A new approach to fast neutron diagnostic simulation: Monte Carlo with shower and drizzle splittings and finite close-collision treatment

}'rill{_2 HI (}r~ H }~Cl/,III1

\ [ I FI~h~. Ig'x~[gM~l

(

~ ItJ }'Zr~ i{1],,T1 }'FI.N. ~h]L

A NEW A P P R O A C H TO FAST N E U T R O N D I A G N O S T I C SIMULATION: MONTE C A R L O WITH S H O W E R AND D R I Z Z L E SPLITTINGS AND FINITE CLOSE-COLLISION TREATNIENT '" N Ea * , L. I.'GROSSO N * , J. S. BRzos~:o+, B. V. R o u o ¢ ' c H , K. Ht:u~ H. KLEIN--. and S. GL:LDB \KKE:~

Associazione E U R A T O M - E N E A sulla Fusione, Centro Ricerche Energia Frascati, C.P. 65. ()0044 Frascati, Rome, Italy "lnstitut far Angewandte Physik, Universitat Heidelberg, F.R.G. -Stevens Institute of Technology, Hoboken, NJ 07030, U.S.A. - Physikalisch-Technische Bundesansalt (PTB) Braunsweig. F.R.G.

ABSTRACT The paper presents a new approach to Monte Carlo simulation of neutron diagnostics that leads to an acceleration of the convergence of the variances with substantial CPU-time saving. The acceleration is achieved due to (i) improvement in the nuclear reaction-channel probing, (ii) improvement in space sampling, and (iii) a simplified and precise close-collision description. An example of a simulation of the ASDEX tokamak shows that the ratio in CPU-time consumption for a Shower & Drizzle OFF and ON is 8 to 20. The new procedures form intrinsic parts of both VINIA3DAMC and 3D-MCSC-RWR analogue-ME software sets that operate in continuous space and energy representations, on point-wise data file inputs, and w i t h o u t any simplification. 1. INTRODUCTION Modern nuclear technology requires the simulation of radiation migration (neutron, gamma) in complex and sophisticated systems. For diagnostics, Monte Carlo treatments successfully use the fluxat-a-point method (Kalos M.H. ,1963) tO obtain meaningfu statistics of useful contributions at the detector. The method is normally used in MCNP (Los Alamos Monte Carlo Group ,1981) , TRIPOLI {Nimal J.C. et al. ,1980), and VINIA-3DAMC (Brzosko J.S., Robouch B.V., and Ir~rosso L., 1987) software for neutron diagnostics applied to complex structures such as those of fusion tokamaks. However, if rare-but-strong-events (RSE) are not to be neglected in a study, one has to cope with realistic CPUtime consumption. By RSE we refer particularly to two classes: the first (RSE-1) is related either to a material with a disproportionately large mean-free-path of radiation, or to a material with a low product of isotopic abundance and reaction-channel cross section. Both conditions may give rise to a strong contribution in an otherwise quiet part of the spectrum. The other (RSE-2) is due to thin (again with respect to the mean-free-path) material located in the vicinity of the detector. Such thin spaces stop neutrons only rarely, but when they do, the event produces intense detector tallies. The situation is agravated when any of these RSE events contributes to a narrow energy interval of interest. These strong but rare events, out of proportion with the rest of the data accumulated, are detrimental to the convergence rate of the overall variance. To avoid such a situation and ensure that the significant contributions be constantly in proportion, we now propose the analogue SHOWER and DRIZZLE splittings, which reproduce the probabilities of physical events. Although they are presented here as applied to a flux-at-a-point detection, they are powerful when used, for example, in a) blanket tritium-breeding evaluations, b) evaluating radioactivity of the surface layers 409

41~)

B.V.

