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On irradiation experiments in view of fusion condition simulation
311
Journal of Nuclear Materials 174 (1990) 311-318 North-Holland
On irradiation experiments in view of fusion condition simulation E.A. Koptelov, V.V. Korolev and A.A. Semenov Institutefor Nuclear Research, Academy of Sciences of the USSR, 60th October Anniversary Prospect 7a, Moscow I1 7312, USSR
Charged particle accelerators of meson physics facilities provide certain possibilities for simulation experiments in radiation damage and radiation material investigations for fission and fusion reactors. The problem of the adequacy of such experiments noses some questions. The possible influence of the time structure of linear machines, such as the Moscow Meson Facility proton accelerator, on the radiation kinetics is discussed to outline the validity of simulation experiments in fusion materials studies.
1. Introduction The resolution of the problems arising from fusion materials hampered by the absence of neutron sources
with spectra and fluxes reproducing the irradiation conditions at planned fusion facilities. In this regard it is interesting to consider the possible use of intensive proton and secondary neutron beams of high intensity meson facility accelerators in irradiation physics and nuclear materials investigations. Such accelerators are known to operate in the USA, Switzerland and Canada. Analogous construction work on the research complex at the Moscow Meson Facility (MMF) of the Institute for Nuclear Research (INR) has entered the concluding stage. Experimental investigations carried out at the meson physics facilities at Los Alamos (USA) and at Villigen (Switzerland) have demonstrated the effectiveness of using these nuclear physics facilities for researchers on radiation physics of metals and alloys [1,2]. As regards investigations on nuclear materials, the extra potentialities offered by meson facilities are connected with the availability of intensive proton and secondary neutron beams [3-51. Experimental and theoretical investigations of physical mechanisms defining the radiation damage kinetics can assist in selecting construction materials for fission and fusion power reactors. Metals and alloys to be used in future power installations have to resist irradiation up to doses of the order of hundreds of displacements per atom (@a) or - 102’ neutrons/m2. For this reason one has to investigate various phenomena such as radiation emb~t~ement, swelling, effects of cyclic loading and tem-
perature changes, effects of hydrogen, helium and other irradiation-produced impurities on mechanical properties of metals and alloys [6,7]. The working conditions for the first walls of fusion reactors, that are defined by the plasma irradiation and operating mode of installations such as tokamaks, are summarized in paper [7]. The authors of ref. [7] have analysed the main processes that define the utilization of materials in several fusion reactor projects. The present report deals with aspects of simulation studies of the radiation resistance of fusion materials, that can be carried out on the basis of intensive proton and secondary neutron beams of meson physics facilities.
2. Meson physics facilities potential for simulation investigations of irradiation processes in fusion materials
As is already known, intense neutron generators based on the (T, d)-reaction with rotating targets (for example, RTNS-II) provide 14 MeV neutrons, but in a rather limited volume of a few cm3 and with a low density not exceeding 1016 n/m2 s. Such fluxes are ten times lower than the normal flux even for the hybrid thermonuclear reactor. Various irradiation facilities can be used for simulation inves~gations of the irradiation processes in fusion materials. The scope of phenomena that can be investigated in a given installation depends critically on its characteristics, such as damage rate K (dpa/s), helium and hydrogen production rates Ku, and K, (appm/s),
0022-3115/90/$03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)
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E.A. Koptelou et al. / Irradiation experiments in view
respectively, depth of damage zone as well as the capability of creation of controlled mechanical stresses and temperature conditions in the area being irradiated. The possibilities of conducting experiments in radiation materials physics in the proton and secondary neutron beams of the Moscow Meson Facility (MMF) have been considered in some previous works [3-5,8,9]. The main characteristics of primary and secondary beams of MMF have been presented elsewhere [4,5]. The facility includes an accelerator for hydrogen ions with an energy of 600 MeV at an average current rent of 0.5-l mA. The temporal structure of the primary beam is characterized by the pulse rate w = 100 Hz and the pulse duration 7 = lop4 s in the normal regime, but can be altered through a wide range by making use of the proton storage ring (PSR-like) stretcher and compressor [IO]. Certain possibilities for the radiation testing of firstwall fusion materials under conditions close to reality, can be created at the neutron target structure or beam stop for the proton beam of the experimental complex of MMF (INR, the USSR) [5].
3. Formulation of the problem Comparison of radiation damage by intensive proton beams and by characteristic neutron spectra with respect to damage rate, helium production rate and their ratio only gives a basis for an approximate assessment of the possibilities for simulation investigations of the behaviour of radiation materials. The problem of the adequacy for predictions of property changes of metals and alloys in neutron fields based on radiation effects investigations with proton beams gives rise to a number of questions. We shall outline below the following two points: (1) the effect of the temporal structure of the meson facility proton beam on the growth kinetics of radiation defect clusters; (2) the role of temperature pulsations in the evolution of a void system. These problems represent a particular case of a more general problem connected with the pulsed operating regime of various irradiation facilities and fusion reactors [7,11]. Some general features of radiation defect cluster growth under nonstationary irradiation conditions are considered in refs. [12-141 and will be described below. Theoretical analysis of the radiation damage kinetics relies upon the following concepts. A set of point and
offusion condition simulation
extended defects in irradiated metals and alloys represents a particular case of open non-equilibrium systems with reactions and diffusion. In such systems the processes of development of spatial and temporal structures (self-organization) [15,16] are possible. Simultaneously, there exists the hierarchy of times in such systems [16]. The existence of different time ranges in the case of radiation defects results in a large variety of experimentally observed dependencies of the microstructure kinetics on pulse characteristics during pulsed irradiation [ll]. As is usually the case with non-equilibrium systems with reactions and diffusion, a significant difference in the diffusion coefficients for interstitials and vacancies defines the differences between the time ranges of various processes of the defect kinetics. So, if 7, and 7” are the lifetimes (times of absorption by sinks and recombination) for interstitials and vacancies. respectively, T, and ~a are characteristic growth times for interstitial and vacancy clusters. respectively, then usually Ti K 7, K rv K 7a.
