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Spatial variations of damage parameters in FMIT and their implications
Journal of Nuclear Materials 85 & 86 0 North-Holland Publishing Company
(1979)49 l-495
SPATIAL VARIATIONS OF DAMAGE PARAMETERS IN FMIT AND THEIR IMPLICATIONS J. 0. SCHIFFGENS,R. L. SIMONS, F. M. MANN, and L. L. CARTER Hanford EngineeringDevelopmentLaboratory,Richland, Washington, 99352 USA The major conclusionis that the variation in damage rates in FMIT will be dominatedby changes in flux, not spectrum. Throughoutthe test region where the flux is greater than 1014 n/cm2.s, the flux varies by a factor of about 20, while the spectral-averageddisplacementand helium production cross sections for copper vary by less than factors of two and four, respectively. The correspondinghelium-to-dparatios bracket a fusion reactor first wall value for copper (i.e., 7.7 appm He/dpa). With the Li(d,n) yields and with the copper damage energy and helium production cross sections used in this study, the test volumes for which the displacementand total helium productionrates are greater than those at a D-T fusion reactor first wall (with a loading of 1.0 h/m2) are about 139 and 208 cm3, respectively. 1.
INTRODUCTION
The Fusion Materials IrradiationTest (FMIT) facility is an accelerator-basedneutron source which will provide, within a reasonabletest volume, a high damage rate with high energy neutrons in potential fusion reactor materials In FMIT, neutrons from Li(d,n) reactions [ll. are expected to populate spectra throughoutthe test volume which are broadly distributedin energy comparedwith fusion first wall spectra, as shown in Figure 1. Until a fusion test reactor is operating,data from FMIT, Rotating Target Neutron Source-II (RTNS-II),fission reactors, and charged particle irradiationfacilities,together with a strong understandingof the physical processes that occur during irradiationwill provide the basis for initial component design-lifecriteria.
PRISTINE SPECTRA X y
2
km)
ooo--0 2 o0 0 * --___-
1500--.
The Damage Analysis and FundamentalStudies (DAFS) program has been formulatedprimarily to develop dsmage correlationmodels and procedures. A key step in the program strategy is the verification of the methodology in FMIT. Hence, the program plan specificallycalls for characterization of the MIT neutron field, the initial step of which requires analyses of the spatial variation of damage parameters in the irradiation test cell. Characterizationof the expected neutron field in terms of damage parameters is also essential for the developmentof approximate experimentaltest assemblies and for the determinationof required data accuracies. Since both needs must be reflected in the design of the facility, an FMIT damage parameter sensitivity study is in progress [2,3]. This paper summarizessome of the results thus far obtained. Spectrum and rate variations among neutron irradiation facilitiesare typically described in terms of primary knock-on atom (PKA) spectra, spectral-averagedcross sections for displacements per atom (dpa) and gas atoms generated from transmutationreactions (appm He or H), and the respectiveproduction rates. We have concentratedon the calculationsof displace-
PERTURBED SPECTRA
I
0
10
20 30 40 50 NUETRON ENERGY (MeV)
I
@I
FIGURE 1. Calculatedneutron spectra at four positions (see Figure 3) within the F%lIT irradiation cell (for Ed=35 MeV and I=O.l amp) compared with a D-T fusion reactor first wall specThe trum (for lMW1m2, with $=3.81x101%/cm2.s). total flux at each position is shown in Table 1. ment and helium production,with emphasis on the assessmentof the variations anticipatedunder likely operating conditionsat locations of most
491
492
J. 0. Schiffgens et al. / Spatial variations of damage parameters in FMIT
TABLE 1. Spectral-averaged cross sections * for copper within the FMIT test volume; Ed = 35 MeV, I = 0.1 amp, 1 x 3 cm Gaussian s*uree Position
Pristine
