Needs total 50-60 pages DUE BY 13 MAY

NUCLEAR WEAPON’S LATENCY CALCULATION TO VERIFY A HISTORICAL CASE

A Research Proposal
by

Chair of Committee:

February 2021

Major Subject: Nuclear Engineering
Copyright 2021

OBJECTIVE

The main objective of this study is to calculate the break out time (time required to acquire a minimum amount of nuclear material needed for a nuclear weapon) and nuclear weapons latency (time required to produce a nuclear weapon) for the historical case of India (the 1974 plutonium bomb test in Rajasthan-Pokhran). A software developed at Texas A&M will be used to calculate the latency value, further verifying the validity of the tool. To get an accurate latency value, we need to make three basic assumptions. First, predict the date of the decision to proliferate nuclear weapons. Second, build a possible proliferation pathways based on existed nuclear complexes and R&D. Third, set needed times for each activity in the proliferation pathways. To reveal the bias or possible errors of the tool, sensitivity analyses by varying activity time alterations to the proliferation pathways are planned. The entire Indian Nuclear fuel cycle and R&D complexes will be analyzed.

Introduction

From 1968, 191 countries have signed the Treaty on the Non-proliferation of Nuclear Weapons (NPT).1 However, India, Israel, Pakistan, North Korea, and South Sudan are not party to the NPT. India, Pakistan, and North Korea have openly claimed successful nuclear weapons tests, and it is generally believed that the same is true in the case of Israel. Moreover, some countries are taking steps toward the development of non-peaceful nuclear technologies. For example, recently, on January 13, 2020, the International Atomic Energy Agency (IAEA) reported Iran’s plans to conduct R&D activities on uranium metal production.2 Within global political-economic changes and existing advanced nuclear technologies, any state’s willingness to have nuclear weapons components is a significant concern for international nonproliferation community. It is prudent to estimate breakout time and nuclear weapons latency using software tools that will use openly available information about the type of nuclear fuel cycles followed by the countries. A Nuclear Weapons Latency Tool (NWLT) 3 developed at Texas A&M is used for this study to analyze the historical case study of India’s “peaceful nuclear explosion” of 1974.
The Indian nuclear program was started by Dr. H.J. Bhabha along with other scientists in the late 1940s.4 They developed a very complex three-stage nuclear power production program. The beginning of the program was successfully working and was only for civilian purposes. However, since China tested its first atomic bomb in 1964, 5 and the Indian government did not sign NPT in 1968, it was argued that India may start its military nuclear program. Indo-China b tensions in 1967 also gave strength to this argument.
In this thesis study, we assume that the intent to proliferate was made by India in 1968 when the Jaduguda uranium mine and milling got to its full capacity. Before 1968, India did not possess the needed nuclear material to proliferate since all other imported nuclear materials were under IAEA safeguards monitoring. By this time, India already had a plutonium-producing research reactor, Canada India Reactor Utility Services (CIRUS), which was ideal for weapons-grade plutonium production. The fuel for the CIRUS was supplied by Canada, but India kept control over the reactor’s produced plutonium.6 The spent fuel from CIRUS was reprocessed in PHOENIX reprocessing plant. CIRUS was designed and built with support of Canada and the United States. The works on fission bomb study and fabricating of plutonium metal alloys were started after the visit of Indian scientists to the Soviet’s plutonium-fueled pulsed fast reactor in 1968-69. Subsequently, Indian scientists designed the Plutonium Reactor for Neutron Investigation in Multiplying Assemblies (PURNIMA).6
Therefore, the known value of nuclear weapons latency for India’s historical case is about five years (1969-1974). Hence, the analysis of this historical case will verify the efficacy of Texas A&M’s NWLT.