(1)
The expressions and estimates for these times can be found, for example, in refs. [14,17]. The evolution of defect clusters under pulsed irradiation must be governed by the relation between the characteristic times of the defect kinetics and temporal parameters of irradiation in fusion installations or simulation facilities. We introduce the following notations: C,, Ci are the concentrations of vacancies and interstitials, respectively; K(t) is the damage rate; p is the recombination coefficients for coefficient; D,, Di are the diffusion vacancies and interstitials, respectively, p is the density of dislocation network, pL is the density of interstitial dislocation loops; pd = p + p,_ is the total dislocation density, b is the modulus of the Burger’s vector; N is the loop density, R, is the loop radius; N, is the void number density; R is the void radius; ps = 4mN,,R; Z,, Z, are the bias factors for interstitials and vacancies, respectively, 7v,i = [ D,,i( Zv,ip, + ps)]-‘. The kinetics of radiation defects can then be described by the rate equations [13]:
d&l dt
=K(t)-ucic”-~
(2)
“.I
here a: = p( Di + 0,). In eq. (2), the time dependence of sink densities must be taken into account. We can account for the role of evaporation terms in eq. (2) and in cluster growth in numerical solutions of the full set of equations. (See table 1.) We shall consider the time structure of irradiation typical of intense proton beams of meson facilities
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EA. Koptelou et al. / Irradiation experiments in view offusion condition simu~ut~on
based on linear accelerators. varies as follows: Ko, 0 i7
K(t)=
The damage rate K(t)
OItI7,
the “on-time”
r
the “off-time” interval.
interval;
(3) Here Ka is the amplitude of the damage rate; 7 is the pulse duration; or is the pulsing period of irradiation. The average value of the damage rate is (K) = K,,( 7/q). For 7r = 0.01 s and the duty factor T/T~= 0.01 one has (K) < K,. So the problem of comparison of radiation damage by some steady irradiation with the damage rate K = (K) and by pulsed irradiation with the average damage rate (K) exists.
4. Interstitial dislocation loop fonuation
under pulsed
109
-0
f0-5
10-s
10-l
IRRADIATION
IO’
103
TIME (s 1
Fig. 1. The time dependence of the interstitial dislocation loop density pL and the loop number density N in Ni under continuous irradiation. Ti, = 373 K. The damage rate fc = 10e4 dpa/s. Values of N,,, and p,,, correspond to estimations based on eqs. (5) and (6) in the text.
and continuous irradiation
Let us consider first of all the formation of interstitial dislocation loops in irradiated metals. This process can be important if the density of pre-existing dislocations is small enough, p < ,D_,where the value of pC, is determined by irradiation conditions [17]. Assuming this inequality to be satisfied, the estimation of the loop nucleation time is as follows To= ({~)~~i)-1’2.
(4) After the nucleation stage the loop growth process takes place. Under continuous irradiation the resulting loop number density iV and the density of dislocation loops p,_ can be written in the form: N, = n2’3[(K)/‘pDi]1’2 PL=r
1’3W[ ( K)/~Di]1’2(
(5) Di/D,)“4.
(6)
Here w = S( r&Z)- ‘/* fi is the atomic volume. The corresponding time scale is of the order of [17]: 7[= &($
In 3 - arctg 4).
On the basis of eqs. (5) and (6) one can estimate the parameters of interstitial loop structure forming under certain continuous irradiation. Fig. 1 shows the results of such estimations and of numerical solutions of eq. (2). Under pulsed irradiation in high intensity beams of the meson physics facility, the pulse duration T is longer than the loop nucleation time 7. - ( KO~.Di)-1~2. In this case the loop number density N,, according to (S), must be proportional to Ki12. This means that under the pulsed irradiation considered, the loop density NL( Ko)
Table 1 Material parameters used in the calculations Parameter
Notation
Vacancy formation energy Interstitial formation energy Vacancy migration energy Interstitial migration energy Vacancy diffusion pre-exponential InterstitiaI diffusion pre-exponential Surface energy Recombination coefficient Atomic volume Interstitial dislocation bias factor Vacancy dislocation bias factor Initial void radius Melting temperature
Nickel
E6
2.83x10-19
E,m
1.6x10-I9 24x10-” 1.9x10-5 8.0x10-’
Ef
Eim D 0:; B
P f2
1.0x102’ 1.09x 10-29
zi
Z” Ro %I
1728
SS 316
Album
2.56x10-i9 6.41 x lo-l9 2.1x10-‘9 3.2 x 1O-2o 5.0x10-s 1.0x 10-7 2.0 1.0x10~0 8.0x10-30 1.08 1.00 1.0x10-s
1.06~10-‘~ 5.19x10-‘9 9.12~10-‘~ 1.6x10-20 4.0x10-6 8.0x10-6 1.0 1.86 x 10’9 1.25 x 10-29 1.08 1.00 1.0x10-s 933
Molybdenum 6.8X1O-‘p
144x10-‘* 2.45 x lo-i9 1.36x lo-” 3.0x 10-6 1.6~10-~ 2.05 1.34 x 10’9 2.03~10-*~ 1.08 1.00 1.0x10-s 2893
units J J J J m’/s m’/s J/m2 mm2 m3
E
314
E.A. Koptelav et al. / Irradiation
experiments
iI
0
kc__-. 0
1.
._/
100 IRRADIATION
0
200
TIME (pulses 1
Fig. 2. Comparison of interstitial dislocation loops generation
in nickel under pulsed (pulse rate 100 Hz, duty factor 10-2) and conontinuousirradiations with the same averaged damage rate (K) =10m4dpa/s, qTi,,= 373 K.
can be expected to be higher than N,(( K)) under the continuous irradiation with the same average damage rate K = (K). The difference must be of the order of prove ( 5/T 1I/* > 1. Results of numerical computations this conclusion. The total dislocation length under the pulsed irradiation considered is also greater than under the comparable continuous irradiation (see fig. 2). If the pulse duration T is small as compared to the nucleation time Q, then the kinetics of dislocation loop formation has no specific features connected with the pulsed beam time structure [XX]. The model used considers the loop nucleation via di-interstitials and neglects the vacancy cluster formation. So the numerical resutls are limited to sufficiently short irradiation times [17] 1
f <
-4
8Z
3 = D”&~ fln*-z,
71
i
where 7s is the time for vacancy cluster nucleation. The increase in interstitial dislocation density under the pulsed irradiation considered can be dominant in radiation defect structure evolution for irradiation temperatures I;,, < 0.3T”, where ‘&, is the absolute melting temperature. For higher temperatures such modified dislocation densities must be accounted for as the starting conditions for void growth kinetics.
5. The void growth kinetics under pulsed irradiation This process was analysed numerically by Kmetyk et al. [19-21f for the pulsed irradiation with the time
m view of fusion condition slmuiation
structure of the Los Alamos Meson Physics Facility. According to their results for aluminium and molybdenum, damage rate pulsing is not important for void growth, while associated irradiation temperature oscillations enhance swelling at temperatures lower than the peak swelling temperature and retard it above that temperature. We shall show that damage rate pulsing can influence void growth markedly if two conditions are satisfied simultaneously: (i) point defect lifetimes are shorter than the pulse period; (ii) during the “ontime” period point defect recombination dominates over point defect absorption by sinks. Both conditions follow from simple analytical considerations 1131, as can be seen below. Void sizes do not change significantly during the pulse period. The growth equations for clusters are linear in point defect concentrations. So extended defects grow similarly under pulsed and continuous irradiations if average concentrations of point defects for both cases are equal. In quasistationa~ conditions the point defect concentrations at the beginning and at the end of each irradiation period are the same. Then one has from eq. (2): cK)
- ff(cJ~)
-
(G,i)/‘v.,.i
=O.
