may turn out to be useless if adeviation of ion distributions from the Maxwellian form
appears. To make a final conclusion one should know realistic
distributions of fuel ions in experimental devices.
We have shown that in the plasma burning phase at Ti >10 keV the nT /nD density ratio could be measured by meansof γ -ray spectroscopy. This technique requires a simultaneous
detection of two 0.429- and 0.478-MeV γ rays and may be
applicable even if some distortion of ion distributions exists.
The γ -ray signals can be resolved and counted in the presenceof background typical of CIT and TFTR. This conclusion isvery likely to be also valid for ITER.

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Acknowledgments
The authors would like to thank the referee for valuablecomments and suggestions.

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