ISSN 1562-6016. PASТ. 2019. №5(123), p. 18-24. 

UDC 612.039.517 

SPHERICAL STANDING BURNING WAVE WITH EXTERNAL 

AUTOMATIC REACTIVITY CONTROL 

Yu.Y. Leleko, V.V. Gann, A.V. Gann  
 National Science Center “Kharkov Institute of Physics and Technology”, 

Scientific and Technical Complex “Nuclear Fuel Cycle” 

Center for Reactor Core Design, Kharkiv, Ukraine  

E-mail: makswell.com@gmail.com 
 

Neutron kinetics of a nuclear burning wave in moving incompressible neutron-multiplying medium in the pres-

ence of nuclear reactions is developed. A spherical reactor is considered, where fuel moves with acceleration to the 

center of the reactor at a velocity V(r)=VR(R/r)
2
, and the burning wave travels radially from the center to periphery. 

The fuel that came to the origin was unloaded from the reactor, and U-238 was loaded to the peripheral area at the 

same rate. Comparison of theoretical results with computer simulation using MCNPX code was performed. 

 

INTRODUCTION  

In this article, the theory of nuclear reactor on spher-

ical standing burning wave is developed. The neutron 

kinetics of a nuclear burning wave in a moving neutron-

multiplying medium in the presence of nuclear reactions 

was developed. Computer simulation of moving and 

standing spherical burning waves in a nuclear reactor 

was performed using MCNPX code [1].  

The reactor core consists of four areas: the outer 

zone made of U-238, the breading zone where produc-

tion of Pu-239 takes place according to the scheme      

U-238 + n = U-239 → Np-239 → Pu-239, the inner 

region in which Pu-239 is burning, and central area con-

sists of burnt fuel. The fuel moves with acceleration 

from periphery to the center of the reactor. It is shown 

that in such a system a spherical standing wave travels 

radially from the center zone to periphery. The burning 

wave consists of two regions: the external  breading 

zone and the internal  burning area. Distributions of 

the neutron flux, the U-238, Np-239, and Pu-239 iso-

tope concentrations and the specific power in the stand-

ing spherical burning wave are obtained in this paper. 

The conditions for existence of spherical standing burn-

ing waves are investigated. It is shown that an operation 

mode of the standing-wave reactor is characterized by 

two combinations of nuclear cross sections and single 

function defining the stability boundaries of the stem. 

Stability region of spherical waves was found to be 

broader then stability region of one-dimensional travel-

ing burning waves in an infinite medium. A state dia-

gram of such a reactor has been obtained. 

Concept of the traveling wave nuclear reactor 

(TWR) is one of the brilliant ideas of 20-th century. It 

suggests using depleted uranium (or thorium) as fuel 

and promises to supply inexhaustible source of energy 

worldwide. This idea was proposed by S.M. Feinberg, 

realized in theory by L.P. Feoktistov [2] and developed 

in many publications (see bibliography in [3]), in which 

several ways of its practical implementation were sug-

gested. One of the most promising designs of TWR is a 

fast reactor, which is able to work in maneuverable 

mode [3, 6]. Mathematical modeling of TWR using 

MCNPX code was performed in [4, 7, 8].  

Computer simulation of reactor on standing and 

traveling spherical burning wave has been carried out in 

present article. The computer model of the reactor using 

the MCNPX code is a ball of 2 m radius filled with ura-

nium dioxide fuel. In the traveling spherical wave mode, 

nuclear burning begins in the central zone of the core 

enriched with uranium. When concentration of Pu-239 

in U-238 becomes high enough due to breeding mecha-

nism according to the scheme U-238 + n = U-239 → 

Np-239 → Pu-239, a spherical burning wave appears; 

then it breaks away from the ignition region and contin-

uously moves to the edges of the core during   

~ 150 years. In our model at a power of 240 MW, the 

burning wave velocity was 0.5 cm/year. The mode of a 

standing spherical burning wave (SWR) was achieved 

by selecting the values of fuel speed and reactor power. 

Radial distributions of neutron flux, power density and 

the concentrations of Pu-239 and U-238 in the spherical 

standing burning wave were obtained using MCNPX 

code. A comparison of theoretical results with the data 

of numerical simulation has been carried out. Possibility 

of using depleted uranium as a nuclear fuel in reactors 

on spherical burning wave is confirmed. 