1
0.0
0.0
0.0
2
5.0
0.0
0.0
3 10.0 4 15.0
0.0 0.0
0.0 0.0
5 0.0 6 5.0 7 10.0
2.0 2.0 2.0
0.0 0.0
9.49
0.0
1.07
8 9
0.0
2.0
::;
0.0
1.06 .8g6
10 0.0 11 2.0 12 5.0 13 10.0
0.0 0.0 0.0 0.0
2.0 2.0 2.0 i.5
14 15 16
0.0 5.0
2.0 2.0 2.0
2.0 2.0 2.0
3.7
0.0
0.0
3.0
1.56
0.0
2.0
22.3 3.54 1.53 .837
2.13
Perturbed
13.31
36.4 38.7 39.6
8.L 10.6 10.9 11.0
24.0
3.45 3.56 3.61
8.45 11.96 12.78
2.60 3.31 3.49
20.3 33.7 37.1
7.8 10.2 10.6
10.4 1.83 .721
5.99 7.47
2.11 2.40
11.3 16.6
2:;
1.19 .973
5.28 6.21
2.15
11.9 22.6 30.1 36.8
2:: 9.6 10.6
3.72 2.64 1.48 .780
5.56 7.81 9.24 io.8
9.17
12.60
13.12
2.75
23.0
2.88 .969 .419
8.48 11.0 11.5 12.1
10.9
6.21 9.14 11.04
1.09
12.74
2.72 3.12 3.47
2.16
5.86
2.08
1.66 1.10
8.44
2.58 3.01
20.0 10.7
::;
2.47 1.89
28.0
9.3
1.14
5.19 7.00 8.66
2.04
9.93
4.9
1.81
4.99
10.6 5.66
20.9 31.1 33.2 35.9
7.71 2.43 16.1 10.1 2.89 27.6
2.35 1.48
3.29
2.59 3.09 3.18 3.32
3.06
30.9
1.93 2.09
9.63 13.2
1.98 2.42 2'.72 3.03
10.3 18.6 24.3 30.4
1.91 2.27 2.59
9.12 16.1 22.2
1.86
8.48
* Damage energy cross sectionswere convertedto displacementcross sectionsby multiplyingby where Ed for copper is 30 eV.
interestfor irradiationtesting (i.e., where the displacementrate in stainlesssteel is greater than about 6 dpa/yr). Because both damage energy and helium productioncross sections are availablefor copper over the energy range of interest [4], copper was chosen as the referencematerial for this study. The results of some stainlesssteel and iron dpa calculationsare also included for comparison. The damage energy 141 and helium production [5] cross sectionsused in this study are shown in Figure 2. All damage rates presentedhere assume a plant factor of 1.0.
8.0 10.1 10.4
10.8 7.5 9.5 10.1 5.0 6.3
::: 9.0 10.0
0.8/2
4.8 ii:'6 4.6
Ed,
im,'7.,lm
2. RESULTS WIT preliminarydesign calls for a 0.1 amp beam of 35 MeV deuteronsto strike the surface of flowing lithium 2 em thick. The deuteron ion density is to peak at the center of the target area and be Gaussian in the vertical and horizontal directionswith full-widths-at-half maximum (FWM) of I.cm and 3 cm, respectively. Calculationsof the spatial variationsof damage parametershave been made for the pristine neutron field as well as for the field perturbedby a representativeirradiationtest module. The test module is taken to be composedof three regions, as shown in Figure 3. These regions, labeled A, B, and C, have bulk densitieswhich are 50, 25, and I.0percent that of stainlesssteel.
----I
MlRAPDtATlON
FIGURE 2. Damage energy and helium production [5] cross sections versus neutron energy.
493
J. 0. Schiffgens et al. / Spatial varfations of damage parameters in FMIT
FIGURE 3. Configurationof a representativeirradiation test module and positions at which neutron spectra were calculated.
FIGURE 5. First quadrant helium productionrate contour maps for a 1 x 3 cm FWHM Gaussian source distribution(Ed=35 MeV and I=O.l amp). Total volumes within the contours are shown.
2.1 Pristine neutron field Contour maps for copper displacementrate and helium productionrate in the pristine neutron field are plotted in Figures 4 and 5. Note that the volumes for which the dpa and the total helium productionrates are greater than those in a D-T fusion reactor first wall with a wall loading of 1.0 MW/m2 are about 139 and 208 cm3, respectively. Current fusion reactor design studies envisionwall loadings up to 3-5 MW/m2. Note that the smallest contours in Figures 4 and 5, enclosing6-11 cm3, have displacementand heLium production rates in excess of those corresponding to a first wall loading of 5 MW/cm2. The rates at which these volumes shrink with increasing damage rate is further demonstratedin Figures 6 and 7. These figures show plots of dpa rate and helium production rate versus distance (x) normal to the flowing lithium surface for various y-z coordinates. The damage rate in the x-direction changes fastest near the beam axis where the damage rate is highest.
