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VACUUM ULTRA-VIOLET SPECTROSCOPY ON
T.F.R. TOKAMAK PLASMAS
T. Group
To cite this version:
JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 7 , Tome 39, Juillet 1978, page C4-86
VACUUM ULTRA-VIOLET SPECTROSCOPY ON T.F.R. TOKAMAK PLASMAS
T.F.R. GROUP(presented by C . Breton)
Association EURATOM-CEA sur la fusion
Dtpartement de Physique du Plasma et de la Fusion ContrGlCe Centre d7Etudes Nucleaires, BP 6, 92260 Fontenay aux Roses, France
RCsumC. - On expose les mesures faites, dans le domaine de longueur d'onde 5-2 000
A,
sur le plasma du Tokamak de Fontenay-aux-Roses. Ce plasma est une source de grand volume, a haute temperature (kT,-
2 keV) et de densite relativement petite (n,-
8 X 1013 cm-3). Le gaz de travail(H, ou D,) est contamini: par des impuretes Iegkres ( 0 , C, N) et lourdes (MO, Fe). Les premieres sont complktement ionisees dans la rtgion centrale, l& secondes existent &-tat d'ions fortement charges possirdant encore quelques electrons (Mo30+).
Les spectres inconnus des ions du molybdkne sont Ctudies en detail dans le domaine 5-100 A ;
le comportement spatio-temporel des divers ions des impuretes dans le domaine 100-2 000
A.
Les radiances (W. cm- sr- l ) sont interprttees a B'aide de modeles bases sur l'approximation coronalesoit a I'equilibre (centre du plasma durant le plateau de courant) soit en regime transitoire (debut de la decharge et zone peripherique du plasma). Les pertes d'energie en sont deduites.
Dans le domaine 1 200-2 000
A,
la temperature des ions est mesuree i partir de l'elargissement par effet Doppler de raies emises par les ions des impuretes Iegkres.Abstract. - Spectroscopic measurements in the range 5 to 2 000
A
on T.F.R. are presented. This machine is a source of large volume, high temperature (kT,-
2 keV) and relatively low density (n,-
8 X 1013 cm-3). The working gas (H, or D,) is contaminated by light ( 0 , C, N) or heavy (MO,Fe) impurities, the former being fully ionized in the central region of the the latter existingas highly charged ions with some remaining bound electrons (Mo30+).
Unknown spectra of molybdenum ions are studied in details in the range 5-100
A
; spatio- temporal behaviour of the various impurity ions is studied between 100 and 2 000 W . Radiances (W .cm-L sr-l) are interpreted in terms of ions densities through models which are all based on the corona1 approximation either a t equilibrium (central part of the plasma during current plateau) or in the transient regime (beginning of the discharge and peripheral zone of the plasma). Total radiation losses are deduced.In the range 1 200-2 000
A,
ion temperature is deduced from Doppler measurements of some light impurity lines.1. Introduction. - One of the critical points for the understanding of Tokamak plasmas is the role played by impurities, present in the plasma as a result of sputtering and desorption of the walls and limi- ter [l, 21. The main effect of these impurities is to increase the losses (mainly by line radiation) that the input power (ohmic plus eventual additional heating) has to overcome, thus possibly -limiting the attainable ion and electron temperatures. Both light and heavy impurities exist in the plasma. Light impurities (oxygen, nitrogen, carbon) have ionization potentials for the last ions which are lower than the central electron temperature of typical Tokamak plasmas; they are, therefore, completely ionized at the plasma center and do not radiate there. Heavy impurities (iron, molybdenum), on the other hand, have ionization potentials for the last ions which are
much higher, than the central electron temperature ; they are, therefore, only partially ionized in the plasma center, and are an important source of line radiation. However, since the electron temperature decreases toward the plasma border, all the ionization states (from neutral up to the maximum ionization degree obtained in the center) exist in the plasma. Typical values for the central concentration of the most important impurities are a few for oxygen and a few O / o , for molybdenum (as compared to the
electron density)..
