ELSEVIER

Nuclear Instruments and Methods in Physics Research B 102 (1995) 322-325

Beam Interactions with Materials & Atoms

Simulation of heavy-ion cluster impact fusion

Yasunori Yamamura *, Tetsuya Muramoto Okayama University of Science, Ridai-cho, Okayama 700, Japan

Abstract A computer simulation by the time-evolution Monte Carlo code DYACAT has been performed in order to investigate the

possibility of heavy-ion cluster impact fusion due to heavy-ion cluster impacts on a TiD 2 target. As a heavy-ion cluster, (AI) N, (Ti) N and (Ag) N clusters are considered. These three cluster impacts can produce a well-defined, long-lived quasi-equilibrium state. It is found that A1 clusters can transfer their energy to target deuterium atoms most efficiently among these three clusters. For the (A1) s cluster impacts, the temperature of target deuterium atoms in the impact region is well represented by kT=E113/79.6 exp[ - t /~ - ] , where E 0 is the cluster energy per atom in eV, and r is the cooling time constant which is given as ~" = 2.1 × 102N°l°/E °'12 fs. The total fusion yield per cluster impact is of the order of 10-11 for

50 keV/a tom (Al)2o o cluster impacts.

I. Introduction

Cluster impact on solid surfaces is one of the most interesting subjects in particle-solid interaction. It pro- duces very high particle and energy densities in a very small impact region of the target material. There are a lot of interesting problems in cluster impact phenomena. Computer simulation is one of the most powerful ap- proaching methods for investigating cluster impact phe- nomena. At present there are two computational methods which can treat cluster impact phenomena. One is the molecular dynamics (MD) [1,2], and the other is the time-evolution binary collision approximation (TEBCA) code which was developed by Yamamura. There are two types of TEBCA codes, i.e,, the DYACAT code [3,4] and the DYACOCT code [5]. The DYACAT code is for an amorphous target, and the DYACOCT for a crystalline target.

Several years ago, Beuhler, Friedlander, and Friedman (BFF) of Brookhaven National Laboratory (BNL) showed that deuteron-deuteron fusion occurred when singly charged clusters of 25 to 1300 D20 molecules, accelerated to 200 to 325 keV, impinged on a TiD target [6]. At present, however, the BFF's high fusion rate is recognized to be due to highly accelerated small-ion impurities pro- duced in the acceleration column [7].

The motivation of this paper is that if one uses heavy-ion clusters one can avoid the contribution of highly acceler- ated cluster d atoms. At the same time, recently, Yama-

* Corresponding author

mura and Muramoto [8] showed that the target d atom plays an more important role for the total fusion yield than the cluster d atom when the D20 clusters are bombarded on a TiD target.

In this paper, using the time-evolution Monte Carlo code DYACAT, we investigate the energy properties such as energy spectrum, the effective temperature and the cooling time constant of the cluster impact region due to heavy ion cluster impacts on a TiD 2 target, where as initial cluster energies per atom, which is denoted by E o in this paper, 10 keV, 20 keV and 50 keV are used, and as the cluster sizes 50, 100 and 200 atoms clusters are consid- ered.

2. Model of simulation

The DYACAT program was developed for the time- evolution dynamical simulation of atomic collisions in an amorphous target within the framework of the binary collision approximation. It is the dynamical mode of the ACAT code [9]. The details of the DYACAT code are described elsewhere [10], and only a brief introduction of the DYACAT program is presented here.

In the DYACAT code, the cluster particles and the recoil atoms are followed throughout their slowing-down process in time until their energies fall below predeter- mined-cutoff energies E c. The displacement threshold en- ergy is set to be zero during the slowing-down period, but if T - E B < Ec, the target atom is not added to the cas- cade, where T is the kinetic energy transferred to a target atom after collision, and E B is the bulk binding energy. In the present calculations, E B is set to be 1.0 eV for all

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Y. Yamamura, T. Muramoto / Nucl. Instr. and Meth. in Phys. Res. B 102 (1995) 322-325 323

cases, and the Moli~re potential is used as the interatomic potential for elastic scattering. The electronic energy loss in solids is estimated by using the Oen-Robinson local model [11], where the parameters included in the electronic stopping formula are calculated from the Lindhard formula [12] and Ziegler's table [13] for a heavy ion and a d atom, respectively.

The cluster shape is assumed to be spherical for the heavy ion cluster, and the binding energy between con- stituent atoms is neglected, because the cluster energy of present interest is larger than the cohesive energy of the cluster atom, and the average lattice constant is set to be equal to that of the solid. The atomic fraction of deuterium atoms in TiD x is usually less than 2.0, but recently the Tsukuba group in Japan [14] reported that a TiD 2 target has been successfully obtained. The density of TiD x is calculated according to the following formula:

+ XMD PTiD x = (1 -- a ) MTiMT i pTi, (1)

where MTi and M D are the atomic masses of Ti and D atoms, respectively, PTi is the density of Ti, and A is the expansion factor which the titanium lattice undergoes dur- ing TiD= production [14]. For TiD 2 we used A = 0.10.

