Determination of Main Reactor Parameters for Flibe (Li2BeF4)

DETERMINATION OF MAIN REACTOR PARAMETERS 

FOR FLIBE (Li2BeF4) COOLED PEACEFUL NUCLEAR 

EXPLOSIVE REACTORS (PACER) 

Sebahattin Ünalan* and Selahaddin Orhan Akansu 

Mühendislik Fakültesi, Erciyes Üniversitesi 

Kayseri, Turkey 

ﺔــﺻﻼﺨﻟا 

ﺔﻓﺮﻏ ﻢﺠﺡو ،رﺎﺨﺒﻟا 

ﻂﻐﺿ ﻞﺜﻣ ﺔﻴﺳﺎﺳﻷا ﻞﻋﺎﻔﻤﻟا ( تاﺮﺘﻴﻣارﺎﺑ) 

تاﺰﻴﻤﻣ ﻞﻴﻠﺤﺘﺑ ﺔﺳارﺪﻟا ﻩﺬه ﻰﻨﻌﺗ 

ﺔﻴﻤﻠﺴﻟا ضاﺮﻏﻸﻟ PACER ﻞﻋﺎﻔﻣ ﻲﻓ ﻲﻥوﺮﺗﻮﻴﻨﻟا كﻮﻠﺴﻟاو ،ةراﺮﺤﻟاو 

،ﻂﻐﻀﻟا نزاﻮﺗو ،رﺎﺠﻔﻥﻻا 

ﺖﻣﺪﺨﺘﺳا ﺪﻗو . ةدوﺪﺤﻣ 

ﺔﻴﻨﻣز ةﺮﺘﻓ لﻼﺥ ةرﺮﻜﺘﻤﻟا تارﺎﺠﻔﻥﻻا ماﺪﺨﺘﺳﺎﺑ ﺔﻴﺋﺎﺑﺮﻬﻜﻟا ﺔﻗﺎﻄﻟا جﺎﺘﻥﻹ 

ﺎﻬﻟو ،مﻮﻴﺘیﺮﺘﻟا 

ﻦﻣ ﺔﻴﻓﺎآ ﺔﻴﻤآ ﻰﻠﻋ يﻮﺘﺤﺗو (DRc) ﺔﻔﻠﺘﺨﻣ ﺔآﺎﻤﺳو (DR) ﺔﻔﻠﺘﺨﻣ ﻊﺿاﻮﻣ ﻲﻓ تادﺮﺒﻣ 

(Li2BeF4) ﻲﺒﻴﻠﻔﻟا ماﺪﺨﺘﺳا ﺚﺤﺒﻟا اﺬه ﻲﻓ ﺎﻥﺮﺙﺁ ﺪﻗو . جﺎﻣﺪﻥﻻا ﻦﻋ ﺔﺠﺗﺎﻨﻟا ﺔﻗﺎﻄﻟا صﺎﺼﺘﻣا 

ﻰﻠﻋ ةرﺪﻗ 

تﺎﺑﺎﺴﺤﻠﻟ ًﺎﻘﻓوو . 1540 K و 823 K ﺎهرﺪﻗ ﺔﻴﺋاﺪﺘﺑا ةراﺮﺡ تﺎﺝرد ﺪﻨﻋ ﺔﻔﻠﺘﺨﻣ ﺔﻴﻤﺠﺡ ﺐﺴﻨﺑ ةدﺮﺒﻤآ 

ﺔﺝرد ﻰﻠﻋ لﻮﺼﺤﻟا ﻢﺗ (DRc) ـِﻟ ﺔﻨﻴﻌﻣ 

ﻢﻴﻗ ﺪﻨﻋ جﺎﻣﺪﻥﻻا ﺔﻗﺎﻃ صﺎﺼﺘﻣﻻو ،مﻮﻴﺘیﺮﺘﻟا 

جﺎﺘﻥﻹ ﺔﻴﻥوﺮﺗﻮﻴﻨﻟا 

ﺐﻴﺼﺨﺘﻟا ﺔﺒﺴﻨﻟ ﻊﺒﺸﺘﻟا ﻢﻴﻗ ﺖﻥﺎآو ،ًﺎﻴﺑ 

ً رﺎﻘﺗ ًﺎآﻮﻠﺳ صﺎﺼﺘﻣﻻاو 

ﺐﻴﺼﺨﺘﻟا ﻦﻣ ٌﻞآ ﻚﻠﺳ ﺚﻴﺣ ﻊﺒﺸﺘﻟا 

ماﺪﺨﺘﺳﺎﺑ (m) ةدﱢﺮﺒـُﻤﻟا ةدﺎﻤﻟا ﺔﻠـﺘآ بﺎﺴﺤﺑ ﺎﻨﻤﻗ ﺪﻗو . (M = 1.07) 

صﺎﺼﺘﻣﻻا ﺔﺒﺴﻥو (TBR = 1.27) 

ﻦﻴﺣ ﻦﻃ ٦٥٠٠ – ﻦﻃ ٢٠٠ ﻦﻣ ﺮﻴﻐﺘﺗ ﺚﻴﺡ (DR) ةدﺎیز ﻊﻣ دادﺰﺗ ﺎﻬﻥأ ﺎﻥﺪﺝوو (DRc) ﺔﻤﻴﻗو (DR) 

