P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

P. H. Liem, T. M. Sembiring, B. Arbie and I. Subki

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Analysis of the optimal fuel composition
for the Indonesian experimental power reactor
The optimal fuel composition of the 10 MWth Experimental
Power Reactor (RDE), to be built by the Indonesian National
Nuclear Energy Agency (BATAN), is a very important design
parameter since it will directly affect the fuel cost, new andspent fuel storage capacity, and other back-end environmental
burden. The RDE is a very small sized pebble-bed high temperature gas-cooled reactor (HTGR) with low enriched uranium (LEU) UO2 TRISO fuel under multipass or oncethrough-then-out fueling scheme. A scoping study on fuel composition parameters, namely heavy metal (HM) loading per
pebble and uranium enrichment is conducted. All burnup, criticality calculations and core equilibrium search are carried out
by using BATAN-MPASS, a general in-core fuel management
code for pebble bed HTGRs, featured with many automaticequilibrium searching options as well as thermal-hydraulic calculation capability. The RDE User Requirement Document issued by BATAN is used to derive the main core design parameters and constraints. The scoping study is conducted overuranium enrichment in the range of 10 to 20 w/o and HM loading in the range of 4 g to 10 g/pebble. Fissile loading per unit
energy generated (kg/GWd) is taken as the objective function
for the present scoping study. The analysis results show thatthe optimal HM loading is around 8 g/pebble. Under the constraint of 80 GWd/t fuel discharge burnup imposed by the technical specification, the uranium enrichment for the optimal
HM loading is approximately 13 w/o.
Analyse der optimalen Brennstoffzusammensetzung für den
Indonesischen experimentellen Leistungsreaktor. Die optimale Brennstoffzusammensetzung des von der indonesischen National Nuclear Energy Agency (BATAN) geplanten 10 MWthexperimentellen Leistungsreaktors (RDE) ist ein wichtiges
Ausgestaltungsmerkmal, da dadurch direkt Brennstoffkosten,
Lagerkapazitäten für neue und abgebrannte Brennelementesowie Umweltbelastungen betroffen sind. Der RDE ist ein kleiner gasgekühlter Hochtemperatur-Reaktor (HTGR) mit niedrig angereichertem Uran (LEU) UO2 TRISO Brennstoff. Eine
Voruntersuchung der Parameter der Brennstoffzusammensetzung, wie die Schwermetall-Beladung und die Urananreicherung eines Kugelbrennelements wurde durchgeführt. Alle
Abbrand-, Kritikalitäts- und Gleichgewichtsberechnungenwurden mit Hilfe von BATAN-MPASS, einem Brennstoffmanagementcode für Kugelhaufenreaktoren durchgeführt. Das
von BATAN ausgestellte Dokument für die RDE-Benutzeranforderungen wird verwendet um die wichtigsten Auslegungsparameter und ihre Beschränkungen abzuleiten. Die Voruntersuchung wurde durchgeführt über einen Bereich der
Urananreicherung von 10 bis 20 w/o und einer SchwermetallBeladung von 4 g bis 10 g/Kugel. Die Beladung mit spaltbarem
Material pro erzeugte Energieeinheit (kg/GWd) wurde als objektive Funktion für die Voruntersuchung verwendet. Die Er78

gebnisse der Analyse zeigen, dass die optimale Schwermetall-Beladung bei etwa 8 g/Kugel liegt. Aufgrund der von den
technischen Spezifikationen auferlegten Beschränkung von
80 GWd/t für den Entladebrand liegt die Urananreicherung
bei optimaler Schwermetall-Beladung bei etwa 13 w/o.