R~,t~{,c ~ H e t a[.

of the facility (for safe lathing after shut down), c) neutron detector callibration in the vicinity of a massive structure. In essence, MC migration has to probe the space and the nuclear reaction channels in order to gather information about the model's properties; the better the probing, the more credible the results. SHOWER enhances the probing of nuclear reactions, while DRIZZLE, with its beam-probing, greatly enhances the space probed. In addition, neutron detection with close or internal collisions requires particular consideration. The importance of attaining small variances is far greater in diagnostics than in detection. In fact, in detection a value is measured and the standard deviation error is determined. In diagnostics, as a parameter is varied, one aims to detect the variation in the measured signal. To detect such a variation, the o-errors of the detected signal must be smaller than half the variation in the signal. The aim of the paper is to introduce SHOWER, DRIZZLE, and the close-collision treatments we have developed to accelerate the convergence of variances. They have successfully been applied to a) fast-neutron diagnostics (B~itzner R. et al. lgg0) , b) fast-neutron radiography (Brzosko J.S., et al. 1990), and c) elemental analysis (Brzosko J.S. 1989). The simulation below refers to the first of the applications. 2. MONTE CARLO SIMULATION OF NEUTRON DIAGNOSTICS FOR TOKAMAKS The interpretation of neutron diagnostics for large fusion devices requires numerical simulation of the full experiment: starting from the neutron emission in a plasma with known parameters; following the migration of the neutrons through the complicated structures of the device and the detector (see Fig:l ); concluding with the response of the detectors used. Such an extensive numerical simulation requires MC treatments of the following problems: 1 - description of the plasma neutron-source: spatial distribution, anisotropy of emission, and energy spectrum (thermonuclear plasmas, plasmas with additional heating, etc...); 2- calculation of the spectra and fluence of neutrons arriving at the detector; 3- determination of detector response to the different fluence components (direct or scattered; structural part in which scatter occurred, etc ...). For a full understanding of neutron diagnostics, the following data have to be stored in the output file: a) coordinates of the points of emission, collisions and detection for each story; b) time of emission or collision, necessary for time-of-flight detection or other time-resolved studies; c) weight (i.e., probability) and energy of the neutron contribution arriving at the detection point; d) identifiers for the origin of neutron re-emission: collided nuclide and reaction branch, tokamak structural element (region}, and the partition of space as observed by the detector (zone). Of course, the uncertainties and statistical errors at each step of the calculation sum up nonlinearly and determine the overall quality of the simulation. The distinct MC software sets designed to solve each one of the above three problems are strongly correlated. The output of the neutron source program serves as input to the neutron migration software, whose output is used as input for the several software programs for simulating the response of the different detectors. In this paper we concentrate on the neutron migration software, in which close-collision treatment, SHOWER, and DRIZZLE are CPU time savers. 2.1 Close-collision treatment. The simulation of neutron diagnostics for tokamaks has to be as realistic as possible, especially in the treatment of the detector vicinity and tokamak parts in direct view of the detectors. In fact, the reduction of the detected intensity, by material structures and due to the distance, limits the space of origin of the important contributions to but a few mean-free-paths around the detector. We concentrate our attention on the problems intrinsic to this vicinity. In applying the flux-at-a-point biassing and evaluating the expected value estimator in its uncollided flux estirnatorversion, the expression for the fluence reaching the point-detector per unit area is given (Kalos M.H. ,1963) by ~=

Id3rldEIdE'I~(re,E) [~tzg~/rd-re---e,E-.E')-e-t~(E')Ird-reld.___..~} t

Ir d - rel

(1)

4r~l r d - rel

Here, rd and re are respectively the point of the detection and the point of the event (emission or collision); d r= Ird - tel; e ~ (rci-re)/d; E and E' are, respectively, the incident neutron energies and those exiting from the event; ll(E') is the total attenuation coefficient of the scattered neutron, and g is the probability of scattering a neutron of energy E' in a direction (e, e + de). In Eq. (1) we are faced with the singularity introduced by the 1/4 ~d2 term and the necessity of having to use the once collided estimator or some other similar treatment (Steinberg H.A. and Kalos

M.H., 1971;Drawbough D.W. ,Ig61;TroubetzkoyE.S. & Cohen M.O.,1967;Kali H.J. and Cashwell E.D.,

k:tst ncutr~m dia~n,~[ic qmuiat~tm

~tll

1977;Steinberg H. and L i c h t e n s t e i n H. ,1973;Podlivaiev I.F.& Ruzu Yu.I ,t973; Dubi A . , H o r o w i t z Y.S., and R i e f H., t 9 7 9 ; F r a l e y S.K. and H o f f m a n T.J. ,1979; H i r o m a s a Iida and Yasushi Seki ,1980).