(TBR > 1) مﻮﻴﺘیﺮﺘﻟا 

ﻦﻣ ﺔﻴﻓﺎآ ﻢﻴﻗ ﻰﻠﻋ لﻮﺼﺤﻠﻟ ﻪﻥأ ﻲﻨﻌی اﺬهو ، ﻢﺳ 

٧٠٠ – ﻢﺳ ٥٠ ﻦﻣ (DR) دادﺰﺗ 

ةدﺎیز ﻰﻟإ يدﺆی ﺪﻗ اﺬه ﻦﻜﻟو ،ﺔﻨﻜﻤﻣ 

ﺔﻤﻴﻗ ﻞﻗأ (DR) ﺬﺨﺘﺗ ْنأ ﺐﺠی (M = 1) جﺎﻣﺪﻥﻻا ﺔﻗﺎﻃ ﻦﻣ ﻚﻟﺬآو 

ﺐﺠی ،ﻞﻋﺎﻔﺘﻟا ﺔﻓﺮﻏ نارﺪﺝ ةراﺮﺡ ﺔﺝرد ةدﺎیز ﻦﻋ ﺔﺠﺗﺎﻨﻟا راﺮﺿﻷا ﻞﻴﻠﻘﺘﻟو . دﺮﺒﻤﻟا ةراﺮﺡ ﺔﺝرد 

بﺎﺴﺤﻟ تﻻدﺎﻌﻣو ﺔﻴﺤﻴﺿﻮﺗ تﺎﻣﻮﺳر ﺚﺤﺒﻟا اﺬه ﻲﻓ درﻮُـﻥ 

فﻮﺳو 

. نارﺪﺠﻟا ﻦﻣ ًﺎﺒیﺮﻗ دﺮﺒﻤﻟا ﻊﺿو 

ناﺰﺗﻻا ﻂﻐﺿو ،رﺎﺨﺒﻟا ﺔﻴﻤآو ،ةدﺮﺒـُﻤﻟا 

ةدﺎﻤﻟا ﺔﻠﺘآو ،رﺎﺠﻔﻥﻻا ةﺮﺠﺡ ﻢﺠﺡ ﻞﺜﻣ تاﺮﺘﻴﻣارﺎﺒﻟا ﻦﻣ ﺪیﺪﻌﻟا 

. ﺔﻤﺋﻼﻣ ةراﺮﺡ ﺔﺝردو ﻞﻋﺎﻔﺘﻠﻟ ﺞﺗﺎﻥ يأ ﺪﻨﻋو ،تﺎﺒﺜﻟا 

ﺔﻟﺎﺡ ﺪﻨﻋ 

* To whom correspondence should be addressed. 

January 2004 The Arabian Journal for Science and Engineering, Volume 29, Number 1A. 27

Sebahattin Ünalan and Selahaddin Orhan Akansu 

ABSTRACT 

This study analyzed main reactor parameters such as vapor production possibility, 

explosion chamber volume, equilibrium pressure–temperature, and neutronic behavior 

of a PACER (peaceful nuclear explosive reactor) producing electrical energy by means 

of repetitive explosions during certain periods for different values of coolant zone 

position (DR) and coolant zone thickness (DRc), with enough tritium breeding and 

more fusion energy absorption. Flibe (Li2BeF4) with different volume fractions is 

preferred as a coolant. In addition, the flibe inlet temperatures were selected as 

Tin = 823 K and 1540 K. 

According to neutronic calculations, for tritium breeding and fusion energy 

absorption at certain DRc values, a saturation level is reached. In other words, tritium 

breeding and fusion energy absorption behave asymptotically after a certain DRc, 

although the flibe thickness increases. The saturation TBR (Tritium Breeding Ratio) 

and M (fusion energy absorption ratio) values are 1.27 and 1.07, respectively. The 

saturation points for the TBR are higher than the saturation points reached by M. This 

means that the flibe mass requirement for maximum M will be lower than that for TBR. 

The flibe mass (m) calculated by DR and the saturated DRc increase with increasing 

DR. Thereby, the flibe mass requirement increases from ≈200 tonnes to ≈6500 tonnes 

with increasing DR from 50 to 700 cm. Thus, to reduce the flibe mass required for 

sufficient tritium breeding (TBR > 1) and more fusion neutron energy absorption 

(M = 1), DR must be as low as possible. However, low flibe mass can cause a higher 

flibe temperature in the reactor chamber. To decrease mechanical and chemical 

damage caused by high temperature on the chamber wall, the flibe zone must be 

selected at a place adjacent to the wall. Figures and equations are obtained from which 

the explosion chamber volume, flibe mass, vapor amount, and equilibrium pressure at 

saturation conditions can be calculated easily for any given explosion yield and desired 

flibe temperature. For example, for flibe mass higher than 2500 tonnes (DR > 400 cm) 

and low explosive charge yield (≈2 kt-TNT = 8.37×10 12 J), only saturated flibe vapor 

or heated liquid flibe can be produced at the PACER. In this case, an exchanger model 

with two loops, similar to those in pressurized water reactors, for vapor production 

should be preferred. 

28 The Arabian Journal for Science and Engineering, Volume 29, Number 1A. January 2004


DETERMINATION OF MAIN REACTOR PARAMETERS FOR FLIBE (Li2BeF4) COOLED 

PEACEFUL NUCLEAR EXPLOSIVE REACTORS (PACER) 

1. INTRODUCTION 

In order to produce electrical energy from fusion power, investigations have been concentrated by some researchers on 

three reactor models, which can be explained as based on Magnetic Confinement Fusion (MCF), Inertial Confinement 

Fusion (ICF), and peaceful nuclear explosive reactor (PACER). MCF and ICF fusion reactors have some complex 

problems such as plasma instability, high material damage, high radiation, sensitive fluid jet design, high driver power 

requirement, expensive material requirement, higher cost of electrical power, etc. Today, based on the energy projection 

of the world, it is assumed that solutions of these economical and technological problems will be impossible in a short 

time. However, the PACER, which has simpler problems, seems more attractive than other fusion reactors. Therefore, 

the PACER will be a robust model for providing the world energy requirement in the near future. 

