Journal of Modern Physics, 2013, 4, 528-550
http://dx.doi.org/10.4236/jmp.2013.44075 Published Online April 2013 (http://www.scirp.org/journal/jmp)
KamLAND-Experiment and Soliton-Like Nuclear
Georeactor. Part 1. Comparison of Theory with
Experiment
V. D. Rusov1*, D. A. Litvinov1, E. P. Linnik1, V. N. Vaschenko2, T. N. Zelentsova1,
M. E. Beglaryan1, V. A. Tarasov1, S. A. Chernegenko1, V. P. Smolyar1,
P. O. Molchinikolov1, K. K. Merkotan1, P. E. Kavatskyy3
1Department of Theoretical and Experimental Nuclear Physics,
Odessa National Polytechnic University, Odessa, Ukraine
2State Ecological Academy for Postgraduate Education and Management, Kyiv, Ukraine
3Research Institute of Sustainable Development Technologies “Live Earth”, Kyiv, Ukraine
Received December 2, 2012; revised January 5, 2013; accepted February 1, 2013
Copyright © 2013 V. D. Rusov et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
We give an alternative description of the data produced in the KamLAND experiment, assuming the existence of a
natural nuclear reactor on the boundary of the liquid and solid phases of the Earth core. Analyzing the uncertainty of
antineutrino spectrum of georeactor origin, we show that the theoretical (which takes into account the soliton-like nu-
clear georeactor) total reactor antineutrino spectra describe with good accuracy the experimental KamLAND-data over
the years of 2002-2007 and 2002-2009, respectively. At the same time, the parameters of mixing (25
21 2.5 10m


252
21 7.49 10eVm
 2
12
tan 0.436
eV2,
) calculated within the framework of georeactor hypothesis substantially differ from the parameters of
mixing (,
2
12
n 0.437  ta

) obtained in KamLAND-experiment for total exposure over the pe-
riod of 2002-2009. By triangulation of KamLAND and Borexino data we have constructed the coordinate location of
soliton-like nuclear georeactors on the boundary of the liquid and solid phases of the Earth core.
Keywords: KamLAND Experiment; Borexino Experiment; Nuclear Georeactor; Neutrino Oscillations; Parameters of
Mixing
1. Introduction
It is obvious now that the experiments by the Kam-
LAND-collobaration over the last 8 years [1-5] are ex-
tremely important not only for observation of reactor
antineutrino oscillations, but because they make it possi-
ble for the first time to verify one of the most vivid and
mysterious ideas in nuclear geophysics—the hypothesis
of natural nuclear georeactor existence [6-20]. In spite of
its singularity and long history, this hypothesis becomes
especially attractive today because it lets one explain
clearly from the physical standpoint different unrelated,
at the first glance, geophysical anomalous phenomena
the fundamental nature of which is beyond any doubt.
First of all it concerns the problem of 3He and 4He iso-
topes origin in the Earth interior, the concentration ratio
of which, as is well known, “mystically” increases towards
the center of Earth [21,22]. This is practically impossible
to explain by existing models of the origin of the anoma-
lous 3He concentration and 3He/4He ratio distribution in
the Earth interior since they have serious contradictions.
For example, Anderson et al. has pointed out [23]: “The
model whereby high 3He/4He is attributed to a lower
mantle source, and is thus effectively an indicator of
plumes, is becoming increasingly untenable as evidence
for a shallow origin for many high 3He/4He hot spots ac-
cumulates. Shallow, low 4He for high 3He/4He are logi-
cally reasonable, cannot be ruled out, and need to be rig-
orously tested if we are to be understand the full implica-
tions of this important geochemical tracer”. Apparently,
the most advanced model, which is devoid of the men-
tioned contradictions, is the so-called Gonnermann-Muk-
hopadhyay model, preserving noble gases in convective
*Corresponding author.
C
opyright © 2013 SciRes. JMP

V. D. RUSOV ET AL. 529
mantle [24]. However this model ignores the possible
high concentrations of 238U and 232Th in the outer core
(as it is shown by numerous laboratory experiments [16,
18,20]), and this is the weak point of this model. At the
same time, it is shown [17] that, if the nuclear georeactor
exists, within the framework of model, which takes into
account the georeactor thermal power and distribution of
238U and 232Th in the Earth interior, it is possible also to
obtain a good description of the known experimental
3He/4He distributions in the crust and mantle.
A potent argument in favour of the nuclear georeactor
existence are the results of recent seismo-tomography re-
searches of the anomalous high heat flow (13 ± 4 TW) on
the core-mantle boundary. This heat is much higher than
the radiogenic heat in the lower mantle (D''-region) [25].
To explain such an anomalous high heat flow the authors
of this paper have advanced the hypothesis of young
solid core of the Earth with its crystallization energy as a
cause of anomalous temperature effect.
In full measure it concerns the known problem of na-
ture of an energy source maintaining the convection in
the Earth liquid core or, more precisely, the mechanism
of magneto-hydrodynamic dynamo generating the Earth
magnetic field. It is obvious, that the well-known 40K-
mechanism of radiogenic heat production in the solid
core of the Earth does not solve the problem on the
whole, because it can not explain the heat flows balance
on the core-mantle boundary (see [26] and refs therein).
It is also worth mentioning the so-called mechanism of
the Earth magnetic field inversions closely associated
with the problem of convection in the Earth liquid core.
It seems to be strange, but both these fundamental prob-
lems have a simple and physically clear solution within
the framework of hypothesis of existence of the natural
nuclear georeactor on the boundary of the liquid and
solid phases of the Earth [17,27].
If the georeactor hypothesis is true, the fluctuations of
georeactor thermal power can influence on Earth global
climate in the form of anomalous temperature jumps in
the following way. Strong fluctuations of georeactor ther-
mal power can lead to the partial blocking of convection
in the liquid core [27] and the change of an angular velo-
city of liquid geosphere rotation, thereby, by virtue of a
conservation law of Earth angular moment to the change
of angular velocity of mantle and the Earth surface, respec-
tively. It means that the heat or, more precisely, dissipa-
tion energy caused by friction of Earth surface and bot-
tom layer can make a considerable contribution to total en-
ergy balance of the atmosphere and thereby to influence
significantly on the Earth global climate evolution [27].
However, in spite of the obvious attractiveness of this
hypothesis there are some difficulties for its perception
predetermined by non-trivial properties which georeactor
must possess. At first, natural, i.e. unenriched, uranium
or thorium must be used as a nuclear fuel. Secondly, tra-
ditional control rods are completely absent in the reactiv-
ity regulation system of reactor. Thirdly, in spite of the
absence of control rods a reactor must possess the prop-
erty of so-called inner safety. It means that the critical
state of reactor core must be permanently maintained in
any situation, i. e. the normal operation of reactor is auto-
matically maintained not as a result of operator activity,
but by virtue of physical reasons-laws preventing the ex-
plosive development of chain reaction in a natural way.
Figuratively speaking, the reactor with inner safety is the
“nuclear installation which never explodes” [28].
It seems to be strange, but reactors satisfying such un-
usual requirements are possible in reality. For the first
time the idea of such a self-regulating fast reactor (so-
called mode of breed-and-burn) was expressed in a gen-
eral form at II Genevan conference in 1958 by Russian
physicists Feynberg and Kunegin [29] and relatively re-
cently “reanimated” as an idea of the self-regulating fast
reactor in traveling-wave mode of nuclear burning by L.
Feoktistov [30] and independently by Teller, Ishikawa
and Wood [31].
To interpret the experimental KamLAND antineutrino
spectra [3-5] we consider below the properties of such an
unusual reactor.
2. Soliton-Like Nuclear Georeactor and
the KamLAND Antineutrino Spectra
(Experiments over the Period of
2002-2004)
The main idea of reactor with inner safety consists in
selection of fuel composition so that, at first, the charac-
teristic time τ

of nuclear burning of fuel active (fissile)
component is substantially greater than the characteristic
time of delayed neutrons production and, secondly, nec-
essary self-regulation conditions are fulfilled during the
reactor operation (that always take place when the equi-
librium concentration of fuel active component is greater
than its critical concentration [30]). These very important
conditions can practically always be attained, if among
other reactions in a reactor core the chain of nuclear
transformations of the Feoktistov uranium-plutonium cy-
cle type [30]



238239 239
239
U,U Np
Pu ,fission
β
β
n
n




 (1)
or the Teller-Ishikawa-Wood thorium-uranium cycle type
[31]



232233 233
233
Th ,ThPa
U,fission
β
β
n
n




 (2)
are appreciable enough.
In both cases the active components of nuclear fuel are
the generated fissile isotopes of 239Pu (1) or 233U (1). The

V. D. RUSOV ET AL.
JMP
530
n

n
characteristic time of such a reaction, i.e. the respective
β-decay time, is approximately equal to τ

= 2.3/ln2 ≈ 3.3
days and τ

≈ 39.5 days for reactions (1) and (2), respec-
tively. This is several orders of magnitude greater than
the time of delayed neutrons production.
uranium cycle (2), but in time τ

= 39.5 days.
The details of the system of kinetic equations for com-
ponents of nuclear fuel and neutrons (as a diffusion ap-
proximation) in such chains are rather simple and were
described in detail in our paper [17]. Typical solutions
for such a problem have the form of soliton-like concen-
tration wave of nuclear fuel components and neutrons
(Equations (3)-(9) in [17]) and are shown in Figure 1.
Within the framework of soliton-like fast reactor theory
it is easy to show that the phase velocity u of nuclear
burning is determined by following approximate equality
[32]
Self-regulation of nuclear burning process (under indi-
cated above relation between the equilibrium and critical
concentrations of fuel active components [30]) takes
place because such a system, being left by itself, cannot
pass from a critical state to reactor runaway mode as the
critical concentration is bounded above by the finite
value of plutonium equilibrium concentration, i.e. Pu >
crit . On phenomenological level the self-regulation of
nuclear burning is manifested as follows. Increase of a
neutron flux due to some reasons will result in rapid
burn-up, for example, of plutonium, i.e. in decrease of its
concentration, and therefore in decrease of neutron flux,
while the new nuclei of 239Pu are produced with the same
rate during τ

