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Diagnostics of high temperature deuterium and tritium plasmas by spectrometry of radiative capture reactions
Nuclear Instruments and Methods in Physics Research 221 (1984) 449-452 North-Holland, Amsterdam
449
D I A G N O S T I C S O F H I G H T E M P E R A T U R E D E U T E R I U M A N D T R I T I U M P L A S M A S BY SPECTROMETRY OF RADIATIVE CAPTURE REACTIONS F.E. C E C I L Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
D a v i d E. N E W M A N GA Technologies Inc., San Diego, CA 92138 USA
Received 13 June 1983
The high resolution gamma ray spectrometry of the ground state radiative capture reactions d(p, y)3 He, t(p, y)4 He, d(t, y )~He and d(d,y)4 He is proposed as a temperature diagnostic of energetic hydrogen plasmas. Counting rates for these reactions for temperatures and densities characteristic of current CTR research are estimated.
The measurement of the ion temperatures of hydrogen, deuterium and tritium plasmas is an essential component of the CTR diagnostic effort. Medley and Hendel [1] have recently noted the possible use of the d(t,-/)SHe and d(3He, ~,)5Li reactions as ion temperature diagnostics. In this paper we propose the high resolution measurement of the energy of gamma rays produced by the reactions d(t,y)SHe, d(d,3,)4He, p(t,y)4He and p(d,~,)3He as a technqiue for the measurement of ion temperatures. The essential point of the proposed technique is that the precise energy of these gamma rays will be an easily predictable function of the plasma temperature. The energy of a gamma ray produced in the general reaction 1(2,7)3 between nuclei with masses and kinetic energies M~ and E 1, etc. is given in the center-of-mass frame (primed) by
E~ = Q + E{ + E~- E;,
(1)
where Q = M I + M s - M 3. The values of Q for the d(t,y)SHe, d(d,y)4He, p(t,y)iHe and p(d,y)3He reactions are 16.696, 23.84"/1, 19.814, and 5.4936 MeV, respectively. In the laboratory frame, the gamma energy will be Ey = E 0 + Q(1 - Q / 2 M 3 ) ( 1 + flCM COS0),
(2)
where E 0 = E{ + E~, flcr~ is the velocity of the centeror-mass frame, and 0 is the direction ~of motion of the center-of-mass relative to the observex. In eq. (2) we have made the approximation E i << Q << M i (i = 1,2,3). This approximation is appropriate for current plasma applications. In a thermalized plasma characterized by an ion 0167-5087/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
temperature T~ the reaction rate is greatest when E 0 is equal to the "Gamow peak" energy E~, given by [2]: E c = ( ~ a Z 1Z2 kT~ )2/3( M/2)1/3,
(3)
where a is the fine structure constant and M = M 1M2/ (M~ + 342). Physically this peak corresponds to the maximum in overlap of the Maxwell distribution of the plasma (which drops off rapidly at high energies) and the reaction cross section (which drops off rapidly at low energies). The energies of the observed gamma rays will then constitute an approximately symmetric distribution, with a centroid at E, -- a ( 1 - Q / 2 M 3 ) + E G,
(4)
and a width (fwhm) of 2
A ~ (16E~kTi/3 + 8 ln2Q kTJM3)
1/2
.