The PACER concept considered for electrical energy production from repetitive nuclear explosions has been studied in 

the literature [1–9]. In these studies, it has been assumed that the fusion explosions have been carried out in the central 

region of a closed explosion chamber. The explosion chamber, having a cylindrical form or spherical form, has been 

considered to be in an underground cavity because of environmental considerations. In addition, to reduce mechanical 

damage caused by shock forces or shock waves from the explosions on the rock structure, a chamber wall with stainless 

steel liner has been considered. The liner is protected by the rock with regularly spaced and pre-stressed rock tendons. 

At the PACER, the energy from fusion explosions is absorbed by various working fluids flowing vertically and 

surrounding the explosion region for protection of the chamber wall against the explosion shocks. The fusion explosion 

produces neutrons of 14.1 MeV and alpha particles of 3.5 MeV, and they carry 80% and 20% of the total energy arising 

from a fusion explosion, respectively. Shock waves from the explosion would be produced by these particles. If these 

energetic neutrons and particles cannot be stopped by means of various coolant materials, they will reach the wall and, 

therefore, cause very high material damage to the wall of the explosion chamber. Therefore, the fusion neutrons and 

alpha particles have to be absorbed by the coolant fluid surrounding the explosion region, before they can reach the 

chamber wall. For that purpose, the coolant fluid has to have high capability in terms of nuclear reactions such as 

neutron absorption and elastic scatter. In general, the coolant zone has a liquid cylindrical form with a certain shell 

thickness. At the coolant zone configuration, shell thickness of the coolant zone that confines the explosion region will 

be important. The thickness value required for the wall protection does not vary closely as a function of the coolant zone 

space. A fluid having thickness of 1–2 cm can easily stop alpha particles. However, to absorb the fusion neutrons, 

a material having very high neutron absorption capability and enough thickness, should be preferred as a coolant 

material. Therefore, the shock waves can be eliminated by good coolant selection. In other words, heating in the coolant 

zone would considerably reduce the shock waves or forces from the fusion explosion. This approach would be valid 

because nuclear reactions can occur in very short time (≈10 –3 seconds). At the same time, the selected fluid is heated by 

the above-mentioned nuclear reactions. On the other hand, the coolant fluid heated by the explosion vaporizes wholly or 

partially. Therefore, the energy absorbed by coolants could be converted into electricity via steam cycles. Thereby, the 

pressure and temperature caused by vaporization process in the closed explosion chamber vary as a function of the 

produced vapor amount. In previous studies, the main parameters of a reactor such as explosion yield, repetition period, 

and cavity radii were varied between 2-kt and 20-kt equivalent trinitrotoluene (TNT), 40 minutes and 7 hours and 20 m 

and 100 m, respectively [2–9]. In general, flibe (Li2BeF4) was preferred as the working fluid, because it has excellent 

nuclear (high tritium breeding and good neutron energy absorption) and thermal (high evaporation temperature 

leading to lower working pressure) performance [5–9]. In a recent study, neutronic performance and structural specifics 

of the PACER and the activation hazard caused by fusion neutrons in rocks and stainless steel liners have been 

investigated for the optimal coolant thickness required for more energy absorption, enough tritium breeding, and 

operation period of 30 years [9]. To determine the equilibrium pressure and temperature in the explosion chamber of the 

PACER with flibe, a calculation model has been derived [6]. However, in that study, different coolant zone positions in 

the chamber have not been considered, and it was assumed that 70% or all of the explosion energy was absorbed by a 

certain coolant amount in any position. This approach is not realistic because the fusion neutron flux reduces with a 



factor R 2 (R: inner radius of the explosion region). In contrast, the fusion neutron flux from the fusion explosion expands 

in the radial direction as a spherical surface. In this case, for example, the energy amount absorbed by unit coolant mass 

varies for different places of the explosion chamber. On the other hand, for tritium breeding and energy absorption 

capability of the flibe, saturation was reached at a certain flibe thickness [9]. Therefore, if it is assumed that the 

saturation values, which indicate the lowest flibe thickness required for enough tritium breeding and high fusion energy 

absorption, would be nearly the same for all flibe zone positions, the absorption energy of a unit flibe mass is affected by 

the flibe zone, since the flibe mass varies as a function of the coolant zone position. Thus, further flibe zone positions 

from the explosion region have higher flibe mass because of the flibe zone volume expansion with the same shell 

thickness. Thus, equilibrium pressure and temperature, the neutronic performance, and the coolant mass required for 

absorption of all explosion energy vary as a function of the flibe zone position and the flibe zone thickness. Certainly, 

the flibe thickness or mass has to provide maximum fusion neutron energy absorption and tritium breeding. On the other 

hand, the fusion explosive yield must have minimal values due to mechanical considerations and larger explosion 

chamber requirement. In addition, the flibe requirement of the reactor also has to be a minimal value because of 

economical considerations. These facts mean that the explosion yield and the required flibe mass are not arbitrary 

variations. Therefore, for new PACER designs, knowing the relationship between the explosive-charge yield, the 

saturation point, coolant mass, the explosion chamber volume, and the coolant zone position is important from the 

standpoint of coolant vaporization. For example, this information helps in determination of whether a one-loop system 

(without exchanger), based on vaporized liquid, or a two-loop system (with exchanger), based on heated liquid, is 

preferred. Temperature, pressure, and mass parameter values of vapor and liquid should be given for designing the 

turbine, exchanger systems, vapor separators, and the superheated system. 

