1
NEUTRON PROBLEMS OF REACTOR-PUMPED LASER
SYSTEMS: THEORY AND EXPERIMENT
Andrey V. Gulevich, Alexander P. Barzilov, Genady A. Bezhunov,
Peter P. Dyachenko, Oleg A. Elovsky, Oleg F.Kukharchuk, Genady N.Fokin,
Eugeny A. Pashin, Yury A. Prokhorov, Pavel A.Yakubov, Anatoly V. Zrodnikov
Institute for Physics & Power Engineering
1. Bondarenko Sq., Obninsk, Kaluga reg. RUSSIA, 249020
Lately, a coupled reactor systems have been widely used in reactor physics. In
particular, systems of a coupled burst reactor with a subcritical module provide the
opportunity to expand the sphere of application for the standard pulse reactors. It is
presumed that a similar facility, consisting of a fast burst reactor together with a thermal
subcritical laser module, could be used to make inertial confinement fusion realization
possible Ref.[1]. It is important to note that such a system has to operate in the mode of
high power of prompt neutron pulses
Theoretical and experimental investigation of fundamental processes of neutron
transport, as well as the nuclear safety of system described are the important and
challenging problems of modern reactor and neutron physics.
The basic element of this concept is the nuclear pumped amplifier (NPA). A twincore “Bars-6” fast burst reactor is used as the ignition module (see. Fig1). The reactor
parameters are as follows: dimensions of active cores - 220 x 220 mm; distance between
cores - 1500 mm; number of fissions in two cores - 51017; pulse duration - 40 s [4].
The laser module (LM) is a cylindrical structure sized to provide the space required
for housing the two cores of reactor module and the other components of the system see Fig.2. The diameter of laser module is 1700 mm, and the length is 2500 mm. The
LM consists of the laser active elements (LAEL’s), LAEL imitators and neutron
moderator elements. The laser module is surrounded by the two rows of neutron
reflector elements as shown in Fig.2.
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
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2
Figure 1. The twin-core fast burst reactor.
Figure 2. The laser module.
The LAEL assembly consists of a thin-wall stainless steel tube 50 mm in outer
diameter and 2500 mm in length and whose internal surface is coated with ~ 5 mm thick
uranium-235 metal and includes optical windows filled with a laser active medium. ArXe mixture (200:1), at approximately normal pressure, is used as a laser active medium
and has been chosen for this application because it is the medium mostly used in studies
performed at the present time.
The internal reflector consists of a thin-wall stainless tube with paraffin. If required,
the NPA could be provided with an internal neutron reflector of up to 7 cm thick.
The NPA functions as follows. Neutrons from the ignition reactor passing through
the LM are moderated and induce a chain fission reaction of uranium-235 in the coating
of LAEL. The fission fragments captured in Ar-Xe mixture induce plasmas so that the
inversion population of Xe1 levels corresponds to the laser transition with wavelength
1.73 m. The energy stored in the inversion population is extracted from laser module
by the optical system of the model.
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
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Calculation performed show that, in the case where all of the imitators are replaced
with LAEL’s (650 units) the energy of the model laser pulse can reach to the couple of
tens kilojoules for the pumping pulse duration ~ 10 ms.
The system involved has a couple of peculiarities in neutron sense such as: 1) great
difference in the spektra of fast burst reactor (average neutron lifetime is ~ 10-8s) and
thermal laser module (average neutron lifetime is ~ 10-4s); 2) large leakage of neutron (~
40%) from the system; 3) space-time distribution of neutron flux within the LM may be
changed during the pumping pulse; 4) complicated geometry of the system; the sizes of
the basic construction elements may vary from 5 m up to 2.5 meters. To overcome this
difficulties Monte-Carlo MMKFK code was chosen for neuron simulation.
Because of strongly marked space and power separation of the system elements, the
nonstationary neutron transport processes in the coupled system can be described
mathematically in terms of the kinetic models of coupled reactors - point and space
distribution models. There are several formulations for these models, the better known
are described in Refs. [2,3].
The mathematical model for the reactor-laser system dynamics was developed using
as the basis the modified neutron kinetic model of Refs.[3], the equations for feedback
coupling processes in reactor cores, and the equations for determining the cores
reactivity. For this case the equations of modified integral kinetic model are listed
below:
Proc. Intern. Conf. ICENES’98, 1998
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4
t
 r
rr
rb
r
N 1 (t)   11 (t -  ) + 11 (t -  ) N 1 ( )d  