(5)
Here the width A contains contributions from the width of the (approximately Gaussian) Gamow peak and from Doppler broadening. The energy resolution of the detector will cause additional spreading. (In the case of d(t,3,)SHe, the 580 keV natural line width of the 5He ground state will further-broaden the gamma distribution.) The values of E C and A are shown in fig. 1. From eqs. ( 4 ) a n d (5), the observed gamma ray energy and width can each be used to measure ~ with independent statistical and systematic uncertainties. In order to design an actual diagnostic device based upon the measurement of the energies of these gamma rays, it is necessary to estimate the yield for reasonable values of the temperature a n d density of the plasma. Thisyield will have to be high enough' to provide' a statistically significant distinction between the gamma
t::E. ('e('d, D.E. Newman /" ttigh temperature deutemum and trmum
450
140
rately predicted from first principles, but may be determined empirically from laboratory measurements of the reaction cross sections as a function of energy. Since the energy at which the reactions should be measured in order to predict the yield of the corresponding plasma at a certain temperature is the energy of the G a m o w peak, a knowledge of the corresponding nuclear reaction is required at energies under 100 keV for T ~ 20 keV. At these energies, the cross section is usually written as [2]:
130 120 ~_
----
ENERGYEg
/
~ 60
110
t
100 9O
80 ~_ c3
70
o( E ) = S ( E ) / E e x p ( - b / E
30
0o
~
///
5o
/'~
4o
20
g
3o
2o
:,o
lO
I
I
I
I
I
I
I
1
10 18 10 19
7.a 10 20
~ 10-21 "~ 10 22 7- lo-2a
P(D,Y).-
]0-24
10-25 10-26 10-27
10-28 0
I 2
I 4
I 6
I 8
I 10
I 12
I 14
I 10
18,
kTi (keV)
Fig. 1. (a) Predicted energy (dotted) and width (solid) of gamma rays from fusion reactions. The S-factor for P(D,7) was assumed to be [2.4x10 -a +7.9x10 -7 E] (keV-b) (ref. [3]). The S-factor for d(t,7) was assumed to be S(0)/[( E - 69) 2 +1640] (ref. [2]). The S-factors for p(t,y) and d(d,7) were assumed to be constant in this energy range; (b) The reactivities ( o r ) of the ground state transitions in plasmas with thermal distribution of ion energies. ray energies corresponding to plasma temperatures to be differentiated. While the relative temperature dependence of these reactions can be calculated using the well-established techniques of nuclear astrophysics [2], the absolute scale of the reaction yield cannot be accu-
'/e),
(6)
where b = 31.28 Z1ZzA 1/2 keV 1,/2 and S ( E ) is the Sfactor which, in the absence of narrow resonances, is a slowly varying function of energy and where A is the reduced atomic number of the constituent particles. The rate of gamma ray production in a plasma is
Rv=nlnz(ov)cm-3s
1
(7)
where the densities of the reactants are nl and n 2, and ( o r ) is the reactivity [2], obtained by integrating the velocity-weighted product of the Maxwell-Boltzmann distribution and o ( E ) from eq. (6) over the ion energies. Although these reactions have been observed at high energies, only d(p,y)3He has been measured accurately at plasma energies [3]. The measurements are summarized in table 1 and all existing data have been used to extrapolate to the zero energy limit of the S-factor. The indicated error limits reflect the disparity in the measured values of the cross sections. The reactivities were calculated using these values and are shown in fig. 1. Plasma diagnostics currently in use are incapable of measuring the energy shift, E G, in eq. (4), Sodium iodide scintillators have insufficient energy resolution and silicon detectors cannot absorb gamma rays of this energy range [7]. The most precise neutron spectrometry data to date [8,9] barely resolve the effect of ion motion by collecting data over many shots. Charge-exchange analysis will not provide information about the core plasma in future large, high-density machines, because neutral atoms will be efficiently re-ionized before
Table t Summary of low energy measurements of cross sections for radiative capture reaction among hydrogen isotopes. Reaction
Lowest energy (keY)
S(E = 0) (keV-b)
P(D,y)3He P(T,y)4He D(D,7)4He D(T,y)SHe
15 a) 75 h) 675 ~) 60 dl
(2.4±0.5)X10 4 (5±2x10 2 (2+~)x10 -s (10+~0)× 10:2
,,1 Ref. [3] b) Ref. [4] c1Ref. [5] •) Ref. [6].
F.E. Cecil, D.E. Newman / High temperature deuterium and tritium
traversing the plasma. While laser fluorescence and Doppler spectroscopy of atomic transitions appear promising, they all require the presence of atoms with at least one electron remaining bound to the nucleus and typically employ several line-of-sight views to the plasma. G a m m a ray spectrometry using a germanium detector entails none of these limitations. The high-energy gammas from fusion reactions readily pass through the plasma and vacuum vessel wall, yet are detected with an absolute (photopeak) efficiency of the order of 5%. Recently developed n-type intrinsic germanium crystals are much less sensitive to degradation from neutrons than older Ge(Li) types and can be repaired if necessary by in-cryostat annealing [10]. We have measured the energy resolution achievable in this range by observing 11.670 MeV gamma rays from 11B(p,y)12C with a 65 cm 3 Ge(Li) detector. The reaction proceeds through a narrow resonance at 163 keV, resulting in a natural gamma linewidth of 6.3 keV. The spectrum observed with a thick target at 0 ° is shown in fig. 2. The width of the full energy peak is consistent with a detector resolution of 16 keV, or 1.4 × 10 3 of the gamma energy. This width is smaller than the energy shifts and line widths expected from reactions in high temperature plasmas, thus indicating the feasibility of ion temperature measurements using such detectors. To illustrate the application of this technique to a specific plasma diagnostic, we will calculate the ex-
200
.