(9)
Let us define the effective damage rate Kefr as the damage rate of such continuous irradiation, when stationary vacancy and interstitial concentrations are equal to the corresponding average meanings for given pulsed irradiation. For continuous irradiation with the damage rate zr’,, one has
It follows from eqs. (9) and (10) that Keff
=
tK>
-
at(cicv>
or in terms of (C,) Keff
=
(1
+
~T(C”))(CV)/G.
-
(c~>(cv>)*
01)
one has (12)
The second term in the right-hand side of eq. (11) describes possible differences in radiation damage under pulsed and continuous irradiations. To estimate this difference we consider the time dependence of Cv in more detail. For the beam time structure of the meson facility we have 7; << 7 K< 7”
(13)
E.A. Koptelov et al. / ~rrad~at~o~ experiments in view offusion condition simulation
315
Solving eq. (2) in this case one has the following expressions for CV: (i[ (1 + “7iCo)’ + 2~K,7,‘] G(r)
- l}/luTi
for 0 I t 5 7;
=
(14)
0.2
Here Ca = C,(O) is the initial value of the vacancy concentration. The equation for C, has the form:
0
aTiC,Z[exp(27r/TV) - 11 + 2Ca[exp(Tr/T,)
- l] = ~K,T. (1%
Let us consider the following two cases. 5.1. The short pulse period: rf e r, Expanding the left-hand side of eq. (15) up to the second order terms in ?r/r,,, one has 1 +qc.. + 1 + 2qcs
Tf
z
CC”)= s 1 -
i
1
”
(K)
=
1
(17)
lXTiCS 7i” .-----cl. 1 + aTic, 127,”
So in the case of short pulsing period, rr e r,, the void growth under pulsed irradiation develops with the same rate as under continuous irradiation with the average damage rate of the given irradiation, i.e., K,, = (K). This analytical result is illustrated by the two upper curves of fig. 3 where resutls of numerical imputations are presented. Fig. 3 shows the dependence of Kerf versus the pulse duration 7 at different values of the pulsing period TV,but with the constant average damage rate (K > = 10T6 dpa/s_ As the value of rr/rV decreases the curve tends to unity. 52. The long pulsing period:
10-2
IO"
r(s) Fig. 3. Dependence of the effective continuous dalpage rate corresponding to the given pulse regime (in view of the average void growth rate) on pulse duration at various pulse rates w = 0.1; 1, 10 and 100 Hz. The average damage rate (K > is fixed and equal to 10s6 dpa/s. T,*, = 823 K. The material constants for SS 316 were used: q = 0.097 s, ~~= 0.72 x lo- 5 s.
q X- rv
In this case C, = 0. Averaging eq. (14) one has (C,) = [ (1 + 2~Ke~ir)i’~ - I] T”,/aTi~f for
It follows consequently K
rtr (1 + ~cx(K)~~#~ eff
x
(19)
- 1
l+~[(1+2a(K)~~~i)L”-lj).
(20
The values of the ratio Keff/(K) described by expression (20) are shown on fig. 3 by straight dotted lines for ri = 10 s and TV= 1 s. These values agree well with the data of numerical calculations in the domain where ~~s T I 7” * q. Eqs. (19) and (20) can be simplified in two limits: 5.2.1. During the “on-time” dominates, i.e., 2a(K)7,7i >>1
where
recombination
(21) When recombination dominates, eq. (21) is valid for some linear-like part of the curve with 9 = 10 s and to a lesser extent for the curve with or = 1 s. X2.2. During the “on-time” where absorption by sinks dominates, i.e., 2a( K)rfri CC1 In this case, from eq. (19), it follows that (C,) = (K)T,.
$ < 1.
that
wrir
(
+T;t;ics .$p .
It follows from eq. (12) that
(Ku>- Keff
10-L
$
* 1272 Y 1. i Here Cs is the stationary value of vacancy concentration under continuous irradiation with the average damage rate of the pulsed irradiation. Omitting terms of the order of (7/rr) +=s1, one obtains: co = czi l-
10-6
(22)
This relation corresponds exactly to the vacancy concentration under continuous irradiation with the damage rate (K) if absorption by sinks dominates. Conse-
316
E.A. Koptelou
et al. / Irradiation
experimenis
rn view of fusion condition
.simulation
/
cant
16 i
I
500
600
700
800
900
T,,,(K)
Fig. 4. Dependence of the void growth rate on the temperature r,, (SS 316). The average damage rate (K) = 10d5 dpa/s, the pulse duration 7 = 10m4 s and the pulsing period 7, = 10, I, 0.1 and 0.01 s, respectively.
quently, one has Keff = (K) in this case. Fig. 4 shows the temperature dependence of the void growth rate in stainless steel for (K) = lo-’ dpa/s, T = 10-O s and different periods of pulsing TV= 10, 1, 0.1, 0.01 and 10e4 s (continuous regime), respectively. The swelling curves for pulsed and continuous irradiations coincide at low temperatures and become different in the temperature domain where the lifetime of vacancies appears to be less than the period of irradiation pulsing. The curve corresponding to typical i~adiation regime of MMF (TV= 10T2 s) differs slightly from the continuous irradiation curve over the whole temperature domain of void swelling. Finally, the pronounced difference in the void growth under pulsed and continuous irradiations with equal average damage rate can exist in the case of section 5.2.1 when both conditions (i) and (ii) or two inequalities, rr >> r\,
(23)
2ff(K)TrT1 5-> 1,
(241
are simultaneously satisfied. It must be mentioned that energy losses in materials irradiated by intense beams are able to cause temperature pulsing. Figs. 5 and 6 present the numerical data on void growth in aluminum and molybdenum under the irradiation conditions of the Moscow Meson Facil-
L20
I LLL_-
L60
:v) 60
20
0
1000
and
1
500 560 T,,, IK) Fig. 5. Temperature dependence of void growth rate in aluminum under the Meson Physics Facility irradiation (pulse rate 100 Hz, duty factor 10m2). (lu) =10m4 dpa/s, p =1012 me2, NV= 1Ota mm 3, R0 = 10 nm, T, = 933 K. 1 - continuous irradiation; 2, 3 and 4 - pulsed irradiation, including temperature pulses with magnitude of 0, T,/20 and T,/lO, respectively. 380
1000
1200
lLO0
1600
1800
2000
TC,iKl
Fig. 6. Temperature dependence of void growth rate in molybdenum under the Meson Physics Facility irradiation (pulse rate 100 Hz, duty factor lo-*). (K) =10m4 dpa/s, p = 3x 1012 rnm2, NV= 10” rne3, R, = 10 nm, T,, = 2893 K. 1 -- continuous irradiation; 2, 3 and 4 - pulsed irradiation, including temperature pulses with magnitude of 0, T,/20 and T,/lO, respectively.