0

t
t

rr
rb
rs
  12
(t -  ) + 12
(t -  ) N 2r ( )d    11
(t -  )S1 ( )d 

0
0

t

r
rr
rb
r
N
(t)

 2
 22 (t -  ) + 22 (t -  ) N 2 ( )d 

0

t
t
rr
rb
rs

   21
(t -  ) +  21
(t -  ) N 1r ( )d  +   22
(t -  )S2 ( )d 

0
0

t
t


br 
r
br 
r
N b (r , t)   G1 (r , t -  )N 1 ( )d    G2 (r , t -  )N 2 ( )d
0
0







(1)


Here: N ri (t ) , Si ( ) - fission rate and external neutron source intensity in i-th core for a

time moment t, respectively; N b (r , t ) - the space distributed power of laser module for
time moment t;  rr
ij (t - ) - the distribution of secondary fissions in i-th core for time
moment t (the condition being that the first fission was initiated in j-th core at a moment
time );  riis (t - ) - the analogous function for neutrons from the external source with
intensity Si () ;  rijb (t - ) - the distribution of secondary fissions for time moment t in

i-th core initiated by fissions in a laser module; G br
i (r , t - ) - the space distribution of
all fissions in the laser module for time moment t - mathematical analog of Green
rs
rb
function. Note that the calculation of functions  rr
ij (t - ) ,  ii (t - ) ,  ij (t - ) ,

G br
i (r , t - ) is performed only once. This model was tested in the experiments on the
Universal Critical Facility (UCF) (see. Fig.3).
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
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Figure 3. Universal Critical Facility.
1 - central multiplicative zone; 2,3 - internal neutron reflector;
4 - external multiplicative zone; 5 - neutron reflector
UCF is the neutron analog of coupled reactor laser system, which consist of central
uranium critical zone and external subcritical zone. Theoretical and experimental study
was to estimate the nonstationary neutron flux within the external zone from the pulsed
neutron generator (with the output 108n/impuls and duration ~ 1s), which had been
placed into the central zone. Comparison of some experimental and simulation results
are displayed in the Fig.4 a,b.
N, rel.unit
N, rel.unit
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
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6
Ni ,
. .
N
- exper .
- exper.
- cul c.
- cu l c.
a
, s
0.0000
0.0010
0.0020
,s
s
0.0000
0.0004
0.0008
0.0012
a)
b)
Figure 4. Time-dependent distributions of neutron flux: a) in the external zone ( no internal zone);
b) in the external zone ( with internal zone)
The model (1) was also used for the simulation of neutron kinetics of pulsed reactor
BARS-6 and system «BARS-6 with LM». The simplified analytical formula for the
estimation of a power pulse of BARS type reactor is following N r  t  

