Thus, it has been experimentally established that with increase of the irradiation temperature in the range 30-600~ the radiation expansion and impairment of the quartz structure is considerable but decreases monotonically in consequence of the intensification of recombination of Frenkel pairs during irradiation. The most significant temperature effect is observed in the first stage (increase of volume less than 0.5-1%) and below 100~ when an increase of temperature by 30-40~ reduces the expansion of quartz by a factor of i0. At the same time, the nature of the isothermal curves of the dependence of the volume increase on the fluence, the degree of anisotropy of the radiation expansion, and the type of defects originating with increase of the irradiation temperature remain unchanged. LITERATURE CITED 1.
2. 3. 4. 5.
6.
.
M. Wittels, Phil. Mag., 2, 1445 (1957). W. Primak, Phys. Rev., ii0, 1240 (1958). S. Weissman and K. Nakajima, J. Appl. Phys., 34, 611 (1963). G. K. Krivokoneva et al., Neorg. Mater., iO, No. ii, 1998 (1974). B. K. Pergamenshchik and A. V. Samotaev, "Calculation of the number of displacements in quartz during irradiation in a reacton," in: Proceedings of V. V. Kuibyshev Construction Engineering Institute [in Russian], No. 114, Moscow (1974), p. 102. O. V. Shcherbak and V. N. Karyukina, Microfloat for Determining the Specific Weights of Liquids and Minerals (in Liquids) by Torsional and Analytical Balances [in Russian], All-Union Scientific-Research Institute of Metrology and Standardization, Moscow (1972). V. M. Agranovich and V. V. Kirsanov, Usp. Fiz. Nauk, 118, No. i, 1 (1976).
TIME CHARACTERISTICS
OF A BACKSCATTERED X-RAY
PULSE CLOSE TO THE INTERFACE BETWEEN TWO MEDIA L. Ya. Morgovskii and F. L. Gerchikov
UDC 539.166.3
When investigating the characteristics of a nonsteady field of x or y-radiation near the interface between two media, it is necessary to analyze the time characteristics of the back scattered pulse. The existing data, generalized in [I], are confined to the use of a point source, radiating isotropically in a solid angle of 4~; these data have been obtained by the Monte Carlo method. At the same time, the expanding technical use of x radiation in guidance and control systems [2, 3] has necessitated the solution of this problem for collimated sources using simpler operative methods, e.g., albedo approximation. In this present paper, an analytical calculation of the time characteristics of back scattered x-ray pulses is described, for the case of the use of a collimated source and which is of more practical importance in technical applications. A pulsed x-ray emitter (RE) radiates in air in the direction of a semiinfinite reflector, located at a distance H from it, with energy Wo (MeV/sr) in a ~-pulse (Fig. i). The radiation within the limits of the directivity diagram of RE, defined by the angle of collimation 2~o is isotropic, the linear dimensions of RE and of the detector are much less than H, and the line RE-detector D (base b) is parallel to the surface of the reflector. We shall assume the albedo of the reflector to be isotropic, as its slight dependence on the angle of incidence and reflection within the limits of values of ~o a n d b/H of practical importance, can be neglected [4], assuming A = A E/2~ , where A E is the integrated energy albedo. We shall assume also that the detector is isotropic and we shall consider it, e.g., as a small sphere. Then the backscattered pulse received by the detector from the dense medium is: g (t) = A ~ W o G (t,
H);
Translated from Atomnaya Energiya, Vol. 51, No. 3, pp. 185-187, September, 1981. ginal article submitted August 18, 1980. 0038-531X/81/5103-0595507.50
9 1982 Plenum Publishing Corporation
(1)
Ori-
595
RE
b
s
a
4s i
~,,
3g
r
50
100
l
15g
200
4s2s 9
I
U
I
15g
g "o
2~g
o,~
o
~,os
"d
SO
o,, IfY
fog
15g
.... $0
*#a
7, i !00
~
Time, see
Fig. i Fig. i.
Fig. 2
Geometry of the problem.
Fig. 2. Signal of a backscattered x-ray pulse from air (i) and a dense reflector (2), m: a) 2.5; b) 5; c) i0; d) 20. Htgr G(t'H)=2~5
0
2a~ e_~t(p,+p2 ) (t 5' P~P~ cos@8 0
Pl~-P'z ) (2)
rdrdcp,
w h e r e p~ : t t 2 q - r ' Z ; p'.j : H~-[-b"-4- r ~" - - 2br cos (p; cos~p= H/D1; 1~ i s t h e a t t e n u a t i o n air; and c, velocity of light.
factorof
the radiation
in
Integration over the angle ~ is performed by using the properties of the ~-function. The second integration is performed directly. As a result: [ 0, (~<: ~); c0 - 2btH'~
G (% k)
.