E.A. Koptelov et al. / Irradiation experiments in view of fusion condition simulation
ity (MMF). As is shown in fig. 5 for aluminum, damage rate pulsations do not cause any change in the void growth rate, if temperature pulsations are absent. However, if one simultaneously applies temperature pulses with the magnitude of the order of (1/2O)T,, then the void rate decreases markedly near the upper temperature limit of swelling and increases slightly at lower temperatures. These conclusions are in qualitative agreement with the numerical data obtained at LAMPF [19-211. In the case of molybdenum (fig. 6) even in the absence of temperature pulsations (curve 2), pulsed irradiation results in distinguishable differences in void growth rate at higher temperatures. The conditions under which damage rate pulsations lead to a significant decrease of void growth rate were discussed above. The requirements (23) and (24) impose a restriction on the total sink density p,: (DJJ’
K &---z 2p(K)r,.
This
restriction
(K)
= 10m4 dpa/s
(25)
cannot be fulfilled for aluminium at in the temperature range of void swelling, but in molybdenum one can obtain from (25) the following inequalities:
317
early stage of irradiation, by increasing the dislocation density. The problem of the effect of irradiation pulsing on void generation awaits its solution. These details of radiation damage seem to play a secondary role in the long-term behaviour of irradiated metals. So the primary proton beam of the MMF will provide the possibilities for conducting research on radiation damage physics in fission and fusion materials. Also envisaged is irradiation of samples in the beam stops where the fast neutron flux averaged over time and over the volume of - 50 cm3 reaches - 2 x 10” n/m2 s at the total proton current of 0.5 mA. The ratio of damage rate to the helium production rate at the beam stop is close to that for the first-wall materials in fusion reactors. Irradiation with the pure proton beam can provide damage rates which are one to two orders of magnitude greater than the damage rates in the existing neutron irradiation facilities, but with enhanced helium production rate per unit of displacement, compared with the fusion reaction irradiation [4].
Acknowledgements
3.8 x 10” m-* =X pt < 2.7 x 1013 m-*. At higher total sink strengths (about 1.6 x lOi m-* as in refs. [19,21]) in the absence of temperature pulses, the differences are low and do not exceed a few percent. As for temperature pulsations, it follows from the numerical results presented in figs. 5 and 6 that they become important only when temperature pulse amplitudes are of the order of (1/2O)T, or higher. In real experimental environments one can select irradiation conditions such that damage rate pulsations will not affect the void swelling kinetics [13,14]. Temperature pulsations of the order of T,/20 can only be achieved in the very extreme case of maximal focusing of the MMF proton beam. According to our estimates, at the average damage rate (K ) = 10e5 dpa/s, the amplitudes of temperature pulses do not exceed a few tens of degrees.
6. Conclusions One should expect that in experimental studies of the vacancy agglomeration and swelling of metals, the temporal structure of the proton beam of linear accelerator meson facilities (or other installations with similar time structure) will not cause any significant direct changes in the void growth kinetics. However, irradiation pulsations can play an indirect role, at least in the
The authors would like to thank Professors V.M. Lobashev and Yu.Ya. Stavissky for their constant interest and attention to this work. The authors also have great pleasure in maintaining long-termed scientific contacts with Professors V.V. Orlov, I.V. Al’tovsky and S.N. Votinov, who took a great part in developing the program of experimental investigations on radiation materials physics at MMF.
References
PI W.F. Sommer, W. Lohman, K. Graf, I.K. Taylor and R.M. Chaver, in: Proc. 13th Int. Symp. on Effects of Radiation on Materials (Part II), Eds. F.A. Gamer, C.N. Henager and N. Igata, ASM-STP 956 (1987) 718. PI D. Gavillet, R. Gotthardt, J.-L. Martin, S.L. Green, W.V. Green and M. Victoria, in: Proc. 12th Int. Symp. on Effects of Radiation on Materials, Eds. F.A. Garner and J.S. Perrin, ASTM-STP 870 (1985) 394. 131 E.A. Koptelov and Yu. Ya. Stavissky, Institute of Nuclear Research of the Academy of Sciences of the USSR, Preprint P-0053 (1977). [41 E.A. Koptelov, V.V. Korolev and Yu. Ya. Stavissky, Institute of Nuclear Research of the Academy of Sciences of the USSR, Preprint P-0288 (1983). 151S.E. Boriskin, N.V. Kalmychkov, E.A. Koptelov and Yu. Ya. Stavissky, Institute of Nuclear Research of the Academy of Sciences of the USSR, Preprint P-0431 (1985).
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E.A. Koptelov et al. / Irradiation experiments in view of fusion condition simulation
[6] V.F. Zelensky et al., Some Problems in Physics of Radia-
[7] [8]
[9] [lo]
tion Damage of Materials (Naukova Dumka, Kiev, 1979) p. 240 (in Russian). V.V. Orlov and I.V. Al’tovsky, Institute of Atomic Energy, Preprint IAE.3380/8 (1981). B.B. Kadomtsev et al., in: Pro&. 4th All-Union Workshop on the Program of Experimental Research at the Meson Facility of Institute of Nuclear Research of the Academy of Sciences of the USSR, Moscow, 1986, p. 372. I.V. Al’tovsky et al., Institute of Atomic Energy, Preprint IAE-3504/11 (1982). Yu.P. Severgin and I.A. Shukeilo, in: Proc. 4th All-Union Workshop on the Program of Experimental Research at the Meson Facility of the Institute of Nuclear Research of the Academy of Sciences of the USSR, Moscow, 1986, p.
1111 t:H. Packan, Radiat. Eff. 101 (1987) 189. [12] E.A. Koptelov and N.A. Golubev, Voprosy Atomnoj Nauki i Tekhniki, Ser.: Radiation Damage Physics and Radiation Technology Is. 2 (15) (1981) 6.
1131 EA. Koptelov and V.V. Korolev, Voprosy Atomnoj Nauki i Tekhniki, Ser: Radiation Damage Physics and Radiation Technology Is. 2 (40) (1987) 29. [14] E.A. Koptelov and V.V. Korolev, in: Proc. 14th Int. Symp. on Effects of Radiation on Materials, Eds. N.H. Packan, R.E. Stoller and A.S. Kumar, ASTM-STP 1046 (1990) 572. [15] G. Nickolis and I. Prigozhin, Self-Organization in Nonequi~b~um Systems (Wiley, New York, 1977). [16] II. Haken, Synergetics (Springer, Berlin, 1978). [17] EA. Kopteiov, Radiat. Eff. 45 (1980) p. 163. [18] P.A. Bereznyak, A.V. Volobuev, V.V. Gann and N.M. Kiryukhin, Voprosy Atomnoj Nauki i Tekhniki, Ser.: Radiation Damage Physics and Radiation Technology Is. 2 (10) (1979) 77. 1191 L.N. Kmetyk, J. Weertman, W.F. Green and W.F. Sommer, J. Nucl. Mater. 98 (1981) 190. [ZO] L.N. Kmetyk, W.F. Sommer and Weertman, J. Nucl. Mater. 103 & 104 (1981) 1409. [21] L.N. Kmetyk, J. Nucl. Mater. 122 & 123 (1983) 613.