Previous Work

The Indian nuclear fuel cycle and its history were already investigated sufficiently. There is a book by Gopalakrishnan; “Evolution of The Indian Nuclear Power Program,” 7 and a paper by D.S. Dutt; “India and Bomb,”8 which provide very detailed historical data and some analysis. While Woody’s book, India’s Nuclear Fuel Cycle 9, is a combination of the aforementioned two literature documents with modifications and is newer. Woody made some assumptions regarding the production of weapons-grade plutonium for the state’s first bomb. For example, his quote, “India did not have the requisite plutonium for their first device until 1969,” shows that the chosen proliferation starting point as 1968 might be a close number to use in the tool.
In 2002, Sandia National Laboratories developed a Risk-Informed Proliferation Analysis method (RIPA), 10 which calculates the cost and time needed to acquire a nuclear weapon. RIPA method can predict the time and pathways required to produce a nuclear bomb and nuclear material equivalent to a significant quantity (SQ). The IAEA defines an SQ as “the approximate amount of nuclear material for which the possibility of manufacturing a nuclear explosive device cannot be excluded.”11 The NWLT can provide latency value for a conventionally deliverable nuclear weapon.
The tool uses the Generalized Stochastic Petri Net (GSPN) 12 simulation method. While the basics of the method did not include stochastic timing. Petri net was originated by Carl Adam Petri in 1962 at the University of Darmstadt, West Germany.13 It was widely used in mathematical modeling and logical programming. Petri net is a directed bipartite graph. Figure 1 gives the main description of the Petri net where circles show places, boxes are transitions, and arrows are arcs. Arcs connect places and transitions. The black dots in the places are tokens. Distribution of tokens on the places gives the last term, marking. For successful transitions from input place to output places, inputs have to have a minimum of one token. As a result, enabled transitions will be successful.

Fig. 1. The Petri net.

The extension with stochastic timing concept to the classic Petri net theory came by Florin and S. Natkin in 198214, and Molloy in 198115. Later on, additional analysis by Markov-chain brought to the GSPN method. The GSPN model allows to instantly trigger transitions without any switch-on time and have priority over timed transitions.
The NWLT was based on the historical analysis of the U.S. Manhattan Project and was tested for Pakistan, South Africa, and Republic of Korea, as case studies by the tool’s developers. Several cases were used to test NWLT by Johansen16 and Rathore17. However, no tests have been done using the NWLT for the historical case of India yet.

METHODOLOGY

The NWLT can predict the time needed for a non-nuclear-weapon state to develop a conventionally deliverable nuclear weapon and shows states’ proliferation pathways. The project will undertake the following steps:
1. Simulate time-dependent proliferation pathways on Microsoft Visio using the Petri Nets. The pathway is a whole proliferation network that leads to Pu implosion weapon. Figure 2 shows India’s proliferation network that will be used in this thesis study employing NWLT. In the Fig. 2, main aspects are places (symbolized with circles) and transitions (illustrated with boxes). Places represent objects (facilities, parts, designs, people, etc.). Transitions describe an action that is being undertaken. Places connect to transitions by directional arc weights (symbolized with a rounded rectangle), and arcs direct the flow of tokens within the Petri Net. After the simulation on MS Visio, a new MS Excel file will be generated.

Fig. 2. The fragment of the Petri net for India’s Weapons grade Pu production (Microsoft Visio).
2. The generated Excel file has five sheets labeled as Dminus, Dplus, H, Transition Data, and Placed Data. Where, 𝑃 = {𝑝1,𝑝2,…,𝑝n} is the set of n places;

𝑇 = {𝑡1, 𝑡2,…𝑡𝑠} is the set of s transitions, 𝑇 ∩ 𝑃=∅ ;

𝐷 −⊂ (𝑃×𝑇) is the set of s transition input arcs;

𝐷 +⊂ (𝑇×𝑃) is the set of s transition output arcs;

𝐻⊂ (𝑃×𝑇) is the set of s transition inhibition arcs; 𝑀:𝑃→N is the marking which lists the number of tokens in each place with marking 𝑀0.
The Excel sheet needs some NWLT inputs to be entered manually18 using the analyzed and collected data for the specific case study. The transition datasheet will need time in days for the list of transitions. Place datasheet will need a number 0 or 1 to represent the non-enabling or enabling of a specific transition. In Table 1, place-number 1 in the DNWMark’s column means enough nuclear material for one SQ was available at the time. DNWMark decrypts as deliverable nuclear weapon marking, while for the India case, Pu implosion weapon is known. The generated Excel file is an input file for the code written in the MATLAB language.