In previous studies, the required coolant mass and the best position of the coolant zone have not been investigated in 

terms of the chamber volume, more energy absorption, and sufficient tritium breeding. These studies have not given the 

vapor production possibility, or optimal correlation between parameters such as the chamber temperature and pressure, 

inlet and outlet conditions of coolants, thermal and mechanical damage of the wall and pipelines, explosive-charge yield, 

the required flibe mass for enough tritium breeding and energy absorption, and the chamber volume. Particularly, the 

vapor production is affected by fuel-charge yield and chamber volume, coolant type, coolant mass, and coolant zone 

position. The goal of the present study is to address the above issues for the PACER cooled by flibe coolant. 

2. BLANKET GEOMETRY AND PROBLEM DESCRIPTION 

In this study, the main emphasis is on detailed neutronic performance, equilibrium pressure, equilibrium temperature, 

and the vapor production possibility as a function of the chamber volume, the fusion explosion yield, the coolant mass, 

and the coolant zone position for enough tritium breeding and high neutron energy absorption in the explosion chamber 

of the PACER. For that purpose, the neutronic calculations are carried out for various positions of the coolant zone in the 

chamber and different coolant thicknesses. After the neutronic calculations, equilibrium pressure and temperature in the 

explosion chamber are calculated for possible values of the chamber volume, the explosion yield, the coolant mass, and 

the coolant zone position 

The neutronic analysis is carried out on the PACER blanket geometry described in [9]. Figure 1 shows the basic 

structure of the explosion chamber (a) and the coolant zone geometry (b) adapted from [9] for this work. Flibe (Li2BeF4) 

is selected as a coolant because of its highest neutronic performance and best wall protection [9]. All steel structures 

such as pipelines and liners are made of SS-316, which is compatible with the flibe. A realistic approach considered for 

determination of the coolant zone corresponds to a coolant zone configuration that occurs in practice. In this approach, 

before the explosion processes, the flibe zone geometry shown in Figure 1 would occur approximately with injection of 

cold flibe by means of the injection system on the top of the chamber, and the explosion process would carry on 

simultaneously with this coolant zone configuration. At the same time, the flibe injection would stop with the explosion 

process. The injection process is performed by two sub-systems in the injection system. These sub-systems can provide a 

continuous flibe flow and a periodical flibe flow required for confinement of the explosion region by vertical and top– 

bottom sides, respectively. The periodical flow helps in the explosion void formation (or the explosion region) in the 

coolant zone. Thereby, the coolant zone geometry is a liquid cylindrical form surrounding the explosion region in its 


cylindrical form (void). Therefore, 

the working coolant amount as a 

function of the coolant zone position 

(DR) and the coolant zone thickness 

(DRc) can be calculated easily from 

this geometry. In addition, the flibe 

zone geometry serves in realistic 

equilibrium temperature and pressure 

calculations, with coolant mass 

calculated by the geometry and 

neutronic calculations in onedimensional 

spherical geometry, 

because it resembles a spherical 

shell of DRc thickness. Large fluid 

thickness at the top and bottom of 

the flibe zone would provide higher 

safety for reactor parts such as the 

injection and circulation systems 

placed on the top and bottom of the 

explosion chamber. In the calculations, 

reactions such as fission or 

chemical reactions of burned fusion 

fuel, and neutronic, chemical, and 

mechanical effects of these reactions 

on the fusion neutrons, the flibe and 

other parts are ignored. Thereby, an 

anisotropic fusion neutron source of 

14.1 MeV is assumed as a point 

source in the center of the explosion 

region or at the explosion point. For 

simplicity, the neutronic calculations 

are performed in one-dimensional 

spherical geometry. At first sight, 

the neutronic analysis in onedimensional 

geometry for the flibe 

zone geometry may be considered 

invalid. However, for a neutronic 

analysis, the calculation dimensions 

are affected highly by the material 

composition and the source neutron 

flux direction. Approximately, 

fusion neutrons released from the 

explosion scatters in the radial 

direction of the sphere surface. If the 

variation of the material 

composition along the θ and ϕ 

components of the spherical 

coordinate system is homogeneous, 

the one-dimensional analysis with r 

The heated 

liquid flibe 

outlet 

The flibe 

vapour outlet 

Fusion 

explosive 

assembly 

The cold 

flibe inlet 

DRc 

DR 


January 2004 The Arabian Journal for Science and Engineering, Volume 29, Number 1A. 31 

The explosion 

region (void) 

The 

pulverized 

flibe 

H 

2 DR 

Flibe 

injection 

system 

H = 4 (DR+DRc) 

Fusion 

explosive 

Continuous 

flibe flow 

Periodical 

flibe flow 

SS-316 

layer 

Underground Rock Flibe Zone 

Figure 1. Cross-sectional view of the explosion chamber of the PACER (a) and the flibe 

zone geometry (b). 