= 3.3 days. And vice versa, if the neutron
flux is sharply decreased due to external action, the burn-
up rate decreases too and the plutonium accumulation
rate will be increased as well as the number of neutrons
produced in a reactor after approximately same time.
Analogous situation will be observed for the thorium-
6
42
2
2
864
exp ,
29π
3π
π
4
β
crit
fis crit
uτaa
L
n
ann
 

 


 


(3)
where
f
is and crit are the equilibrium and critical
concentrations of active (fissile) isotope, respectively; L
is the average diffusion distance for neutron, τ

is the
delay time caused by active (fissile) isotope production,
which is equal to the effective period of intermediate
nuclei  -decay in the uranium-plutonium cycle (1) or
n
n
Figure 1. Concentration kinetics of neutrons, 238U, 239U, 239Pu in the core of cylindrical reactor with radius of 125 cm and
1000 cm long at the time of 240 days. Here r is the transverse spatial coordinate axis (cylinder radius), z is the longitudinal
patial coordinate axis (cylinder length). s

V. D. RUSOV ET AL. 531
thorium-uranium cycle (2).
Note that Equation (3) automatically contains the self-
regulation condition for nuclear burning because the ex-
istence of a wave is predetermined by the inequality
f
iscrit In other words, Equation (3) is a necessary
physical requirement for the existence of soliton-like
neutron wave of nuclear burning. We indicate for a com-
parison that, as it follows from Equation (3), the upper
bounds of phase velocity of nuclear burning wave are
3.70 cm/day for the uranium-plutonium cycle (1) and
0.31 cm/day for the thorium-uranium cycle (2) at almost
equal average diffusion distance (L ~ 5 cm) for fast neu-
trons (1 MeV) both for uranium and thorium.
nn

2
m
2
12
tan 0.56  
Finally, we consider some important details and prop-
erties of such a soliton-like fast reactor, assuming the exi-
stence of which, we have obtained the theoretical spectra
of reactor antineutrino and terrestrial antineutrino which
are in good agreement with the experimental KamLAND
data [17] corresponding to the first [1] and third [3] ex-
posures.
According to our notions, a soliton-like fast reactor is
located on the boundary of the liquid and solid phases of
the Earth [17]. The average thickness of such a shell-
boundary with increased density and mosaic structure is
~2.2 km [33. In our opinion, the most advanced mecha-
nism for formation of such a shell below the mantle so
far follows from the experimental results by Anisichkin
et al. [16,18] and Xuezhao-Secco [34]. According to
these results, the chemically stable high-density actinide
compounds (particularly uranium carbides and uranium
dioxides) lose most of their lithophilic properties at high
pressure, sink together with melted iron and concentrate
in the Earth core as a consequence of the initial gravita-
tional differentiation of the planet. In the other words,
during early stages of the evolution of the Earth and
other planets, U and Th oxides and carbides (as the most
dense, refractory, and marginally soluble at high pres-
sures) accumulated from a magma “ocean” on the solid
inner core of the planet, thereby activating chain nuclear
reactions, and, in particular, a progressing wave of Feok-
tisov and/or Teller-Ishikawa-Wood type.
What is the thermal power of such a reactor? As a na-
tural quantitative criterion of the georeactor thermal pow-
er we used the well-known (based on the geochemical
measurements) 3He/4He radial distribution in the Earth
interior [17]. It turned out that the experimental average
values of 3He/4He for crust, the depleted upper mantle,
the mantle (minus the depleted upper mantle) and the so
called D''-region in the lower mantle are in good agree-
ment with the theoretical data obtained by the model of
Feoktistov’s uranium-plutonium georeactor with thermal
power of 30 TW [17]. Figure 2 shows the special experi-
mental investigation of geologically produced antineu-
trinos with KamLAND [3] and an alternative description
of these data by our georeactor model [17].
We need to note that, in spite of the fact that the expe-
rimental KamLAND-data are well described within the
framework of georeactor model [17] (see Figure 2),
some geophysicists still have doubts about the existence
of georeactor, and the value of georeactor power (30 TW)
arouses a special mistrust. In this connection we would
like to pay attention to a strange restriction (W ≤ 6.2 TW)
on the value of nuclear georeactor thermal power W,
which, unfortunately, is frequently met in the scientific
literature recently [3,4,35,36], and strongly masks and
distorts the clear understanding of problem of georeactor
existence, which is intricate enough by itself. Below we
ground a complete inconsistency of this restriction. One
of the conclusions of the KamLAND-colloboration is the
upper bound of nuclear georeactor thermal power (W ≤
6.2 TW at 90% C.L.), which is a direct consequence of
uncertainty of KamLAND experimental data [4]. How-
ever, it is necessary to keep firmly in mind that the re-
striction of 6.2 TW on georeactor power is true only for
the specific parameters of mixing, i.e. for 21 = 7.58
× 10−5 eV2, , and takes into account the
Figure 2. The energy spectra in KamLAND [17]. Main
panel, experimental points (solid black dots with error bars)
together the total expectation obtained in KamLAND ex-
periment (dotted black line) [3] and present paper (thick
solid blue line). Also shown are expected neutrino spectrum
(solid green line) from Japan’s reactors, the expected neu-
trino spectrum from georeactor 30 TW (red line), the ex-
pected signals from 238U (dashed red line) and 232Th (dashed
green line) geoneutrinos, 13C(α, n)16O reactions (dashed
blue line) and accidentals (dashed black line). Inset: ex-
pected spectra obtained in KamLAND experiment (solid
black line) [3] and our paper [17] (solid green line) extended
to higher energy.
e
v

V. D. RUSOV ET AL. 532
existence of georeactor within the framework of nonzero
hypothesis [4], but absolutely ignores such a nontrivial
property of the nuclear georeactor as an uncertainty of
georeactor antineutrino spectrum, which in the case of
soliton-like nuclear georeactor reaches ~100%. As it will
be shown below, the this level of uncertainty within the
framework of maximum likelihood function leads (in the
minimization of the χ2-function) to a considerable expan-
sion of restriction on the nuclear georeactor heat power
(~30 TW) and, accordingly, to the new oscillation para-
meters (21 , ) for
reactor antineutrino.
252
10 eV
tan2.5 2
12 0.437
 
Pu PufnV
m
Another widespread error is related to determination of
the Earth geothermal power WEarth. It is known that there
are two estimations of WEarth, i.e., ~33 ± 1 TW [37] and
~44 ± 1 TW [38]. We are not going to participate in the
discussion among the authors of these estimations con-
cerning the necessity of taking into account the hydro-
thermal circulation. We would like only to emphasize
that these estimations are 1.7 - 2.3 times greater than the
radiogenic heat contribution (from the decay 238U, 232Th
and 40K in the mantle and crust), which is 19.5 TW [17].
D.L. Anderson [39] refers to this difference as “the miss-
ing heat source problem” and summarizes the situation in
the following words: “Global heat flow estimates range
from 30 to 44 TW Estimates of the radiogenic con-
tribution (from the decay of U, Th and K in the mantle),
based on cosmochemical considerations, vary from 19 to
31 TW. Thus, there is either a good balance between
current input and output or there is a serious missing
heat source problem, up to a deficit of 25 TW”. Be-
cause of this missing heat, some researchers think that, if
a reactor exists, its thermal power must make up the ex-
istent deficit of geothermal energy. It is correct when it
comes to a thermal power of reactor which operated in
the remote past, but which does not operate today. The
difference between the heat generated now by a reactor
in the Earth interior and the experimentally observed
geothermal heat [37,38] is very significant due to the
high thermal inertia of the Earth. In other words, it is ne-
cessary to take into account that the heat generated in the
Earth interior is not instantly transferred to the surface,
but delays (due to a low heat conductivity) in a time of
thermal relaxation of the Earth (τE ≈ 109 years) [40,41].
From here it follows that it is impossible to sum up the
heat flows which have different spatial and temporal ori-
gin.
3. The Nonstationary Soliton-Like Nuclear
Georeactor and KamLAND Antineutrino
Spectrum (Experiments over the Period
of 2002-2007)
Now we consider the use of idea of soliton-like nuclear
georeactor to describe the KamLAND experimental an-
tineutrino spectra over the period of 2002-2007 [4]. For
this purpose let us estimate an uncertainty of nuclear
georeactor thermal power and an uncertainty of georeac-
tor antineutrino spectrum, respectively. Note that, gener-
ally speaking, such an uranium-plutonium georeactor can
consist of a few tens or hundreds of reactors (with the
total thermal power of 30 TW), which represents the in-
dividual burning “rivers” and “lakes” of an inhomoge-
neous actinide shell located in the valleys of rough sur-
face of the Earth’s solid core [17]. In the general case,
the fission rate of 239Pu nuclei for the uranium-plutonium
cycle (1) in the one-group approximation can be written
down in the form
, (4)



where φ = νn is the neutron-flux density; ν is the neutron
velocity; n is the neutron concentration; σf is the fission
cross-section for 239Pu; nPu is the 239Pu concentration; V is
the volume of burning area.
It is easy to see that due to the random character of cri-
tical and equilibrium concentrations of plutonium in an
actinoid shell and also a stochastic geometry of the “riv-
ers” and “lakes” of actinoid medium, the relative varia-
tions of neutron flux density φ, the plutonium concen-
tration n and the volume of burning areas can run up to
50% and more. Then ignoring the possible variations of
fission cross-section for plutonium, we can write down
the following relation for the relative variation of fission
rate:
12
2
22
Pu Pu
Pu Pu
0.87,
1
nV
nV






  


 

 
 




(5)
On the other hand, it is obvious that a kinetics of geo-
reactor, which operates on the boundary of the liquid and
solid phases of the Earth core at the temperature of 5000
- 6000 K and a pressure of a few hundreds of thousands
atmospheres, must necessarily take into account a heat
transfer kinetics. This is caused by the fact that under
such thermodynamics conditions between these kinetics
non-trivial feed-backs can arise, which will significantly
change the “traditional” kinetics of neutrons and nuclear
reactions. It should be noted that it seems to be the first
time that such a problem is being solved within the
framework of reactor physics. We have obtained the de-
pendence of fission cross-section
f
σ239 Pu for the 94
nuclei averaged over the neutron spectrum on the nuclear
fuel temperature T by the computational experiment with
an allowance for the moderation of neutrons and neutron
resonance absorption (Figure 3).