In this paper we shall describe the spectroscopic work in the ultra-violet spectral region performed on the T.F.R. Tokamak. This machine, and the main results obtained, have been extensively described in the literature (see, for example, [3]). It is a toroidal configuration with major radius of the torus
VACUUM ULTRA-VIOLET SPECTROSCOPY ON T.F.R. TOKAMAK PLASMAS C4-87
R = 9 8 cm, and molybdenum limiter radius grazing incidence (lo), 2 m radius grating a = 20 cm ; maximum plasma current and toroidal (2 400 groovelmm) spectrometer. Several tens of
magnetic field are 400 kA and 60 kG, respectively. discharges are necessary in order to correctly expose The plasma duration is typically 500 ms. Figure 1 the plate (Kodak SC 5 type) for the heavy impurity ion radiation; however, only a few discharges are
Soft x-ray
detecius sufficient for the oxygen ion lines. Figure 2 shows
soft x-ray spectmmeter
Frc. 1. - Position around the T.F.R. torus of the diagnostics discussed in the text.
shows the position around the torus of the diagnostics employed for the measurements described in this paper. Starting from the limiter, in the plasma current direction, we find : at cp = 900, a grazing incidence vacuum ultra-violet duochromator and a visible monochromator ; at cp = 1350, a multichannel HCN laser interferometer, giving the electron density pro- file, and a fast neutral analyzer, for ion temperature measurements ; at cp = 1800, four soft X-ray detectors, using the absorber method in order to obtain the time evolution of the central electron temperature; at cp = 2250, Thomson scattering, giving a shot-to- shot profile of the electron density and temperature, and a multichannel analyzer for the spatial profile of Hp (and, therefore, the spatial profile of the neutral hydrogen, or deuterium, density) ; at cp = 270°, a normal incidence vacuum ultra-violet spectrometer, occasionally used to check the uniformity of irnpu- rities around the torus ; at cp = 3150 and cp = 00, space-resolved bolometry, providing a profile of the
radiation losses ; at cp = 3150, a vacuum ultra-violet monochromator for Doppler broadening measure- ments on impurity ions ; finally, at cp = 00 an extreme grazing incidence vacuum ultra-violet spectrometer. 2. Extreme grazing incidence V.U.V. spectro-
scopy (l). - The 5 &l00
A
spectral region has been studied photographically by means of an extreme(r) With the collaboration of J. L. Schwob, M. Klapisch, N. Schweitzer and M. Finkenthal, Racah Institute of Physics, Jerusalem, Israel. CV CV1 N V I I O V I I ovr I I OVI I I
FIG. 2. - T.F.R. Tokamak and MO spark spectra in the spectral range 16-80 A.
the spectral region from 16
A
to 80A ;
300 discharges were used here, in order to record weak lines of heavy impurities. The identification of 0, N, C lines is straight-forward, since their lines are well known, and, moreover, they are the most intense lines in the spectrum; this fact can obviously be also used in order to check the wavelength scale. The other, weaker, lines belong to different ionization degrees of iron and molybdenum. The identification of iron lines is relatively easy by comparing with well-known solar flare spectra. However, next to nothing is known for the higher ionization degrees of molybde-C4-88 T.F.R. GROUP
energy vacuum sparks using a molybdenum anode ; however, due to the different physical conditions of the spark (higher electron temperature and density, shorter life-time) not all the molybdenum lines are present. The other method is, therefore, to compare the observed wavelengths with the 'most recent and accurate wavelength theoretical calculations [4]. In this way, lines from molybdenum -ions from MO XV
up to MO XXXIII have been identified [5]. Figure 3 shows a portion of the T.F.R. spectrum between 10
A
and 21 A, where most of the highest ionizationd MO)
Identification of FeXlX to FeXXlY by B.C. Fawcett
FIG. 3. - Enlarged portion of T.F.R. spectrum in the range 10 A-
21
A.
stages are found ; this figure gives a clear idea of the extreme difficulty of identification, since not only different degrees of ionization are present, but also several impurities.
Although spectra like those shown are very useful for spectroscopic work (line identification and compa- rison with theoretical calculations), this type of work has little usefulness from the point of view of understanding the plasma physics, since it is very difficult to get from photographic plates reliable absolute values of impurity densities.
3. Spatially-resolved vacuum ultra-violet measure- ments. - A schematic diagram of the vacuum ultra- violet duochromator set-up is shown in figure 4. The duochromator is placed about 4 m from the center of the vacuum chamber; it has an hologra- phically ruled diffraction grating G (1 200 groo- veslmm ; wavelength of maximum efficiency 300 A) working at a grazing angle of 70. Two tungsten cathode magnetic electron multipliers B are moved along the
i
to v l s ~ b l e
1
T F Rrnonochrornotor
l
FIG. 4. - Vacuum ultra-violet spectroscopy experimental set-up.