Journal of Nuclear Materials 174 (1990) 311-318 North-Holland
On irradiation experiments in view of fusion condition simulation E.A. Koptelov, V.V. Korolev and A.A. Semenov Institutefor Nuclear Research, Academy of Sciences of the USSR, 60th October Anniversary Prospect 7a, Moscow I1 7312, USSR
Charged particle accelerators of meson physics facilities provide certain possibilities for simulation experiments in radiation damage and radiation material investigations for fission and fusion reactors. The problem of the adequacy of such experiments noses some questions. The possible influence of the time structure of linear machines, such as the Moscow Meson Facility proton accelerator, on the radiation kinetics is discussed to outline the validity of simulation experiments in fusion materials studies.
1. Introduction The resolution of the problems arising from fusion materials hampered by the absence of neutron sources
with spectra and fluxes reproducing the irradiation conditions at planned fusion facilities. In this regard it is interesting to consider the possible use of intensive proton and secondary neutron beams of high intensity meson facility accelerators in irradiation physics and nuclear materials investigations. Such accelerators are known to operate in the USA, Switzerland and Canada. Analogous construction work on the research complex at the Moscow Meson Facility (MMF) of the Institute for Nuclear Research (INR) has entered the concluding stage. Experimental investigations carried out at the meson physics facilities at Los Alamos (USA) and at Villigen (Switzerland) have demonstrated the effectiveness of using these nuclear physics facilities for researchers on radiation physics of metals and alloys [1,2]. As regards investigations on nuclear materials, the extra potentialities offered by meson facilities are connected with the availability of intensive proton and secondary neutron beams [3-51. Experimental and theoretical investigations of physical mechanisms defining the radiation damage kinetics can assist in selecting construction materials for fission and fusion power reactors. Metals and alloys to be used in future power installations have to resist irradiation up to doses of the order of hundreds of displacements per atom (@a) or - 102’ neutrons/m2. For this reason one has to investigate various phenomena such as radiation emb~t~ement, swelling, effects of cyclic loading and tem-
perature changes, effects of hydrogen, helium and other irradiation-produced impurities on mechanical properties of metals and alloys [6,7]. The working conditions for the first walls of fusion reactors, that are defined by the plasma irradiation and operating mode of installations such as tokamaks, are summarized in paper [7]. The authors of ref. [7] have analysed the main processes that define the utilization of materials in several fusion reactor projects. The present report deals with aspects of simulation studies of the radiation resistance of fusion materials, that can be carried out on the basis of intensive proton and secondary neutron beams of meson physics facilities.
2. Meson physics facilities potential for simulation investigations of irradiation processes in fusion materials
As is already known, intense neutron generators based on the (T, d)-reaction with rotating targets (for example, RTNS-II) provide 14 MeV neutrons, but in a rather limited volume of a few cm3 and with a low density not exceeding 1016 n/m2 s. Such fluxes are ten times lower than the normal flux even for the hybrid thermonuclear reactor. Various irradiation facilities can be used for simulation inves~gations of the irradiation processes in fusion materials. The scope of phenomena that can be investigated in a given installation depends critically on its characteristics, such as damage rate K (dpa/s), helium and hydrogen production rates Ku, and K, (appm/s),
0022-3115/90/$03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)
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E.A. Koptelou et al. / Irradiation experiments in view
respectively, depth of damage zone as well as the capability of creation of controlled mechanical stresses and temperature conditions in the area being irradiated. The possibilities of conducting experiments in radiation materials physics in the proton and secondary neutron beams of the Moscow Meson Facility (MMF) have been considered in some previous works [3-5,8,9]. The main characteristics of primary and secondary beams of MMF have been presented elsewhere [4,5]. The facility includes an accelerator for hydrogen ions with an energy of 600 MeV at an average current rent of 0.5-l mA. The temporal structure of the primary beam is characterized by the pulse rate w = 100 Hz and the pulse duration 7 = lop4 s in the normal regime, but can be altered through a wide range by making use of the proton storage ring (PSR-like) stretcher and compressor [IO]. Certain possibilities for the radiation testing of firstwall fusion materials under conditions close to reality, can be created at the neutron target structure or beam stop for the proton beam of the experimental complex of MMF (INR, the USSR) [5].
3. Formulation of the problem Comparison of radiation damage by intensive proton beams and by characteristic neutron spectra with respect to damage rate, helium production rate and their ratio only gives a basis for an approximate assessment of the possibilities for simulation investigations of the behaviour of radiation materials. The problem of the adequacy for predictions of property changes of metals and alloys in neutron fields based on radiation effects investigations with proton beams gives rise to a number of questions. We shall outline below the following two points: (1) the effect of the temporal structure of the meson facility proton beam on the growth kinetics of radiation defect clusters; (2) the role of temperature pulsations in the evolution of a void system. These problems represent a particular case of a more general problem connected with the pulsed operating regime of various irradiation facilities and fusion reactors [7,11]. Some general features of radiation defect cluster growth under nonstationary irradiation conditions are considered in refs. [12-141 and will be described below. Theoretical analysis of the radiation damage kinetics relies upon the following concepts. A set of point and
offusion condition simulation
extended defects in irradiated metals and alloys represents a particular case of open non-equilibrium systems with reactions and diffusion. In such systems the processes of development of spatial and temporal structures (self-organization) [15,16] are possible. Simultaneously, there exists the hierarchy of times in such systems [16]. The existence of different time ranges in the case of radiation defects results in a large variety of experimentally observed dependencies of the microstructure kinetics on pulse characteristics during pulsed irradiation [ll]. As is usually the case with non-equilibrium systems with reactions and diffusion, a significant difference in the diffusion coefficients for interstitials and vacancies defines the differences between the time ranges of various processes of the defect kinetics. So, if 7, and 7” are the lifetimes (times of absorption by sinks and recombination) for interstitials and vacancies. respectively, T, and ~a are characteristic growth times for interstitial and vacancy clusters. respectively, then usually Ti K 7, K rv K 7a.