1. NEUTRON KINETICS EQUATION  

IN MOVING NEUTRON-MULTIPLYING 

MEDIUM 

Let us consider nuclear burning wave in incompress-

ible uranium-based medium, which moves to the center 

of the reactor at velocity V(r) = VR(R/r)
2
, where VR is 

speed of fuel at periphery of the reactor at r = R. 

The simplest description of neutron kinetics and 

burning of nuclear fuel can be obtained using the coor-

dinate system x ', y ', z ', in which the fuel is stationary: 

1 ˆ ( )
v

f aD S
t




    


;               (1) 

8
8 8a

n
n

t



  


,  

9 9
89 8

89

n n
n

t





  


,  

9 9
9 9

89

a

n n
n

t





  


, 9 92c

f

n
n

t



 


,     (2) 



 

where ( ', )r t  is neutron flow; v is speed of neutrons; 

n8 ( ', )r t  is concentration of  
238

U; 9 ( ', )n r t  is concen-

tration of 
 239

Np; 
9 ( ', )n r t  is concentration of 

239
Pu; 

( ', )cn r t  is concentration of fission products; D̂  neu-

tron transport operator; 
99 nff   macroscopic 

cross-section of fission and 
ccaaa nnn   9988
 

 macroscopic neutron absorption cross section. S  

term describing the reactor operating controls; 89  

transmutation cross-section of 
238

U to 
239

Pu; 89  time 

of the decay in chain 
239

U  
239

Np  
239

Pu; 9f   

fission cross-section of 
239

Pu;   the number of fission 

neutrons; 8a  and 9a   neutron absorption cross-

sections for nuclei 
238

U and 
239

Pu; c  is neutron ab-

sorption cross-section for fission products. To simplify 

we put  8a = 9a = a . 

Boundary conditions have to be added to Eqs. (1) 

and (2): 

Ψ(∞, t) = 0, Ψ'(0, t) = 0, n9(∞, t) = 0, 

 9
~n (∞, t) = 0, nc(∞, t) = 0, n8(∞, t) = n8(0).  (3) 

We need to find a time-independent solution of 

equations (1) in the form of a spherical standing wave 

Ψ(r), n8 (r), n9(r). Consider the movement of fuel mate-

rials rather slow: 89 V<<L, where L is the characteristic 

size of the burning region, then Eqs. (1), (2) can be in-

terpreted as quasi-stationary (v=∞). The operator D̂  we 

choose in diffusion approximation.  

The boundary conditions (3) look as follows:  

Ψ(∞) = 0, Ψ'(0) = 0, n9(∞) = 0, 

nc(∞) = 0, n8(∞) =n0.  (4) 

2. THEORY OF SPHERICAL NUCLEAR 

BURNING WAVE 

Equation for fluence 

Now, instead of the r coordinate we will introduce a 

new variable 

 2

2

( ')
( ) ' ( ') ' '

( ')

a
a

Rr r

r
r dr r r dr

V r V R


 

 


    , 

which is proportional to fluence F(x) and ranges from 0 

to a maximum value of 0 maxaF  . Let us choose 

the function S(x) describing the automatic control on 

excess reactivity ρ as:  fS  . After these 

changes Eqs. (1) and (2) become: 

2 2
4

2 4
(1 ) 0 

2

a
f a

R

D
r

V R


 

 

 
     

  
, (5) 

8
8 n

d

dn



,                (6) 

9898
9 / nn

d

dn
a 


,                            (7) 

af
c n

d

dn



/2 9

,               (8) 

  dQRVP faR /4 2
,              (9) 

9nff  ,                (10) 

ccaa nnn  )( 98 ,              (11) 

where Q is nuclei 
239

Pu fission energy release. 

The boundary conditions (4) for the functions Ψ(φ), 

n8(φ), 9
~n (φ), n9(φ)  look as follows:  

0 9 8 0(0) 0; '( ) 0; (0) 0; (0) 0; (0) ,cn n n n        

(12) 

where 
0 (0)   is the maximum neutron fluence. 

Equation for neutron flux density 

Equations (6) - (8) can be solved: 
  enn 08 )( ,

  enn a 0899 /)( , 

2

89 0( ) 2 / [1 (1 ) ]c f an n e         ,             (13) 

where 
0n  is concentration of U-238 in the initial mate-

rial, and equation (5) becomes: 
4 2

2 4

0

8989

2

( )
2 (1 2 )

2

2 (1 ) ,

a

R

f

a a

D d r d
e

n V d R d

e e



 

 
 

 

 
    

 



 

 
    

 

 
    
 

  (14) 

where 
3

89 /c f a    
 

is a parameter, which 

determines the speed of breeding in the system.  