Number

Places

M1

DNWMark

1

Making uranium metal
(doesn’t need enrichment)

0

0

2

Dismantling from PURNIMA

0

0

3

Weapon

0

1

4

Conversion Facility

0

0

5

Weapons grade Pu Metal

0

0

6

Conversion Facility Design

1

0

Table 1. The fragment of the Placed Data sheet (Excel file)

3. Finally, the data from Excel file is transferred to a MATLAB code and some modification within the codes followed by simulations provides the latency value. It is important to note that changes with the number of interactions, activity time steps, and All Pathway Transition Lists (APTL) selections may give a more accurate value.
The simple representation of NWLT’s performance is shown in Fig. 3. Three green boxes illustrate the used programming methods and their basic functions within the tool. The yellow box is the result of the performance.

Fig. 3. Nuclear Weapons Latency Tool’s main performance.
Developers of NWLT also created an additional code with the Multi-Attribute Utility Analysis (MAUA) 19, 20 pathway selection option. MAUA is a well-known decision modeling method that automatically selects between different proliferation pathways based on multiple attributes. Overall, 15 attributes’ functionalities within the MAUA analyzed.

Table 2. The list of Proliferation Pathway Attributes (15).3

Number of weapons

Industrial capacity

Time to 1st weapon

Nuclear materials

Delivery method

Technical knowledge

Concealability

Fissile material production technology availability

Sustainability

Technical human capital

Survivability

Financial resources

Reliability

Non-nuclear materials

other

Implementing MAUA to NWLT needed additional sheets filled with attribute utility values to the Excel file. The values expressed in Multi-Attribute Utility Equation:

Where Up is the utility of path p, ki is normalized weight attributed to attribute value i, ui is the utility value of attribute i, and xi,p is the value of attribute i for path p. The utility value is evaluated for all events on path p. MAUA can increase the latency value’s accuracy. However, with inappropriate parameters, results can be skewed. Also, it is difficult to get a detailed understanding of decision-making distributors.

Significance

The historical case study of Indian nuclear proliferation will prove the NWLT’s correctness in estimating nuclear weapons latency values. The study can also demonstrate how NWLT can help characterize the proliferation risk for technology informed policy decision making. The results of this research will give more information for future Indian nuclear fuel cycle related proliferation studies. Moreover, simulations with different modifications than the history, will prove the correctness of decisions of that time.