V. D. RUSOV ET AL. 533
Figure 3. Dependence of 239Pu fission cross-section averaged
over the neutron spectrum on fuel medium temperature for
limiting energy (3 kT) of the Fermi and Maxwell spectra.
The similar dependence for the 235U fission cross-section is
shown for comparison.
This dependence has a form of a power function1 in
the 4000 to 6000 K range (see Figure 3):
Pu ,where 2
fT

 . (6)
From Figure 3 follows that the weak variations of tem-
perature in the 4000 to 6000 K range can cause the strong
variations of fission cross-section
f
σ for
239Pu, which
can run up to 100% and more. The variations of fission
cross-section
f
σ for
239Pu will, in their turn, cause the
variations of neutron flux density φ and neutron concen-
tration n. It means that an expression for the fission rate
of 239Pu in uranium-plutonium cycle (1), which is analo-
gous to (4), will be more complicated in the multigroup
approximation.
However, in spite of the difficulties with analytical de-
termination of the plutonium fission rate variation, it is
possible to show (without loss of generality) the lower
estimation of relative variation in the case of multigroup
approximation
Pu
Pu
Pu
Pu
1
f
f





. (7)
Now let us show the uncertainty of georeactor anti-
neutrino spectrum with oscillations due to the relative
error of plutonium fission rate (5). For this purpose we
write down the theoretical form of measured total energy
spectrum

dd
ii
nEnE
 
ii
nE mE

 

in the ith energetic bin
, (8)
where
 
Pu
2
,
,
,,
4π
ip
iijip
ji
mt
N
EEEpEL
L







 
(9)



22
21
22
12
π
,1 sin2sin,
2.48 MeV
where .
eV
l
pEl L
E
LE m
m


 



(10)
Here mλ is the total number of fissions during the expo-
sure time Δt determined by the fission rate λPu;


E 
i is
the average number of detected antineutrino per fission
in the ith energetic bin; ε is the detection efficiency for
positrons in the inverse β-decay reaction; Np is the num-
ber of protons in the detector sensitive volume; Δt is the
exposure time;


,pEL is the neutrino oscillation prob-
ability at the appropriate parameters of mixing and ener-
gy E at a distance of l from the reactor; L is the oscilla-
tion length; θ21 is the mixing angle; 222 mmm 
12 21 is
the mass squared difference; (1/4πL2) is the effective
solid angle;
p


is the antineutrino-proton interaction
cross-section of inverse β-decay reaction with the corre-
sponding radiation corrections; ii is the nu-
clear fuel antineutrino energy spectrum in the ith ener-
getic bin, MeV/fission;

E  
i is the fraction of ith isotope.

Here it should be noted that, in general, normalized
antineutrino energy spectra corresponding to the different
values of reactor heat power may be considered as self-
similar. This fact simplifies the further analysis consid-
erably. At the same time, a self-similarity takes place
only for equilibrium neutrino spectra [42,43], which are
typical for stationary processes in reactor core. And vice
versa, when processes in the reactor core are nonstation-
ary, a self-similarity of equilibrium neutrino spectra is
violated. It means that if, for example, the variations of
neutron energy spectrum (and therefore the variations of
mass yields induced by the fission of 239Pu) in the reactor
core are considerable, the shapes of corresponding neu-
trino spectra are not self-similar. Therefore, the calcu-
lated (“stationary”, i.e. equilibrium) spectra and corre-
sponding experimental (nonstationary) neutrino spectra
may differ up to 10% - 15% and higher [42,43]. The non-
equilibrium effect of neutrino spectra will be considered
in detail in Section 6.
Obviously, due to the stochastic change of the nonsta-
tionary nuclear georeactor power as a consequence of the
239Pu fission cross-section
f
σ and the georeactor
neutrino spectrum shape (9) variations, the relative un-
certainty of georeactor antineutrino spectrum
1It is interesting, that such a behavior of cross-section on the medium


grn
nE
i
with oscillations in the ith energy bin (with an allowance
for Equations (6)-(9)) looks like
temperature is appropriate for the fission cross-section and capture
cross-section of 239Pu and absolutely is not appropriate for similar
cross-sections of the 235U nuclei, which have the classical dependence
of 1/υ. type.

V. D. RUSOV ET AL. 534
12
22
1
ii
i



 

Pu
Pu
grn
grn
i
n
n










, (11)
where

10%  
ii is the relative uncertainty due to
nonstationarity of georeactor neutrino spectrum shape.
Therefore the lower estimation of uncertainty of total
antineutrino spectrum with oscillations with an allow-
ance for Equation (11) and the contribution of uncer-
tainty (4.14%) of antineutrino spectrum


Jap
i
nE

from
the Japanese reactors [4] takes on the form

12
22
grn
i
n




22
,sin 2m
0.0414Jap
ii
nn

. (12)
Note that this uncertainty is the one shown in Figure 4
as a violet band.
Now we are ready to use our model of uranium-Pluto-
nium georeactor [17] for the alternative description of the
data produced in new KamLAND experiment [4]. Obvi-
ously the standard methods of obtaining consistent esti-
mates (e.g. the maximum-likelihood method) normally
used for the determination of the oscillation parameters
12 12

 [1-5] must take into account one more
reactor, or, more specifically, take into account the anti-
neutrino spectrum of georeactor with the power of 30
TW which is located at a depth of L ~ 5.2 × 106 m. How-
ever, following [17], we propose here a simple estimat-
ing approach. The results of its application show that the
hypothesis of the georeactor existence on the boundary
of liquid and solid phases of the Earth core does not con-
tradict the experimental data.
So, we proceed as in [17]; if CPT-invariance is assum-
ed, the probabilities of the ee
and ee νν

 

2
 2 n 0.437  
oscil-
lations should be equal at the same values L/E. On the
other hand, it is known that the variations of Δm2 domi-
nate over the more stable small variations of angle θ at
the spectral distortion (oscillations) of “solar” neutrino
spectrum. Therefore we can assume (on the grounds of
CPT-theorem) that the angle which is determined by the
experimental “solar” equality tan2θ12 = 0.447 [44] may
be used as the reference angle of mixing in the Kam-
LAND-experiment.
Finally, following the computational ideology of [17],
we give the results of verification of the optimal oscilla-
tion parameters (21 , 12 )
by comparing the theoretical (which takes into account
the georeactor operation) and experimental spectra of re-
actor antineutrino based on the KamLAND data over the
period of 2002-2007 (Figure 4). We compare also in
Figure 5 the χ2-profiles for our georeactor hypothesis
and KamLAND nonzero hypothesis, which does not take
into account an uncertainty of reactor antineutrino spec-
trum (see Section 6).
25
2.5 10eV
ta
m
In spite of low statistics of neutrino events (≤150
Figure 4. Prompt event energy spectrum of e candidate
events (2002-2007). The shaded background and geoneu-
trino histograms are cumulative. Statistical uncertainties
are shown for the data; the violet band on the blue histo-
gram indicates the event rate systematic uncertainty. The
georeactor power is 19.5 TW. The georeactor is at a dis-
tance of 5098 km from the KamLAND-detector (see expla-
nation in the text and Table 1).

v
Figure 5. Dependences of χ2/NDF on the mass squared dif-
ference corresponding to KamLAND-hypothesis
without georeactor (blue line, tan2θ12 = 0.56 [4]) and our
georeactor hypothesis (red line, tan2θ12 = 0.437).
2
21
Δm
events/bin), the theoretical reactor antineutrino spectrum
(which takes into account a soliton-like nuclear georeac-
tor with the power of 19.5 TW) describes with an accep-
table accuracy the experimental KamLAND-data (Figure
4) [4]. Below we pay attention to some important mo-
ments.
3.1. Peculiarities of the Low Antineutrino
Statistics Accounting
It is obvious, that a low antineutrino statistics is the rea-
son of high inhomogeneity of filling event density of an
antineutrino spectrum (which is continuous by its nature).
This inhomogeneity intensifies due to energy discretiza-
tion of spectrum (0.425 MeV in KamLAND-experiment).
As a result, the formal procedure of events integration

V. D. RUSOV ET AL. 535
within one energy bin (ΔE = 0.425 MeV) can generate
substantial deviations of the number of events (per bin)
from its true average value. To observe this effect it
would be necessary to decrease the width of energy bin
considerably or, that is the same, to decrease the width of
detector energy window. However, since it is impossible,
we will attempt to show this effect in the following way.
As follows from Figure 4, the significant disagree-
ment between the experimental and theoretical antineu-
trino spectra is observed for the 5, 7 and 9 bins. There-
fore, if the apparent condition




57
1, ,PlpElpEl p

9
,maxEl 
830,7410 km
, (13)
is imposed on oscillations of nuclear georeactor antineu-
trino spectrum, then by Equation (10) and the average
energies of bins Е5 = 2.8 MeV, Е7 = 3.7 MeV and Е9 =
4.5 MeV (see Figure 4) we can obtain a series of the
values l for distances from KamLAND-detector to the
supposed location of georeactor on the surface of Earth
solid core (Figure 6).
5365,5968,6400,6l. (14)
Now let us return to the problem of low antineutrino
statistics. Fulfillment of condition (13) for given dis-
tances (14) makes it possible to recalculate a georeactor
antineutrino spectrum (Figure 4) for these distances by
Equations (8)-(10). Proceeding from a low antineutrino
statistics (in energy bins Е5 = 2.8 MeV, Е7 = 3.7 MeV
and Е9 = 4.5 MeV), the following variants of the location
of a georeactor on the Earth solid core surface are most
acceptable: 1) a georeactor with the thermal power of
30.7 TW at 6400 km distance from KamLAND detector
(Figure 7(a)); 2) a georeactor with the thermal power of
34.7 TW at 6830 km distance from KamLAND detector
(Figure 7(b)); georeactors of equal thermal power but
Figure 6. The spatial frequency distribution P(l) of oscillat-
ing georeactor antineutrinos with energies Е5 = 2.8 MeV, Е7
= 3.7 MeV и Е9 = 4.5 MeV. Shaded area corresponds to the
continuous series of distances l from the KamLAND-de-
tector to the Earth solid core surface.
(a)
(b)
(c)
Figure 7. The theoretical antineutrino spectrum (blue histo-
gram), which takes into account the nuclear georeactor (a)
with thermal power of 30.7 TW (yellow histogram) situated
at a distance of 6400 km from the KamLAND-detector, (b)
with thermal power of 34.7 TW (yellow histogram) situated
at a distance of 6830 km from the KamLAND-detector, (c)
with general thermal power 32.6 TW (yellow histogram)
situated simultaneously at the distances of 6400 and 6830
km from the KamLAND-detector. In all figures one can see
how discrete antineutrino spectra of KamLAND-experi-
ment (blue histogram) and georeactor (yellow histogram)
mask the low statistics effect in corresponding continuous
antineutrino spectra (red and yellow oscillations).