1 Introduction
The National Nuclear Energy Agency of Indonesia (BATAN)
is launching a plan (2014) to build an Experimental Power
Reactor (Reaktor Daya Eksperimental, RDE) [1] in the
Agency’s largest Research Center site, i. e. the Puspiptek
Complex, Serpong, South Tangerang, Banten, as a first strategic milestone for the introduction of large scale nuclear power
plant fleets into the country. The main objective of the plan is
to demonstrate safe and reliable electricity and process heatgeneration from a nuclear reactor. According to the User
Requirement Document [1] issued by BATAN, the RDE
adopted a very small sized pebble-bed high temperature gascooled reactor (HTGR) with a thermal output of 10 MWth,fueled with low enriched uranium (LEU) UO2 TRISO fuelunder multipass or once-through-then-out (OTTO) fuelingscheme. The thermal heat generated in the core is transferred
to steam generator (for electricity generation) and a heatutilization plant via an intermediate heat exchanger (IHX).
The use of IHX is expected to ensure a high degree of plantsafety especially the steam/water ingress events can be
avoided. As will be shown later, the document provides general main specifications of the RDE, however, many detaildesign parameters on the core dimension, fuel composition
etc. are given in term of ranges of value which should befurther optimized during the conceptual, basic and detail design phases.
An optimal fuel composition in the operation of a pebblebed HTGR is a very important design parameter since it will
directly affect the fuel cost, new and spent fuel storage capacity as well as other back-end environmental burden. A scoping study on the fuel composition parameters, namely heavy
metal (HM) loading per pebble and uranium enrichment isconducted. The main goal of this study is to obtain optimal
ranges of HM loading per pebble and uranium enrichment
for the RDE design. HM loading per pebble strongly affects
the neutron moderation (core neutron spectrum) while uranium enrichment is correlated directly with the achievable
discharge burnup. The present work is expected to contributein providing an optimal fuel composition for the RDE, however, only HM loading per pebble and uranium enrichment
are considered in the analysis. Nevertheless, since the rangesof the parameters considered are adequately wide, not only
the optimal fuel composition value but also the trend and im Carl Hanser Verlag, München

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P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

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Table 1. Main design parameters and constraints of the 10 MWth RDE
Design Parameters

Specifications Issued by BATAN

Present Analysis

Thermal Power (MW)1010Core Diameter (m)< 2.5

1.8 [2]

Core Height/Diameter Ratio>1.1

1.1 (Height = 1.97 m)

Ave. Core Power Density (PD, W/cm3)

2.0 £ PD £ 3.0

2.0 (Max. Core Vol.)

Upper Core Void Height (m)–0.4 [2]

Radial Reflector Thickness (m)–0.5Upper and Lower Reflector Thickness (m)

–

1.0

235

U Enrichment (w/o)£ 17

10 – 20 (LEU)HM Loading (g/pebble)£ 20

4 – 10Ave. Discharge Burnup (GWd/t)80

80

Fueling Scheme

Multipass/OTTO

Multipass (5 passes [2])He Inlet/Outlet Temp. (C)250/700

250/700

He Inlet Pressure (MPa)33Table 2. Standard data for pebble fuel element cell calculation
TRISO coated particle fuelmaterial(235U/238U)O2

diameter (lm)500

density (g/cm3)

10.9

Coatings

material

PyC/PyC/SiC/PyC(from inner)

thickness (lm)

90/40/35/35

density (g/cm3)

0.9/1.85/3.2/1.85

KernelPebble fuel element
Fuel matrix

Outer layer

Fuel element

material

graphitediameter (cm)5material

graphitethickness (cm)0.5

diameter (cm)6

Few group structure
Upper bound (eV)

Lower bound (eV)

Range

107

1.11 · 105

fast fission

1.11 · 105

2.90 · 101

slowing down

2.90 · 101

2.38

resonance

2.38*

thermal82 (2017) 1

79

P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

pact of the two design parameters on the core neutronics andburnup characteristics can be obtained.

2 RDE technical specifications
In Table 1, the main design parameters and constraints of the
RDE are listed. The parameters and constraints shown in thesecond column of the table were taken from the URD issued
by BATAN. The thermal output, discharge burnup and thecoolant inlet/outlet temperature and pressure are already
fixed. As for the core dimension, three design constraints are
imposed, that is, the maximum core diameter, minimum
height/diameter ratio and average core power density. On
the other hand, as for the fuel composition, only the maxi-

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Table 3. Nuclides used in BATAN-MPASS code
Heavy metals
Fission products