In the present calculations the cutoff energy E c of a target d atom is set to be equal tD 200 eV, 400 eV and 1000 eV for E o = 10 keV, 20 keV and 50 keV, respec- tively, because the main concern of the present paper is the high-energy tail of the energy spectrum of the target d atom.

3. Simulated results and discussions As a heavy-ion cluster we consider (ml )2oo , (Ti)2o o and

(Ag)2o o clusters. In Fig. 1 we show the normalized energy spectra of the cluster atoms, target Ti atoms and target d atoms at t = 30-40 fs due to 10 keV/a tom 200 a toms/ cluster impacts on a TiD 2 target, where "normal ized" means that these spectra are those per one primary atom. The number of impinged primary dusters is 100. From the energy spectra of Ti atoms and d atoms, it is known that the impact region is already in the quasi-equilibrium state after t = 20 fs. The elastic energy transfer factors 31 of a heavy ion and a target Ti atom are 0.922, 1.0, and 0.852, respectively, and those of a heavy ion and a target d atom are 0.258, 0.155 and 0.0720, respectively. The acceleration rates of cluster atoms, target Ti atoms and target d atoms are about 1.5 for all cases. As a matter of course, the (A1)2o o cluster produces the recoil d atoms with highest energies among three different kinds of cluster impacts.

From the slope of the energy spectrum we can define the temperature of active d atoms in the usual manner, where "ac t ive" means the particles with energies larger than the preassigned cutoff energy. In Fig. 2 we plot the

10"=

10-3 l O k e V / a t o m . . . . target Ti - - target D

10-4 - . =

106 ~ 10-6 10 .7

E 10 "8 o ~ cluster Ti

. . . . target Ti "~ 10 "~ - - target D ~- - l . , t = 30-4Ors

1 0 4 0

.~- 10 s

lO.e

10 .7

O 10"8

,o3 [t~.., - - target D I04F l '-"... t = 30-4Ors

10-~

tO-7

10. 8 - ' I 0 5000 10000 15001

E n e r g y [eV]

Fig. 1. Energy spectra o f cluster atoms, target T i atoms and target d atoms due to 10 k e V / a t o m (Al)200, (Ti)200 and (Ag)2o o cluster impacts on a T i D 2 target at t = 3 0 - 4 0 fs.

temperature of the d atoms in the impact region as a function of time for 10 keV/a tom (A1)200, (Ti)200 and (Ag)200 duster impact, where the solid lines are the best-fit curves which are represented by the following fitting-func- tion:

kT : kT o e x p [ - t / r ] . (2)

The best-fit values of kT o are 4.06 × 102, 2.54 × 102, and 1.67 × 102 eV, respectively, for (A1)20o, (Ti)20 o and

1000 !target O atom" ' lOk'eV / &tom

gtoo o (AI)~o --~ "l'iDz [] (1"i)=oo ~ riD=

10 • (Ag)moo "-* TiD~ 30 40 50 60 70 80 90 100

t i m e [ f s ]

Fig. 2. Plot of the temperature of the target d atom as a function of time for 10 keV/atom (A1)2oo, (Ti)2o o and (Ag)2o o cluster im- pacts on TiD 2 targets.

V. CLUSTER-SOLID INTERACTIONS

324 Y. Yamamura, T. Muramoto /Nucl. Instr. and Meth. in Phys. Res. B 102 (1995) 322-325

I::: 10 "2

~ 10_3

10 "4 t j .--~ 10 ~

10.e

"~ 10.7 E

10"

l)N ~)' TiD2 target D atom eV/atom ~ N = 200

- - N = 1 0 0 . . . . N = 5 0

= 50-60fs

. . . . .

1000 2000 3000 4000

Energy [eV]

Fig. 3. The cluster-size effect on the energy spectrum of target d atoms at t = 50-60 fs for the (A1) N cluster impacts on a TiD 2 target, where the initial cluster energy is 10 keV eV/atom.

10000 target O atom (AI)mo ---> TiD~

~ 1000 ~

tO0 30 40 50 60 70 80 90 100

t i m e [Is] Fig. 5. Plot of the temperature of the target d atom as a function of time for (Al)200 cluster impacts on a TiD E target, where the initial heavy-ion energies are 10 keV eV/atom, 20 keV and 50 keV/atom.

(Ag)200 cluster impact, and r is 1.2 × 102 fs for all cases. The cooling time constant ~" does not depend on the kind of cluster atom, because the cooling is mainly determined by elastic collisions of recoil d atoms with target Ti atoms and d atoms.