$ glrn
- z*O.mcm _______ z.,.m
P i 0
54
0
5 10 DISTANCE IN x - DIRECTION lcml
15
FIGURE 6. Displacementrate versus distance normal to the source surface.
FIGURE L. First quadrant displacementrate contour maps,for a 1 x 3 cm FWRM Gaussian source distribution(Ed=35 MeV and I=O.l amp). Total volumes within the contours are shown.
While test volumes in FMIT are small compared with those available in fiesion reactors, damage rates are expected to be much higher. Figure a shows a bar chart comparingthe neutron flux and damage rates in FMIT to those in other neutron irradiation facilities,namely RFIR, ERR-II, FTR, and RTIVS-II. The data are presented a8 the ratio
494
J.O. Schiffgens et al, /Spatial variationsof damage parametersin FMIT of the neutron flux, the displacementrate, and the total helium productionrate in the given facility to the correspondingquantity at the first xall of a 1.0 M%/m2 D-T fusion reactor. The FMIT source [6] and fission reactors produce displacementsat an acceleratedrate relative to the first wall, but, unlike MIT, fission reactors produce transmutantsat a far lower rate (except for helium productionin nickel). RTNSII, like EMIT, will produce helium-to-dparatios comparableto a first wall, but low fluxes in RTNS-II prohibit the productionof damage at rates close to or greater than those produced at a first wall. Note that with the damage energy cross sectionsused in this study (see Figure 2), the displacementrate in copper at the first wall is 16.7 dpe/yr while that in stainless steel is 12.5 dpa/yr. 2.2 Test module perturbed neutron field
FIGURE 7. Helium productionrate versus distance normal to the source surface.
Figure 3 shows the configurationand composition of a representativeirradiationtest module. Neutron spectra were calculatedwith and without this test module in the irradiationcell. Both the pristine and test module perturbed spectra at four positions are plotted in Figure 1. As shown in Table 1, at points near the source, the total flux is higher in the perturbed spectra than in the pristine spectra, and the reverse is true far from the source. These effects are due to neutron backscatteringthroughoutthe test assembly. The backscatteringlowers the high energy flux and raises the low energy flux, as ohown, with the result that the spectral-averaged damage energy and helium productioncross sections are lower in the perturbed spectra. However, the test module lowers the helium-to-dpa ratio by less than ten percent throughoutthe volume encompassesby the module (see Table 1). Note that the copper helium-to-dparatios in FMIT bracket the first wall value for copper (7.7 appm He/dpa). 3. CONCLUSIONS a) FMIT test volumes for which the displacement and the total helium productionrates in copper are greater than those at a D-T fusion reactor first wall, with a loading of 1.0 MW/m2, are about 139 and 208 cm3, respectively. b) The copper helium-to-dparatio in the FMIT test cell is within a factor of two of that et the fusion reactor first wall (7.7 appm He/dpe). c) While throughoutthe cell volume encompassed by the test module the neutron flux varies by as much as a factor of twenty, the helium-to-dparatio varies by less than a factor of two. Hence, damage rates are expected to be much more affectedby variationsin flux than variationsin spectra.
FIGURE 8. Ratios of flux and damage rates in various neutron irradiationfacilitiesto values at a 1.0 MN/m2 D-T fusion reactor first wall.
J.O. Schiffgens et al. / Spatial variations of damage parameters in FMIT
ACKNOWLEDGMENTS The authors gratefullyacknowledgeprofitable discussionswith D. G. Doran. This work was supportedby the U. S. Department of Energy. REFERENCES [l] E. W. Pottmeyer,Jr., this conference. [2] J. 0. Schiffgens,R. L. Simons, F. M. Mann, and L. L. Carter, Damage Analysis and FundamentalStudies QuarterlyTechnical Progress Report, April - June 1978, p. 39, DOE/ET006512. [3] J. 0. Schiffgens,R. L. Simons, F. M. Mann, and L. L. Carter, Damage Analysis and FundamentalStudies QuarterlyTechnical Prog&e;;6;Tort, July - September 1978, p. 42, DOE/
[4] C. Y. Fu and F. G. Perey, J. Nucl. Mat. $& (1976) P. 153. [5] The total helium productioncross section for copper which was used here was derived as part of this study and agrees well with recent measurements,see H. Farrar IV and D. W. Nneff, Damage Analysis and FundamentalStudies Quarterly Technical Progress Report, January - March 1978, p. 58, DOE/F%0065/l.