System excess reactivity calculation 

Integrating equation (14) over φ taking into account 

the boundary condition Ψ(0) = 0, we obtain: 

4 2

2 4

0

( )
( )

2

a

R

D r d
f

n V R d

 





 ,              (15) 

where        ( ) 2 (1 2 )( 1)f e          

8989

2
2 (1 ) [1 (1 ) ]

f

a a

e 
 

   
 

 
      
 

. 

Substituting φ = φ0 in (15) and using the boundary 

conditions (12), we obtain the equation for the system 

excess reactivity ρ: 

0( ) 0f   .    (16) 

Solving Eq. (16) we obtain expression for excess re-

activity, which is necessary for the existence of a sta-

tionary solution: 

 
2

0

89

a

f

c q



  

      (17) 

 

 



 

where 

0

0

0
0

0

2 (1 2 )( 1)

1 (1 )

e
q

e





 







  


 
, and 

891 2
f

a a

c
 

 
 

 
   
 

.             (18) 

Eq. (17) and (18) relate excess reactivity ρ to the 

maximum fluence in unloaded fuel φ0. This value lies in 

the range 0 ≤ φ0 ≤ χ, where χ is the maximum fluence in 

the flat burning wave [4] (Eq. (19) and Fig. 1): 

22

22

)1(2]1)1[(

)1(



















ee

ee .  (19) 

0 2 4 6 8 10 12 14

0

1

2

3




 

Fig. 1. Dependence χ(β) 

Neutron field calculation 

Substituting (17) to (15) we obtain: 

4 2

1 02 4

0

( )
( , ),

2

a

R

D r d
f q

n V R d

 





           (20) 

where 
1 0 0 0( , ) 2 (1 2 )( 1)f q q e q e           . 

The function 1 0( , )f q  has the following analytical 

properties [7, 8]: 1 0(0, ) 0f q  , 
1 0 0( , ) 0f q  ; it be-

comes zero at the ends of the range 
00   . 

Substituting expression 

2

R

a

V R d

r dr





 
    

 
 in 

equation (20) and introducing new dimensionless varia-

bles 
2

0 0R a

D D

n V R n R



  ;  

0( ) /an D r   ,  

we get the system of equations: 

2

1( ) /
d

f
d


 


  ,               (21) 

2d

d





                  (22) 

with boundary conditions 

0( ) 0, (0) , ( ) .         (23) 

Set 0 in the interval 0< 0 < χ and solve equations 

(21), (22) with boundary conditions (23) by the shooting 

method: choose a value 0 and start from 0   with 

initial conditions
0(0)   and (0)   ; we ob-

tain solutions ( )   and ( )   diverging at   . 

We select 0 so that the region of divergence was as 

far as possible. 

Returning to the variables r, φ(r), and Ψ(r), we find 

the radial dependences of the neutron fluence φ(r), and 

flux )(r , as well as the concentration profiles of plu-

tonium 
)(

0899 )(/)( r

a ernrn   ,                         (24) 

uranium 
)(

08 )( renrn   and fission products  

 2 ( )

89 0( ) 2 / [1 1 ( ) ]r

c f an r n r e        .    (25) 

We also get the expression for power: 

fP Q dV     

02 2

0 89 04 / [1 (1 ) ]R f aQV R n e
     

   .     (26) 

The speed of fuel movement is proportional to the 

power of the reactor. The burning wave profile remains 

unchanged. 

The main result of theory is that spherical standing-

burning wave can be described with tree parameters: 

two combinations of nuclear cross sections c, β and neu-

tron fluence φ0 in unloaded fuel. 

Fig. 2 shows an example for radial profiles of the 

neutron flux in standing burning waves for material pa-

rameter β = 1 (when χ = 2 – the maximal value of φ0) 

and different values of the parameter φ0. 

 

0 5 10 15

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045
 

0
=0.3

 
0
=0.5

 
0
=1

 
0
=1.3

 
0
=1.5

 
0
=1.7





  

Fig. 2. Radial dependences of the neutron flux 

ψ(ζ) in standing waves, χ = 2 

The maximum of neutron flux in the burning wave 

(see Fig. 2) moves away from the center of the core 

when φ0 increases and goes to infinity at φ0 = χ.  