(b) 

(a)


component would be equal to a three-dimensional analysis. Therefore, a one-dimensional spherical geometry for this 

study provides enough sensitivity. At the first stage of the neutronic calculations, the best position for the coolant zone 

(DR from the explosion point) in the reactor chamber and the optimal coolant thickness (DRc) for each position in terms 

of higher energy absorption and enough tritium breeding with lower flibe amount are investigated. In the calculations, 

while the positions of the coolant zone are selected as DR = 50, 400, 700, and 1000 cm, the coolant zone thickness are 

varied between DRc = 0 – 425 cm. The explosion chamber radius is assumed as 4×DR for neutronic calculations. 

In addition, the calculations are repeated for different volume fractions of flibe and void to symbolize the pulverization 

process that will occur during the flibe injection in practice. The flibe expanding to larger volume creates an easier 

vaporization process because the vaporization surface is increased. That is, the vaporization capability of the flibe can be 

increased by expanding to a higher volume by means of the pulverized flibe. For that purpose, volume fractions are 

preferred as 100% flibe, 25% void +75% flibe, 50% void +50% flibe, and 75% void +25% flibe. After the neutronic 

calculations, the equilibrium pressure and temperature is calculated by calculation models derived at previous and 

present papers. For these calculations, while the chamber pressure is assumed as 1 atm (= 10 5 Pa) before the explosion 

process, the preferred flibe inlet temperatures are 823 K for heated liquid flibe and saturated flibe vapor production and 

1540 K (the saturation temperature of flibe at 10 5 Pa) for only superheated vapor production. Atomic densities of 

materials are not given in this text as they have been presented in [9]. In addition, the heat transfer calculation, design 

calculations, and more advanced information for other parts such as the separators, the coolant system, and the turbine 

island of the PACER are not given because this is beyond the scope of the paper. Especially, the heat transferring 

calculations and analyzing of turbine systems will not be required because they could be directly adapted from the 

turbine systems of pressured water reactors (PWR). 

3. NUMERICAL RESULTS 

3.1. Calculational Tools 

The neutronic calculations have been performed on a PC with a Pentium III coprocessor at 500 Mhz by solving the 

Boltzman Transport Equation with the neutron transport code ANISN/PC [10] using the neutron transport and activity 

cross section data libraries MATXS10 [11] and CLAW-IV [12]. The neutron cross sections are averaged over 30 energy 

groups using the Bondarenko [13] flux approximation with a fusion, fission, 1/E and thermal weight function. 

The energy structure has 12, 9, and 9 neutron groups between 1.353 MeV and 17 MeV, 1.235 KeV and 1.353 MeV, and 

0.000139 eV and 1.235 KeV, respectively. The integration of the angular neutron flux has been done in the S16–P3 

approximation by using Gaussian quadrature sets. The numerical output of the ANISN calculations has been further 

processed using the auxiliary code ERDEMLI [14] to evaluate specific information for this work. 

3.2. Tritium Breeding and Energy Absorption 

While the best flibe zone position in the reactor chamber and the optimal coolant thickness is determined, main 

parameters are selected as high absorption of fusion neutron energy released from repetitive explosions and enough 

tritium breeding. Therefore, high fusion neutron absorption concludes lower radiation damage on the explosion chamber 

wall. Namely, many of the fusion neutrons should be absorbed by the flibe to decrease damage effects on the first wall 

material (SS-316), to breed tritium and to capture the fusion neutron energy. However, tritium breeding of a fusion 

reactor must be slightly higher than tritium consumption (Tritium Breeding Ratio: TBR > 1). 

Figures 2–5 show M (Fusion Energy Absorption Ratio = total energy in MeV released in the reactor / 14.1 MeV) and 

TBR versus DRc for DR and flibe percentages of 25%, 50%, 75%, and 100%. As seen in these figures, TBR and M values 

increase rapidly with increasing DRc values, then a saturation with TBR = 1.27 and M = 1.07 is reached at certain DRc 

values. That is, TBR and M behave asymptotically after a certain DRc value, although the flibe thickness increases. 

The DRc values providing the saturation point, which indicates the beginning point of the asymptotic behavior, are about 

350, 175, 125, and 100 cm for 25%, 50%, 75%, and 100%, respectively. In practice, the flibe thickness must be equal to 

the saturation values because of the economical considerations. However, if DRc at the saturation point cannot provide 

the coolant mass requirement of the PACER, the flibe thickness can be selected higher than the saturation point. 

In addition, Figures 2–5 show that the effect of the coolant zone position DR on TBR and M at the saturation point can be 



Figure 2. Variation of M and TBR versus Flibe Thickness (DR C) for 25 % Flibe case. 












almost ignored. In other words, the saturation point is not affected by various flibe zone positions. However, this 

approach has to be supported with clearer calculations because clear saturation values may not be selected from these 

figures. For that purpose, DRc saturation points calculated by means of linear interpolation for M = 1.07 and TBR = 1.27 

from Figures 2–5 are shown in Table 1. Table 1 shows that the DRc saturation values from Figures 2–5 are almost the 

same for all DR values and flibe percentages. The difference between TBR values calculated for DR = 50 and 1000 cm 

are 48 cm (= 421.9 – 374.6) and 4 cm (= 101.4 – 96.7) with 25% flibe and 100% flibe percentages, respectively. 

However, the same approach cannot be claimed for flibe mass values to be determined with the saturation DRc and DR 

because volume of the flibe zone having the cylindrical geometry is fairly affected by radius. 