M, : tilting gold-coated mirror ; M, : removable mirror ; a :
scanned angle ; D : rectangular diaphragm ; S : spectrometer slits ;
B : magnetic electron multipliers ; R : Rowland circle.
1 m radius Rowland circle R, e a ~ h having in front an adjustable exit slit S. The electron multiplier working at higher wavelengths has a cathode coated with CsI, thus allowing to extend the measurements up to 2 000
A.
The wavelength resolution used in the work reported here is 2A.
Space resolution was obtained by using a tilting gold-coated mirror M, (working at an incidence angle of between 5O and 40°),the duochromator being used with the entrance slit set horizontally. An adjustable rectangular dia-
phragm D placed just behind the gold-coated mirror, provides the desired space resolution. We have generally used a 10 mm space-resolution, since several profiles made with 3 mm resolution have shown that it is a good choice in order to take into account both'resolution and signal-to-background ratio. This system allows a shot-to-shot scan of the upper half of the plasma in a torus section placed at 90° from the limiter.
The absolute intensity calibration of this system has been performed in situ by the branching ratio method [6], using a visible monochromator viewing the plasma along the same chord (by means of the removable mirror M,). The visible monochromator has been calibrated down to about 3 800
A
by means of a standard tungsten ribbon lamp set up with the same optical arrangement as for plasma observations. The method depends on the appropriate selection of atoms or ions which emit pairs of lines from the same upper level i, one line (i, m) being in the visible, and the other (i, j) being in the V.U.V. Then the ratio of the radiances B, as measured by the two spectrometers, isB(i, m) A (i, m)
-=
B(i, j) A 6, j)
VACUUM ULTRA-VIOLET SPECTROSCOPY O N T.F.R. TOKAMAK PLASMAS C4-89
visible as a function of incidence angle having been measured previously to assembly). Figure 5 shows the results of this calibration along the central chord, for the short wavelength electron multiplier. The points at Lya - 1 216
A
and He I1 - 256 A, 304A
are based on calculated relative populations of the levels involved [7]. Two more calibration points (He I, 537 A-5 015 A, and He I, 522 A-3 965 A) never gave consistent results, probably because of problems with self-absorption. Needless to say, helium was purposely added to the initial deuterium gas for the calibration. Figure 5 clearly shows the major short-
photons cm"
FIG. 6. - Experimental radiance B(h) of the 0 V1 1032 A line, Abel-lnverted volume emission E(r), and density no5+(l;).
FIG. 5. - Calibration curve for the short wavelength ( B , ) electron multiplier. and branching-ratio line pairs used.
coming of this calibration method : only a few experi- mental points are available in the spectral region of interest, so that one has to rely on interpolations. However, the minimum of the calibration curve agrees with what is expected from the grating effi- ciency; moreover, most of the observed lines in T.F.R. are below 400
A
and above 1 000 A, thus reducing the possibility of errors. The calibration curve does not extend below 100 A, since this is the lower useful limit of our spectrometer, background light being dominant below this wavelength. All things considered, we estimate the error on the abso- lute intensity values at approximately 50%.
Figure 6 shows an example of the data processing for a peripheral line. The data refer to the 0 V1 1 032
A
line, and have been determined with a 140 kA, 26 kG deuterium discharge. B(h) is the experimental radiance (photons S-' cm-' sr-') versus chordheight h. The line through the experimental points is a smoothed, hand-drawn, fit which has been used
in the Abel-inversion procedure (assuming cylindrical symmetry). E(r) is the (Abel-inverted) plasma volume emission (photons S-' cmp3) ; to obtain E(r) it must
also be assumed that the plasma radiates isotropi- cally. nO5+(r) is the density profile of the ion 0 5 + .
This has been obtained in the corona1 approximation (certainly valid for impurities at Tokamak electron densities), i.e., E,(r)
-
n,(r) n,(r) Q(T,), where n, is the density of ions of charge Z of the considered atomic species, and Q is the excitation rate coefficient, function of radius through T,(r) (see [g] for the for- mulae used to calculate Q). Since all lines detected (except for the 0 V11 1 623A
line) are resonance transitions of the ns-np type which are excited from the ground state and can decay radiatively only to it (n is here the principal quantum number), Q is a weak function of T,. As a consequence, the peak positions of E,(r) and n,(r) are almost coincident, n,(r) peaking only a few mm outside (since n,(r) isa decreasing function of r).