(1)
The expressions and estimates for these times can be found, for example, in refs. [14,17]. The evolution of defect clusters under pulsed irradiation must be governed by the relation between the characteristic times of the defect kinetics and temporal parameters of irradiation in fusion installations or simulation facilities. We introduce the following notations: C,, Ci are the concentrations of vacancies and interstitials, respectively; K(t) is the damage rate; p is the recombination coefficients for coefficient; D,, Di are the diffusion vacancies and interstitials, respectively, p is the density of dislocation network, pL is the density of interstitial dislocation loops; pd = p + p,_ is the total dislocation density, b is the modulus of the Burger’s vector; N is the loop density, R, is the loop radius; N, is the void number density; R is the void radius; ps = 4mN,,R; Z,, Z, are the bias factors for interstitials and vacancies, respectively, 7v,i = [ D,,i( Zv,ip, + ps)]-‘. The kinetics of radiation defects can then be described by the rate equations [13]:
d&l dt
=K(t)-ucic”-~
(2)
“.I
here a: = p( Di + 0,). In eq. (2), the time dependence of sink densities must be taken into account. We can account for the role of evaporation terms in eq. (2) and in cluster growth in numerical solutions of the full set of equations. (See table 1.) We shall consider the time structure of irradiation typical of intense proton beams of meson facilities
313
EA. Koptelou et al. / Irradiation experiments in view offusion condition simu~ut~on
based on linear accelerators. varies as follows: Ko, 0 i7
K(t)=
The damage rate K(t)
OItI7,
the “on-time”
r
the “off-time” interval.
interval;
(3) Here Ka is the amplitude of the damage rate; 7 is the pulse duration; or is the pulsing period of irradiation. The average value of the damage rate is (K) = K,,( 7/q). For 7r = 0.01 s and the duty factor T/T~= 0.01 one has (K) < K,. So the problem of comparison of radiation damage by some steady irradiation with the damage rate K = (K) and by pulsed irradiation with the average damage rate (K) exists.
4. Interstitial dislocation loop fonuation
under pulsed
109
-0
f0-5
10-s
10-l
IRRADIATION
IO’
103
TIME (s 1
Fig. 1. The time dependence of the interstitial dislocation loop density pL and the loop number density N in Ni under continuous irradiation. Ti, = 373 K. The damage rate fc = 10e4 dpa/s. Values of N,,, and p,,, correspond to estimations based on eqs. (5) and (6) in the text.
and continuous irradiation
Let us consider first of all the formation of interstitial dislocation loops in irradiated metals. This process can be important if the density of pre-existing dislocations is small enough, p < ,D_,where the value of pC, is determined by irradiation conditions [17]. Assuming this inequality to be satisfied, the estimation of the loop nucleation time is as follows To= ({~)~~i)-1’2.
(4) After the nucleation stage the loop growth process takes place. Under continuous irradiation the resulting loop number density iV and the density of dislocation loops p,_ can be written in the form: N, = n2’3[(K)/‘pDi]1’2 PL=r
1’3W[ ( K)/~Di]1’2(
(5) Di/D,)“4.
(6)
Here w = S( r&Z)- ‘/* fi is the atomic volume. The corresponding time scale is of the order of [17]: 7[= &($
In 3 - arctg 4).
On the basis of eqs. (5) and (6) one can estimate the parameters of interstitial loop structure forming under certain continuous irradiation. Fig. 1 shows the results of such estimations and of numerical solutions of eq. (2). Under pulsed irradiation in high intensity beams of the meson physics facility, the pulse duration T is longer than the loop nucleation time 7. - ( KO~.Di)-1~2. In this case the loop number density N,, according to (S), must be proportional to Ki12. This means that under the pulsed irradiation considered, the loop density NL( Ko)
Table 1 Material parameters used in the calculations Parameter
Notation
Vacancy formation energy Interstitial formation energy Vacancy migration energy Interstitial migration energy Vacancy diffusion pre-exponential InterstitiaI diffusion pre-exponential Surface energy Recombination coefficient Atomic volume Interstitial dislocation bias factor Vacancy dislocation bias factor Initial void radius Melting temperature
Nickel
E6
2.83x10-19
E,m
1.6x10-I9 24x10-” 1.9x10-5 8.0x10-’
Ef
Eim D 0:; B
P f2
1.0x102’ 1.09x 10-29
zi
Z” Ro %I
1728
SS 316
Album
2.56x10-i9 6.41 x lo-l9 2.1x10-‘9 3.2 x 1O-2o 5.0x10-s 1.0x 10-7 2.0 1.0x10~0 8.0x10-30 1.08 1.00 1.0x10-s
1.06~10-‘~ 5.19x10-‘9 9.12~10-‘~ 1.6x10-20 4.0x10-6 8.0x10-6 1.0 1.86 x 10’9 1.25 x 10-29 1.08 1.00 1.0x10-s 933
Molybdenum 6.8X1O-‘p
144x10-‘* 2.45 x lo-i9 1.36x lo-” 3.0x 10-6 1.6~10-~ 2.05 1.34 x 10’9 2.03~10-*~ 1.08 1.00 1.0x10-s 2893
units J J J J m’/s m’/s J/m2 mm2 m3
E
314
E.A. Koptelav et al. / Irradiation
experiments
iI
0
kc__-. 0
1.
._/
100 IRRADIATION
0
200
TIME (pulses 1
Fig. 2. Comparison of interstitial dislocation loops generation
in nickel under pulsed (pulse rate 100 Hz, duty factor 10-2) and conontinuousirradiations with the same averaged damage rate (K) =10m4dpa/s, qTi,,= 373 K.
can be expected to be higher than N,(( K)) under the continuous irradiation with the same average damage rate K = (K). The difference must be of the order of prove ( 5/T 1I/* > 1. Results of numerical computations this conclusion. The total dislocation length under the pulsed irradiation considered is also greater than under the comparable continuous irradiation (see fig. 2). If the pulse duration T is small as compared to the nucleation time Q, then the kinetics of dislocation loop formation has no specific features connected with the pulsed beam time structure [XX]. The model used considers the loop nucleation via di-interstitials and neglects the vacancy cluster formation. So the numerical resutls are limited to sufficiently short irradiation times [17] 1
f <
-4
8Z
3 = D”&~ fln*-z,
71
i
where 7s is the time for vacancy cluster nucleation. The increase in interstitial dislocation density under the pulsed irradiation considered can be dominant in radiation defect structure evolution for irradiation temperatures I;,, < 0.3T”, where ‘&, is the absolute melting temperature. For higher temperatures such modified dislocation densities must be accounted for as the starting conditions for void growth kinetics.