DR 

[cm] 

Saturation value of 

DR c (cm) for 25% flibe 

Table 1. DR c Saturation Points Provided by TBR = 1.27 and M = 1.07. 







TBR = 1.27 M = 1.07 TBR = 1.27 M = 1.07 TBR = 1.27 M = 1.07 TBR = 1.27 M = 1.07 

50 421.98 312.18 208.87 151.60 140.20 99.41 101.46 74.26 

400 391.17 282.69 193.91 140.72 127.69 94.76 97.79 71.89 

700 381.84 274.37 190.97 138.16 124.83 93.70 97.21 71.39 

1000 374.60 270.36 188.69 136.20 124.23 92.84 96.72 70.96 

At this point, determination of the flibe mass values 

providing the saturation point would be important. In 

this case, the flibe mass needed for the PACER chamber 

can be calculated as function of DR, DRc, and flibe 

density (ρ) from the flibe zone geometry in Figure 1(b) 

by means of following equation: 

m = 2πρ[2(DR + DRc) 3 – DR 3 ] . (1) 

Variation of the flibe mass calculated by Equation (1) 

for DRc saturation points versus flibe zone position DR 

is given in Figure 6. As expected, m values providing 

enough tritium breeding and energy absorption increased 

with increasing of DR. For high TBR and M values with 

lower flibe amount, the flibe zone must be as close to the 

explosion region as possible. Thus, a lower flibe mass 

serves to give a lower cost for electrical energy. That is, 

for the best flibe zone position, DR has to be selected at 

the lowest value allowed by the reactor operation 

conditions. According to Figure 6, the flibe masses 

required for saturation of TBR are slightly higher than 

the values required for M. In this case, if the saturation 

point with TBR were selected, the same point would also 

provide high enough M values. At this stage, it would be 

interesting if the required flibe mass with TBR = 1.27 

and M = 1.07 for the flibe zone position in the explosion 

chamber were known analytically, because the determination 

of equilibrium temperatures–pressures and vapor 

production as a function of this flibe mass, the explosion 

Figure 6. Variation of m values with TBR=1.27 and M=1.07 versus DR. 



chamber volume, and any explosive 

yield would be important in terms of 

reactor operation conditions and 

reactor safety. For a more practical 

approach, the shapes of the curves 

in Figure 6 can be analytically 

explained by a polynomial function 

following: 

DR = A + B.m + C.m 2 + D.m 3 . (2) 

In Equation (2), DR and m are in 

cm and tonnes, respectively. For A, 

B, C, and D coefficients requiring 

the calculation within an accuracy of 

1% are given in Table 2. 

Therefore, if the m requirement is 

known, DR and DRc can be 

calculated by Equations (1) and (2). 

3.3. The Equilibrium Pressure–Temperature and Flibe Vapor Production 

In this section, flibe vapor production possibility, equilibrium pressures and temperatures for the investigated cases 

will be calculated. The meaning of the equilibrium is that the high turbulence that occurred in the few seconds following 

the explosion process has finished. Flibe vapor production possibility, equilibrium pressure, and temperature are 

important in terms of mechanical considerations, operation conditions, and reactor safety. Operation pressure and 

temperature of the reactor have to be lower than the values given for metallic parts. After the explosion process, up to a 

later explosion, the pressure and temperature values of the flibe vapor in the chamber decrease continuously because of 

the vapor transferred to the turbine system. For this reason, the outlet temperature must be regulated to a constant value. 

This operation also depends on the equilibrium pressure and temperature. In addition, the quality of the produced vapor 

(saturated vapor or superheated vapor) also would be important from the standpoint of the selection of a turbine system 

working with or without condensation. The equations needed for calculation of the equilibrium pressure (Pf) and 

equilibrium temperature (Tf) can be adapted from [6] as follows: 

where, 

T 

f 

E − mv 

( ∆h 

− RTv 

) − mC p ( Tv 

−Ti 

n) 

+ mv 

Cv 

Tv 

= (3) 

m C 

v 

v 

mv 

RTf 

Pf 

= , (4) 

V 

E : the explosive energy yield = 2.95×10 24 ×[n/shot] 17.6 [MeV/n] 1.602×10 –13 [J/MeV]×M 

mv : mass of the vaporized flibe (m ≥ mv) 

V : the chamber volume of the PACER reactor [m 3 ] 

∆h : latent heat of flibe vapor = 2079 J/g 

Tv : the saturated vapor temperature: [K] 

Tin : inlet temperature of flibe: [K] 

Cv : 1.88 J/g K 

Cp : 2.35 J/g K 

R : 0.47 J/g K. 

Table 2. Numerical Coefficients for Equation (2). 

The case A B C D 

25%-TBR –88.0968 0.22493 –2.24936.10 –5 8.32157.10 –10 

50%-TBR 0.7992 0.23279 –2.58172.10 –5 9.94182.10 –10 

75%-TBR 21.4882 0.22411 –2.40462.10 –5 8.33179.10 –10 

100%-TBR 32.7906 0.20319 –1.97084.10 –5 5.91985.10 –10 

25%-M –42.2288 0.32536 –4.80213.10 –5 2.64298.10 –09 

50%-M 19.1456 0.30891 –4.58881.10 –5 2.24291.10 –09 

75%-M 33.1814 0.27705 –3.66058.10 –5 1.49366.10 –09 

100%-M 38.5927 0.24771 –2.88471.10 –5 9.98872.10 –10 



Pf and Tf can be calculated by means of Equations (3) and (4). However, the saturation temperature Tv, that depends on 

the saturation pressure (Pv), must be defined. According to [6], Pv in Pascal and Tv in K can be found by: 

v 

9. 