.
.
.
.
.
.
.
.
.
.
.
180
.
.
.
.
.
.
.
.
.
T . . . . . . . . .
]
. . . . .
Ge(Li) SPECTRUM OF 11.670 MeV GAMMA RAYS
160 140 z
120
~'
lOO
-~
80
>=
=
pected response of a large (200 cm 3) germanium detector placed 4 m from the plasma of a large machine, collimated to view 30% of the plasma, and shielded by lead sheets from X-ray backgrounds. For this case we will take np = n D = 8 × 1013/cm 3 and assume a uniform ion temperature of k ~ = 8 keV within the 1 m 3 core volume. Reactions from the cooler, less dense outer regions of the plasma will be ignored, as will beamplasma reactions due to non-thermal ions. Plasmas approximating these conditions are anticipated at Big Dee, T F T R , and M F T F - B in the coming years [1,11]. From fig. 1, the yield is about 4 × 101° 5.5 MeV gammas from p(d,7) and 6 x 10 s 24 MeV gammas from d(d,7) per s. Assuming a detector efficiency of 5% and a gamma attenuation of 50% in the intervening material, the detection rate would be about 104/s of the lower energy gammas with E G = 24 keV and A = 38 keV, plus 102/s of the higher energy gammas with E G = 25 keV and A = 88 keV. (Detection rates in excess of this, result in additional broadening.) These measurements yield a value of ~ to about 10% in 10 -2 to 10 -3 s. The first and second escape peaks [7] due to both reactions can additionally be used for centroid energy and width determinations with a precision nearly equal to that of the photopeak. In all, 12 statistically independent measurements of T, would be derived from a single energy spectrum. In addition, if the efficiency of the detector is known, the deuteron density can be determined from the observed rate of 24 MeV gamma rays, and the product of the proton and deuteron densities can be found from the 5.5 MeV rate, using T, from the energy measurements. Precise yet non-invasive diagnostic techniques sensitive to nuclear reactions in plasmas are necessary for the next generation of experimental plasma machines. Continued progress in gamma ray diagnostic development requires that the poorly-known radiative cross sections be measured at plasma energies, that the spectral shape due to non-thermal ion energy distributions be evaluated, and that fusion gammas be measured at existing plasma devices. We are grateful to Sid Medley and Torkil Jensen for stimulating discussions. This work was supported by U S D O E Contract DE-AC02-83ER40091 and by a G A Technologies Internal Research and Development grant.
5:
60 ,,~ >
40
451
20
References 0 2000
2050
2100
2150
2200
2250
2300
2350
2400
CHANNEL NUMBER
Fig. 2. Pulse height distribution of 11.670 MeV gamma rays from NB(p,y)12C observed with a Ge(Li) detector. The full energy peak and peaks due to the escape of one and two 511 keV annihilation gammas are seen.
[1] S.S. Medley and HG. Hendel, Bull Am. Phys. Soc. 26 (1982) 980 and PPPL-1950 (Nov. 1982). [2] C. Rolfs and H. Truatvetter, Ann. Rev. Nucl. and Part. Sci (1978) 115. [3] G.M. Griffiths et al., Can. J. Phys. 41 (1963) 724. [4] J.E. Perry and S.J. Bane, Phys. Rev. 99 (1955) 1368.
452
b~E. Cecil, D.E. Newman / High temperature deuterium and tritium
[5] R.W. Zurmuhle et al., Phys. Rev. 132 (1963) 751. [6] V.M. Bezotosnyi et al., Sov. J. Nucl. Phys. 10 (1970) 127: W. Buss et al., Phys. Lett. 4 (1963) 198. [7] G.F. Knoll, Radiation detection and measurement (John Wiley, New York, 1979). [8] K. Steinmetz, Private communication (1982). [9] W.A. Fisher, S.H. Chen, D. Gwinn and R.R. Parker, Bull Am. Phys. Soc. 27 (1982) 938.
[101 L.S. Darken, Jr., R.C. Trammell, T.W. Randorf, R.tt. Pehl, and J.H. Elliott, Nucl. Instr. and Meth. 171 (1980) 49: R,H. Pehl, N.W. Madden, J,H. Elliott, I'.W. Randorf. R.C. Trammell and L.S. Darken, Jr., IEEE Trans. Nucl. Sci. NS-26 (1979) 321. [11] D.E. Baldwin and B.G. Logan (eds.) UCID-19359 (1982); .t.M. Rawls et al., GA-AI6143 (1980).