In the ensuing discussions we will calculate the depen- dence of the cluster energy and the cluster size on the energy property of the impact region for the (Ag) N cluster impacts on a TiD 2 target. In Fig. 3 we compare the energy spectra of d atoms at t = 50-60 fs for (A1)5o, (Al)lo o and (A1)2oo, where the cluster energy E o is 10 keV, and the numbers of primary impinging clusters in the simulation is chosen in such a manner that the total number of imping- ing cluster atoms is equal to 20 000. The cluster effect on the energy spectra is observed only in the high energy tail. On the other hand, the dependence of the cluster energy on the energy spectrum is shown in Fig. 4 for the (A1)lO o cluster impact, where the energy spectra of target d atoms at t = 50-60 fs are drawn. As a matter of course, the cluster energy is an important factor for the energy prop- erty of the impact region. While the acceleration effect becomes weak with increase of the cluster energy.

One of the most important parameters for estimating the fusion rate per cluster impact is the dependence of the

I=: 10"2

10 -3

-~ 10 4

.¢= 10 "s

~ 10 "6

"~ 10. 7 E o 10 ~ <:

iAl~oo ~ TiDa " "target O'atom - - 10kaY

. - - 2 0 k e V

~ 5 0 k e V

5000 10000

Energy [eV]

Fig. 4. The cluster energy dependence of the (Al)2o o cluster on the energy spectrum of target d atoms at t = 50-60 fs, where the initial heavy-ion energies are 10 keV eV/atom, 20 keV and 50 keV/atom.

cluster energy and the cluster size on the temperature of the target d atom in the impact region. As an example, in Fig. 5 we plot the temperatures of d atoms as a function of time for the (A1)2o o cluster impacts with energies 10 keV, 20 keV and 50 keV. The solid lines in Fig. 5 correspond to Eq. (2) with corresponding best-fit parameters, where (kT o, ~') of 10 keV, 20 keV and 50 keV are (4.06 × 102, 1.2 × 102), (8.57 × 102, 1.1 × 102) and (2.44 × 103, 9.4 × 101), respectively. The data analysis of the best-fit values gives the following simple expression of the tem- perature for the (A1) N cluster impact on TiD 2 target:

Eo 1.13

k T = 79.6 e x p ( - t / ~ - ) , (3)

where r = 1.2 × 1 0 2 N ° l ° / E °'12 fs. The N-dependence is very weak, as was expected.

Fusion events may be caused by fast d atoms colliding with stationary target d atoms or by collisions between two fast d atoms. Here, let us obtain a rough estimate of the total fusion yield per cluster impact. The total fusion yield per cluster impact is given as

¢¢ Y = f dt N d ( t ) R ( k T ( t ) ) , (4)

t 0

where t o is the time at which the impact region becomes in the quasi-equilibrium, N O is the number of d atoms in the hot spike, R is the fusion rate per d atom, and kT(t) is the temperature of the hot spike given by Eq. (3). The volume of the hot spike is determined by the computer simulation, and the fusion cross section included in the fusion rate R is given as O'F=S//E e x p [ - F / v ~ - ] , where F = 3 1 . 2 8 keV 1/2, and S = 5.5 × 10 -23 cm 2 keV. Fig. 6 shows the cluster energy dependence of fusion yield per cluster im- pact for (A1)lo o and (A1)2o o cluster impacts, where t o is set to be 10 fs. The fusion yield of the present calculation is proportional to E 4"8 in this energy region for (A1)20 o cluster impacts. The cluster effect on the fusion rate is mainly due to the size of the cascade volume induced by (Al)lo o and (Al)2o o cluster impacts. The calculated fusion

Y. Yamamura, T. Muramoto / Nucl. Instr. and Meth. in Phys. Res. B 102 (1995) 322-325 325

~ 10-1o

~'- 10-11

~ 10-12

-~1o -13

"10 10-14

10-15 0 '~ 10-16 O.

~ 5 ...... 10 100

Energy / atom [keV]

Fig. 6. The total fusion yield per cluster impact as a function the cluster energy E 0 for (Al)100 and (Al~zoo cluster impacts on a TiD 2 target.

yield for 50 k e V / a t o m (Al)20 o cluster impacts is 1.4 × 10 -11 , which is qualitatively consistent with the recent experimental results due to small (HeO)NH + cluster im- pacts on heavy ice [7].

4. Conclusions

A computer simulation by the time-evolution Monte Carlo code DYACAT has been performed in order to investigate the possibility of the heavy-ion cluster impact fusion on TiD e , The temperature of the impact region due to (A1)~v cluster impacts is represented by kT = Eo1'13/79.6 e x p [ - t / ~ ' ] with the definition of ~-= 2.1 × 1 0 2 N ° l ° / E o °'12 fs, where E o is the incident energy per atom in eV. As a result it is expected that the proton yield per dus ter impact is of the order of 10-11 for 50 k e V / a t o m

(A1)20 o impact on a TiD 2 target.

Acknowledgement

This work was supported by a Grand-in-Aid of The Ministry of Education, Science. The author is grateful to Dr. H. Tawara of the National Institute for Plasma Science for his valuable discussions.

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V. CLUSTER-SOLID INTERACTIONS