232Th, 233Pa, 233U, 234U, 235U, 236U, 237Np,
239Np, 239Pu, 240Pu, 241Pu, 242Pu

83Kr, 95Zr, 95Mo, 97Mo, 99Tc, 101Ru, 103Ru,

103Rh, 105Rh, 105Pd, 106Pd, 109Ag, 113Cd, 131I,

131Xe, 133Xe, 135Xe, 136Xe, 133Cs, 134Cs, 141Pr,
143Pr, 143Nd, 145Nd, 146Nd, 147Pm, 148 mPm,

148 g

Pm, 147Sm, 148Sm, 149Sm, 150Sm, 151Sm,
Sm, 153Eu, 154Eu, 155Eu, 155Gd, 156Gd,
157Gd, Non-saturating FP

152

Moderators

12C, 16O

Poisons

B, Impurity in C

Fig. 1. Fissile loading requirement as function of heavy metal loading
and uranium enrichment

80

Fig. 2. Average discharge burnup as function of heavy metal loading
and uranium enrichment

Fig. 3. Pebble fuel residence time as function of heavy metal loading anduranium enrichment

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P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

Fig. 4. Maximum power density as function of heavy metal loading anduranium enrichment

Fig. 5. Conversion ratio as function of heavy metal loading and uranium
enrichment

82 (2017) 1

mum uranium enrichment (17 w/o) and maximum HM loading (20 g/pebble) are imposed.
The third column of Table 1 gives the design parameters
taken for the present scoping study. The core diameter is set
to 1.8 m (derived from the Chinese 10 MWth HTR-10 [2])while the core height/diameter ratio and average power density are set to its minimum and maximum value, i. e. 1.1 and2 W/cm3, respectively, to obtain good neutron economics.
The void cavity at the top of the core is necessary and its
height is set to be approximately 40 cm [2]. As for the fresh
fuel composition, the scoping study is conducted over uranium enrichment in the range of 10 to 20 w/o and HM loadingin the range of 4 to 10 g/pebble. Cases of uranium enrichment
higher than the maximum design constraint (17 w/o) are also
considered for the sake of completeness since the possible
maximum uranium enrichment for LEU is 20 w/o. Cases with
HM loading less than 4 or higher than 10 g/pebble are excluded through preliminary screening calculations.
The URD issued by BATAN allows the RDE to be operated under the multipass or once-through-then-out (OTTO)
fueling scheme. However, OTTO fueling scheme is not included in the present scoping study since from the point ofview of axial power peaking factor the multipass fuelingscheme is favorable. The multipass fueling scheme is selected
for the present study and the number of pass is adopted fromthe Chinese 10 MWth HTR-10 [2], i. e. 5 passes.
Since detail fuel specification and core-reflector structuresand dimensions etc. are not presently available, we assume
no boron (equivalent) impurity in the fuel, 50 cm (radial)
and 100 cm (axial) thickness of pure graphite reflectors withgraphite density of 1.75 g/cm3. For the multipass refuelingstrategy, we assume no radial zoning.

Fig. 6. In-core fissile inventory as function of heavy metal loading anduranium enrichment

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P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

3 Analytical code and group constants

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The pebble fuel movement, burnup, core criticality calculations and core equilibrium search are carried out by BATAN-MPASS [3], a general in-core fuel management codefor pebble-bed HTGRs, featured with many automatic equilibrium and criticality searching options as well as thermal-hydraulic calculation capability. The code has been validatedwith the German HTR-Module design, the validation results
have also been used as a comparative solution for other code
[4].
The TRISO coated particle fuel and pebble fuel element
specifications are shown in Table 2. The microscopic crosssections (4 energy groups, Table 2) and their self-shielding

factors as a function of temperature and composition wereprepared using several parts of the VSOP code system [5]:ZUT-DGL, THERMOS and GAM. In Table 3, the heavy
metals, fission products, moderators and poisons nuclides
used in the burnup chain of BATAN-MPASS are listed.
Group constants for the cavity at the top of the core are determined according to the method developed by Gerwin andScherer [6]. Using their method, different axial and radial diffusion coefficients can be obtained. The detail discussion of
the in-core thermal-hydraulic model used in the BATANMPASS code was already given by Liem and Sekimoto [7].
By using the core equilibrium search option, all calculation
cases converged to an equilibrium core with effective multiplication factor (keff) equals to 1.0 (critical).