449
D I A G N O S T I C S O F H I G H T E M P E R A T U R E D E U T E R I U M A N D T R I T I U M P L A S M A S BY SPECTROMETRY OF RADIATIVE CAPTURE REACTIONS F.E. C E C I L Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
D a v i d E. N E W M A N GA Technologies Inc., San Diego, CA 92138 USA
Received 13 June 1983
The high resolution gamma ray spectrometry of the ground state radiative capture reactions d(p, y)3 He, t(p, y)4 He, d(t, y )~He and d(d,y)4 He is proposed as a temperature diagnostic of energetic hydrogen plasmas. Counting rates for these reactions for temperatures and densities characteristic of current CTR research are estimated.
The measurement of the ion temperatures of hydrogen, deuterium and tritium plasmas is an essential component of the CTR diagnostic effort. Medley and Hendel [1] have recently noted the possible use of the d(t,-/)SHe and d(3He, ~,)5Li reactions as ion temperature diagnostics. In this paper we propose the high resolution measurement of the energy of gamma rays produced by the reactions d(t,y)SHe, d(d,3,)4He, p(t,y)4He and p(d,~,)3He as a technqiue for the measurement of ion temperatures. The essential point of the proposed technique is that the precise energy of these gamma rays will be an easily predictable function of the plasma temperature. The energy of a gamma ray produced in the general reaction 1(2,7)3 between nuclei with masses and kinetic energies M~ and E 1, etc. is given in the center-of-mass frame (primed) by
E~ = Q + E{ + E~- E;,
(1)
where Q = M I + M s - M 3. The values of Q for the d(t,y)SHe, d(d,y)4He, p(t,y)iHe and p(d,y)3He reactions are 16.696, 23.84"/1, 19.814, and 5.4936 MeV, respectively. In the laboratory frame, the gamma energy will be Ey = E 0 + Q(1 - Q / 2 M 3 ) ( 1 + flCM COS0),
(2)
where E 0 = E{ + E~, flcr~ is the velocity of the centeror-mass frame, and 0 is the direction ~of motion of the center-of-mass relative to the observex. In eq. (2) we have made the approximation E i << Q << M i (i = 1,2,3). This approximation is appropriate for current plasma applications. In a thermalized plasma characterized by an ion 0167-5087/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
temperature T~ the reaction rate is greatest when E 0 is equal to the "Gamow peak" energy E~, given by [2]: E c = ( ~ a Z 1Z2 kT~ )2/3( M/2)1/3,
(3)
where a is the fine structure constant and M = M 1M2/ (M~ + 342). Physically this peak corresponds to the maximum in overlap of the Maxwell distribution of the plasma (which drops off rapidly at high energies) and the reaction cross section (which drops off rapidly at low energies). The energies of the observed gamma rays will then constitute an approximately symmetric distribution, with a centroid at E, -- a ( 1 - Q / 2 M 3 ) + E G,
(4)
and a width (fwhm) of 2
A ~ (16E~kTi/3 + 8 ln2Q kTJM3)
1/2
.