However, one has to note that in the above expression the fluence is implicitly expressed per unit area (Ua) of a spherical surface while, rigorously speaking, we ought to be referring it to the unit area (Ua) of a plane surface. The transformation factor is the ratio o f the solid angles subtending a unit area on the plane ~lMane(Ua,d) to that subtending a unit area on the sphere ~sphere(Ua,d). Clearly ~sphere(Ua,d) = Ua/d2. For the plane, assuming for simplicity that the unit area Ua be a circle of radius ' a", i.e., ha2 = Ua, the solid angle ~p|ane(Ua,d) it subtends at a distance d is cosO= d , ' V / ~ + a 2

~plane (Ua' d) = 2 u [l - ;cosOl)

f(d) -

12pi,me (Ua' d) 2n(t - IcosOI) 2nd'Z [ flaphere (Ua' d) ~ Ua/d2 - ~ a l

d ~/d 2 +

] a2

At large distances, d2 >a2 -- Ua/n, a Taylor expansion of f(d) in series of ~ = (aid)2 gives t~d2,>a 2~ Ua/n= t/n)=

Thus, f o r

2rtd 2 1

2

U---~"2-

3 az <_10-2 i.e 4 d2

3

2

2 + Ore2)

t-~"

~-a

4 d2

,

--d > _ 5 x / 3 a = 5x/31u

the corrections are less than 1% for d => 5. As was to be expected, this simply restates that for large radii the Ua of the spherical surface coincides with the Ua of the plane tangent to it. At the other extreme we have

f(d~O)-,2ud2/Ua

which, inserted in Eq. (1), cancels out the singularity, leaving a finite factor that increases monotonically to 0.5. This simply restates that a plane Ua-surface can intercept at most half of the emission from an emitting point as it approaches the surface. By incorporating this transformation coefficient into our software, i.e., using U I

(1

2Ua

~

r~)

insteadof

~/d 2 ; U J

4nd2

our estimator is regular (i.e., has no singularity) and thus needs neither the once collided estimator nor other similar special treatments to tackle even the very close collisions (see B~[tzner R. et al., 1990 for instance). 2.2 The SHOWER splitting concept. At any collision a neutron has a certain probability of following any of the branches of the reaction with any of the nuclides present at this point. As the starting situation for the next migrative step, the Monte Carlo procedure randomly selects one of these possible reactions and, traditionally, a flux-at-a-point tally is sent to the detecting point only for the selected reaction branch, i.e., we have one nuclear reaction-channel tally per point. In this approach, as mentioned above, both lowprobability branches and minor nuclidic constituents, w h e n they do occur, create rare and disproportionately large event contributions (RSE-1). Thus, for a selected type of detected radiation for which RSE-1 contributions are or are not superposed upon the radiation coming from the rest of the device, the distribution converges to a meaningful value only after the simulation of a large number of neutron stories. To avoid these perturbations and the large number of neutron stories they would need, we introduced the SHOWER splitting. Consider Eq. (1). In MC, the integrations become sums of tallies, and, in particular, the integral over dE' becomes the sum over all the reaction-channel branchenergies E', ~E'- We have just seen that, traditionally, from each collision only one tally is considered and associated to the full v2 assigned to a single reaction channel. We, instead, retain EVERY contribution of ~'E' from each collision. To do this analogically, ty(E,r) is split proportionately to the product of the density (n (r)) of the nuclide (i) multiplied by its cross secion Oi,r for the reaction branch (r) which determines E': ku = ~" i

~" ku~.r with r

k~i.r = ku x n o . / ~

n( --\- o,r). t

c

41-~

B. V R~m~uc'u et" d/.

Thus, the signal delivered to the detecting point is a shower of tallies, each one duly reduced to account for anisotropy, space dispersion, and attenuation by the material crossed. None of them is ever out of proportion. This treatment totally eliminates perturbations introduced by rare nuclear reactions due to trace elements or low cross-section branches and guarantees a full probing through all possible nuclear reactions.