References

1. Nuclear Non-Proliferation Treaty, 2009. NPT States Parties [PDF Document]. URL https://web.archive.org/web/20130311220936/http://dtirp.dtra.mil/pdfs/npt_status_2009.pdf/ (accessed 11.28.20).
2. ‘Grave military implications’: Iran making uranium metal alarms Europe [WWW Document]. URL https://www.theguardian.com/world/2021/jan/17/grave-military-implications-iran-making-uranium-metal-alarms-europe, (accessed 01.18.21).
3. Sweeney J. D., 2014. Nuclear Weapons Latency (Ph.D. Dissertation). Center for Nuclear Security Science & Policy Initiatives, Texas A&M University, College Station, TX.
4. TIFR: History and Vision [WWW Document]. URL https://www.tifr.res.in/portal/history.php (accessed 11.28.20).
5. Walter C. Clemens., 1967. Chinese Nuclear Tests: Trends and Portents, Cambridge University Press, University of Cambridge.
6. India’s Nuclear Weapons Program: Historical Background [WWW Document]. URL https://nuclearweaponarchive.org/India/IndiaOrigin.html (accessed 10.28.20).
7. Gopalakrishnan A., 2002. Evolution of the Indian Nuclear Power Program, Harvard University, Cambridge, MA.
8. Major‐General D., Som D., 1966. India and the Bomb.
9. Woddi V.K.T., Charlton W.S., Nelson P., 2009. India’s Nuclear Fuel Cycle: Unraveling the Impact of the U.S.-India Nuclear Accord. Scientech: A Curtiss-Wright Flow Control Company, Texas A&M University.
10. Rochau G., 2002. Risk-Informed Proliferation Analysis, SAND2001-2020, Sandia National Laboratory.
11. International Atomic Energy Agency, 2002. IAEA safeguards glossary, 2001-ed., Vienna.
12. Van der Aalst W.M.P., Van Hee K.M., Reilers H.A., 2000. Analysis of discrete-time stochastic Petri nets, Statistica Neerlandica, pp. 6-7.
13. Petri C.A., 1962. Kommunikation mit Automaten (Ph.D. Dissertation). Institut f¨ur instrumentelle Mathematik, Bonn.
14. Florin G., Natkin S., 1982. Evaluation based upon Stochastic Petri Nets of the Maximum Throughput of a Full Duplex Protocol. Springer-Verlag, Berlin.
15. Molloy M.K., 1981. On the Integration of Delay and Throughput Measures in Distributed Processing Models (Ph.D. Dissertation). University of California, Los Angeles.
16. Johansen M., 2016. The Nuclear Weapons Latency Value of the Joint Comprehensive Plan of Action with the Islamic Republic of Iran. Texas A&M University, College Station, TX.
17. Rathore K., Chirayath S. S., 2019. Investigation on Iran’s Nuclear Weapon Latency Time in case of Non-Compliance with JCPOA. Texas A&M University, College Station, TX.
18. Sweeney D. J., 2015. Nuclear Weapons Latency Tool Manual and Operation. Texas A&M University, College Station, TX.
19. Keeney R.L., Raiffa H., 1976. Decisions with Multiple Objectives, Wiley & Sons, New York, NY.
20. Brucker P., Drexl A., Mohring R., Neumann K., and Pesch E., 1999. Resource-constrained project scheduling: Notation, classification, models, and methods. European Journal of Operational Research.

Initiate weapons R&D
Design Pu implosion (existing weapon design)
Build Pu Implosion Weapon
Initial Weapons R&D
Pu Implosion type weapons R&D
Pu Implosion type design
1
1
1
1
1
8
CIRUS
Spent Fuel from CIRUS
1
1
Reprocessing PHOENIX
8
Reprocessed Pu

1
Jaduguda mine
Jaduguda Mill
Jaduguda mine
1
Jaduguda Mill
1
1
Build Pu metal conversion facility
Operate WGPu metal conversion facility
Conversion Facility Design
WGPu Metal
1
1
1
1
Conversion Facility
Serve at PURNIMA

Plutonium Implosion Weapon
1
PURNIMA
1

Making uranium metal
(doesn’t need enrichment)
Making uranium metal
(doesn’t need enrichment)
1
1

1

Initiate weapons R&DDesign Pu implosion (existing weapon design)Build Pu Implosion Weapon Initial Weapons R&D Pu Implosion type weapons R&DPu Implosion type design111118CIRUSSpent Fuel from CIRUS11Reprocessing PHOENIX8Reprocessed Pu1Jaduguda mineJaduguda MillJaduguda mine1Jaduguda Mill11Build Pu metal conversion facility Operate WGPu metal conversion facilityConversion Facility DesignWGPu Metal1111Conversion FacilityServe at PURNIMAPlutonium Implosion Weapon 1PURNIMA1Making uranium metal(doesn¶t need enrichment) Making uranium metal(doesn¶t need enrichment)111