(5)
Here the width A contains contributions from the width of the (approximately Gaussian) Gamow peak and from Doppler broadening. The energy resolution of the detector will cause additional spreading. (In the case of d(t,3,)SHe, the 580 keV natural line width of the 5He ground state will further-broaden the gamma distribution.) The values of E C and A are shown in fig. 1. From eqs. ( 4 ) a n d (5), the observed gamma ray energy and width can each be used to measure ~ with independent statistical and systematic uncertainties. In order to design an actual diagnostic device based upon the measurement of the energies of these gamma rays, it is necessary to estimate the yield for reasonable values of the temperature a n d density of the plasma. Thisyield will have to be high enough' to provide' a statistically significant distinction between the gamma
t::E. ('e('d, D.E. Newman /" ttigh temperature deutemum and trmum
450
140
rately predicted from first principles, but may be determined empirically from laboratory measurements of the reaction cross sections as a function of energy. Since the energy at which the reactions should be measured in order to predict the yield of the corresponding plasma at a certain temperature is the energy of the G a m o w peak, a knowledge of the corresponding nuclear reaction is required at energies under 100 keV for T ~ 20 keV. At these energies, the cross section is usually written as [2]:
130 120 ~_
----
ENERGYEg
/
~ 60
110
t
100 9O
80 ~_ c3
70
o( E ) = S ( E ) / E e x p ( - b / E
30
0o
~
///
5o
/'~
4o
20
g
3o
2o
:,o
lO
I
I
I
I
I
I
I
1
10 18 10 19
7.a 10 20
~ 10-21 "~ 10 22 7- lo-2a
P(D,Y).-
]0-24
10-25 10-26 10-27
10-28 0
I 2
I 4
I 6
I 8
I 10
I 12
I 14
I 10
18,
kTi (keV)
Fig. 1. (a) Predicted energy (dotted) and width (solid) of gamma rays from fusion reactions. The S-factor for P(D,7) was assumed to be [2.4x10 -a +7.9x10 -7 E] (keV-b) (ref. [3]). The S-factor for d(t,7) was assumed to be S(0)/[( E - 69) 2 +1640] (ref. [2]). The S-factors for p(t,y) and d(d,7) were assumed to be constant in this energy range; (b) The reactivities ( o r ) of the ground state transitions in plasmas with thermal distribution of ion energies. ray energies corresponding to plasma temperatures to be differentiated. While the relative temperature dependence of these reactions can be calculated using the well-established techniques of nuclear astrophysics [2], the absolute scale of the reaction yield cannot be accu-
'/e),
(6)
where b = 31.28 Z1ZzA 1/2 keV 1,/2 and S ( E ) is the Sfactor which, in the absence of narrow resonances, is a slowly varying function of energy and where A is the reduced atomic number of the constituent particles. The rate of gamma ray production in a plasma is
Rv=nlnz(ov)cm-3s
1
(7)
where the densities of the reactants are nl and n 2, and ( o r ) is the reactivity [2], obtained by integrating the velocity-weighted product of the Maxwell-Boltzmann distribution and o ( E ) from eq. (6) over the ion energies. Although these reactions have been observed at high energies, only d(p,y)3He has been measured accurately at plasma energies [3]. The measurements are summarized in table 1 and all existing data have been used to extrapolate to the zero energy limit of the S-factor. The indicated error limits reflect the disparity in the measured values of the cross sections. The reactivities were calculated using these values and are shown in fig. 1. Plasma diagnostics currently in use are incapable of measuring the energy shift, E G, in eq. (4), Sodium iodide scintillators have insufficient energy resolution and silicon detectors cannot absorb gamma rays of this energy range [7]. The most precise neutron spectrometry data to date [8,9] barely resolve the effect of ion motion by collecting data over many shots. Charge-exchange analysis will not provide information about the core plasma in future large, high-density machines, because neutral atoms will be efficiently re-ionized before
Table t Summary of low energy measurements of cross sections for radiative capture reaction among hydrogen isotopes. Reaction
Lowest energy (keY)
S(E = 0) (keV-b)
P(D,y)3He P(T,y)4He D(D,7)4He D(T,y)SHe
15 a) 75 h) 675 ~) 60 dl
(2.4±0.5)X10 4 (5±2x10 2 (2+~)x10 -s (10+~0)× 10:2
,,1 Ref. [3] b) Ref. [4] c1Ref. [5] •) Ref. [6].
F.E. Cecil, D.E. Newman / High temperature deuterium and tritium
traversing the plasma. While laser fluorescence and Doppler spectroscopy of atomic transitions appear promising, they all require the presence of atoms with at least one electron remaining bound to the nucleus and typically employ several line-of-sight views to the plasma. G a m m a ray spectrometry using a germanium detector entails none of these limitations. The high-energy gammas from fusion reactions readily pass through the plasma and vacuum vessel wall, yet are detected with an absolute (photopeak) efficiency of the order of 5%. Recently developed n-type intrinsic germanium crystals are much less sensitive to degradation from neutrons than older Ge(Li) types and can be repaired if necessary by in-cryostat annealing [10]. We have measured the energy resolution achievable in this range by observing 11.670 MeV gamma rays from 11B(p,y)12C with a 65 cm 3 Ge(Li) detector. The reaction proceeds through a narrow resonance at 163 keV, resulting in a natural gamma linewidth of 6.3 keV. The spectrum observed with a thick target at 0 ° is shown in fig. 2. The width of the full energy peak is consistent with a detector resolution of 16 keV, or 1.4 × 10 3 of the gamma energy. This width is smaller than the energy shifts and line widths expected from reactions in high temperature plasmas, thus indicating the feasibility of ion temperature measurements using such detectors. To illustrate the application of this technique to a specific plasma diagnostic, we will calculate the ex-
200
.
