SolitonSoliton--like Regime of Neutron like Regime of Neutron Transport in a Multiplying Medium. Transport in a Multiplying Medium.

Physical Ground of Traveling Wave ReactorPhysical Ground of Traveling Wave Reactor

S.P. FominS.P. Fomin, A.S. Fomin, M.S. Malovytsia, V.V. Pilipenko, N.F. Shul, A.S. Fomin, M.S. Malovytsia, V.V. Pilipenko, N.F. Shul’’gaga

Akhiezer Institute for Theoretical PhysicsAkhiezer Institute for Theoretical PhysicsNSC NSC ““Kharkov Institute of Physics and TechnologyKharkov Institute of Physics and Technology””

e-mail: sfomin@kipt.kharkov.ua

Channeling 2018 23Channeling 2018 23--28 September 201828 September 2018 Ischia, ItalyIschia, Italy

National Academy of Sciences of UkraineNational Academy of Sciences of UkraineNational Science Center National Science Center

““Kharkov Institute of Physics and TechnologyKharkov Institute of Physics and Technology””

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Outlook:Outlook:

• Historical introduction• Nuclear Burning Wave concept• Mathematical approach• Results of our calculations• Mixed Th-U-Pu fuel cycle• Stability study of NBW regime• Negative reactivity feedback (!)• Transient processes in NBW reactor• Main features of NBW reactor & possibility

to solve the nuclear power problems

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Nuclear Burning Wave concept

Lev Feoktistov (USSR, 1988):L.P. Feoktistov. Preprint IAE-4605/4, 1988.L.P. Feoktistov. Sov. Phys. Doklady, 34 (1989) 1071.

Edward Teller (USA, 1997): Traveling Wave Reactor Monte Carlo simulation

E.Teller. Preprint UCRL-JC-129547, LLNL,1997. Th-U fuel cycleHiroshi Sekimoto (Japan, 2001): CANDLE Deterministic approach

H.Sekimoto et al., Nucl. Sci. Eng., 139 (2001) 306. U-Pu fuel cycle, Stationary problem: x = z + Vt

238U (n,) 239U () 239Np () 239Pu (n,fission) ...T1/2 2.35 days

Concept & Analytical approach

Feoktistovcriterion

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8 8 Pu2 Pua a fn nD vn N Nt z

88 8 ;a

N vn Nt

9

8 8 91

aN vn N Nt

Pu9 PuPu

1a f

N N vn Nt

x z Vt

8 8Pu aeq Pu Pu

f a

NN

( 1)ai iPu i

cr Puf

NN

Pu Pueq crN N

Goldin & Anistratov (USSR, 1992): Nuclear Burning Wave Deterministic approachV. Goldin, D. Anistratov. Preprint IMM RAS # 43, 1992. U-Pu fuel cycle 1d non-stationary problem

232232ThTh 233Th

233Pa

233233UU 234U 235U 236U 237U

T½ = 22.2 min

T½ = 27 days

237NpT½ = 6.75 days

238238UU 239U

239Np

239239PuPu 240Pu 241Pu 242Pu 243Pu

T½ = 23.5 min

T½ = 2,35 days

243Am

T½ = 4.98 hours

241Am

T½ = 14,3 years

ThTh--U fuel cycleU fuel cycle

UU--Pu fuel cyclePu fuel cycle

Nuclear fuel reproductionNuclear fuel reproduction

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L z

rR

Lign

j ext

Breeding zoneIgnition zone

238 U 100 %238 U 90 %

239 Pu 10 %

2D Non2D Non--Stationary Theory of Nuclear Burning WaveStationary Theory of Nuclear Burning WaveS. Fomin, et al. - 1st IC “Global 2009”, Paris, paper 9456.

Nuclear Burning Wave

/ / / / / /

/ / /

1 1

1

1 1 1

1 1

( ) ( )

g g gg g g g g g g g g g

a in mod in modg

gG Gg g g j j g g j j j g g gf f f d l f f l d l l inj l j l

g g g

rD Dv t r r r z z

C

( 1) ( 1) ( 1)g gg gl

al l l c l l lg g

N N Nt

Non-Stationary Nonlinear Multi-Group Diffusion Equation of Neutron Transport

Together with Fuel Burn-up Equations and Equations of Nuclear Kinetics

of Precursor Nuclei of Delayed Neutrons

96 6

N Nt

10

1,4,5,6,7

ggfl l

l g

N Nt

( )j

j j j g g gll l l f f l

g

C Ct

Metal fuel (44%)Metal fuel (44%)

PbPb--Bi coolant (36%)Bi coolant (36%)