Fig. 3 shows dependence the power of the standing 

burning wave on the fluence φ0 at χ = 1. The fundamen-

tal difference between a spherical standing-wave reactor 

and a one-dimension traveling-wave reactor is that its 



 

power can be physically limited by choosing a suffi-

ciently small parameter φ0 and small dimensions of the 

core. Spherical standing-wave differs from a traveling 

burning wave Feoktistov’s type, in which the power and 

neutron fluxes are much more than modern structural 

materials can allow.  

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

P


  

Fig. 3. Dependence of power of the standing burning 

wave on the fluence φ0 with χ = 1 

0 1 2 3

0.0

0.1

0.2

 Pu-239

 Fissium





C
o

n
c
e

n
tr

a
ti
o

n
, 
P

u
-2

3
9

, 
fi
s
s
iu

m





 

Fig. 4. Dependences of Pu-239 concentrations and fis-

sion products on the radius 

0 1 2 3

0.7

0.8

0.9

1.0

1.1





C
o

n
c
e

n
tr

a
ti
o

n
, 
U

-2
3

8





 

Fig. 5. Dependence of U-238 concentration on the radi-

us in the standing burning wave 

Figs. 4,5 show the dependences of the concentra-

tions of Pu-239, U-238 and fission products on the radi-

us in the standing burning wave of a spherical shape. 

From Fig. 5 one can see that in the standing burning 

wave with the specified parameters, the uranium isotope 

U-238 burns out by 18%, and in the spent fuel there are 

still ~ 6% Pu-239. 

3. ANALYSIS OF STABILITY THE 

SPHERICAL BURNING WAVE 

In Fig. 6 the family of phase trajectories ψ(φ) for 

different values of φ0 is shown. 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.00

0.05

 
0
=0.1

 
0
=0.3

 
0
=0.5

 
0
=1

 
0
=1.3

 
0
=1.5

 
0
=1.7

 
0
=1.8





  
Fig. 6. Dependence ψ(φ) for a some values of φ0  at 

χ = 2 

A necessary condition for stability of a standing 

burning wave is the positivity of the values of φ and ψ 

along the trajectory of the solution ( )   and ( )  . 

Thus, the entire trajectory of the dependence φ(ψ) 

should lie in the first quadrant. As can be seen in Fig. 6 

this condition is valid. 

Calculation of the minimum value of the parame-

ter with the scope of the solution 

The condition ρ ≥ 0 for the existence of a standing 

spherical wave gives a relation: 

c ≥ q0(β, φ0).      (27) 

Relation (27) determines сmin(φ0)  the minimum 

value of с, for which a stationary solution still exists for 

a given value of φ0. The dependence сmin(φ0) has the 

form: 

0

0

0
min 0

0

2 (1 2 )( 1)
( , ) .

1 (1 )

e
c

e





 
 







  


 
          (28) 

The dependence сmin(φ0, β) calculated using (28) for 

the value β = 1 is shown in Fig. 7. The wave exists in 

the open region of the graph. The dependence сmin(φ0, β) 

has a minimum, indicated in the graph as cmm(β), which 

is located below the line q(β) corresponding to a plane 

burning wave. One can see from Fig. 7 that a standing 

spherical burning wave is more stable than a plane burn-

ing wave, and two times lower fluency φ0 is required for 

existence of a standing wave. 



 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

0

2

4

6

8

10

q
0
(


)

 

c
mm

()




c

q()

 

Fig. 7. Dependence of сmin(φ0, β) on φ0 with β=1,(χ= 2) 

State diagram of a reactor on the standing spheri-

cal burning wave 

The dependence of cmm(β) is shown in Fig. 8 with 

dotted line. It represents the lower limit of parameter c 

for standing burning wave stability in a spherical reac-

tor. For comparison, the lower limit of c for a plane 

burning wave stability in an infinite medium q(β) [4] is 

shown in the same graph.  

0 1 2 3 4

0

2

4

6

8

10

12

14

c
mm

()



c

q()

 

Fig. 8. State diagram of the reactor on a standing 

spherical burning wave 
 

The state diagram of a reactor on a standing spheri-

cal burning wave is shown in Fig. 8. In the pink shaded 

region there are no standing waves, in the region shaded 

in yellow the spherical standing waves exist only for 

some values of φ0. In the open region of the Fig. 8 the 

waves exist for any values of φ0. 