495
(1979)49 l-495
SPATIAL VARIATIONS OF DAMAGE PARAMETERS IN FMIT AND THEIR IMPLICATIONS J. 0. SCHIFFGENS,R. L. SIMONS, F. M. MANN, and L. L. CARTER Hanford EngineeringDevelopmentLaboratory,Richland, Washington, 99352 USA The major conclusionis that the variation in damage rates in FMIT will be dominatedby changes in flux, not spectrum. Throughoutthe test region where the flux is greater than 1014 n/cm2.s, the flux varies by a factor of about 20, while the spectral-averageddisplacementand helium production cross sections for copper vary by less than factors of two and four, respectively. The correspondinghelium-to-dparatios bracket a fusion reactor first wall value for copper (i.e., 7.7 appm He/dpa). With the Li(d,n) yields and with the copper damage energy and helium production cross sections used in this study, the test volumes for which the displacementand total helium productionrates are greater than those at a D-T fusion reactor first wall (with a loading of 1.0 h/m2) are about 139 and 208 cm3, respectively. 1.
INTRODUCTION
The Fusion Materials IrradiationTest (FMIT) facility is an accelerator-basedneutron source which will provide, within a reasonabletest volume, a high damage rate with high energy neutrons in potential fusion reactor materials In FMIT, neutrons from Li(d,n) reactions [ll. are expected to populate spectra throughoutthe test volume which are broadly distributedin energy comparedwith fusion first wall spectra, as shown in Figure 1. Until a fusion test reactor is operating,data from FMIT, Rotating Target Neutron Source-II (RTNS-II),fission reactors, and charged particle irradiationfacilities,together with a strong understandingof the physical processes that occur during irradiationwill provide the basis for initial component design-lifecriteria.
PRISTINE SPECTRA X y
2
km)
ooo--0 2 o0 0 * --___-
1500--.
The Damage Analysis and FundamentalStudies (DAFS) program has been formulatedprimarily to develop dsmage correlationmodels and procedures. A key step in the program strategy is the verification of the methodology in FMIT. Hence, the program plan specificallycalls for characterization of the MIT neutron field, the initial step of which requires analyses of the spatial variation of damage parameters in the irradiation test cell. Characterizationof the expected neutron field in terms of damage parameters is also essential for the developmentof approximate experimentaltest assemblies and for the determinationof required data accuracies. Since both needs must be reflected in the design of the facility, an FMIT damage parameter sensitivity study is in progress [2,3]. This paper summarizessome of the results thus far obtained. Spectrum and rate variations among neutron irradiation facilitiesare typically described in terms of primary knock-on atom (PKA) spectra, spectral-averagedcross sections for displacements per atom (dpa) and gas atoms generated from transmutationreactions (appm He or H), and the respectiveproduction rates. We have concentratedon the calculationsof displace-
PERTURBED SPECTRA
I
0
10
20 30 40 50 NUETRON ENERGY (MeV)
I
@I
FIGURE 1. Calculatedneutron spectra at four positions (see Figure 3) within the F%lIT irradiation cell (for Ed=35 MeV and I=O.l amp) compared with a D-T fusion reactor first wall specThe trum (for lMW1m2, with $=3.81x101%/cm2.s). total flux at each position is shown in Table 1. ment and helium production,with emphasis on the assessmentof the variations anticipatedunder likely operating conditionsat locations of most
491
492
J. 0. Schiffgens et al. / Spatial variations of damage parameters in FMIT
TABLE 1. Spectral-averaged cross sections * for copper within the FMIT test volume; Ed = 35 MeV, I = 0.1 amp, 1 x 3 cm Gaussian s*uree Position
Pristine
1
0.0
0.0
0.0
2
5.0
0.0
0.0
3 10.0 4 15.0
0.0 0.0
0.0 0.0
5 0.0 6 5.0 7 10.0
2.0 2.0 2.0
0.0 0.0