V. D. RUSOV ET AL.
Co JMP
536
with the total power of 32.6 TW at 6400 and 6830 km
distance from KamLAND detector (Figure 7(c)).
bases of cones with a vertex in KamLAND and generat-
ing sides with lengths equal to the corresponding dis-
tances from KamLAND detector to the Earth solid core
surface (Figure 8).
These results force us to recalculate the georeactor
thermal power obtained for KamLAND data over the
period of 2002-2004 [17]. The parameters of nuclear
georeactors obtained by two calculation methods of anti-
neutrino spectra over the periods of 2002-2004 and 2002-
2007 are collected in Table 1.
3.2. Non-Stationary Nature of Soliton-Like
Nuclear Georeactor
Analyzing Table 1, we can see that within the frame-
work of modified method for calculation of antineutrino
spectrum (Figure 7), the average thermal power of geo-
reactor changes from ~50 TW (during the exposure of
749.1 days in 2005 [3], Figure 2) to ~30 TW (at total
exposure of 1890.25 days in 2008 [4]). There is no doubt
The considered peculiarities of low antineutrino statis-
tics make it possible not only to determine the possible
distances from KamLAND detector to supposed nuclear
georeactor on the Earth solid core surface (Figure 6), but
to construct the map of located on the Earth surface lines
radially conjugate to lines-circumferences formed by the
Table 1. Nuclear georeactor thermal power depending on a distance to detector and exposure time in the KamLAND and
Borexino experiments.
Period 2002-2004 2002-2007 2005-2007 2002-2009 2008-2009 2008-2009
Experiment KamLAND Borexino
Exposure, days 749.10 1890.25 1141.15 2135 244.75 537.20
Distance, km Nuclear Georeactor Power, TW
5098 30.0 19.5 12.6 17.3 4.7 -
6400 47.3 30.7 19.8 28.0 7.1 -
6830 53.4 34.7 22.4 31.6 7.7 -
6400 + 6830 50.2 32.6 21.1 29.7 7.3 -
6711 - - - - - 5.0
0 40 5060708090100110150
mW/m2
6400 km 5365 km
5968 km 6830 km
7410 km
Figure 8. Distribution of geothermal power density on the Earth [45] superposed with the conjugated “pseudoreactor” cir-
cumferences, which are generated by “georeactor” circumferences located on the perimeters of the bases of cones with a ver-
tex in KamLAND (36.43˚N and 137.31˚E) and generating sides with lengths from KamLAND-detector to the Earth solid core
urface equal to 7410 (sky blue), 6830 (orange), 6400 (green), 5968 (blue) and 5365 (pink) km. s
pyright © 2013 SciRes.

V. D. RUSOV ET AL. 537
that it is the reflection of a non-stationary nature of geo-
reactor. Taking into account that total exposure (1890.25
days) is a sum of two consecutive exposures (749.1 and
1141.15 days, respectively), in fact the change in the
average thermal power of georeactor is even more, i.e.
from ~50 TW over the first exposure to ~20 TW over the
second consecutive exposure (see Table 1).
From the physical standpoint, the decrease of geore-
actor thermal power (during the two successive expo-
sures) almost by a factor of two means that the variances
of fission cross-section
f
σ for the 94 nuclei
during total exposure over the period of 2002-2007 also
changed in two times, or more exactly, went almost 100%
down. It means that the variance of fission cross-section
239 Pu
f
σ for the nuclei reaches practically 100%
and this is in good agreement with our estimation of
variance of fission rate (7).
239
94 Pu
At the same time, we asserted before that the main
cause of change of fission cross-section
f
σ
239 Pu
252
7.65 10eVm  2 sin 0.304  
252
21 2.5 10eVm
 2 tan 0.437  
2
sin 0.304  

Euro
i
nE
for the
94 nuclei under extreme thermodynamics conditions
are the temperature variations of fuel medium. Therefore,
there is a natural question as to what (except the geore-
actor) is the reason of the fuel temperature variations, or
more exactly, what is the physical nature of independent
source of the fuel temperature variations, which in the
end plays the role of external modulator of nuclear geo-
reactor thermal power. The answer to this very important
question related to finding out the physical reasons of non-
stationary nature of soliton-like nuclear georeactor will
be given in the second part of the present paper [46].
Briefly summarizing the results of this section, we can
say that in spite of the low statistics of neutrino events
(≤150 events/bin), the theoretical reactor antineutrino
spectrum (which takes into account the soliton-like nu-
clear georeactor with the power of 30 TW) describes
with acceptable accuracy the experimental KamLAND-
data [4] (see Figures 4 and 7). Here we pay attention to
some important moments. First, the average georeactor
heat power is changed from ~50 TW at the exposure time
of 749.1 days in 2005 [3] (Figure 2) to ~30 TW at total
exposure of 1890 days in 2008 [4] (Figure 3). This re-
flects the nonstationary nature of the georeactor.
4. The Borexino and KamLAND
Experiments and Triangulation of
Soliton-Like Nuclear Georeactors
Location
As is generally known, the first stage of Borexino experi-
ment (Laboratory Nationali del Gran Sasso, Italy) [47]
was recently completed, ideology of neutrino measure-
ments in which is practically analogical to that of the
neutrino measurements in KamLAND experiment. It means
that the joint use of the Borexino and KamLAND data
opens up non-trivial possibility for the solving of very
important problem of spatial identification of nuclear
georeactor location on the Earth solid core surface, or in
other words, the triangulation of the soliton-like nuclear
georeactor location on the boundary of the liquid and
solid phases of the Earth core.
4.1. Borexino Antineutrino Spectrum (Exposure
over the Period of 2008-2009)
We give here the alternative analysis of the Borexino
data collected between December 2007 and December
2009, corresponding to 537.2 days of live time [46]. The
fiducial exposure after all selection cuts is 252.6 ton·yr.
The determination of the expected neutrino signal from
reactors, which, as usual, was calculated by Equation (8),
required the collection of the detailed information on the
time profiles of power and nuclear fuel composition for
nearby reactors. In Equation (8) the main contribution
comes from 194 reactors in Europe, while other 245 re-
actors around the world contribute only 2.5% of the total
reactor signal. Information on the nominal thermal power
and monthly load factor for each European reactor origi-
nate from IAEA and EDF [47].
It is important to note that to describe the antineutrino
spectra in the Borexino experiment, the parameters of
mixing (21 , 12 [48])
based on the global three-flavour analysis of solar (SNO)
and reactor (KamLAND) experimental data were used.
At the same time, for the alternative description of the
Borexino data (Figure 9) we use the parameters of mix-
ing , 12, or in other
words, 12 obtained by our model, which
takes into account the existence of natural nuclear reactor
on the boundary of the liquid and solid phases of the Earth
core [17].
It is obvious, that in spite of very low statistics of neu-
trino (reactor) events (1 - 2 events/bin), the theoretical
reactor antineutrino spectrum (which takes into account a
soliton-like nuclear georeactor with the power of 5 TW)
describes with an acceptable accuracy the experimental
Borexino data (Figure 9) [47]. Note that the lower esti-
mation of uncertainty of total antineutrino spectrum with
oscillations (which is headlined in violet colour in Fig-
ure 9) was calculated by Equation (12) at the uncertainty
of antineutrino spectrum from European reac-
tors equal to 5.38% [47].
4.2. Peculiarities of the Low Antineutrino
Statistics Accounting
As follows from Figure 9, the considerable disagreement
between the experimental and theoretical antineutrino
spectra is observed for 5, 6, 7 and 11 bins. Therefore, if
the apparent condition

V. D. RUSOV ET AL. 538
Figure 9. The e
v energy spectra in Borexino [47]. Experi-
mental points (solid black dots with error bars) together
with the total expectation obtained in Borexino experiment
(red solid histogram) [3] and in the present paper (blue
solid histogram). Also shown are the expected neutrino
spectrum from European reactors calculated using our
parameters of mixing (blue dashed histogram) and obtained
in Borexino-experiment (red shaded area). The expected
neutrino spectrum from the georeactor of 5 TW located at a
distance of 6711 km from the Borexino-detector (green line)
is also shown (see explanation in the text).









