Oksana Katsuro-Hopkins, Paper Journal Moscow Physics Society, Fission Degradation. 1997

8/14/2019 Oksana Katsuro-Hopkins, Paper Journal Moscow Physics Society, Fission Degradation. 1997

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J. Moscow Phys. Soc. 7 (1997) 153-162.

The space-tim e evolution of the track of an a tomic nucleusf ission fragm ent in a helium -m etal vapour m ixture

Oks a n a K a t s u r o - H o p k i n s , 2 n d A u t h o rA P Budnik, I V D obrovol'skaya, and 0 N K atsuroState Scienti f ic Center of the Ru ssian Federat ionInstitute of Physics and PowerEngin eerin g, Bonda ren ko sq. 1, 249020 Obninsk , Kaluga Region, Russia

Received 25 September 1996

Abstract. Resul ts o f mathem atica l model ling o f the space- t im e ev o lut ion o f thetrack o f a f i ss ion f ragm ent a re presen ted. The degradat ion o f the energy o f nuc learf ission f ragments in a hel ium -cadmium m ixture are studied.

1. Introduction

T he degradation o f the energy of fission fragme nts in inert gases is very impo rtantfor the development of a device to generate nuclear energy at optical wavelengths(a "flash-lamp" a nuclear-pumped laser). The theory of energy degradation for rapidelectrons in gases is currently well developed. The state of the theory of energy degra-dation of m ultiply-charged ions, including fission fragments, is considerably w orse.Th e interaction of fission fragments w ith matter is fundamentally different from theinteractions of other charged particles with matter due to the strong influence of so-called track effects. Because of these effects, the kinetics of the energy degradation offission fragments are, as a rule, significantly inhomoge neous.In recent years, a theory for the spacetime evolution of the tracks of fissionfragments in inert gases has been developed [1-3]. T his theory is capable of rathercorrectly taking ac coun t of a who le series of processes: the diffusion of electrons inions, the energy relaxation of electrons du ring collisions, electronion recom bination,the creation of an electric field and the drift of charged particles under its influence.Th is paper concerns the theoretical study of the energy degradation of fission frag-men ts in mixtures of helium and m etal vapours. We present results of mathem aticalmodelling of the spacetime evo lution of a fission fragment track in a heliumc admiummixture. In contrast to previous studies [1-3], we take account of electronelectron

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The f iss ion f ragmen t t rack space - t ime evo lut ionhoand St e e (fo) is the electron-electron collision integral. In (5), the sum over acorresponds to various inelastic collisions between electrons and atoms, with2eaU l = U 2 +or elastic collisions5a)rn2eU 2 = Uor superelastic collisions5h)mwhere ea is the excitation energy for atoms in the a state.S t ee (fo), representing the flux of electrons in velocity space due to electron-electron collisions, is determined by the formulas4re 2 ) 2 1St ee = (----nu 2 e u I n A2 fo ( r , w ,t ) dw fo (r , u, t )0

1(u0 0 fo ( r u , t+ -iu-4/0(r,w,t)dw u 31 wfo (r, w, t).dwu6)where A is the ratio of the Debye radius ID to the Coulom b radius ro, defined askTet )e 22e 23k7; (6b)

where Te is the effective temperature.We write the boundary conditions for the system of equations (1)-(3) in the form8-07 fo(r,u,t)l. 0 = 07)88 7 Nik ( r , t ) I r =0 = 08)E(r, t ) ir=0 = 0(9o(r, u, t)l.10)

N i k (r ,o 011) 0 4 .12 'In order not to excessively complicate the problem, we will describe the evolutioof a track at a m oment in time w hen the electrons have experienced several collisiotafter the flight of the fragment. In this time, the electrons diffuse over a distancethe order of several mean free paths. Consequently, examining the evolution for mulonger times, we can w ith some small error specify the electron and ion concentratitto be G aussian distributions. Then, the initial conditions can be writtenN iim der(e)2fo(r, Olt=o =4ru d e 7 k ir r47e4""kU1\\-1_,Ar4 %to1 / 2 (6a)


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T he fiss ion fragment t rack space-tim e evolutionTable 2

Plasma-chemical reactions in the He-Cd plasma model

N o Reaction R eaction rate1 He+ .+He+He=He: +He 0.3x 10-31 cm 6 / s2 He++He+He+He=He:+He+He 1.82x 10' 1 cm 9 /s3 He : +CdsCd** + +H e +H e 6.12x10' cm3 / s4 He: +Cd=Cds+ + He i -He 7.92x 10-1 cm 3 / s5 He (20.6 )+Cd=CdPs++Hq+e 0.35x 10' 3 cm 3 / s6 He(20.6)+Cd=CdP**++He+e 0.35x 10" I cm 3 / s7 He (20.6 )+Cd=CdS++He+e 2.55x 10' cm3 / s8 Cd**+=CdPs++hv i 2.9x 10+ 6 s"9 Cds+ =Car"' +hv2 1.2x 10+6 s'