41ta.c~ {(-~:__s
s ~ ( ~ - - ~.~) ,-(~.~_~)2+s
I• %=
X
(3)
], (~ ~ * ~ %);
[ O, ( % < ' ~ ) ~lt .... (k+E2) 1/~, (tg~%~k); scc •,, 4- [1 4- (2k-- tg %,)21112
(tg r ~ 7v);
see @,,+ It + (2X + tg %)qW '2 "Lz=
2
where dimensionless variables are introduced, which take account of the geometrical factors =
ctl2H,
k =
b12It.
For large distances H (~<< I) , formulas 0,
(3) are simplified considerably ( 0 ~ < ~ < t);
c0 - 2 btH'~
G (T, ~) =
2Ha.c--------T - ; (t ~.~ "~~.~ see ~o); 0, (sec *o < ~).
The backseattered pulse from the air medium can be obtained by considering the layered scattering in the volume of the cone bounded by the angle of collimation ~o. If the backscattering coefficient of the layer dz (it is also assumed to be isotropic) is equal to A b then we can write the corresponding signal in the form 596
gb (t)
Ab~WoF (t, It),
where
(4)
Z,2( t, H)
F (t, H) =
(5)
G (t, z) dz. t/
z~(t, H) As a result
0, ( 0 ~ < z < k ) I Fl,(k~<~
(tg % ~> k);
1% (zll ~< ~ ~< ~,~)
co - 2~HT
(6)
F (% %) - - b~
o,
(o~-~
(tg % <~ ~,). [ O, (z~ < ~)
F 1 --(1--%~T2 ~] (D_--D+)-yDu
D_-X;
F~ = Du 1-- ( I-- X2 ) D+;
F3-- ( t-- ~'~-2.~) (Do-- D+)+ Du
D~I;
[ ~,2COS2,0 ]1/2 D• . . . . 1-~ (~ _+ k sin %)2 }2
DU - [ t +
(T2_~2P
(7)
]i/2
In the expressions given, no account is taken of the contribution of multiple scattering in the air and the mixed processes of interaction of the medium and the air and vice versa. Within the limits of the region bounded by 1-2 mean free paths and the buildup time of ]0 -710 -6 sec, the contribution of multiple scattering, as the estimates based on the results of [i] show, is insignificant. Thus, analytic expressions (3), (6), and (7) completely describe the time distribution of the prompt backscattered x-ray pulse on the density of the medium and air in functions of the geometric factors (b, ~o, H). Using the formulas obtained, the time distribution of the backscatter signals for an x-ray pulse of finite duration f(t) can be reduced to an elementary integration t
W(t)= J g(t--x)/(x)dx.
(8)
0
F i g u r e 2 shows t h e c h a r a c t e r i s t i c s , from the backscattering of a bell-shaped w i t h b = 0 . 9 m a n d ~o = 45 ~ 9 The p u l s e e n e r g y i s 50 keV.
calculated o n t h e M-4030 c o m p u t e r , o f t h e s i g n a l s x-ray probing pulse for an air--concrete boundary length at half-height i s 15 n s e c and t h e e f f e c t i v e
Thus, the formulas obtained, w i t h o u t r e c o u r s e t o m o d e l i n g b y t h e Monte C a r l o m e t h o d , will allow the amplitude--time characteristics of a backscattered x-ray signal to be obtained in arbitrary geometry for a collimated source. LITERATURE CITED 1.
2. 3. 4. 5.
V. A. Klimanov et al., Propagation of Ionizing Radiations in Air [in Russian], Atomizdat, Moscow (1979). I. K. Zykov and S. B. Varyushchenko, Ionizing Radiations in Aviation and Space Technology [in Russian], Atomizdat, Moscow (1975). B. P. Bulatov and N. F. Andryushin, Backscattered y Radiation in Radiation Technology [in Russian], Atomizdat, Moscow (1971). B. P. Bulatov et al., Albedo of y Radiation [in Russian], Atomizdat, Moscow (1968). F. L. Gerchikov, Pis'ma Zh. Tekh. Fiz., 5, No. 18, 1121 (1979). 597