.
.
.
.
.
.
.
.
.
.
.
180
.
.
.
.
.
.
.
.
.
T . . . . . . . . .
]
. . . . .
Ge(Li) SPECTRUM OF 11.670 MeV GAMMA RAYS
160 140 z
120
~'
lOO
-~
80
>=
=
pected response of a large (200 cm 3) germanium detector placed 4 m from the plasma of a large machine, collimated to view 30% of the plasma, and shielded by lead sheets from X-ray backgrounds. For this case we will take np = n D = 8 × 1013/cm 3 and assume a uniform ion temperature of k ~ = 8 keV within the 1 m 3 core volume. Reactions from the cooler, less dense outer regions of the plasma will be ignored, as will beamplasma reactions due to non-thermal ions. Plasmas approximating these conditions are anticipated at Big Dee, T F T R , and M F T F - B in the coming years [1,11]. From fig. 1, the yield is about 4 × 101° 5.5 MeV gammas from p(d,7) and 6 x 10 s 24 MeV gammas from d(d,7) per s. Assuming a detector efficiency of 5% and a gamma attenuation of 50% in the intervening material, the detection rate would be about 104/s of the lower energy gammas with E G = 24 keV and A = 38 keV, plus 102/s of the higher energy gammas with E G = 25 keV and A = 88 keV. (Detection rates in excess of this, result in additional broadening.) These measurements yield a value of ~ to about 10% in 10 -2 to 10 -3 s. The first and second escape peaks [7] due to both reactions can additionally be used for centroid energy and width determinations with a precision nearly equal to that of the photopeak. In all, 12 statistically independent measurements of T, would be derived from a single energy spectrum. In addition, if the efficiency of the detector is known, the deuteron density can be determined from the observed rate of 24 MeV gamma rays, and the product of the proton and deuteron densities can be found from the 5.5 MeV rate, using T, from the energy measurements. Precise yet non-invasive diagnostic techniques sensitive to nuclear reactions in plasmas are necessary for the next generation of experimental plasma machines. Continued progress in gamma ray diagnostic development requires that the poorly-known radiative cross sections be measured at plasma energies, that the spectral shape due to non-thermal ion energy distributions be evaluated, and that fusion gammas be measured at existing plasma devices. We are grateful to Sid Medley and Torkil Jensen for stimulating discussions. This work was supported by U S D O E Contract DE-AC02-83ER40091 and by a G A Technologies Internal Research and Development grant.
5:
60 ,,~ >
40
451
20
References 0 2000
2050
2100
2150
2200
2250
2300
2350
2400
CHANNEL NUMBER
Fig. 2. Pulse height distribution of 11.670 MeV gamma rays from NB(p,y)12C observed with a Ge(Li) detector. The full energy peak and peaks due to the escape of one and two 511 keV annihilation gammas are seen.
[1] S.S. Medley and HG. Hendel, Bull Am. Phys. Soc. 26 (1982) 980 and PPPL-1950 (Nov. 1982). [2] C. Rolfs and H. Truatvetter, Ann. Rev. Nucl. and Part. Sci (1978) 115. [3] G.M. Griffiths et al., Can. J. Phys. 41 (1963) 724. [4] J.E. Perry and S.J. Bane, Phys. Rev. 99 (1955) 1368.
452
b~E. Cecil, D.E. Newman / High temperature deuterium and tritium
[5] R.W. Zurmuhle et al., Phys. Rev. 132 (1963) 751. [6] V.M. Bezotosnyi et al., Sov. J. Nucl. Phys. 10 (1970) 127: W. Buss et al., Phys. Lett. 4 (1963) 198. [7] G.F. Knoll, Radiation detection and measurement (John Wiley, New York, 1979). [8] K. Steinmetz, Private communication (1982). [9] W.A. Fisher, S.H. Chen, D. Gwinn and R.R. Parker, Bull Am. Phys. Soc. 27 (1982) 938.
[101 L.S. Darken, Jr., R.C. Trammell, T.W. Randorf, R.tt. Pehl, and J.H. Elliott, Nucl. Instr. and Meth. 171 (1980) 49: R,H. Pehl, N.W. Madden, J,H. Elliott, I'.W. Randorf. R.C. Trammell and L.S. Darken, Jr., IEEE Trans. Nucl. Sci. NS-26 (1979) 321. [11] D.E. Baldwin and B.G. Logan (eds.) UCID-19359 (1982); .t.M. Rawls et al., GA-AI6143 (1980).