4. COMPUTER SIMULATION  

OF SPHERICAL TRAVELLING BURNING 

WAVE 

Computer model of STBW is a sphere with radius     

R =2 m, filled with uranium dioxide based fuel, which is 

divided into spherical layers with thickness of 5 cm. In 

order to reach criticality an igniter containing enriched 

uranium was located in the central part of the reactor 

core.  Due to transmutation under fast neutron irradia-

tion the 
238

U isotope converts to 
239

Pu according to the 

chain: 
238

U + n = 
239

U  
239

Np  
239

Pu. When concen-

tration of 
239

Pu in the fuel reaches high level, spherical 

burning wave appears; it breaks away from the central 

area and moves to the edges of the active zone during 

30 years. In this model the speed of the burning wave is 

~0.5 cm/year at 240 MW power (see Figs. 9 and 10 in 

which radial distributions of neutron flux and power are 

shown). 

0 10 20 30 40 50 60 70 80 90 100 110 120 130

0.0

2.0x10
14

4.0x10
14

6.0x10
14

8.0x10
14

1.0x10
15

1.2x10
15

1.4x10
15

 0 years

 5 years

 10 years

 20 years

 30 years

F
lu

x
, 
n

/c
m

2
/s

r, cm  
Fig. 9. Radial dependences of the neutron flux density in 

a traveling spherical burning wave for period  

of 30 years 

0 20 40 60 80 100 120 140

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Spherical travelling nuclear burning wave 

 0 years

 5 years

 10 years

 15 years

 20 years

 25 years

 30 years

P
o

w
e

r 
fr

a
c
ti
o

n
, 

r 
=

 5
 c

m

r, cm

SWRSh8, 30 years, Power 240 MW

 
Fig. 10. Radial distribution of power fraction of the 

layers in the traveling spherical burning wave during  

30 years at 240 MW power 

5. COMPUTER SIMULATION OF 

SPHERICAL STANDING BURNING WAVE 
 

In SWR model fuel is moving towards the burning 

wave at the same speed, that ensures the stationarity of 

breading and burning processes in the reactor. The re-

sults of computer simulation of a standing nuclear burn-

ing wave during 20 years are shown in Fig. 11. It shows 

that parameters of the model ensure stationary of the 

spherical nuclear burning wave when reactor is fed with 

depleted uranium. Figs. 11–13 show dependences of 

power density and concentrations of Pu-239 and U-238 

on the radius, which were obtained using MCNPX 

computer simulation of the spherical standing burning 

wave. They are in qualitative agreement with the theo-

retical results (see Figs. 3–5).  

 

 



 

0 10 20 30 40 50 60 70 80 90 100 110 120

0.00

0.02

0.04

0.06

0.08

0.10

0.12
 0 years

 5 years

 10 years

 15 years

 20 years

P
o

w
e

r 
fr

a
c
ti
o

n
, 

r 
=

 5
 c

m

r, cm

SWRS, 20 years, Power 240 MW

Spherical standing nuclear burning wave 

 
Fig. 11. Radial distribution of power fraction of the 

layers in a standing spherical burning wave over a   

period of 20 years 

0 10 20 30 40 50 60 70 80 90 100 110 120

0

1

2

3

4

5

6

7

8

9

10

 Pu-239

C
o

n
c
e

n
tr

a
ti
o

n
, 
%

r, cm

SWRS, 20 years, Power 240 MW

Spherical standing nuclear burning wave 

 
Fig. 12. Dependence of Pu-239 concentration on the 

radius in the standing burning wave 
 

0 10 20 30 40 50 60 70 80 90 100 110 120

0

10

20

30

40

50

60

70

80

90

100

110

 U-238

 Pu-239

C
o

n
c
e

n
tr

a
ti
o

n
, 
%

r, cm

SWRS, 20 years, Power 240 MW

Spherical standing nuclear burning wave 

 
Fig. 13. Dependence of the concentrations of U-238 and 

Pu-239 on the radius in the standing burning wave 

 

CONCLUSION 

• Standing nuclear burning wave can exist not only 

in one-dimensional geometry, but in systems with cy-

lindrical and spherical symmetries as well.  