C4-90 T.F.R. GROUP
translation of the peripheral Te and n, profiles in order to have the correct value at the last measured point).
Finally, a word of caution must be given on the impurity density profiles obtained in this way. Indeed, the wings of these profiles must be taken with some precaution. The inner wing is affected by the poor precision of the Abel-inversion procedure in this region, due to deep central depression of B(h). The outer wing, on the other hand, suffers from the poor knowledge of ne(r) in the plasma periphery, and also from the inaccuracy with which the hand- drawn smoothing procedure sends to zero the B(h) profile. These two wings will, therefore, be dis- regarded in the following. Moreover, although more accurate measurements are necessary (and difficult to perform), our simplified numerical model of impurity diffusion [9] indicates that the outer increase is not due to excitation of recombining ions.
FIG. 7. -Time evolut~on of the radial profile of the density of oxygen ions five times ionized.
Figure 7 shows, as an example of the data obtained for low ionization potential ions, the time evolution of the radial density profile of the ion OS+. LOW ionization potential ions appear in the discharge right at the beginning (in the first few ms). At the time of the ionization, their distribution in the plasma is uniform. The temperature and density being low, deep penetration of the impurities into the discharge is possible. This emission is, therefore, characteristic of volume ionization ; this fact has been used, with the help of a uniform, one-impurity, plasma numeri- cal model, to estimate the initial amount of impurities present in the plasma [l]. This procedure invariably shows that the Zeff value
Zii n' being the effective charge
is already large (typically 3 to 4) in the first ten ms. However, after this initial ionization .phase, the electron temperature and density rapidly increase, and penetration to the center of the incoming impurity atom flux is no more possible ; the ion density profile then develops a cylindrical shell structure. The variation of the emitting shell position with time corresponds to the evolution of the peripheral electron temperature. Indeed, the peak of the density profile of a given ion always occurs at the same electron temperature (Te 2: 113
xi,
wherexi
is the ionizationpotential of the ion considered) and, therefore, as Te increases the shell position moves outwards.
FIG. 8 - Emisslon profiles of five success~ve oxygen ions. norma- 11zed to thelr peak values.
Figure 8 shows the radial profiles of the emission of five successive ionization degrees of oxygen ( 0 I11 to 0 VII), normalized to their peak value. These results have been obtained with a 140 kA, 26 kG deuterium discharge, at 200 ms (on the current plateau). The radial positions of the peaks are in the right order, taking into account their respective ionization potentials and the decrease of the electron temperature towards the plasma edge. Corona equili- brium calculations [g] show that the temperature at the position of the experimental peaks is always higher than the temperature of maximum abundance at ionization equilibrium (except, perhaps, . ..for - . 0 . . . VII). . . . -
At a given radius, therefore, light atomic species are less ionized than at corona equilibrium; this is due to the fact that they are diffusing inwards. Comparing these results with those obtained by means of a numerical model for impurity diffusion [g] (in which the impurities diffuse inwards with a constant velocity V, in a background plasma repre- sented by the experimental density and temperature profiles) it is possible to estimate the inward velocity and the recycling flux density. Typical values for oxygen are V. = 103 cm S-' and
VACUUM ULTRA-VIOLET SPECTROSCOPY ON T.F.R. TOKAMAK PLASMAS
This is done by writing down the rate equations for the ion densities; since the recombination terms can be neglected, the experimental knowledge of T,(r), n,(r), and the radial density profiles of two successive ions nj(r) and njWi(r) is sufficient to estimate the flux density term rj(r). The values obtained in this way agree within a factor of two with those mentioned above.
Moreover, it must be pointed out that it is not necessary to have space-resolved measurements in order to estimate the impurity atom flux density To [l]. It can be easily shown that the value of the radiance on axis (that is, for h = 0) of the line of a peripheral ion j is related to the incoming atom flux density
by the relation
where A is the branching ratio for the observed line, Sj the ionization rate coefficient of the ion considered, Q the excitation rate coefficient of the transition observed, and p the radius at which the ion is produced. The values obtained in this way again agree within a factor of two with those given above.