5. The void growth kinetics under pulsed irradiation This process was analysed numerically by Kmetyk et al. [19-21f for the pulsed irradiation with the time
m view of fusion condition slmuiation
structure of the Los Alamos Meson Physics Facility. According to their results for aluminium and molybdenum, damage rate pulsing is not important for void growth, while associated irradiation temperature oscillations enhance swelling at temperatures lower than the peak swelling temperature and retard it above that temperature. We shall show that damage rate pulsing can influence void growth markedly if two conditions are satisfied simultaneously: (i) point defect lifetimes are shorter than the pulse period; (ii) during the “ontime” period point defect recombination dominates over point defect absorption by sinks. Both conditions follow from simple analytical considerations 1131, as can be seen below. Void sizes do not change significantly during the pulse period. The growth equations for clusters are linear in point defect concentrations. So extended defects grow similarly under pulsed and continuous irradiations if average concentrations of point defects for both cases are equal. In quasistationa~ conditions the point defect concentrations at the beginning and at the end of each irradiation period are the same. Then one has from eq. (2): cK)
- ff(cJ~)
-
(G,i)/‘v.,.i
=O.
(9)
Let us define the effective damage rate Kefr as the damage rate of such continuous irradiation, when stationary vacancy and interstitial concentrations are equal to the corresponding average meanings for given pulsed irradiation. For continuous irradiation with the damage rate zr’,, one has
It follows from eqs. (9) and (10) that Keff
=
tK>
-
at(cicv>
or in terms of (C,) Keff
=
(1
+
~T(C”))(CV)/G.
-
(c~>(cv>)*
01)
one has (12)
The second term in the right-hand side of eq. (11) describes possible differences in radiation damage under pulsed and continuous irradiations. To estimate this difference we consider the time dependence of Cv in more detail. For the beam time structure of the meson facility we have 7; << 7 K< 7”
(13)
E.A. Koptelov et al. / ~rrad~at~o~ experiments in view offusion condition simulation
315
Solving eq. (2) in this case one has the following expressions for CV: (i[ (1 + “7iCo)’ + 2~K,7,‘] G(r)
- l}/luTi
for 0 I t 5 7;
=
(14)
0.2
Here Ca = C,(O) is the initial value of the vacancy concentration. The equation for C, has the form:
0
aTiC,Z[exp(27r/TV) - 11 + 2Ca[exp(Tr/T,)
- l] = ~K,T. (1%
Let us consider the following two cases. 5.1. The short pulse period: rf e r, Expanding the left-hand side of eq. (15) up to the second order terms in ?r/r,,, one has 1 +qc.. + 1 + 2qcs
Tf
z
CC”)= s 1 -
i
1
”
(K)
=
1
(17)
lXTiCS 7i” .-----cl. 1 + aTic, 127,”
So in the case of short pulsing period, rr e r,, the void growth under pulsed irradiation develops with the same rate as under continuous irradiation with the average damage rate of the given irradiation, i.e., K,, = (K). This analytical result is illustrated by the two upper curves of fig. 3 where resutls of numerical imputations are presented. Fig. 3 shows the dependence of Kerf versus the pulse duration 7 at different values of the pulsing period TV,but with the constant average damage rate (K > = 10T6 dpa/s_ As the value of rr/rV decreases the curve tends to unity. 52. The long pulsing period:
10-2
IO"
r(s) Fig. 3. Dependence of the effective continuous dalpage rate corresponding to the given pulse regime (in view of the average void growth rate) on pulse duration at various pulse rates w = 0.1; 1, 10 and 100 Hz. The average damage rate (K > is fixed and equal to 10s6 dpa/s. T,*, = 823 K. The material constants for SS 316 were used: q = 0.097 s, ~~= 0.72 x lo- 5 s.
q X- rv
In this case C, = 0. Averaging eq. (14) one has (C,) = [ (1 + 2~Ke~ir)i’~ - I] T”,/aTi~f for
It follows consequently K
rtr (1 + ~cx(K)~~#~ eff
x
(19)
- 1
l+~[(1+2a(K)~~~i)L”-lj).
(20
The values of the ratio Keff/(K) described by expression (20) are shown on fig. 3 by straight dotted lines for ri = 10 s and TV= 1 s. These values agree well with the data of numerical calculations in the domain where ~~s T I 7” * q. Eqs. (19) and (20) can be simplified in two limits: 5.2.1. During the “on-time” dominates, i.e., 2a(K)7,7i >>1
where
recombination
(21) When recombination dominates, eq. (21) is valid for some linear-like part of the curve with 9 = 10 s and to a lesser extent for the curve with or = 1 s. X2.2. During the “on-time” where absorption by sinks dominates, i.e., 2a( K)rfri CC1 In this case, from eq. (19), it follows that (C,) = (K)T,.
$ < 1.
that
wrir
(
+T;t;ics .$p .
It follows from eq. (12) that
(Ku>- Keff
10-L
$
* 1272 Y 1. i Here Cs is the stationary value of vacancy concentration under continuous irradiation with the average damage rate of the pulsed irradiation. Omitting terms of the order of (7/rr) +=s1, one obtains: co = czi l-
10-6
(22)
This relation corresponds exactly to the vacancy concentration under continuous irradiation with the damage rate (K) if absorption by sinks dominates. Conse-
316
E.A. Koptelou
et al. / Irradiation
experimenis
rn view of fusion condition
.simulation
/
cant
16 i
I
500
600
700
800
900
T,,,(K)
Fig. 4. Dependence of the void growth rate on the temperature r,, (SS 316). The average damage rate (K) = 10d5 dpa/s, the pulse duration 7 = 10m4 s and the pulsing period 7, = 10, I, 0.1 and 0.01 s, respectively.
quently, one has Keff = (K) in this case. Fig. 4 shows the temperature dependence of the void growth rate in stainless steel for (K) = lo-’ dpa/s, T = 10-O s and different periods of pulsing TV= 10, 1, 0.1, 0.01 and 10e4 s (continuous regime), respectively. The swelling curves for pulsed and continuous irradiations coincide at low temperatures and become different in the temperature domain where the lifetime of vacancies appears to be less than the period of irradiation pulsing. The curve corresponding to typical i~adiation regime of MMF (TV= 10T2 s) differs slightly from the continuous irradiation curve over the whole temperature domain of void swelling. Finally, the pronounced difference in the void growth under pulsed and continuous irradiations with equal average damage rate can exist in the case of section 5.2.1 when both conditions (i) and (ii) or two inequalities, rr >> r\,
(23)
2ff(K)TrT1 5-> 1,
(241
are simultaneously satisfied. It must be mentioned that energy losses in materials irradiated by intense beams are able to cause temperature pulsing. Figs. 5 and 6 present the numerical data on void growth in aluminum and molybdenum under the irradiation conditions of the Moscow Meson Facil-
L20
I LLL_-
L60
:v) 60
20
0
1000
and
1
500 560 T,,, IK) Fig. 5. Temperature dependence of void growth rate in aluminum under the Meson Physics Facility irradiation (pulse rate 100 Hz, duty factor 10m2). (lu) =10m4 dpa/s, p =1012 me2, NV= 1Ota mm 3, R0 = 10 nm, T, = 933 K. 1 - continuous irradiation; 2, 3 and 4 - pulsed irradiation, including temperature pulses with magnitude of 0, T,/20 and T,/lO, respectively. 380
1000
1200
lLO0
1600
1800
2000
TC,iKl
Fig. 6. Temperature dependence of void growth rate in molybdenum under the Meson Physics Facility irradiation (pulse rate 100 Hz, duty factor lo-*). (K) =10m4 dpa/s, p = 3x 1012 rnm2, NV= 10” rne3, R, = 10 nm, T,, = 2893 K. 1 -- continuous irradiation; 2, 3 and 4 - pulsed irradiation, including temperature pulses with magnitude of 0, T,/20 and T,/lO, respectively.