2.3 The DRIZZLE splitting concept. The second type of perturbation (RSE-2), due to thin material close to the detector, is particularly a problem in the simulation of detectors with thin protective shields (for light, X-rays, thermal neutrons) around them. The same situation occurs when detectors inserted in the tokamak vessel come close to thin shields installed for other purposes. An example for both such situations is given in Fig.1. Here, a pneumatic system transports the detectors very close to the plasma edge. The protection tubes, the transport tube, and the transport boxes are made as thin as possible. The full detector installation crosses a thin stainless steel shield which protects the diverter chamber. In a traditional MC treatment, such surfaces exhibit a cumulative effect due to the sporadicity of their emissions. The rare, lumped, strong contributions would totally offset the variance of the collected distribution. However, the correct simulation of the processes in all the shields shown in the figure is really essential. All together they attenuate the neutron fluence passing to the detector by about 25%, while contributing, on the other hand, about 16% of the collided fluence arriving at the detector. The use of DRIZZLE splitting satisfies the need to get results with a small variance, in a reasonable CPU-time. To present DRIZZLE, let us recall the usual forced-collision treatment (Cashwell E.D.a~d Everett C.J.,1959) of a neutron migrating through material space. Here, for every migratory step, one first calculates the weight attenuation (due to the various materials traversed) which the neutron would suffer along its line of flight up to the outermost surface of the material space of the tokamak model. Then, one point of collision is selected stochastically along this line of flight, taking into account the absorption in the different regions. It is then that this full interacted-weight is scattered from the selected point and sends a contribution - or in our treatment is split into a shower of contributionsto the detector. This interacted weight then proceeds to the next migratory step, starting from this point of collision. The neutron migrative collision naturally stops preferably in thick or in dense regions. Only seldom does one have collisions in thin or rare regions; but when they do occur, the full interacted weight is assigned to them. Again, as in the SHOWER case, this is equivalent (having replaced integration over d3r by a summation, Zr, over all the space traversed) to taking a single tally from only one of the points, with the full v2 attributed to it. To overcome this statistically valid approach, which however introduces a distortion in the statistical distribution, we apply the DRIZZLE splitting. DRIZZLE spreads the scattered signal into its regional components along the line of flight, reproducing more faithfully ~r. ln fact, here a tally is scattered from each region into the detector, proportional to the interacted weight in that region. The point of emission along the line of flight is selected randomly in the region, using the same algorithm as adopted for the neutron migration. Thus, for each migratory step, we still have one point of collision that is the starting point for the next migrative step. On the other hand, for tally collection, the innovation consists in having one scattering point for each structural element (or subelement) of the experimental set up encountered along the line of flight. Such a treatment eliminates accumu!ated sporadic perturbations of the second type, as it ensures that each solicited region contributes by an amount proportional to its capacity to interact. 3. EXAMPLES OF MC SIMULATION WITH SHOWER, DRIZZLE, AND THE NEW CLOSE-COLLISION APPROACH. The example presented in this section is related to a simulation of neutron diagnostics that is being currently tackled. Simulating the Garching ASDEX tokamak with its several hundred structural volumes, each with its proper chemical composition involving several decades of nuclides with an average of half a dozen reaction channels each, is a CPU-time-consuming job. Moreover, detection is particularly sensitive to collisions close to, and unshielded from, the detector - whence the importance of close collisions. The simulations were done with the analogue VINIA-3DAMC software, using the pointwise-data of EFF-1 and JEF-1 nuclear data banks (Oruppelaar H. , Nierop D., 1986; OECD Report, 1985, respectively). It iS to be noted that calculations and outputs of both VINIA-3DAMC and 3DMCSC-RWR are in absolute units and do not use any parameters or normalization factors. We compare the MC simulation results from DRIZZLE + SHOWER (D + S) with those from Classical (C) as applied to the ASDEX experiment (see Fig.1). The results obtained with the full use of SHOWER, DRIZZLE, and the new close-collision estimator show a very good agreement (_+ 15%) between the experimental and the VINIA-3DAMC numerical absolute fluences at the detector (B~tzner R.. et al. , 1990). Both D + S and C simulations include the new close-collision treatment. The specific spectra given in Fig. 2 represent thefluence of neutrons arriving f r o m a particular part of the device; they

Fast n e u t r o n d~agn,.)stic ,,imuLttion

; i

413

i Pneumatic transport systemwith , \-i ~ ~ m p l e .

S ;

;IL ...........