407−10054 

/ T 

v 

P = 133( 

10 

) 

(5) 

mv 

RTv 

Pv 

= . (6) 

V 

Considering that Equations (3–6) are closed functions, it is clear that their solutions can be found by means of 

iteration methods. These calculations for liquid flibe and flibe vapor (assuming ideal gas behavior) are performed in light 

of following scenario: 

• Liquid flibe having temperature of Tin will heat up to Tv at the constant pressure of 1 atm. If E values are lower than 

[mCp (Tv–Tin)], only the liquid flibe heated up to Tv will be obtained. 

• If E values are higher than [mCp (Tv–Tin)], heat the liquid flibe up to Tv and vaporize the liquid of mv at Pv pressure 

and constant volume. If E values are lower than [mCp(Tv–Tin) +m(∆h –RTv)], the saturated flibe vapor of mv and 

the heated liquid flibe of m–mv at Pv pressure and Tv temperature will be obtained. 

• If E values are higher than [mCp (Tv–Tin) + m(∆h – RTv)], superheat up to Tf at constant volume and calculate Pf. 

In this case, the superheated flibe vapor of m = mv at Pf pressure and Tf temperature will be obtained. 

If all the liquid flibe mass converted to the vapor phase, the mv value would be equal to the m value. In this case, 

superheated vapor production would be possible. If Tf = kTv and EV = E/V, Equations (2–5) can be converted as follows: 

133( 

10 

EV = 

rT 

9. 

407−10054/ 

Tv 

v 

) 

[ ∆h 

+ C kT 

− C T ] 

v 

v 

p in 

, (7) 

where k indicates the produced vapor quality. If k = 1, the flibe vapor is at the saturation condition. For the superheated 

vapor production, k has to be higher than unity (k > 1). EV is the ratio of the fusion explosion yield (E) to the explosion 

chamber volume (V). The EV value at any k and Tv or Tf (= kTv) can be calculated from Equation (6). However, it would 

be more useful to show Equation (6) in a Figure because it cannot be easily solved. Therefore, Tf values found for 

various k values as a function of EV (in MJ/m 3 ) can be shown in Figure 7 for Tin = 823 K and Tin = 1540 K, respectively. 

On the other hand, if m = mv for full vaporization and Cp = R+Cv, the reactor volume and flibe mass required for any 

explosion yield E can be calculated from: 

E 

V = (8) 

EV 

E 

m = . (9) 

C T + ∆h 

− C T 

v 

f 

p in 

In addition, the equilibrium pressure Pf for m and V are found from Equation (4). Consequently, the equilibrium 

pressure (Pf), equilibrium temperature (Tf), reactor volume (V) and flibe mass (m) required for the desired explosion 

yield (E) value can be determined by Figures 6 and 7 and Equations (4), (8), and (9). 

For example, for Tin = 823 K, Tf = 2250 K, and k = 1.2 [1.2 means Tv = 1875 K and a temperature decrease of 375 K 

(≈2250–1875 K) at the turbine system], EV is found as 7 MJ/m 3 from Figure 7. Therefore, for explosion yield of 

8.37×10 12 J (= 2 kt equivalent TNT), m and V can be calculated as 1913 tonnes from Equation (8) and 1195714 m 3 

(corresponding to a spherical geometry having a radius of 65 m) from Equation (8). In addition, the equilibrium pressure 

is found as 17×10 5 Pa from Equation (4). At the given conditions, the critical coolant position DR with the saturation 

point of TBR should be about 265 cm from Equation (2) for m = 1913 tonnes and 25% flibe. In this case, the flibe zone 

thickness would be equal to DRc = 415 cm from Equation (1). However, an m value of 1913 tonnes also can be provided 



Tin=823 o K 

Tin = 1540 K Tin = 823 K 

k=2.4 

k=2.5 

k=2.5 

k=2.4 

Tin=1540 o K 

k=2.3 

k=2.3 

k=2.2 

k=2.2 

k=2.1 

k=2.0 

k=1.9 

k=1.8 

k=1.7 

k=1.6 

k=1.5 

k=2.1 

k=2.0 

k=1.9 

k=1.8 

k=1.7 

k=1.6 

k=1.5 

Tf (K) 

40 The Arabian Journal for Science and Engineering, Volume 29, Number 1A. January 2004 

k=1.4 

Figure 7. Variation of T f versus EV (the explosive yield/the chamber volume) in various k values for T in=1540 K and 823 K. 

k=1.4 

k=1.3 

k=1.3 

k=1.2 

k=1.2 

k=1.1 

k=1.1 

k=1.0 

k=1.0 

0 5 10 15 20 25 30 35 40 45 50 55 60 

0 5 10 15 20 25 30 35 40 45 50 55 60 

EV (MJ/m 3 EV (MJ/m ) 3 ) 

EV (MJ/m 3 ) 

EV (MJ/m 3 )


by DR < 265 cm and DRc > 415 cm. At this point, while the case given lowest flibe mass can be preferred, it must be 

attended that distribution of energy absorption across the flibe zone spatial is flatted. For the flatted energy absorption in 

the flibe zone after the explosion process, the temperature difference between inner-side and outer-side of the flibe zone 

should be the lowest value. The very much temperature difference can cause instantaneous fluid explosion and unsteady 

behavior, which may be hazard for the reactor safety. Thereby, the DR with the saturation point will be enough. For inlet 

temperature of Tin = 1540 K, the same values are about 15 atm, 5 MJ/m 3 , 3100 tonnes, 1674000 m 3 , and DR ≈ 550 cm, 

respectively. These values show that high inlet temperature cause high chamber volume and flibe mass. 