Fig. 7. Axial distributions of group neutron flux and power

Fig. 8. Radial distributions of group neutron flux and power

82

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P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

4 Results and discussion

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The scoping analysis results are shown in Figs. 1 to 6. Figure 1
shows the fissile loading requirement as a function of HM
loading for 4 values of uranium enrichment. The fissile loading requirement per unit energy generated (kg/GWd) decreases as the uranium enrichment increases. For all valuesof uranium enrichment, one can find an optimal value of
HM loading per pebble, which is around 8 g/pebble. This optimal composition also indicates the optimal moderation for
the reactor.
Figure 2 shows the pebble fuel element discharge burnup as
a function of HM loading for 4 values of uranium enrichment.

From the figure, it can be observed an almost linear proportionality of discharge burnup to uranium enrichment. Similar
to Fig. 1, for a particular value of uranium enrichment one
can find an optimal value of HM loading per pebble, whichis also around 8 g/pebble. If the design constraint of 80 GWd/
t discharge burnup is imposed then for the optimal HM loading of 8 g/pebble case, the uranium enrichment is found to bearound 13 w/o. For the case of optimal HM loading and uranium enrichment of 13 w/o, the pebble fuel residence time inthe core is around 4.4 years (indicated by a red dot in Fig. 3).
Figure 4 shows the maximum power density (kW/pebble) as
a function of HM loading. This parameter is not too sensitive
to the uranium enrichment. For HM loading higher than 6 g/

Fig. 9. Thermal and flow analysis results

Fig. 10. Nuclide density distributions after the first pass82 (2017) 1

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P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

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pebble, the maximum power density increases almost linearlywith the HM loading. The trend can be explained from thefact that higher HM loading will result in a longer pebble fuelresidence time and the axial power density profile will produce higher peak. Nevertheless, even for 10 g/pebble HM
loading cases the maximum power density is still lower than
0.65 kW/pebble, that is one order smaller than the maximum
allowable value.
Figure 5 shows the conversion ratio as a function of HM
loading. As expected, lower uranium enrichment gives better
conversion ratio. Higher HM loading per pebble also significantly increases the conversion ratio. With higher HM load-ing, the pebble fuel resides longer in the core and the fertile
to fissile conversion is enhanced.
The in-core fissile inventory shown in Fig. 6 can be used toestimate the required amount of fissile inventory to start a reactor per GW thermal power unit. For the RDE consideredhere (thermal power of 10 MW) at the optimal HM loading,
the required amount of fissile inventory (235U) is around
80 kg.
For the optimal HM loading and uranium enrichment of 13
w/o, the axial and radial distributions of group neutron flux
and power are shown in Figs. 7 and 8, respectively. From
Fig. 7, it can be observed that axial power shows no strong

Fig. 11. Nuclide density distributions after the third pass

Fig. 12. Nuclide density distributions after the fifth pass84

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P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

skewed profile which indicates that 5 passes are adequate forthe present design. The thermal and flow analysis result isshown in Fig. 9. The maximum pebble fuel center temperature, as expected, appears at the bottom of the core but its
value is lower than 800 8C.
Under the optimal HM loading and uranium enrichment of
13 w/o condition, the axial nuclide distributions of some important nuclides are shown in Figs. 10, 11 and 12 for the firstpass, third pass and fifth pass, respectively. These nuclide densities are averaged by radial mesh volume. After the first pass,
one can observe that fertile 238U is slowly converted to fertile239
Pu and 241Pu while the original fertile 235U is depleted
slowly. After the third and fifth passes, the axial nuclide distributions show almost flatter profiles. The profile of the homogenized nuclide density for the 5 different passes (histories)
is shown in Fig. 13. It can be observed that 5 passes for thepresent multipass scheme are adequate to obtain flat nuclide
distributions, except for 239Np which is a short-lived nuclide.
While a superior characteristic of the multipass scheme canbe expected to boost the core burnup performance, the neutron loss in term of leakage is considerably high for this smallcore. The overall result is a rather poor neutron economic
condition.