_~. ":" . . . . . . . . . .

67

~,~ "72 "79

Fig.l: A poloidal cross-section of ASDEX through the vacuum chamber and the detecting transport tube (as seen by the computer). Numbers refer to a selection of parts of the device, some of which are treated in Fig:2. Parts shown are Main section: 3-ASDEX vacuum chamber, 5-ohmic field coils, 18-divertor, 26-carbon shield, 65 -67-thin stainless steel shield protecting the diverter chamber. Blow-up: 81-nuclear emulsion or indium sample; 79 & 72-protective tubes; 59transport tube; (e) transport box.

are normalized to one neutron emitted by the plasma and expressed as per square centimeter of the detector. The ASDEX plasma source (neutraI-D injection heating) emits neutrons with an effective energy F,n = 2.45 MeV distributed over a 0.6 MeV range. At the position of the detector, the total probability of neutron detection is 6.83-10-6/cm2; of these neutrons, 57% are scattered due to the massive structure of ASDEX. As the detector has a threshold energy of 0.33 MeV, the cut-off energy for the calculation is set at that value. To simplify the comparison, we ran a unique set of 1000 random walk stories. Using this set of 1000 trajectories, we then estimated the spectra that would be delivered by the two approaches being compared. We then extended the C-run to a total of 6000 neutron stories so that the total CPUconsumption was just above that of the 1000 stories D +S run (both shown in Fig,2). In the same Fig.2, the results of the simulations of 125 stories with D + S are also shown. The statistics presented are of course poor (see the values of R in Fig.2), because of (al the large volume of the neutronemitting toroidal-plasma source and (b) the particular position of the detector, right at the edge of the plasma source. On the other hand, they are suitable to show the evolution of the quality of spectra delivered by the D + S treatment, w i t h o u t going into a sophisticated mathematical analysis. Some of the conclusions that can be drawn from Fig. 2 are as follows: 1. Spectra of neutrons rescattered from massive structural elements of ASDEX (like REG:3) have a quality that is independant of the approach used, provided the same CPU-time is consumed. 2. Spectra of neutrons rescattered from thin sheaths or the detector structure itself (REG:80,81) have their quality improved if D + S is used: D + S with 125 neutron stories delivers a spectrum quality comparable to that of 6000 stories of a C-treatment i.e., a CPU-time saving by a factor of 8. 3. Spectra from the detector (REG =81), which are particularly sensitive to close collisions, converge still faster with D + S. 4. Spectra of neutrons scattered from extended but small density volumes(such as air, REG = 1) reveal an even greater improvement. In the present situation the saving factor is estimated to be 20

414

B.V.

REG

= I

R,.m,')~,. H ~'t ~d. l~,.

= 3

REG

REG

REG = 8 ~

= ~30

/

"=j

L ~

,]

i,

,Sd.

,i r

, t

I

tJ

I

~

-'2.

Z

,== [

4

2!

,-, I

.

f

.

I

I a

N ;~.

.

~ " S jLi;;

-4 i

,

"!

' !

[ ~ ! i i J L , ~' I,

'I

!

,

,

•

,

'h

1.

80B

[,0.

o

~

i

-

}l,J~-;

-i

::,, +

J

=

~ 182

ii N

£ r

--

1

,I

.!

Fig.2: Comparison of DRIZZLE + SHOWER (D + S) and classical (C) MC simulations of scattered specific neutron spectra at the detector (region = 81), from different parts of ASDEX structure. Each graph corresponds to a different region. I: the integral fluence and its statistical deviation. R: C-case - number of migrative collisions; D + S-case number of migrative + DRIZZLE collisions (due to SHOWER, the number of tallies is still larger).