9.49
0.0
1.07
8 9
0.0
2.0
::;
0.0
1.06 .8g6
10 0.0 11 2.0 12 5.0 13 10.0
0.0 0.0 0.0 0.0
2.0 2.0 2.0 i.5
14 15 16
0.0 5.0
2.0 2.0 2.0
2.0 2.0 2.0
3.7
0.0
0.0
3.0
1.56
0.0
2.0
22.3 3.54 1.53 .837
2.13
Perturbed
13.31
36.4 38.7 39.6
8.L 10.6 10.9 11.0
24.0
3.45 3.56 3.61
8.45 11.96 12.78
2.60 3.31 3.49
20.3 33.7 37.1
7.8 10.2 10.6
10.4 1.83 .721
5.99 7.47
2.11 2.40
11.3 16.6
2:;
1.19 .973
5.28 6.21
2.15
11.9 22.6 30.1 36.8
2:: 9.6 10.6
3.72 2.64 1.48 .780
5.56 7.81 9.24 io.8
9.17
12.60
13.12
2.75
23.0
2.88 .969 .419
8.48 11.0 11.5 12.1
10.9
6.21 9.14 11.04
1.09
12.74
2.72 3.12 3.47
2.16
5.86
2.08
1.66 1.10
8.44
2.58 3.01
20.0 10.7
::;
2.47 1.89
28.0
9.3
1.14
5.19 7.00 8.66
2.04
9.93
4.9
1.81
4.99
10.6 5.66
20.9 31.1 33.2 35.9
7.71 2.43 16.1 10.1 2.89 27.6
2.35 1.48
3.29
2.59 3.09 3.18 3.32
3.06
30.9
1.93 2.09
9.63 13.2
1.98 2.42 2'.72 3.03
10.3 18.6 24.3 30.4
1.91 2.27 2.59
9.12 16.1 22.2
1.86
8.48
* Damage energy cross sectionswere convertedto displacementcross sectionsby multiplyingby where Ed for copper is 30 eV.
interestfor irradiationtesting (i.e., where the displacementrate in stainlesssteel is greater than about 6 dpa/yr). Because both damage energy and helium productioncross sections are availablefor copper over the energy range of interest [4], copper was chosen as the referencematerial for this study. The results of some stainlesssteel and iron dpa calculationsare also included for comparison. The damage energy 141 and helium production [5] cross sectionsused in this study are shown in Figure 2. All damage rates presentedhere assume a plant factor of 1.0.
8.0 10.1 10.4
10.8 7.5 9.5 10.1 5.0 6.3
::: 9.0 10.0
0.8/2
4.8 ii:'6 4.6
Ed,
im,'7.,lm
2. RESULTS WIT preliminarydesign calls for a 0.1 amp beam of 35 MeV deuteronsto strike the surface of flowing lithium 2 em thick. The deuteron ion density is to peak at the center of the target area and be Gaussian in the vertical and horizontal directionswith full-widths-at-half maximum (FWM) of I.cm and 3 cm, respectively. Calculationsof the spatial variationsof damage parametershave been made for the pristine neutron field as well as for the field perturbedby a representativeirradiationtest module. The test module is taken to be composedof three regions, as shown in Figure 3. These regions, labeled A, B, and C, have bulk densitieswhich are 50, 25, and I.0percent that of stainlesssteel.
----I
MlRAPDtATlON
FIGURE 2. Damage energy and helium production [5] cross sections versus neutron energy.
493
J. 0. Schiffgens et al. / Spatial varfations of damage parameters in FMIT
FIGURE 3. Configurationof a representativeirradiation test module and positions at which neutron spectra were calculated.
FIGURE 5. First quadrant helium productionrate contour maps for a 1 x 3 cm FWHM Gaussian source distribution(Ed=35 MeV and I=O.l amp). Total volumes within the contours are shown.
2.1 Pristine neutron field Contour maps for copper displacementrate and helium productionrate in the pristine neutron field are plotted in Figures 4 and 5. Note that the volumes for which the dpa and the total helium productionrates are greater than those in a D-T fusion reactor first wall with a wall loading of 1.0 MW/m2 are about 139 and 208 cm3, respectively. Current fusion reactor design studies envisionwall loadings up to 3-5 MW/m2. Note that the smallest contours in Figures 4 and 5, enclosing6-11 cm3, have displacementand heLium production rates in excess of those corresponding to a first wall loading of 5 MW/cm2. The rates at which these volumes shrink with increasing damage rate is further demonstratedin Figures 6 and 7. These figures show plots of dpa rate and helium production rate versus distance (x) normal to the flowing lithium surface for various y-z coordinates. The damage rate in the x-direction changes fastest near the beam axis where the damage rate is highest.