1 0 CdP**+=CdS++hv3 5.15x10+" s"II CdPs+ sCdS++ hv4 4.314x 10+" s-1

cross-sections for collisions between electrons and helium atom s from and cross-sections for the excitation of helium atoms by electrons from [81. Data on associativeionization, the conversion of atomic to molecular helium ions, and dissociative recom-bination were adopted from [9-111. The probabilities for transitions between excitedstates of helium were calculated using the oscillator strengths presented in [121.In the model, w e took ac count of such plasma-chemical reactions determiningthe character of processes in the helium-cadmium plasma as Penning ionization of thecadmium atoms, the conversion of atomic helium and cadmium ions to molecular ions,the recharging of molecular helium ions on cadmium atoms, and processes involvingthe plasma electronsionization and recombination processes, and excitation anddeexcitation of the helium atoms by electrons ; etc. In addition, we allowed for radiativetransitions between exc ited states of the helium atoms and c admium ions. Table 1presents all components of the plasma considered w ith their formation energies, andTab le 2 presents the plasma-chem ical reactions in w hich they take part, togetherwith the corresponding reaction rates and their dependence on the temperature of thfmedium.

3. Results

We carried out mathematical modelling of the evolution of a track of a fission fragrin a neutral gas a mixture of helium (N H. = 2 .68 x 10 1 9 cm -3) and satuicadmium vapours at a temperature of 650 K. W e take the parameter (r2 ) 0equal to ( r 2 ) = 4 x 10-8cm 2 . F igures 1-9 show the results of our c alculationsradial dependence of the concentrations of electrons, atomic and molec ular 7atoms (He+,nd cadmium ions in the ground (CdS ) and excited 4d 9 5s 2state (Cd*+ ) at various times after the passage of the fission fragment are s l


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10 9 t= 0.13 ns10'= 1.2 ns1111t=3010 510 310 '

60000000 r , 1 0 -5 cm0000 t = 45 n sThe fission fragment track space-time evolution59N Cd .*, CITC 3Figure 4. Radial dependence of the concentration of cadmium ions Cd in the exitedstate 4d9 5 8 2 2 D s/3 (Ce+ ) at various times.N Cd S 9cm -310 6

10 4

10 2

10000000000000 r, 10 -5 CMFigure 5. Radia l depen dence of the concentrat ion of cadm ium ions in the groun d state(CdS) at various t im es.F igures 1-5. It is clear (F igure 1) that the electrons rapidly leave the region near thetrack axis due to diffusion, so that a rather strong electric field 10 2 V/cm ) arisesthere.The electrons create a significant num ber of He+ ions via inelastic collisions; theconcentration of these ions rapidly grows, especially far from the track axis (F igure 2 ).Th e concentration of atomic helium ions He+ then decreases due to diffusion and

drift, and, especially, due to conversion into mo lecular helium ions H et (F igure 2 ).The c oncentration of molecular helium ions thus grows due to the cerversion process(F igure 3); due to recharging, the concentration of atomic cadmium io ns also grows(Figures 4-5). F igure 6 show s the concentrations of various plasma com ponents attime 45 ns. W e can see that near the track, the comp onent with the largest concen-tration is molecular helium ions Het ; the concentration of positive ions significantlyexceeds the c oncentration of electrons near the track ax is.Superelastic collisions significantly affect the evolution of the track. In particular,even at large times, these collisions determine the electron energy distribution near


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E, V / cm2001 5 0

1 0 0

5 00

The fission fragment track space-time evolution6 1f(s) , eV - 3 1 21 0 - 1 41 0 - ' 710 -2 010 -2 31 0 -261 0 -291 0 421 0 -35

....1

00505 e, eVFigure 8. Electron energy distribution function f(Ea distance r f rom the t rack axisat time t.45 ns.00 0000000 500 r, 10 -s c m

Figure 9. Radia l dependen ce of the e lectr ic f ie ld st rength at the t rack at v ar ious t imes.

com plex com position (helium with cadmium vapours). Our results may be useful forthe developm ent of the theory of m icroscopic kinetic processes in nu clear-pum pedlasers based on me tal vapou rs, takin g account of the track structure of the plasma .

Refe r ences[1 ] Budnik A P, Sokolov Yu V , and Vak u lovskiy A S 1994 H yp e r f i n e In t e r a c t i o n s 88 185[2 ] Budnik A P, Vak u lovskiy A S, and Sokolov Yu V 1992 Proc. Conf. "LYaN-92" vol 1

(Obninsk : Physical -Energ etic Institute) p 178[3 ] Budnik A P, V aku lovskiy A S, Dobrovol 'skaya I V, an d Sokolov Yu V 1993 P h y s i c a l - E ne rg e t i c

Institute Prep rint-2315[4 ] Georjuoy E 1966 Phys. Rev . 148 54[5 ] Reym ann K , Schartner K-H, Somm er B, and Tra bert E 1988 Phys. Rev. A 38 2290[6 ] Nikerov V A and Sholin G V 1985 Kinetika D e g r a d a t s i o n n y k h P r o ts e s s o v (Moscow:

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Oksana Katsuro-Hopkins, Paper Journal Moscow Physics Society, Fission Degradation. 1997