E.A. Koptelov et al. / Irradiation experiments in view of fusion condition simulation
ity (MMF). As is shown in fig. 5 for aluminum, damage rate pulsations do not cause any change in the void growth rate, if temperature pulsations are absent. However, if one simultaneously applies temperature pulses with the magnitude of the order of (1/2O)T,, then the void rate decreases markedly near the upper temperature limit of swelling and increases slightly at lower temperatures. These conclusions are in qualitative agreement with the numerical data obtained at LAMPF [19-211. In the case of molybdenum (fig. 6) even in the absence of temperature pulsations (curve 2), pulsed irradiation results in distinguishable differences in void growth rate at higher temperatures. The conditions under which damage rate pulsations lead to a significant decrease of void growth rate were discussed above. The requirements (23) and (24) impose a restriction on the total sink density p,: (DJJ’
K &---z 2p(K)r,.
This
restriction
(K)
= 10m4 dpa/s
(25)
cannot be fulfilled for aluminium at in the temperature range of void swelling, but in molybdenum one can obtain from (25) the following inequalities:
317
early stage of irradiation, by increasing the dislocation density. The problem of the effect of irradiation pulsing on void generation awaits its solution. These details of radiation damage seem to play a secondary role in the long-term behaviour of irradiated metals. So the primary proton beam of the MMF will provide the possibilities for conducting research on radiation damage physics in fission and fusion materials. Also envisaged is irradiation of samples in the beam stops where the fast neutron flux averaged over time and over the volume of - 50 cm3 reaches - 2 x 10” n/m2 s at the total proton current of 0.5 mA. The ratio of damage rate to the helium production rate at the beam stop is close to that for the first-wall materials in fusion reactors. Irradiation with the pure proton beam can provide damage rates which are one to two orders of magnitude greater than the damage rates in the existing neutron irradiation facilities, but with enhanced helium production rate per unit of displacement, compared with the fusion reaction irradiation [4].
Acknowledgements
3.8 x 10” m-* =X pt < 2.7 x 1013 m-*. At higher total sink strengths (about 1.6 x lOi m-* as in refs. [19,21]) in the absence of temperature pulses, the differences are low and do not exceed a few percent. As for temperature pulsations, it follows from the numerical results presented in figs. 5 and 6 that they become important only when temperature pulse amplitudes are of the order of (1/2O)T, or higher. In real experimental environments one can select irradiation conditions such that damage rate pulsations will not affect the void swelling kinetics [13,14]. Temperature pulsations of the order of T,/20 can only be achieved in the very extreme case of maximal focusing of the MMF proton beam. According to our estimates, at the average damage rate (K ) = 10e5 dpa/s, the amplitudes of temperature pulses do not exceed a few tens of degrees.
6. Conclusions One should expect that in experimental studies of the vacancy agglomeration and swelling of metals, the temporal structure of the proton beam of linear accelerator meson facilities (or other installations with similar time structure) will not cause any significant direct changes in the void growth kinetics. However, irradiation pulsations can play an indirect role, at least in the
The authors would like to thank Professors V.M. Lobashev and Yu.Ya. Stavissky for their constant interest and attention to this work. The authors also have great pleasure in maintaining long-termed scientific contacts with Professors V.V. Orlov, I.V. Al’tovsky and S.N. Votinov, who took a great part in developing the program of experimental investigations on radiation materials physics at MMF.
References
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318
E.A. Koptelov et al. / Irradiation experiments in view of fusion condition simulation
[6] V.F. Zelensky et al., Some Problems in Physics of Radia-
[7] [8]
[9] [lo]
tion Damage of Materials (Naukova Dumka, Kiev, 1979) p. 240 (in Russian). V.V. Orlov and I.V. Al’tovsky, Institute of Atomic Energy, Preprint IAE.3380/8 (1981). B.B. Kadomtsev et al., in: Pro&. 4th All-Union Workshop on the Program of Experimental Research at the Meson Facility of Institute of Nuclear Research of the Academy of Sciences of the USSR, Moscow, 1986, p. 372. I.V. Al’tovsky et al., Institute of Atomic Energy, Preprint IAE-3504/11 (1982). Yu.P. Severgin and I.A. Shukeilo, in: Proc. 4th All-Union Workshop on the Program of Experimental Research at the Meson Facility of the Institute of Nuclear Research of the Academy of Sciences of the USSR, Moscow, 1986, p.
1111 t:H. Packan, Radiat. Eff. 101 (1987) 189. [12] E.A. Koptelov and N.A. Golubev, Voprosy Atomnoj Nauki i Tekhniki, Ser.: Radiation Damage Physics and Radiation Technology Is. 2 (15) (1981) 6.
1131 EA. Koptelov and V.V. Korolev, Voprosy Atomnoj Nauki i Tekhniki, Ser: Radiation Damage Physics and Radiation Technology Is. 2 (40) (1987) 29. [14] E.A. Koptelov and V.V. Korolev, in: Proc. 14th Int. Symp. on Effects of Radiation on Materials, Eds. N.H. Packan, R.E. Stoller and A.S. Kumar, ASTM-STP 1046 (1990) 572. [15] G. Nickolis and I. Prigozhin, Self-Organization in Nonequi~b~um Systems (Wiley, New York, 1977). [16] II. Haken, Synergetics (Springer, Berlin, 1978). [17] EA. Kopteiov, Radiat. Eff. 45 (1980) p. 163. [18] P.A. Bereznyak, A.V. Volobuev, V.V. Gann and N.M. Kiryukhin, Voprosy Atomnoj Nauki i Tekhniki, Ser.: Radiation Damage Physics and Radiation Technology Is. 2 (10) (1979) 77. 1191 L.N. Kmetyk, J. Weertman, W.F. Green and W.F. Sommer, J. Nucl. Mater. 98 (1981) 190. [ZO] L.N. Kmetyk, W.F. Sommer and Weertman, J. Nucl. Mater. 103 & 104 (1981) 1409. [21] L.N. Kmetyk, J. Nucl. Mater. 122 & 123 (1983) 613.