5 Concluding remarks and future works
A scoping study on the optimal fuel composition (heavy metal loading per pebble and uranium enrichment) for the
10 MWth RDE, with LEU UO2 TRISO fuel under multipass
fueling scheme, was conducted using BATAN-MPASS code.
The objective function for the optimization is the fissile loading requirement per energy generated (kg/GWd). The optimal heavy metal loading was found around 8 g/pebble while
the uranium enrichment corresponding to the 80 GWd/t discharge burnup constraint is approximately 13 w/o.
The results of the present scoping study can be improved in
the future when other detail design parameters become available in the basic and detail design phases. These include thedetail core-reflector structures and dimensions, control rod
and reserved shutdown absorber in the radial reflectors, impurities in fuel and graphite etc. The results of safety evaluation in the future may provide feedback to the present scoping study and the optimal composition of the fuel slightly
shifts from the above mentioned values.
(Received on 8 March 2016)

References
1 User Requirement Document – Reaktor Daya Eksperimental –.
BATAN, 2014.
2 Xu, Y.; Zuo, K.: Overview of the 10 MW High Temperature Gas
Cooled Reactor – Test Module Project. Nuclear Engineering and
Design 218 (2002) 13 – 23, DOI:10.1016/S0029-5493(02)00181-4
3 Liem, P. H.: BATAN-MPASS: A general fuel management code forpebble-bed high-temperature reactors. Annals of Nuclear Energy
21 (5) (1994) 281 – 290, DOI:10.1016/0306-4549(94)90012-4
4 Tery, W. K.; Gougar, H.D.; Ougouag, A.M.: Direct deterministic
method for neutronics analysis and computation of asymptotic burnup distribution in a recirculating pebble-bed reactor. Annals of Nuclear Energy 29 (2002) 1345 – 1364,
DOI:10.1016/S0306-4549(01)00110-4
5 Teuchert, E. et al.: VSOP – Computer Code System for Reactor Physics and Fuel Cycle Simulation. Jul-1649 (1980)
6 Gerwin, H.; Scherer, W.: Treatment of the Upper Cavity in a PebbleBed High Temperature Gas-Cooled Reactor by Diffusion Theory.
Nuclear Science and Engineering 97 (1987) 9 – 19
7 Liem, P. H; Sekimoto, H.: Neutronic and Thermal Hydraulic Designof the Graphite Moderated Helium-Cooled High Flux Reactor. Nuclear Engineering and Design 139 (2) (1993) 221 – 233,
DOI:10.1016/0029-5493(93)90158-6

The authors of this contribution
Dr. Peng Hong Liem
Nippon Advanced Information Service (NAIS Co., Inc.)
416 Muramatsu, Tokaimura, Ibaraki
Japan
Tel.: +81-29-2705000
Fax. +81-29-2705001
E-mail: liemph@nais.ne.jp

Fig. 13. Nuclide density distributions of all passes (homogenized)

82 (2017) 1

85

P. H. Liem et al.: Analysis of the optimal fuel composition for the Indonesian experimental power reactor

Ir. Tagor Malem Sembiring
Center for Nuclear Reactor Technology and Safety
National Nuclear Energy Agency of Indonesia (BATAN)
Kawasan Puspiptek, Serpong, Tangerang Selatan, Banten
Indonesia
E-mail: tagorms@batan.go.id
Dr. Bakri Arbie
PT MOTAB Technology
Kedoya Elok Plaza Blok DA 12
Jl. Panjang, Kebun Jeruk, Jakarta Barat
Indonesia
E-mail: dayatek@yahoo.com

Kerntechnik downloaded from www.hanser-elibrary.com by Hanser - Library on March 30, 2017
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Ir. Iyos Subki MSc
PT MOTAB Technology
Kedoya Elok Plaza Blok DA 12
Jl. Panjang, Kebun Jeruk, Jakarta Barat
Indonesia
E-mail: isubki01@gmail.com

Bibliography
DOI 10.3139/124.110679
KERNTECHNIK
82 (2017) 1; page 78 – 86
ª Carl Hanser Verlag GmbH & Co. KG
ISSN 0932-3902