1,PlpEl
pEl p


56
711
1,
,,max,
pEl
E l


128,7490 km
(15)
is imposed on the oscillations of nuclear georeactor anti-
neutrino spectrum, then by Equation (15) for p(E, l) and
the bin average energies Е5, Е6, Е7 and Е11 (see Figure 9)
we can obtain a series of the values l for possible distances
from Borexino-detector to the supposed location of geo-
reactor on the surface of Earth solid core (Figure 10).
5310,5400,6310,6711,7l. (16)
Returning to the problem of low antineutrino statistics,
note that the fulfillment of the condition (15) for given
distances (16) makes it possible to recalculate by Equa-
tions (8)-(10) a georeactor antineutrino spectrum (Figure
9) for these distances. Proceeding from a low antineu-
trino statistics (in energy bins Е5, Е6, Е7 and Е11), the
most acceptable location of a georeactor on the Earth
solid core surface is at 6711 km distance from the Bore-
xino detector (Figure 10). It is easy to show that the ther-
mal power of such a nuclear georeactor is ~5 TW.
It is necessary to note that the restriction on the nu-
clear georeactor thermal power obtained within the frame-
work of the Borexino experiment is ~3 TW [47]. Though
this restriction is obtained within the framework of non-
zero georeactor hypothesis, it does not take into account
the high uncertainty of georeactor antineutrino spectrum.
The consequences of neglect of this uncertainty come
into a question in Section 6.
Figure 10. The spatial frequency distribution P(l) of oscil-
lating georeactor antineutrinos with energies corresponding
to 5, 6, 7 and 11 bins in Borexino-spectrum in Figure 9.
Shaded area corresponds to the continuous series of the
distances l from the Borexino-detector to the surface of the
Earth solid core.
4.3. Triangulation of the Locations of
Soliton-Like Nuclear Georeactors
By triangulation of the KamLAND and Borexino data we
have constructed the ”pseudogeoreactor” coordinate lo-
cation conjugate to the real location of soliton-like nu-
clear georeactors on the boundary of the liquid and solid
phases of the Earth core (Figure 11).
Analyzing Figures 6 and 7 and also Figure 10 (by
which it is possible to determine the most probable dis-
tances between the detector and a nuclear georector), we
have divided georeactors into two groups-operating re-
actors and probable low-power reactors (Figure 11).
Naturally, a question is the following: What is the
cause of sufficiently high degree of correlation between
“conjugate pseudoreactors” and the regions of higher
geothermal power of the Earth in Figure 11? Below we
consider physical reasons causing such a correlation.
Here it should be recalled, that according to our as-
sumption [17], nuclear georeactors are located in the thin
uranium-containing high-density layer (about 2.2 km)
[33], which is the peculiar physical boundary of the liq-
uid and solid phases of the Earth core. According to the
results of seismic tomography [33], this layer has a mo-
saic structure with typical size of ~200 km. This means
that the spatial history of nuclear burning wave, or in
other words “burning spot”, is completely determined by
the area of one patch of a mosaic structure. Since the area
on the Earth surface conjugate to the single patch of a
mosaic structure has the typical size ~1000 km, this value
is the size of the uncertainty domain for the “conjugate
burning spot” on the Earth surface.
On the other hand, we know that the time of heat
transmission from the “burning spot” to the “conjugate

V. D. RUSOV ET AL.
Copyr JMP
539
burning spot” has the order of 109 years. Taking into ac-
count the average velocity of nuclear burning wave (~1
m/year), we obtain that for 109 years the “burning spot”
will cover the total distance of 106 km on the Earth sur-
face. Since this distance easily goes into the area of one
patch of a mosaic structure in the form of a certain frac-
tal-broken curve, the domain of uncertainty of thermal
flow (on the Earth surface) coincides with the domain of
uncertainty of the “conjugate burning spot”. This coinci-
dence is indeed a reason of good correlation between
“conjugate burning spots” location and the areas of
higher geothermal power in Figure 11. In other words, a
map of geothermal power distribution on the Earth is at
the same time a rough approximation of the nuclear geo-
reactors that are acting or had been acting in the past with
their locations determined in this case with an accuracy
up to 1000 km.
It is interesting that if any considerable geothermal
heat release is absent in the places, where the nuclear
georectors location is supposed (see Figure 11), the large
so-called solitary volcanoes (hot spots), e.g. in the Cen-
tral and South-East Africa (Figure 12), or active volca-
noes, e.g. Erebus in Antarctica (Ross Sea coast), Decep-
tion (South Scotch Islands) and a recently discovered
0 405060708090100110150
mW/m2
Figure 11. Distribution of geothermal power density on the Earth [45] superposed with the conjugate “pseudogeoreactor”
ellipsoidal closed curves, which were built on basis of KamLAND (red lines) and Borexino (blue lines) experimental data.
(☆)—operating nuclear georeactors; (О) and (◦)—nuclear georeactors with a power (if they are operating) of an order of
magnitude and more less than the thermal power of reactors designated by (☆).
Figure 12. The map of spatial location of “pseudureactors”, hot spots and deep-focus earthquakes over the period of 1993-
006. The map of “pseudureactors” and earthquakes was built on basis of the plate boundaries map [50]. 2
ight © 2013 SciRes.

V. D. RUSOV ET AL. 540
nameless volcano (Hudson Mountains in the West Ant-
arctica [49]) are necessarily there.
5. Non-Stationary Soliton-Like Nuclear
Georeactor and New KamLAND
Antineutrino Spectrum (Exposure over
the Period of 2002-2009)
At the time this paper was written, another data of Kam-
LAND experiment obtained over the years of 2002-2009
were published [5]. In spite of this, we decided not to
change the structure of the paper, but to add the analysis
of these data to existing material, because such an analy-
sis is the natural illustration of inner consistency of the
considered above georeactor hypothesis.
KamLAND Antineutrino Spectrum
We give here the alternative description of KamLAND-
data [5] collected from March 9, 2002, to November 4,
2009, corresponding to 2135 days of live time. The num-
ber of target protons within the 6.0-m-radius spherical
fiducial volume is calculated to be (5.98 ± 0.12) × 1031
for the combined data set which corresponds to an expo-
sure to electron antineutrino e of 3.49 × 1032 proton-
years. The determination of the expected neutrino signal
from reactors, which was traditionally calculated by
Equation (8), required the collection of the detailed in-
formation on the time profiles of power and nuclear fuel
composition for nearby reactors. The relative fission
yields, averaged over the entire live-time period, for iso-
topes (235U:238U:239Pu:241Pu) are (0.571:0.078:0.295:
0.065), respectively. In Equation (8) the main contribu-
tion comes from 56 Japanese nuclear power reactors,
while the contributions from Korean reactors and the re-
mainder of the global nuclear power industry is estimated
to be (3.4 ± 0.3)% and (1.0 ± 0.5)% of the total reactor
signal, respectively. Information on the nominal thermal
power and monthly load factor for each Japanese reactor
originate from consortium of Japanese electric power
companies [5].
ν

It is obvious, that the theoretical reactor antineutrino
spectrum (which takes into account a soliton-like nuclear
georeactor with the power of 29.7 TW (see Table 1))
describes with an acceptable accuracy the new experi-
mental KamLAND-data (Figure 13). Let us note that the
lower estimation of uncertainty of total antineutrino spec-
trum with oscillations is calculated by Equation (12) with
an allowance for the contribution of the uncertainty 4.5%
(which corresponds to the variant DS-2 [5]) of total anti-
neutrino spectrum from the Japanese reactors.
It follows from Table 1 that the average thermal pow-
er Wt of nuclear georeactor sharply decreases in Kam-
LAND experiments corresponding to the exposures over
the periods of 2002-2004, 2002-2007 and 2002-2009
Figure 13. Prompt event energy spectrum of e candidate
events (exposure over the years of 2002-2009). The shaded
background and geoneutrino histograms are cumulative.
Statistical uncertainties are shown for the data; the violet
band on the blue histogram indicates the event rate system-
atic uncertainty in the framework of georeactor hypothesis.
The total georeactor power is 29.7 TW. Georeactors are
located at a distance of 6400 and 6830 km from the Kam-
LAND-detector (see explanation in the text and Table 1).
 v
Such a power jump indicates that the nuclear georeactor
is strongly nonstationary. It is a very important fact for
the correct calculation of reactor geoneutrinos, which in
the end are the integral part of KamLAND antineutrino
spectrum (within the framework of georeactor hypothe-
sis). To illustrate such a strong nonstationarity we give
below the change of the georeactor average thermal pow-
er over the period of 2002-2009.
Using the average values of nuclear georeactor thermal
power Wt reconstructed within the framework of geore-
actor hypothesis (Table 1), which correspond to expo-
sures over the years of 2002-2004, 2002-2007 and 2002-
2009, it is possible to determine the values Wt corre-
sponding to “latent” exposures over the years of 2005-
2007 and 2008-2009 by obvious expression
12
12
12 12
12
,
where .
tt t
tt
WWW
tt tt
tt t



(17)
The values of nuclear georeactor thermal power Wt
extended in that way with consideration of exposure over
the period of 2002-2004 (see Table 1) make it possible
to build the time evolution of the georeactor average
thermal power W over the years of 2002-2009 (Figure
14).
Thus, the sharp change of the georeactor average
thermal power W during the years of 2002-2009 must be
necessarily taken into account in the calculation of the
georeactor neutrino spectra, which are the part of the
KamLAND antineutrino spectra within the framework of
georeactor hypothesis. For that purpose, within the

V. D. RUSOV ET AL. 541
Figure 14. Evolution of reconstructed average thermal pow-
er W of nuclear georeactor over the years of 2002-2009.
framework of traditional calculations of effective neutri-
no spectra of both individual nuclides and their mixture
[42,43], it is necessary to take into account the high de-
gree of nonequilibrium of neutrino spectra due to strong
nonstationarity of nuclear georeactor power [42,43].
It is very important to note, that in the real experiment
exactly the high degree of nonequilibrium of neutrino
spectra due to the “latent” nonstationarity of radiation
source can become the reason of sharp change of the
expected “equilibrium” shape of resulting neutrino spec-
trum. In this sense, ignoring of the high degree of neu-
trino spectrum nonequilibrium or, in other words, de-
scription of experimental effective neutrino spectrum by
the equilibrium neutrino spectra of individual nuclides or
their mixture can result in serious mistakes in fitting the
experimental neutrino spectrum. Let us consider this in
more detail.
6. On Some Important Features of
Alternative Treatment Procedure of
KamLAND Experimental Data
6.1. Time Variation of the Reactor Antineutrino
Flux and Upper Limit of Georeactor Power
In the paper by KamLAND-collaboration [2], where the
results of the second exposure (551.1 days) are analyzed,
the original and very interesting method for determina-
tion of antineutrino rate suppression factor, which de-
scribes the degree of distortion of antineutrino spectrum,
is presented. For that purpose the time variations of the
reactor antineutrino flux assuming no antineutrino oscil-
lation were estimated (see Figure 15(a)).
Analysis of the linear dependence of the observed e
Figure 15. Adapted from [2]. (a) Estimated time variation of
the reactor flux assuming no antineutrino oscillation. (b)
Observed e event rate versus no-oscillation reactor e flux.
Data points correspond to intervals of approximately equal
e flux. The dotted black line is a fit [2]; the 90% C.L. is
shown in gray [2]. The solid black line is a fit constrained to
the expected background [2]. The dotted red line is a con-
tinuation of the dashed black line, the intercept of which in
this case is equal to the sum of expected background and e
flux from unknown source (for example, a georeactor). The
reactor distance distribution for e events in the absence of
oscillation is shown in the inset.
e
v
 v v
 v

v

v
main points of this method. The solid black line in the
Figure 15(b) is the linear KamLAND-fit (90% C.L.)
constrained to the expected background [2]. As analysis
of this experiment shows, the value of this expected back-
ground corresponds to the sum of background contribu-
tions from different background nuclear reactions to the
e



e
signal above 2.6 MeV and is equal to 17.8 ± 7.3
events. Here it is important to note that to obtain such a
fit, the authors of Ref. [2] use the strict assumption that
“the intercept is consistent with known background,
but substantially larger backgrounds cannot be excluded;
hence this fit does not usefully constrain speculative
sources of antineutrinos such as a nuclear reactor at the
Earth core [15] ”. In other words, being applied to the
analysis of the observed


event rate on the no-oscillation reactor e

 flux and as-
sumption that the slope can be interpreted as e

 rate
suppression factor and the intercept as the reactor-inde-
pendent constant background rate (Figure 15(b)) are the