Consequently, in order to design a PACER, the main parameters such as the flibe zone position, the flibe thickness, the 

explosion chamber volume, and flibe mass for given explosive and flibe inlet conditions can be determined by the above 

figures and equations. It can be decided whether a design should have a double loop with a heat exchanger, as for PWRs, 

with the heated liquid flibe, or one loop, as for BWRs, with the saturated flibe vapor. 

4. CONCLUSIONS AND RECOMMENDATIONS 

In this study, the vapor production possibility, the equilibrium pressure, and temperature occurring in the explosion 

chamber of a PACER producing electrical energy from fusion explosions repeated in a certain repetition period for 

different coolant zone positions (DR) and coolant zone thickness (DRc), with enough tritium breeding and more fusion 

energy absorption, are analyzed. Flibe (Li2BeF4) with various volume fractions is preferred as a coolant. The analysis 

expands to two inlet temperatures (Tin) of 823 K and 1540 K. The main conclusions are as follows: 

1. For tritium breeding and energy absorption at a certain flibe mass (or certain flibe thickness), saturation is reached. 

TBR and M values calculated at the saturation point are equal to 1.27 and 1.07, respectively. The saturation mass of 

the flibe increases with increasing DR. For the same explosive yield, low DR indicates high flibe temperature. 

However, for the sake of reactor safety, a high enough working temperature can be provided by higher flibe mass 

or high DR value. To decrease the flibe mass required for sufficient tritium breeding (TBR > 1) and more fusion 

neutron energy absorption (M = 1), DR must be as low as possible. 

2. As an example, for a working temperature of 2250 K with the explosive yield of 8.37×10 12 J (2 kt equivalent TNT) 

and Tin = 823 K, a flibe mass of 1913 tonnes, an explosion chamber volume of 1195714 m 3 , and DR = 265 cm are 

enough. For Tin = 1540 K, the flibe mass, the chamber volume, and DR values are about 3100 tonnes, 1 674 000 m 3 , 

and 550 cm. Therefore, high flibe inlet temperature requires higher flibe mass and chamber volume. 

The following recommendations can be given for future studies: 

1. Effects of chemical or fission mechanisms required for initiation of fusion explosions on neutronic performance, 

flibe, and other reactor parts must be determined. 

2. Chemical and mechanical damage caused by high impact velocity on the SS-316 liner have to be investigated for 

better selection of flibe zone placement in the explosion chamber. 

3. The effects of the shock waves from the explosions on the reactor plant and the integrity of the reactor vessel must 

be investigated both theoretically and experimentally. 

REFERENCES 

[1] E. Teller, W. Talley, and G. Higgins, Constructive Uses of Nuclear Explosives. New York: McGraw-Hill Book Company, 1968. 

[2] H.W. Hubbard et al., Project PACER Final Report. RDA-TR-4100-003, R&D Associates, 1974. 

[3] R.P. Hammond et al., “Practical Fusion Power”, Mech. Egn., 104 (1982), p. 34. 

[4] W. Seifritz, “PACER: A Grand Design for Fusion Power”, Fusion, 4 (1980), p. 22. 

[5] R.W. Moir, “PACER Revisited”, Fusion Technology, 15 (1989), p. 1114. 

[6] C.J. Call and R.W. Moir, “A Novel Fusion Power Concept Based on Molten-Salt Technology: PACER Revisited”, Nuclear 

Science and Engineering, 104 (1990), p. 364. 

[7] A. Szöke and R.W. Moir, “A Practical Route to Fusion Power”, Techno. Rev., 94 (1991), p. 20. 



[8] A. Szöke and R.W. Moir, “A Realistic, Gradual and Economical Approach to Fusion Power”, Fusion Technology, 20 (1991), 

p. 1012. 

[9] S. Şahin, R.W. Moir, and S. Ünalan, “Neutronic Investigation of A Power Plant Using Peaceful Nuclear Explosives”, Fusion 

Technology, 26 (1994), p. 1311. 

[10] W.W. Engle, Jr., ANISN, A One-Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering. K1693, 

Oak Ridge National Laboratory, 1970. 

[11] R.E. MacFarlane, MATXS10, 30-Neutron, 12-Group Photon Cross Sections from ENDF/B-IV with TRANSX-2. Los Alamos 

National Laboratory, 1994. 

[12] T.A. Al-Kusayer, S. Şahin, and A. Drira, “CLAW-IV, Coupled 30 Neutrons, 12 Gamma Ray Group Cross Sections with 

Retrieval Programs for Radiation Transport Calculations”, Radiation Shielding Information Center, RSIC Newsletter, Oak Ridge 

National Laboratory, May 1988, p. 4. 

[13] Group Constants for Nuclear Reactor Calculations. ed. I.I. Bondarenko. New York: Consultants Bureau, 1964. 

[14] S. Şahin, H. Yapici, and S. Ünalan, ERDEMLI, A Computer Program to Process ANISN Output Data. Gazi University, Ankara, 

Turkey, 1991. 

Paper Received 6 November 2000; Revised 8 December 2001; Accepted 12 February 2003.

Determination of Main Reactor Parameters for Flibe (Li2BeF4)

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