Books · Bücher
Safety of Research Reactors. IAEA Safety Standards Series
No. SSR-3, Published by the International Atomic Energy
Agency 2016, ISBN 978-92-0-104816-5, 125 pp, 58.00 EUR.
The main objective of this Safety Requirements publication
is to provide a basis for safety and for safety assessment for all
stages in the lifetime of a research reactor by establishing requirements on aspects relating to regulatory supervision, management for safety, site evaluation, design, manufacture, construction, commissioning, operation, including utilization andmodification, and planning for decommissioning.
Technical and administrative requirements for the safety of
research reactors are established in accordance with this objective. This publication is intended for use by organizations
involved in the design, manufacture, construction, operation,
modification, maintenance and decommissioning of research
reactors, in safety analysis, verification and review, and in theprovision of technical support, as well as by regulatory bodies.
The safety requirements established in tins publication are
applicable for the site evaluation, design, manufacture, construction, commissioning, operation, including utilization andmodification, and decommissioning of research reactors, including critical assemblies and subcritical assemblies. The safety requirements established in this publication are also to be applied
to existing research reactors to the extent practicable.
Research reactors with power levels in excess of several
tens of megawatts, fast reactors and reactors using experimental devices such as high pressure and temperarme loops andcold or hot neutron sources may require the application of
supplementary measures or even the application of requirements for power reactors and/or additional safety measures(e. g. in the case of reactors used for testing hazardous material). For such facilities, the requirements (and engineering
standards) to be applied, the extent of then application andany additional safety measures that may need to be taken
are required to be proposed by the operating organizationand to be subject to approval by the regulatory body. Homogeneous reactors and accelerator driven systems are out of
the scope of this publication.
All the requirements established here are to be applied unless it can be justified that, for a specific research reactor, critical assembly or subcritical assembly, the application of certain
requirements may be graded. Each case in which the application of requirements is graded shall be identified, with accounttaken of the nature and possible magnitude of the hazards presented by the given facility and the activities conducted. Hereafter, subcritical assemblies will be mentioned separately only
if a specific requirement is not relevant for or is applicable only
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86

considered in deciding whether the application of certain requirements established here may be graded.
This Safety Requirements publication follows the relationship between the safety objective and safety principles, and between requirements for nuclear safety functions and design
criteria and operational criteria for safety. It consists of nine
sections, two appendices and two annexes. Section 2 introduces the general safety objectives, concepts and principles
for the safety of nuclear installations, with emphasis on the radiation safety and nuclear safety aspects of research reactors.
Section 3, which draws on IAEA Safety Standards Series No.
GSR Part 1 (Rev. 1). Governmental. Legal and Regulatory
Framework for Safety deals with the general requirements on
legal and regulatory infrastructure as far as these are relevant
for research reactors. Section 4 deals with requirements on topics relating to the management and verification of safety. Thissection is based on IAEA Safety Standards Series No. GSRPart 2. Leadership and Management for Safety. Section 5 establishes requirements regarding the evaluation and selectionof the research reactor site and deals with the evaluation of
new sites and the sites of existing research reactor facilities.
This section is based on IAEA Safety Standards Series No.
NS-R-3 (Rev. 1). Site Evaluation for Nuclear Installations.
Section 6 establishes requirements for the safe design of all
types of research reactor, with account taken of the considerations mentioned in paras 1.8 and 1.9. Coherence is ensured
with the Safety Requirements publication on the same subject
for nuclear power plants. IAEA Safety Standards Series No.
SSR-2/1 (Rev. 1). Safety of Nuclear Power Plants: Design, Section 7 establishes requirements for the safe operation of research reactors, including commissioning, maintenance, utilization and modification. Coherence is likewise ensured with the
Safety Requirements publication on the same subject for nuclear power plants. IAEA Safety Standards Series No. SSR-2/
2 (Rev. 1). Safety of Nuclear Power Plants: Commissioning
and Operation. Section 8 establishes requirements for the preparation of the safe decommissioning of research reactors on
the basis of IAEA Safety Standards Series No. GSR Part 6.
Decommissioning of Facilities, while Section 9 establishes requirements for the interfaces between safety and security. Appendix I provides a list of the selected postulated initiating
events to be considered in the safety analysis for a research reactor. Appendix II deals with the operational aspects warranting particular consideration. Annex I lists selected safety functions of the safety systems for research reactors and of othersafety related items usually included in the design of research
reactor. Annex II provides an overview of the application of
the safety requirements to subcritical assemblies.
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