• Phenomenological theory of standing spherical nu-

clear burning wave was developed 

• Existence of a standing spherical nuclear burning 

wave was proved for a reactor with fuel continuously 

moving toward the center. 

• State diagram of such a reactor was proposed and 

the boundaries of the standing wave existence were de-

fined.  

• Mathematical modeling of reactor on spherical 

standing burning wave was carried out using MCNPX 

code, and obtained numerical results are in agreement 

with results of the phenomenological theory. 

REFERENCES 

1. MCNPX User’s Manual Version 2.5.0, April. 

2005 LA-CP-05-0369 

2. L.P. Feoktistov. Neutron-fission wave // Rep. 

Academy Sciences of the USSR. 1989, v. 309, p. 864-

867. 

3. T. Ellis, R. Petroski. Traveling-Wave Reactors: 

A Truly Sustainable and Full-Scale Resource for Global 

Energy Needs // Proceedings of ICAPP ’10, San Diego, 

CA, USA, June 13-17, 2010, 10189 p. 

4. V.V. Gann, A.V. Gann. Benchmark on traveling 

wave fast reactor with negative reactivity feedback ob-

tained with MCNPX code // 4 International Conference 

“Current Problems in Nuclear Physics and Atomic En-

ergy” (NPAE-Kyiv 2012), September 37, 2012, Kyiv, 

Ukraine. Proceedings Part II, p. 421-425.  

5. Yu.Y. Leleko, V.V. Gann, A.V. Gann. Computer 

Simulation of Stationary Burning Wave Reactor //  4th 

International Conference “Computer modelling in high-

tech” (CMHT-Kharkov 2016), May 2631, 2016, Khar-

kov, Ukraine, p. 206 

6. TERRAPOWER, LLC Traveling Wave Reactor 

Develop Program Overview //  

http://dx.doi.org/10.5516/NET.02.2013.520 

7. Yu.Y. Leleko, V.V. Gann, A.V. Gann. Nuclear 

reactor on cylindrical standing burning wave with an 

external negative reactivity feedback // Problems of 

Atomic Science and Technology. 2017, № 2(108), p. 

138-143. 

8. V.V.Gann, Yu.Y.Leleko, A.V.Gann Computer 

simulation of nuclear reactor on cylindrical standing 

burning wave // Proceedings of NUCLEAR 2017 the 

10th International Conference on Sustainable Develop-

ment through Nuclear Research and Education, Pitesti,  

2017, May 2426, p. 161-168. 

 

Article received 07.11.2018 

 

 

 

http://dx.doi.org/10.5516/NET.02.2013.520


 

 

СФЕРИЧЕСКАЯ СТОЯЧАЯ ВОЛНА ЯДЕРНОГО ГОРЕНИЯ С ВНЕШНИМ 

АВТОМАТИЧЕСКИМ КОНТРОЛЕМ РЕАКТИВНОСТИ 

Ю.Я. Лелеко, В.В. Ганн, А.В. Ганн 

Была развита нейтронная кинетика стоячей волны ядерного горения в нейтронно-размножающей среде, 

которая не сжимается и является подвижной, при наличии ядерных реакций. Рассмотрен сферический реак-

тор, в котором волна ядерного горения движется радиально от центра, а топливо – в центр реактора. Пока-

зано, что при подпитке такой системы 
238

U в ней может существовать сферическая стоячая волна ядерного 

горения. Проведено сравнение теоретических результатов с данными численного моделирования такого ре-

актора с использованием кода MCNPX.  

 

СФЕРИЧНА СТОЯЧА ХВИЛЯ ЯДЕРНОГО ГОРІННЯ З ЗОВНІШНІМ АВТОМАТИЧНИМ 

КОНТРОЛЕМ РЕАКТИВНОСТІ 

Ю.Я. Лелеко, В.В. Ганн, А.В. Ганн 

Була розвинена нейтронна кінетика стоячої хвилі ядерного горіння в нейтронно-розмножуючім середо-

вищі, котре не стискається та є рухомим, при наявності ядерних реакцій. Розглянуто сферичний реактор, в 

якому хвиля ядерного горіння рухається радіально від центра, а паливо – до центра реактора. Показано, що 

при підживленні такої системи 
238

U в ній може існувати сферична стояча хвиля ядерного горіння. Проведено 

порівняння теоретичних результатів з даними чисельного моделювання такого реактора з використанням 

коду MCNPX.