CM CM -- Fe (20%)Fe (20%)

jjext ext ~ ~ 10101155 cmcm--22 ss--11

ttoff off = 400 days= 400 days

( 1 8);, l

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NBW Reactor : R=117 cm, L = 500 cmNBW Reactor : R=117 cm, L = 500 cm , , ttoff off = 950 days= 950 days

,1017 cм-2 с-1

,1021 cм-3

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NBW reactor with mixed ThNBW reactor with mixed Th--UU--Pu fuelPu fuelSS. . Fomin et al.,Fomin et al., ICAPP 2010ICAPP 2010 (San Diego, USA)(San Diego, USA) paper 10302.paper 10302.SS. . Fomin et al.,Fomin et al., Progress in Nuclear Energy,Progress in Nuclear Energy, 52 52 ((2012011) 8001) 800--805.805.

L z

r

R

L зап

Jext

Breeding zoneIgnition zone

238 U 50 %238 U 90 %

239 Pu 10 % 232Th 50 %

ExampleExample: Metallic fuel : Metallic fuel 232232Th (62%) + Th (62%) + 238238U (48%) volume fraction = 55%, U (48%) volume fraction = 55%, fuel porosity p = 0.35;fuel porosity p = 0.35; Coolant (Pb-Bi eutectic) vol. frac. = 30%,frac. = 30%,

Constr. materials (Fe) vol. frac. = 15%; R = 390 cmfrac. = 15%; R = 390 cm

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Fuel burnFuel burn--upup for Thfor Th--UU--Pu cyclePu cycle

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Stability of the NBW Regime Stability of the NBW Regime -- Negative Reactivity FeedbackNegative Reactivity Feedback (!)(!)

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Variation of the reactivity ρ (dollars) with time t (days) along the variation of the volume-averaged neutron flux Fav (1015 cм-2 с-1)

-1 0 1 2 3 4 5 6 7 8

1

2

3

4

t - t0

av

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

av

Stability of the NBW Regime Stability of the NBW Regime -- Negative Reactivity FeedbackNegative Reactivity Feedback (!)(!)

S. Fomin et al., IC “Fast Reactors 20132013“ (Paris, France) paper CN-199-457

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Stability of the NBW RegimeStability of the NBW Regime(enriched region in the breeding zoon)(enriched region in the breeding zoon)

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Stability of the NBW RegimeStability of the NBW Regime

0 10 20 30 40 50

2468

1012141618

Pint , GW

t, years

62% Th, R=230 cm, 5% brick, z=300÷320 cm

62% Th, R=230 cm, 10% brick, z=300÷320 cm

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0 1 2 3 4 5 6 7

5

10

15

20

25

30

P, GW

t, years

Smooth Startup of the NBW Reactor

O. Fomin et al., Journal of Kharkiv National University, #1041, physical series «Nuclei, Particles, Fields», 2 /58/ (20132013) 49-56.

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0 1 2 3 4 5 6 7

5

10

15

20

25

30

P, GW

t, years

Smooth Startup of the NBW Reactor

0

1

2

3

4

0 10 20 30 40 50 60 70 80 90-4

-3

-2

-1

0, $ P, GW

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

N Np , N Pu

t, days

0

1

2

3

4

0 10 20 30 40 50 60 70 80 90-4

-3

-2

-1

0, $ P, GW

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

N Np , N Pu

t, days

Shutdown and Restart of the NBW ReactorShutdown and Restart of the NBW Reactor

Shutdown and Restart of the NBW ReactorShutdown and Restart of the NBW Reactor

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0 30 60 90 120 150 180 210 240 270 300-7

-6

-5

-4

-3

-2

-1

0

1

t , days

, $ P , GW

t = 250Restart

ShutdownRestart

0 30 60 90 120 150 180 210 240 270 3000

10

20

30

40

ShutdownRestart

NNp

NU233

NPu

NPa

N & N , 1017cm-3

t , days

S. Fomin et al., IC Global 20201515 (Paris, France) paper 5254.

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- negative feedback on reactivity - intrinsic safety (!!!)

- long-term (decades!!) operation without refueling and external control

- possibility of 232Th and 238U utilization as a fuel

- fuel burn-up depth for both 238U and 232Th ≈ 50% (one through cycle !)