-spectra, this assumption is

V. D. RUSOV ET AL. 542
equivalent to acceptance of the so-called zero Kam-
LAND-hypothesis, which a priori rules out the existence
of nuclear georeactor or, at least, rejects the significant
influence of an additional e

 flux from the nuclear
georeactor (even if it exists) on the observed e


e
-spectra.
In the last case, taking into account the parameters of
mixing obtained within the framework of zero Kam-
LAND-hypothesis, “the predicted KamLAND rate for
typical 3 TW georeactor scenarios is comparable to the
expected 17.8 ± 7.3 event background and would have
minimal impact on the analysis of the reactor power de-
pendence signal” [2].
On the other hand, the simple analysis of the dashed
black line in Figure 15(b) shows that the alternative, i.e.
nonzero, KamLAND-hypothesis, which recognizes the
existence of nuclear georeactor with considerable heat
power, has all the rights to exist. Note that the dotted
black line is a fit [2], the 90% C.L. is shown in gray [2]
and the dotted red line is our prolongation of the dashed
black line, the intercept of which in this case is equal to
the sum of expected background and

 flux from an
unknown source.
Below we assume that the nuclear georeactor plays the
role of unknown e


00.32n
95n
0.6pp
source. Let us estimate its heat
power W. It will be recalled that for determination of re-
actor power in neutrino experiments, according to Equa-
tions (8)-(10) and under other conditions being equal, it
is necessary to know 1) the location of georeactor, i.e. the
distance between the georeactor and detector; 2) fuel
composition and the corresponding equilibrium (or non-
equilibrium2) concentrations of fission products; 3) geo-
reactor antineutrino spectrum uncertainty; 4) the survival
probability p or the neutrino oscillation parameters. Let
us assume that for the nuclear georeactors with the heat
power W0 ~ 3 TW (the zero KamLAND-hypothesis [2]
and W (the alternative nonzero KamLAND-hypothesis)
the conditions 1) and 2) are identical. Then, taking into ac-
count that the intercepts and slopes of straight lines in Fig-
ure 15(b) corresponding to the solid black line (the zero
KamLAND-hypothesis) and the dotted red line (the alter-
native nonzero KamLAND-hypothesis) are

,

and 0, 0.10.4

, respectively, it is
easy to obtain the approximate estimation of the nuclear
georeactor heat power W within the framework of alter-
native nonzero KamLAND-hypothesis:
00 22 TW
npWpWW




.
rate shape syst
0
00
pW n

0.4p
. (18)
It is necessary to notice that the survival probability
is not characterized by the neutrino oscillation
parameters computed for the zero hypothesis any more.
In our opinion, the given example, which shows some
details of the reactor antineutrino flux variations applica-
tion, is extremely obvious and significant since it sub-
stantiates in a natural way the possibility of existence of
the two alternative (but physically equal in rights) hypo-
theses for the interpretation of experimental KamLAND-
data.
In this sense it is interesting to examine the results by
Fogli et al. [51], who analyzed the KamLAND neutrino
spectra in energy and time exactly for the second expo-
sure [2]. They acted on the premise that “while the en-
ergy spectrum KamLAND events allows the determina-
tion of the neutrino oscillation parameters, the time spec-
trum can be used to monitor known and unknown neu-
trino sources”. By using available monthly-binned data
on event-by-event energies in KamLAND and on reactor
powers in Japan, they performed a likelihood analysis of
the neutrino event spectra in energy and time, and not
only confirmed the results of KamLAND-collaboration,
but also set the upper bound on hypothetical georeactor
power in the framework of nonzero hypothesis (W ≤ 13
TW at 95% C.L.).
Here a natural question arises: “Why do we obtain the
different values of the neutrino oscillation parameters
and upper bound on hypothetical georeactor power in
comparison with Fogli et al. analyzing the same Kam-
LAND-experiment within the framework of the same
nonzero hypothesis?” Obviously it has nothing to do with
the likelihood analysis ideology, which is clearly stated
in the paper by Folgi [51] in detail, but rather is a cones-
quence of the completely different understanding of the
hypothetical nuclear georeactor physical properties, some
of which are discussed above (see derivation of Equation
(12)). Let us demonstrate this.
In general, the KamLAND unbinned likelihood func-
tion can be written as [1,2,51,52]

LLLL (19)
where the three factors embed information on the total
event rate, on the spectrum shape and on the systematic
uncertainties.
According to [51], we remain the second and third
likelihood factors in Equation (19) unchanged and con-
sider only the first likelihood factor, which can be written
as (see also [1,2,51,52]):

2
22
12
1
2π
,sin; ,,
1
exp 2
rate
rate
theor obs
rate
Nm N





















L
(20)
where (δm2, sin2θ12) are the mass-mixing parameters,

is the systematic energy offset,
2For the details of the calculations of nonequilibrium neutrino spectra
see below (Section 6).

 and


 are free

V. D. RUSOV ET AL. 543
(positive) parameters, Nobs is the total number of observ-
ed events and the total error is the sum of the statistical
and systematic uncertainties

2
r theor
NsN

2
0,
grn
sN 

2
rate theo
 , (21)
where s is a fraction of systematic uncertainty.
Here is the key moment which reveals the physical
distinction between our nonzero hypothesis and nonzero
hypothesis by Fogli et al. [51]. In general case, when the
additional antineutrino source (i.e. a nuclear georactor) is
taken into account within the framework of the nonzero
hypothesis, it is also necessary to take into account the
uncertainty of georeactor antineutrino spectrum. As is
shown above (see Equation (12)), this uncertainty ap-
pears due to the change of fission cross-section of 239Pu
(which is the main component of nuclear fuel) with
change of nuclear fuel temperature and, in particular,
with change of temperature near the Earth solid core sur-
face (see Figure 3). As a result, in the case of nonzero
hypothesis Equation (21) must have, according to Equa-
tion (12), the following form:

2
2
01,
ratetheortheor grn
NsNN
ss


 


(22)
where Ntheor = Njap + Ngrn, NJap is the total number of
events from Japanenese nuclear reactors, Ngrn is the total
number of events from nuclear georeactor, s0 is a contri-
bution from systematic uncertainty of the number of
georeactor antineutrino.
It is obvious that Equation (22) in contrast to Equation
(21) allows higher values of the nuclear georeactor heat
power. This, in its turn, leads to a change in survival
probability and, consequently, to a change in the neutrino
oscillation parameters. In this sense, it is clear that even a
very accurate account taken of the time variation of the
reactor antineutrino flux (for example, monthly or even
daily neutrino flux) and of another not less important
features of antineutrino spectrum does not lead to a con-
siderable change of the antineutrino survival probability
(see Figure 15(b), solid black line), if the specific un-
certainty of georeactor antineutrino spectrum is not taken
into account as well. And vice versa, taking into account
such a feature of georeactor antineutrino spectrum let us
obtain the new restrictions on the georeactor heat power
and corresponding values of the neutrino oscillation pa-
rameters (Figure 5) by likelihood analysis of the Kam-
LAND energy spectrum (Figure 4) and minimization of
corresponding χ2-function based on Equation (19).
Returning to the known KamLAND estimation of geo-
reactor heat power, we would like to cite Ref. [4]: “The
KamLAND-data, together with solar

data, set an
upper limit of 6.2 TW (90% C.L.) for a e

 reactor
source at the Earth center [15] assuming that the reactor
produced a spectrum identical to that of a slow neutron
artificial reactor”. Although it does not evidently follow
from the paper, we suppose that within the framework of
likelihood analysis of the KamLAND neutrino spectra in
energy and time the authors used the nonzero georeactor
hypothesis by adding a 57th reactor at L = 6400 km to the
56 Japanese nuclear power reactors. At the same time,
the nontrivial properties of some components of nuclear
fuel (for example, the 239Pu fission cross-section (see
Figure 3)) were not taken into account at all in this paper
as well as in all other papers by KamLAND-collabora-
tion. As is shown above, such a neglect of anomalous
behavior of the 239Pu fission cross-section at high tem-
peratures (in the 2500 to 6000 K range (Figure 3)) im-
plies, according to Equation (22), the ignoring of high
uncertainty of georeactor antineutrino spectrum, which
within the framework of maximum likelihood analysis
will immediately cause the distortion of “true” values of
reactor heat power and corresponding values of the neu-
trino oscillation parameters.
Finally it is worth mentioning that a nonstationary re-
gime of nuclear georeactor operating, caused by the
change of the 239Pu fission rate (Equation (5)) mainly due
to the strong variation of the 239Pu fission cross-section
(Equation (7)), which is a nonlinear function of medium
temperature (see Figure 3), is the main reason of high
uncertainty of georeactor antineutrino spectrum. Such a
nonstationary regime generates yet another, quite deep
and nontrivial problem, i.e. the so-called problem of non-
equilibrium neutrino spectra. Rejection of this problem
can lead to serious errors in fitting of the experimental
neutrino spectra. Below we consider this in more detail.
6.2. On the Reasons and Degree of the
Antineutrino Spectra Nonequilibrium in
KamLAND Experiments
To describe the nuclear fuel antineutrino radiation, the
nuclide equilibrium concentrations of fission-product mix-
ture and, accordingly, equilibrium antineutrino spectra
obtained for hypothetical infinite irradiation time, which
provides a secular equilibrium of all without exception
fission products, are traditionally used as a zero-order ap-
proximation.
On the other hand, it is obvious that the equilibrium
approximation is not true for the non-stationary nuclear
georeactor (Figure 14). Therefore, there is a question,
how the strategy of calculation of effective neutrino
spectra changes in this case and, in particular, how the
resulting neutrino spectrum shape changes due to taking
into account the nonequilibrium neutrino spectra instead
of equilibrium neutrino spectra, which are used for sta-
tionary nuclear reactors.
As is known, a direct summation method of β,