4. FINAL REMARKS The useful property of DRIZZLE is that it probes the material space, or gathers information, beam-wise, distributingthe contributions proportionately among the regions traversed. This avoids having contributions that are out of proportion. SHOWER, on the other hand, prevents the sporadicity of contributions from rare nuclidic reactions. The close-collision treatment, with the uncollided flux estimator referred to a plane surface, eliminates the divergence of the variance. The combined use of all three ensures comparable variances when adding estimations coming from different contributors. Therefore, the estimated values tend smoothly to the asymptotic values. The D + S approach results in a sensible saving of CPU-time (by a factor of 8 to 20, depending on the problem} as compared to the classical approach, in spite of the fact that the splitting treatment requires a longer time per neutron story. It is important to stress that the total fluence of detected neutrons is in agreement with the measured fluence. In this paper we have discussed the DRIZZLE-SHOWER combination as applied to flux-at-a-point treatments of diagnostics or detection. However, the beam probing of DRIZZLE is more powerful than regional biassing when applied to tritium-breeding blankets of thermonuclear facilities or in

Fa>t n e u t r o n

dia~no~,tic ~ir'nukition

4

i ~'

estimating safety hazards from radioactivity of surface layers to be lathed after a shut down of the tokamak. For such studies we recommenda full DRIZZLE+SHOWER biassed to the reactions of interest. It is to be noted that all three concepts: DRIZZLE, SHOWER, and the new close-collision estimator are functional and integral parts both of VINIA-3DAMC (B~tznet R. et al., 1990) and 3DMCSC-RWR (Brzosko J.S. et al., [990); The work was performed in the framework of the Fusion Technology Program and involved the collaboration of scientists from the Ass. EURATOM-IPP, MPI, Garching, Germany, Ass. EURATOMKfA, J01ich, Germany, a n d t h e i n s t i t u t i o n s o f t h e a u t h o r s o f t h i s p a p e r . REFERENCES BATZNER R., HUBNER K., INGROSSO L., WAGNER R., BOMBA B., BOSCH S., KUClNSKI J., ROBOUCH B.V., BRZOSKO J.S., van CLAKER C., KLEIN H., GULDBAKKE S. (1990): 17th EPS Conf. on Controlled Fusion & Plasma Heating, Amsterdam 25-29/6/1990, 14B, IV p. 1520 BRZOSKO J.S., ROBOUCH B.V., and INGROSSO L. (1987):"Openings in a fusion reactor blanket (Tokamak type) - trends in nuclear characteristics",lEEE T r a n s . P l a s m a Sc.,PS-15,16-27. BRZOSKO J.S. (1989) private communication: R&D, DARPA unpublished report. BRZOSKO J.S., ROBOUCH B.V., INGROSSO L.,NARDI V.,BORTOLOTTI A. (1990): "Fast neutron radiography of massive instruments", in preparation for publication in: Material Evaluation. CASHWELL E.D., and EVERETT C.J.(1959): " M o n t e Carlo method for random walk problems", Pergamon Press, New York GRUPPELAAR H., and NIEROP D. (1986): "EFF-1 summary information"NERF-ECN, Petten EFF-Doc-12 - OECD Report (1985)"JEF-1 Nuclear Data Library", NEADATA Bank, Gif-sur-Yvette, France KALOS M.H. (1963): NucI.Sci.Engineering,16,111-117. LOS ALAMOS Monte Carlo Group (1981):"MCNP - A general Monte Carlo code for neutron and photon transport",Los Alamos Nat.Lab. Rep. LA-7396-m,. NIMAL J.C. et al. (1980): "TRIPOLI-2, Three dimensional polyenergetic Monte Carlo radiation transport program".Radiation Shielding Information Center,CCC-372/TRIPOLI-2, CEA,Saclay,France. STEINBERG H.A. and KALOS M.H.(1971) NucI.Sci.Engin., 4406 - DRAWBOUGH D.W. (1961) NucI.Sci.Engin.,9, 185 - DUBI A.,HOROWITZ Y.S.,and RIEF H.(1979) NucI.Sci.Engin.71,29 - FRALEY S.K. and HOFFMAN T.J. (1979) Nud.Sci.Engin.70, 14 - HIROMASA lida and YASUSHI Seki (1980) Nucl.Sci.Engin.74, 213 - KALI H.J. and CASHWELL E.D. (1977) Trans.Am.Nucl.Soc.27, 3702 - STEINBERG H. and LICHTENSTEIN H.(1973) Trans.Am.NucI.Soc.17,259 -TROUBETZKOY E.S. and COHEN M.O.(1967)Trans.Am.Nucl.Soc.,104 - PODLIVAIEV I.F. and RUZU Yu.I (1973) USSR-Comp.Math.Phys,12,336