$ glrn
- z*O.mcm _______ z.,.m
P i 0
54
0
5 10 DISTANCE IN x - DIRECTION lcml
15
FIGURE 6. Displacementrate versus distance normal to the source surface.
FIGURE L. First quadrant displacementrate contour maps,for a 1 x 3 cm FWRM Gaussian source distribution(Ed=35 MeV and I=O.l amp). Total volumes within the contours are shown.
While test volumes in FMIT are small compared with those available in fiesion reactors, damage rates are expected to be much higher. Figure a shows a bar chart comparingthe neutron flux and damage rates in FMIT to those in other neutron irradiation facilities,namely RFIR, ERR-II, FTR, and RTIVS-II. The data are presented a8 the ratio
494
J.O. Schiffgens et al, /Spatial variationsof damage parametersin FMIT of the neutron flux, the displacementrate, and the total helium productionrate in the given facility to the correspondingquantity at the first xall of a 1.0 M%/m2 D-T fusion reactor. The FMIT source [6] and fission reactors produce displacementsat an acceleratedrate relative to the first wall, but, unlike MIT, fission reactors produce transmutantsat a far lower rate (except for helium productionin nickel). RTNSII, like EMIT, will produce helium-to-dparatios comparableto a first wall, but low fluxes in RTNS-II prohibit the productionof damage at rates close to or greater than those produced at a first wall. Note that with the damage energy cross sectionsused in this study (see Figure 2), the displacementrate in copper at the first wall is 16.7 dpe/yr while that in stainless steel is 12.5 dpa/yr. 2.2 Test module perturbed neutron field
FIGURE 7. Helium productionrate versus distance normal to the source surface.
Figure 3 shows the configurationand composition of a representativeirradiationtest module. Neutron spectra were calculatedwith and without this test module in the irradiationcell. Both the pristine and test module perturbed spectra at four positions are plotted in Figure 1. As shown in Table 1, at points near the source, the total flux is higher in the perturbed spectra than in the pristine spectra, and the reverse is true far from the source. These effects are due to neutron backscatteringthroughoutthe test assembly. The backscatteringlowers the high energy flux and raises the low energy flux, as ohown, with the result that the spectral-averaged damage energy and helium productioncross sections are lower in the perturbed spectra. However, the test module lowers the helium-to-dpa ratio by less than ten percent throughoutthe volume encompassesby the module (see Table 1). Note that the copper helium-to-dparatios in FMIT bracket the first wall value for copper (7.7 appm He/dpa). 3. CONCLUSIONS a) FMIT test volumes for which the displacement and the total helium productionrates in copper are greater than those at a D-T fusion reactor first wall, with a loading of 1.0 MW/m2, are about 139 and 208 cm3, respectively. b) The copper helium-to-dparatio in the FMIT test cell is within a factor of two of that et the fusion reactor first wall (7.7 appm He/dpe). c) While throughoutthe cell volume encompassed by the test module the neutron flux varies by as much as a factor of twenty, the helium-to-dparatio varies by less than a factor of two. Hence, damage rates are expected to be much more affectedby variationsin flux than variationsin spectra.
FIGURE 8. Ratios of flux and damage rates in various neutron irradiationfacilitiesto values at a 1.0 MN/m2 D-T fusion reactor first wall.
J.O. Schiffgens et al. / Spatial variations of damage parameters in FMIT
ACKNOWLEDGMENTS The authors gratefullyacknowledgeprofitable discussionswith D. G. Doran. This work was supportedby the U. S. Department of Energy. REFERENCES [l] E. W. Pottmeyer,Jr., this conference. [2] J. 0. Schiffgens,R. L. Simons, F. M. Mann, and L. L. Carter, Damage Analysis and FundamentalStudies QuarterlyTechnical Progress Report, April - June 1978, p. 39, DOE/ET006512. [3] J. 0. Schiffgens,R. L. Simons, F. M. Mann, and L. L. Carter, Damage Analysis and FundamentalStudies QuarterlyTechnical Prog&e;;6;Tort, July - September 1978, p. 42, DOE/
[4] C. Y. Fu and F. G. Perey, J. Nucl. Mat. $& (1976) P. 153. [5] The total helium productioncross section for copper which was used here was derived as part of this study and agrees well with recent measurements,see H. Farrar IV and D. W. Nneff, Damage Analysis and FundamentalStudies Quarterly Technical Progress Report, January - March 1978, p. 58, DOE/F%0065/l.
495