-

V. D. RUSOV ET AL. 544
spectra of individual nuclides [42,43] composing the fis-
sion-product mixture with regard to the specific modes of
fuel irradiation in a nuclear reactor, and proper total ef-
fective β,

-spectrum of the nuclear system k

k
j
E

k
jjj
NE 

E 
, (23)
are used as the calculation algorithm when passing from
the β-spectrum to the antineutrino spectrum. Here λj is
the decay probability of jth nuclide; Nj is the number of
nuclei of jth nuclide in the system k; j is the total
β,

-spectrum of jth nuclide normalized by the nuclear
decay:
 
,,ijij
i
EE 


E 
,ij
,
j
j
ij
i
K


. (24)
where λjNj is the activity of jth nuclide depending on irra-
diation mode (fuel initial composition, neutron flux den-
sity, fuel burn-up and other parameters influencing on
accumulation of each jth nuclide); Kj is the branching
factor for β-decay channel, i.e. the number of β-particles
per decay; ,ij is the partial β-transition spectrum
of jth nuclide;

is the β-transition intensity of jth nu-
clide.
A priori knowledge (based on calculation or experi-
mental estimation) of the initial concentration Nj(t) of jth
fissionable actinoid and the one-group integral neutron
flux density makes it possible to determine the ac-
cumulation of one or another jth fission product in the
reactor core by solving the following system of kinetic
equations3

1
11
11
d
d
p
j
j
jcjfi
ijji
i
jj
mj mcm
mj
mm
NNN N
t
NN
 




 



(25)
which describes the time change of the jth nuclide con-
centration in fission-product mixture at the initial
condition

i
Nt

0
0
j
j
NN at the time t linked with the
activity of the jth nuclide in the following way


Qt
j

; index “m” relates to precursor nucleus, m < j;

·
jj
Nt 
ij

is the independent yield of the jth nuclide due to
the fuel ith component fission averaged over the effective
neutron spectrum; λmj is the decay probability of mth nu-
clide into the jth nuclide due to β-, β+-decay, electron
capture, isomeric transition etc.; fi is the one-group
fission cross-section for the ith fissionable actinoid;

ci

is the one-group (n, γ), (n, 2n) reaction cross-sec-
tion for ith nuclide; cmj is the (n, γ), (n, 2n) reaction
cross-section for mth nucleus with jth nucleus formation.

Finding the time dependence of nuclide concentration
of fission-product mixture (see (25)) is a sufficiently la-
bor-consuming problem, and its solution depends on the
specific conditions of fuel irradiation, i.e. the time depen-
dence of neutron flux density, neutron flux spectral com-
position and also the initial composition of the fuel [42,
43]. Therefore the exact solution of the kinetic system of
Equations (25) becomes practically unachievable in the
study of fission-product build-up in nonstationary nu-
clear reactors with nonconstant or in general unknown
parameters. All said above applies in full measure to the
nonstationary nuclear georeactor, the thermal power
evolution of which is shown in Figure 14. Moreover, in
this case a situation is aggravated by the fact that the
239Pu fission cross-section (the main active component of
georeactor nuclear fuel) is a strongly nonlinear magni-
tude, which grows by the power law in the temperature
range 3000 - 5000 K (Figure 3), which is typical for the
near-surface layers of the Earth solid core.
How much is better, when the reactor is stationary. In
this case, the left-hand sides of the system of the Equa-
tions (25) can be set equal to zero, and the system itself
transforms into the system of linear algebraic equations,
the solution of which (the so-called equilibrium nuclide
concentrations of fission product mixture) does not de-
pend on initial conditions and irradiation time. The ob-
tained equilibrium nuclide concentrations of fission pro-
duct mixture make it possible (according to Equation (23)
to determine equilibrium partial and total neutrino spec-
tra, which are usually used for description of effective
neutrino spectra of stationary neutrino sources and, in
particular, stationary nuclear reactors.
Finally, returning to the analysis of concrete Kam-
LAND neutrino spectra, it is necessary to state that with-
in the framework of georeactor hypothesis an integral
fraction of reactor geoantineutrino is sufficiently great
and makes up almost the half of integral fraction of anti-
neutrinos produced by all Japanese reactors in the Kam-
LAND-experiment (see Figures 4 and 13). It means that
the non-equilibrium property inherent to the reactor geo-
neutrino spectrum is not only delegated to the Kam-
LAND experimental neutrino spectrum to a considerable
extent, but plays a dominant role in natural distortion of
this spectrum with respect to the KamLAND theoretical
neutrino spectrum, which is based on the ideology of
equilibrium neutrino spectra.
The question arises, to which degree this non-equilib-
rium influences on the effective neutrino spectrum shape
in the general case and, for example, in KamLAND-ex-
periments. As the numerous test experiments related to
the nuclear fuel irradiation under unstable conditions
3Note that the index i changes in the range 1 ≤ i ≤ p, and according to
the known Russian catalogue of radioactive nuclides total β,

-spectra
[42], the index j changes in the range 1 ≤ j ≤ 1028, i.e. the matter is a
necessity to solve the enormous system of enchained differential equa-
tions. The method of solution of the system (25) based on the deriva-
tion of recurrence relations for Nj(t) is in detail described in [53] and
realized as the AFPA program package (Accumulation of Fission
Products and Actinides) in terms of FORTRAN-IV.

V. D. RUSOV ET AL. 545
show [42,53], the non-equilibrium effect manifests itself
as the observed distortion of some pieces of the nonequi-
librium effective spectrum (with respect to an analogical
equilibrium neutrino spectrum), the location of which in
spectrum energy coordinates is completely predetermin-
ed by the time dependence of neutron flux density, neu-
tron flux spectral composition and initial composition of
the fuel [42,53].
On the other hand, the analysis of experimental Kam-
LAND-data obtained over the years 2002-2004, 2002-
2007 and 2002-2009 shows that in all considered cases
the number of recorded events in the fifth (Е5 = 2.8 MeV)
and ninth (Е9 = 4.5 MeV) energy bins of experimental
neutrino KamLAND-spectra differs substantially from
the similar data obtained by fitting or, in other words,
theoretical equilibrium neutrino KamLAND-spectra (see
Figure 1 in [4], Figure 1 in [5] and also Figures 4 and
13). At the same time, the number of recorded events in
the fifth bin is always substantially less than in the fifth
bin of theoretical neutrino KamLAND-spectrum, where-
as an opposite situation is observed for the ninth bin. It is
the so-called problem of 5 and 9 energy bins of neutrino
KamLAND-spectra, which, in our opinion, is caused not
only by detection statistics, but is mainly a manifestation
of substantial non-equilibrium of neutrino spectra. Ac-
cording to [42,43], the amount of non-equilibrium effect,
i.e. the difference between calculated equilibrium neu-
trino spectra and corresponding experimental non-equi-
librium neutrino spectra can reach 10% - 15% and more.
At last, it is necessary to remind that in this paper all
theoretical neutrino spectra (Figures 2, 4, 9 and 13) are
built using the ideology of equilibrium spectra. Within
the framework of georeactor hypothesis such an appro-
ach is reasonable, because the possible high degree of
non-equilibrium of experimental neutrino spectra, which
manifests itself, for example, as the so-called problem of
the 5 and 9 energy bins of neutrino KamLAND-spectra,
is effectively compensated by the high, but reasoned de-
gree of uncertainty of theoretical neutrino spectra.
6.3. Geological (Magnetic) Time-Scale and Time
Evolution of the Nuclear Georeactor Power
Within the framework of the alternative hypothesis we
obtained the time evolution of the average georeactor
heat power over the period of 2002-2009 (Figure 14),
which shows that the average georeactor heat power Wt
drops sharply from 50 TW to 5 - 7 TW in KamLAND-
experiments over the periods of 2002-2004, 2005-2007
and 2008-2009. Here a natural question arises: “What
does such a dynamics reflect or what physical mecha-
nism causes such a dynamics?” In other words, is it a
manifestation of some unknown physics or a trivial con-
sequence of the “luckily guessed calculation rules
which do not represent the true nature of things” [54].
Below we try to give a simple and physically clear inter-
pretation of the possible fundamental mechanism and its
impact on the temporal dynamics of the nuclear georeac-
tor heat power.
It is known that in spite of its long history, the nature
of the energy source maintaining a convection in the
Earth liquid core or, more exactly, the mechanism of the
magneto-hydrodynamic dynamo (MHD) generating the
terrestrial magnetic field has no clear and unambiguous
physical interpretation so far [26,55]. The problem is
aggravated by fact that none of candidates for an energy
source of the geomagnetic field [55] (secular cooling due
to the heat transfer from the core to the mantle, internal
heating by radiogenic isotopes, e.g. 40K, latent heat due
to the inner core solidification, compositional buoyancy
due to the ejection of light element at the inner core sur-
face) can not in principle explain one of the most remark-
able phenomena in solar-terrestrial physics—a strong
(inverse) correlation between the temporal variations of
magnetic flux in the tachocline zone (the bottom of the
Sun convective zone) [56,57] and the Earth magnetic
field (Y-component)4 [59] (Figure 16).
At the same time, supposing that the transversal (radial)
surface area of tachocline zone, through which a magne-
tic flux propagates, is constant in the first approximation,
one can assume that magnetic flux variations describe
also the temporal variations of magnetic field in the solar
tachocline zone. Thus, Figure 16 demonstrates the mir-
ror correlation between the temporal variations of mag-
netic field in the solar tachocline zone and the Earth
magnetic field (Y-component).
To obtain such visual correlations we used the so-call-
ed moving interval averaging algorithm. The procedure
of averaging the series


n
x
in order to derive the av-
eraged (by means of the moving interval of N points)
series


N
n
x was performed using the following ex-
pression:


12
1
1,
where21 3.
N
N
ni nin
ni
xx x
N
Nk










x

(26)
4Note that the strong (inverse) correlation between the temporal varia-
tions of magnetic flux in the tachocline zone and the Earth magnetic
field (Y-component) are observed (Figure 16) only for experimental
data obtained at the observatories where the temporal variations o
f
declination (δD/δt) or the closely associated east component (δY/δt) are
directly proportional to the westward drift of magnetic features [58].
This condition is very important for understanding of physical nature o
f
indicated above correlation, since it is known that the motions of the
top layers of the Earth core are responsible for most magnetic varia-
tions and, in particular, for the westward drift of magnetic features seen
on the Earth surface on the decade time scale. Europe and Australia are
the geographical places, where this condition is fulfilled (see Figure 2
in [58]).