- neutron flux in active zone ≈ 2·1015 n/сm2s

- neutron fluence during the whole reactor campaign ≈ 3·1024 n/сm2

- energy production density in active zone ≈ 200 W/сm3

- total power at the steady-state regime ≈ 1.2 GWt

- wave velocity at the steady-state regime ≈ 2 сm/year

- possibility of nuclear waste burn out (expected)

Main features of NBW reactor with mixed ThMain features of NBW reactor with mixed Th--UU--Pu fuel cyclePu fuel cycleReactor composition (vol. frac.):Fuel = 55% (FTh = 62%, p = 0.20), Coolant = 30%, CM = 15%, R = 215 cm

2010:

http://www.ted.com/talks/bill_gates.html

TravelingTraveling--Wave ReactorWave Reactor

““TerraPowerTerraPower”” ++ ChinaChina == TWRTWR (2020)(2020)

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Minister Zhang of National Energy Minister Zhang of National Energy Administration Received Bill GatesAdministration Received Bill Gates

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Map of World’s Nuclear Power Plants

Reactors Start to Spread in Reactors Start to Spread in Waves Around the WorldWaves Around the World

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List of our publications on the NBW reactor List of our publications on the NBW reactor ::S. Fomin et al., S. Fomin et al., Annals of Nuclear EnergyAnnals of Nuclear Energy, 32 (, 32 (20052005) ) 14351435--1456.1456.S. Fomin et al., S. Fomin et al., Problems of Atomic Science & TechnologyProblems of Atomic Science & Technology, , 6 (6 (20052005) 106) 106--113.113.S. Fomin et al., ICENES (S. Fomin et al., ICENES (20052005) (Brussels, Belgium) paper IC058.) (Brussels, Belgium) paper IC058.S. Fomin et al., S. Fomin et al., Nuclear Science & Safety in EuropeNuclear Science & Safety in Europe. Springer (. Springer (20062006) 239) 239--251. 251. S. Fomin et al., S. Fomin et al., ICAPPICAPP’’06 (06 (20062006) (Reno, USA) paper 6157.) (Reno, USA) paper 6157.S. Fomin et al., S. Fomin et al., Problems of Atomic Science & TechnologyProblems of Atomic Science & Technology, 3 (, 3 (20072007)) 156156––163.163.S. Fomin et al., S. Fomin et al., ICAPPICAPP’’07 07 ((20072007) ) (Nice, France) paper 7499(Nice, France) paper 7499..S. Fomin, S. Fomin, Reactor Physics and Technology. . PINP WS, , StSt--Perersburg, XLPerersburg, XL--XLIXLI (20072007) 154-198.S. Fomin et al., S. Fomin et al., PProgress in Nuclear Energy, 50 (20082008) 163-169.

Yu.Mel’nik et al., Atomic Energy, 107 (20092009) 288-295.S. Fomin et al., Global 20092009 (Paris, France) paper 9456.S. Fomin et al., ICAPP 20102010 (San Diego, USA) paper 10302.S. Fomin et al., Progress in Nuclear Energy, 52 (20120111) 800-805.O. Fomin et al., Journal of KNU, #104, «Nuclei, Particles, Fields», issue 2 /58/ (20132013) 49-56.S. Fomin et al., IC “Fast Reactors 20201313“ (Paris, France) paper CN-199-457.S. Fomin et al., IC “Global 20201515”” (Paris, France) paper 5254.

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1A1A--11--2:2: Sustainable Burning ReactorsSustainable Burning Reactors - Chairs: Kevan Weaver (TerraPower, USA)Traveling-Wave Reactors: Challenges and Opportunities - Kevan Weaver et al. (TerraPower, USA)Feasibility of LBE Cooled Breed and Burn Reactors - Ehud Greenspan (UC, Berkeley, USA)Preliminary Engineering Design of Sodium-Cooled CANDLE Core - Hiroshi Sekimoto (TIT, Japan)Nuclear Burning Wave in Fast Reactor with Mixed Th-U Fuel - Sergii Fomin et al (NSC KIPT, Ukraine)Nuclear Traveling Wave in a Supercritical Water Cooled Fast Reactor – W. Maschek (KIT, Germany)Development and Prospects of TWR Project in China - Zheng Mingguang (Shanghai NER&DI, China)Special PresentationSpecial Presentation: Traveling-Wave Reactors - John Gilliland. (Director of TerraPower, USA)

1A1A--3: Thorium Fuel Reactors3: Thorium Fuel Reactors - Chair: Sergii Fomin (NSC KIPT, Ukraine)(Th-U-Pu) - Mixed Fuel Cycle and Proliferation– E. Kryuchkov et al, (MEPhI, Russia)Large Scale Utilization of Thorium in Gas Cooled Reactors - V. Jagannathan (Bhabha ARC, India). . .

24Thank you for attention !Thank you for attention !