Er
 t 2 

exp  2  .
r

 r 

Here Er and  r - represent the total energy and effective pulse duration respectively. The
results of the mathematical simulation using the computer code TRENAGER BARS-6
and analytical formula for the nominal neutron pulse are presented in the fig.5 in
comparison with the experimental data. The parameters of mathematical model and the
main neutron-physical characteristics of the system «BARS-6 with LM» were calculated
using the Monte Carlo method and the MMKFK-2 code. Calculations were performed
for two laser module designs: one with an internal neutron polyethylene reflector (7-cmthick) and the second without an internal reflector.
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
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E-mail: kuh@ippe.obninsk.ru
7
The basic kinetic parameters, calculated for the two cases are shown in Table 1.
Here: k b - multiplication factor of neutrons for the laser module; k r r - a coupling
coefficient between the burst reactor cores; k rb - the reactivity induced by the laser
Fast neutron flux, rel.units
module on the reactor, G - total number of fissions in the laser module per unit fission in
20.0
the reactor core;  b - average
17.5
prompt neutron lifetime in a laser
module; $=0.0069. The statistical
- experiment
15.0
- numerical simulation
- analytical formula
error of the calculated values
12.5
shown in Table 1 is within 20%.
10.0
The analysis shows, that due to
7.5
the effective shielding of the core
5.0
by
2.5
stationary
the
boron
coating,
energy
the
release
distribution in reactor core is not
0.0
0
100
200
Time,
s
300
400
Figure.5. Time dependent neutron flux in the
BARS-6 reactor during the pulse.
affected by the presence of the
laser module.
Table 1. Neutron parameters coupled system
Parameters
kb
k rr
k rb
 b, s
G
with internal reflector
Calc.
Exp.
0.72
0.67
0.25$
0.46$
0.65$
2.0$
310
270
0.52
-
no internal reflector
Calc.
Exp.
0.78
0.73
0.75$
0.92$
3.0$
3.3$
310
200
1.56
-
Of primary importance is the safety of the system and, in particular, the prevention
of an accidental explosion of the core. One possible solution for preventing such an
accident is the use of a high power level internal neutron source in the reactor, where the
fast control rod is used to generate the pulse.
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
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8
E, 10
17
The
fissions
3.5
power
pulses
were
simulated for the coupled system
3.0
Hypothetical accident energy level
«reactor + LM» furnished with
Safe operation energy level
internal
reflector
with
the
2.5
condition being that the reactivity
input
2.0
into
two
cores
is
simultaneous and at the same
1.5
input rate. The parameters of the
transient
1.0
processes
were
calculated for various reactivity
0.5
1.050 1.075 1.100 1.125 1.150 1.175 1.200 1.225 1.250 1.275 1.300
sys; $
- =220$/s;
- =20$/s;
- =10$/s
(sd=100 ms). The core release
N, W
energy versus a value of the
1
1E+9
below the value of the delay time
to shut down the safety block
Figure 6. Dependence of the core release energy
versus the system reactivity.
1E+10
input rates into the two cores
system reactivity (sys) is shown
2
1E+8
in Fig.6 for various reactivity
1E+7
1E+6
input rates . It is clear that the
1E+5
1E+4
energy release of the reactor core
1E+3
reactor
-
1E+2
-
for the system with internal
LM
1E+1
reflector depends considerably on
1E+0
the reactivity input rate into the
1E-1
1E-2
core. This is because the system
1E-3
1E-4
0.00
0.05
0.10
0.15
0.20
with internal reflector is weak
t, s coupled, in the neutron sense,
Figure 7. Reactor and laser module power for nominal pulses.
and,
therefore,
the
physical
characteristics of the pulses for such a system are similar to those of a reactor without a
LM. The nominal power pulses (of 6MJ energy) for the system operating within the safe
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
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mode are shown in Fig.7 for a laser module with internal reflector (1) and without
internal reflector (2). It is evident that for the first case the pulse duration ten times less
than the second case (5 ms and 50 ms, respectively), but at the same time the energy
release in the LM for the second case ( 20 MJ) is greater than in the first case ( 6 MJ).
The calculations also show that for the first case (laser module with internal reflector)
the magnitude of the change in the system’s reactivity does not significantly affect the
energy of the pulses.
The results demonstrate
that the shape of the energy
release distribution in the
pumped section practically
does not change during the
pulse. The two dimensional
relative energy distribution
in the top area of the LM is
shown in Fig.8.
Figure 8. The energy release distribution in the top area
of the laser module.
From the above it can be
concluded that the coupled
system with internal reflector is considerable safer than a system without internal
reflector, but the trade-off is that the power parameters of the neutron pulses are
considerable lower.
REFERENCES
1. Dyachenko P.P. et al. Fusion Technology, 20, 969 (1991).
2. Avery R. «Theory of coupled reactors,» Second Int. Conf. on Peaceful Uses of
Atomic Energy. Report #1858 (1958).
3. Gulevich A.V. et al. «Modified neutron kinetic model of the reactor-laser system,»
IPPE #2264, Obninsk (1992).
4. Snopkov A.A. et al Proc. of Specialist Conf. on Physics of Nuclear-Induced
Plasmas and Problems of Nuclear-Pumped Lasers. IPPE, Obninsk, Russia, v.1,
pp.144-156 (1992).
Proc. Intern. Conf. ICENES’98, 1998
 - 1998 Institute for Physics and Power Engineering, Technical Physics Laboratory
http://www-tpl.ippe.obninsk.ru
E-mail: kuh@ippe.obninsk.ru