Finally, the experimental results can be used tol estimate the radiation power losses due to impurities. Of course, for the lines observed the power loss is directly given by the measured radiances. However, we only measure a few lines, and therefore the numeri- cal model mentioned above [9] must be used in order to estimate the total radiation power losses due to the measured flux density. These estimates show that the radiation losses in the peripheral region are a considerable fraction of the input ohmic power (generally of the order of 30
X).
Until now we have only discussed low iopization potential ions, characteristic of the peripheral plasma region. In the central region (characterized by an electron temperature of typically between l keV and 2 keV) light impurities are completely ionized, and, therefore, do not emit any line radiation. Heavy impurities, on the other hand, are only partially ionized. Although very little is known about highly ionized molybdenum (the dominant heavy impurity), two transitions in the spectral region of interest have been identified [2]. One belongs to MO XXXI (Mg- like,
xi
= 1 805 eV, 3s'-3s 3p, 'S,-'P,, il = 117 A), and the other to MO XXXII (Na-like,xi
= 1 870 eV, 3s-3p, 2S,12-2P312,1,2, il = 129 A, 177 A). These lines have initially been tentatively identified on the basis of isoelectronic sequence extrapolations, but have now been positively identified by injecting molybdenum in the discharge [l l]. Figure 9 shows the time evolution of the MO XXXI 117A
line, compared to that of the 0 V1 1 032A
line. Also shown here are the plasma current I,, the loop voltage U, the line electron density n, I (along the central chord), and the centralI l l l l , l , , , J . .
0 100 200 300 t [ms] 500
FIG. 9. -Time evolution of plasma current I,, loop voltage U.
l ~ n e electron density n, l (through the central chord), electron tem- perature T,(O), radiance B(0) of 0 V1 1032 A, and radiance B(0) of MO XXXI 117 A (with its background taken several Angstroms
away from the line).
C4-92 T.F.R. GROUP
1
1
50 rnsFIG. 10. - Radial profiles, at two times, of Mo30f and Mo31f ion densities.
Since only two MO ions are seen in the central plasma region, the total central amount cf molybdenum is obtained from the experimental data by using ioniza- tion equilibrium calculations. Typical central values are nMo(0) = 5 X 10'0-~011 cm-3, depending on the
experimental conditions, and nMo(0)/n,,(O) = 3-4. The fact that iron is considerably less abundant than molybdenum is not very surprising, since molybde- num plates cover the liner at several locations around the torus, and moreover, after three years of operation the walls are covered with molybdenum coming from the limiter. It must be stressed at this point that the total density values given rely heavily on ionization equilibrium calculations. The values of the ionization rate coefficients S, recombination
(radiative plus dielectronic) rate coefficients a, and excitation rate coefficients
Q
used in these calculations are based on empirical formulae the precision of which cannot, a priori, be estimated. However, aposteriori, the experimental data support quite strongly our molybdenum ionization equilibrium calcula- tions [l l]. In particular cases, the central electron temperature exhibits saw-tooth modulations, seen on the X-ray radiation (free-free and free-bound transitions) having a period of 2 ms. Such modulations are present either on one central molybdenum line (Fig. 11) or on both of them depending on the temperature. This is consistent with a shift of the
FIG. 1 1. -Effect of electron temperature modulations on MO XXXI 117
A
and MO XXXII 129A
radiances. Top, MO 117A
during the whole discharge; middle, X-ray signal (in phase with T, modu- lations) and MO 117A
; bottom, X-ray signal and MO 129A.
The two last pictures are located in time at about 300 ms from the beginning of the discharge and intensities are increasing downwards.FIG. 12. - MO 117 (bottom) and MO 129 (top) line volume emis- sions calculated in the transient corona1 regime near equilibrium when applying a T, modulation of time shape given by the X-ray signal and amplitude given by Thomson scattering measurements.
VACUUM ULTRA-VIOLET SPECTROSCOPY ON T.F.R. TOKAMAK PLASMAS C4-93
the line radiances. Figure 12 gives the results of a calculation using the measured temperature modu- lation and showing the corresponding modulation on the MO line radiances [l 1, 121. On the basis of these considerations, we estimate the error on total moly6denum central density obtained from spectro- scopic data to be a factor of two.
In the wavelength range studied here, only one other line of comparable intensity, belonging to a highly ionized heavy impurity, has been observed. This is a line of ~ e (Be-like ~ ~
xi
= +1 950 eV, 2s2- 2s 2p 'S,-'P, 133 A) which has been identified bycomparison with solar flare spectra [2]. It presents the same temporal and spatial behaviour as the two MO-lines mentioned above.
Finally, again an estimation of the radiation power losses due to central heavy impurities must compare the experimental results with numerical calcula- tions [l l]. Typically, about 10 % of the input ohmic power is lost as radiation in the center.
4. Doppler broadening measurements in the vacuum ultra-violet. - As already said in the introduction,
in T.F.R. the ion temperature is measured by ana- lyzing the energy of the charge-exchange neutral leaving the plasma. The system used can give a shot-to-shot radial profile of Ti up to 12 cm. In order to have the complete profile of Ti, we have measured the Doppler broadening of lines of impurity ions existing in the peripheral region. This measurement indeed gives the ion temperature, since the impurity ions temperature is, for the plasma conditions existing in T.F.R., equal to the proton (deuteron) tempe- rature (because of the short equipartition time between protons and impurity ions, actually shorter than the electron-proton equipartition time). For the Doppler measurements a 1.25 m focal length mono- chromator (Ebert-Fastie type), with an holographic grating (3 600 grooves/mm ; wavelength of maximum efficiency 1 600
W),
has been used. The entire mono- chromator is under vacuum, and is connected to the torus through a MgF, lens. The shortest wave- length accessible with this system is 1 200 A. The fine wavelength scanning is obtained by rotating a MgF, plate placed just before the exit slit. The instrumental width of this system has been measured by means of an auxiliary ultra-violet source, and it is 0.1 A. The space-resolution of the measured Ti is here insured by the shell distribution of the peripheral impurity ions. We have measured the Doppler broadening of C IV 1 548A
(peak position r = 18 cm for the discharge studied) and 0 V11 1 623A
(peak position r = 12.5 cm). Figure 13 shows Ti(r) and T,(r) for a 140 kA, 30 kG deuterium discharge witha carbon limiter. T,(r) is measured by Thomson scattering up to 12 cm, and then extrapolated following the procedure described in section 3. Ti(r) is measured
FIG. 13. - Electron temperature T, and ion temperature T, profiles in the outer half of the plasma. Solid lines are from Thomson scatter- ing and fast neutrals analysis, respectively. Dotted line for T, is an extrapolation, as explained in the text. The two T, points shown are from Doppler broadening measurements of the Impurity lines
indicated.
by charge exchange up to 12.5 cm; the agreement between the last point measured by charge exchange and the point obtained by measuring the Doppler broadening of 0 V11 1623
A
is quite good. Note that Ti(r) > T,(r) for r > 13 cm ; but is must be stressed that the electron temperature peripheral profile has been extrapolated.T.F.R. GROUP
References
[l] Equipe T.F.R., Nucl. Fusion 15 (1975) 1053. [2] HINNOV, E., Phys. Rev. A 14 (1976) 1533.
[3] T.F.R. Group, Proceed. 5th Intern. Con$ on Plasma Physics
and Controlled Nuclear Fusion Research, Tokyo. IAEA
(Vienna) 1 (1976) 135.
[4] KLAPISCH, M., PEREL, R., WEIL, D., EURATOM-CEA Association Fontenay-aux-Roses (France), Report EUR.
CEA. FC. 827 (1976).
[5] SCHWOB, J. L., KLAPISCH, M,, SCHWEITZER, N., FINKENTHAL, M,, BRETON, C., DE MICHELIS, C., MATTIOLI, M,, Phys.
Lett. 62A (1977) 85.
[6] HINNOV, E., HOFMANN, F. W., J. Opt. SOC. Am. 53 (1963) 1259.
[7] JOHNSON, L. C., HINNOV, E., J. Quant. Spectrosc. Radiat.
Transfer 13 (1973) 333.
[8] BRETON, C., DE MICHELIS, C., MATTIOLI, M., J . Quant. Spec-
trosc. Radiat. ~ransfer 19 (1978) 367.
[g] BRETON, C., DE MICHELIS, C., MATTIOLI, M., NUCL. Fusion 16 (1976) 891.