V. D. RUSOV ET AL.
JMP
546
Figure 16. Time evolution of the magnetic flux variations at the bottom (tachocline zone) of the solar convective zone ((black
dotted line, see Figure 17), variations of the nuclear georeactor thermal power (blue point with bars), geomagnetic field secu-
lar variations (Y-component, nT/year, red dotted line) [59] and prediction (green dotted line) [59]. All curves are smoothed by
sliding intervals in 5 and 11 years. The pink area is the prediction region.
where k is the positive integer.
The smoothed curve of the magnetic flux variations in
the solar tachocline zone, which is shown in Figure 17(c)
(black dotted line), demonstrates the result of such an
averaging of the initial curve (red fill area in Figure
17(c)) by the two sliding intervals in N = 5 and N = 11
years. Physical sense of such a double averaging consists
in the “soft” removing of the 11-year solar cycle influ-
ence and obtaining of the so-called amplitude-modulated
representation of magnetic flux variations in the solar ta-
chocline zone.
It follows from Figure 16 that the degree of averaging
effect on time sample of the variations of solar magnetic
field and the Earth magnetic field (Y-component) sharply
differs in the degree of their smoothing. In our opinion,
this is caused by a considerable delay (10 - 12 years) of
the variations of terrestrial magnetic field (Y-component)
with respect to the solar magnetic field variations, during
which the intermediate deep terrestrial processes con-
trolled by the solar power pacemaker not only activate
and maintain the Earth magnetic field, but also smooth
out some fine “details” of the solar power pacemaker in-
fluence (Figure 17). Below we consider the physical me-
chanism of the one possible intermediate deep terrestrial
process by virtue of which a future candidate for an en-
ergy source of the Earth magnetic field must play not
only the role of a natural trigger of solar-terrestrial con-
nection, but also directly generate the solar-terrestrial
magnetic correlation on its own.
Figure 17. Time evolution of (a) geomagnetic secular varia-
tions (Y-component, nT/year) [59], (b) observed sunspot
area for cycles 12 - 23 [57], (c) integral from 0˚ - 45˚ latitude
of simulated toroidal magnetic flux in bottom shear layer
(red shadow zone) for cycles 12 - 23 [57], plus forecast for
cycle 24 [57]. Black curves are smoothed by sliding intervals
in 5 and 11 years. The green dotted line is the prediction
region.
We assume that the temporal variation of soliton-like
nuclear georeactor heat power can be a global energy
cause of such a fundamental geophysical phenomenon as
the variations of terrestrial magnetic field (Y-component).

V. D. RUSOV ET AL. 547
If it is truth, it must be the Solar magnetic field variations
that “drive” or cause the temporal variations of the nu-
clear georeactor heat power, which, according to our hy-
pothesis, is the energy source of the Earth magnetic field
and, consequently, its variations. One of possible mecha-
nisms generating strong (negative) correlation between
the terrestrial magnetic field and solar magnetic field (see
Figure 16) can be so-called axion mechanism of solar
dynamo-geodynamo connection [60].
The essence of this mechanism is that the total energy
of 57Fe-axions produced mainly in the Sun core is modu-
lated at first by the magnetic field of the solar convective
zone (due to the inverse coherent Primakoff effect [60])
and after that is resonance absorbed by 57Fe in the Earth
core. In other words, the higher the solar magnetic field,
the greater the number of axoins is converted (by the
inverse Primakoff effect) into γ-quanta, the smaller the
number of axoins reach the Earth and are absorbed in the
Earth core, and vice versa.
It results in the fact that the variations of 57Fe-axion
intensity play the role not only of heat source, which
changes the temperature of the Earth core, but also the
modulator of nuclear georeactor thermal power, because
the medium temperature in the range 2500 - 6000 K
modulates the value of the 239Pu fission cross-section
(Figure 3). In other words, the solar axions mechanism
not only explains the nature of heat source in Earth liquid
core, which plays the role of the modulator of nuclear
georeactor thermal power, but in a natural way explains
the cause of experimentally observed strong inverse cor-
relation (Figure 16) between the magnetic field of the
solar convective zone and the Earth magnetic field (Y-
component).
From Figure 16 it follows that the variation of the
Earth magnetic field (Y-component) lags behind the va-
riation of the solar magnetic field about 10 - 12 years. On
the other hand, it is known that a magnetic signal prede-
termined by an extremum of drift velocity of eccentric
dipole of the Earth core lags and therefore is detected on
the Earth surface 5 - 7 years late [61,62]. Within the
framework of georeator hypothesis this means that the
temporal variation of magnetic field energy WSE on the
Earth surface also has the delay of 5 - 7 years with re-
spect to the temporal variation of magnetic field energy
Wcore of the Earth liquid core which, in its turn, is formed
with the delay with respect to the temporal variations of
the nuclear georeactor thermal power W. At the same
time, since Wcore ~ B2, where is the magnetic induc-
tion vector, we can obtain from the obvious relation Wcore
~ W that
B
~BW. (27)
On the other hand, we have found the sampling of
values for the nuclear georeactor thermal power (Table
1), which is obtained by the experimental KamLAND
data handling over the years of 2002-2009. This sam-
pling contains three averaged values: 50.2 TW over the
years of 2002-2004, 21.1 TW over the years of 2005-
2007 and 7.3 TW over the years of 2008-2009. Due to
delay of temporal variation of the nuclear georeactor
thermal power with respect to the variation of the Earth
magnetic field (Y-component) it is obvious that to
smooth out the influence of background processes (the
variations of the Earth liquid core temperature, nuclear
fuel composition etc.) accompanying geodynamo opera-
tion, it is necessary to average the sampling of values of
the nuclear georeactor thermal power by a sliding time
interval with the length of order of a delay time, i.e. N =
5 - 7 years. It is rather easy to show that, using a maxi-
mum possible sliding interval with N = 7 transforms this
sampling composed of the 7 virtual annual values over
the years of 2002-2009 into the sampling which contains
only one term characterizing the average nuclear geore-
actor thermal power
7
430 TWW. (28)
It is obvious that this single term of new sampling
corresponds to the year 2006. If, according to the solar
axion mechanism, we assume the existence of a strong
(inverse) correlation between the variation of the Earth
magnetic field and the value W (see Equation (27))
and also take into account the delay time (5 - 7 years) of
the variation of W with respect to the variation of the
solar magnetic field, it is easy to find the coordinates of
nuclear georeactor in Figure 16. The value of W is at
the intersection of vertical line t = 2006 and the slanting
grey line passing through the extreme point (t = 2001) on
the curve of variation of the solar magnetic field. Let us
remind that the slope of the grey straight line in Figure
16 is the effect of delay under the conditions of strong
(inverse) correlation of the solar magnetic field and the
Earth magnetic field (Y-component).
Note that all the future measurements of annual varia-
tions of neutrino flux in the KamLAND and Borexino
experiments will generate new theoretical data describing
the variations of nuclear georeactor thermal power. If
these variations smoothed by moving-average process
will correlate with the variations of the solar magnetic
field and variations of the Earth magnetic field (Y-com-
ponent), the georeactor hypothesis will obtain another
strong indirect confirmation.
Finally, we would like to remind that within the frame-
work of georeactor hypothesis, a forecast of the above-
mentioned fundamental geophysical processes behavior,
which have a common cause (the temporal variations of
magnetic field in the solar tachocline zone), is possible
only up to a corresponding event horizon predetermined
by delay time of the nuclear georeactor power variation

V. D. RUSOV ET AL. 548
(5 - 7 years) or magnetic Y-field of the Earth (10 - 12
years) with respect the magnetic field in the solar tacho-
cline zone. It is obvious that such a delay effect makes it
possible to predict the behavior of the Earth magnetic
field (Y-component) reliably by experimental observation
of georeactor antineutrino, the variations of which char-
acterize the variations of nuclear georeactor thermal
power.
7. Conclusions
We should note that although the nuclear georeactor hy-
pothesis we used for the interpretation of the Kam-
LAND-experiment seems to be very effective, it can be
considered only as a possible alternative variant for de-
scribing the KamLAND experimental data. Only a direct
measurements of the geoantineutrino spectrum in the
energy range >3.4 MeV in the future underground or
submarine experiments will finally resolve the problem
of the natural georeactor existence and will make it pos-
sible to determine the “true” values of reactor antineu-
trino oscillation parameters. At the same time, the solu-
tion of the direct and the inverse problems of the remote
neutrino-diagnostics for the intra-terrestrial processes
which is essential to obtain the pure geoantineutrino
spectrum and to determine a correct radial profile of the
β-sources in the Earth interior [43,63] will undoubtedly
help us solve the problem of a natural nuclear reactor
existence on the boundary of the liquid and solid phases
of the Earth core.
In the second part of this paper [46] we will consider
some properties of those fundamental geophysical phe-
nomena, which must be observed directly under terres-
trial conditions, if a georeactor hypothesis is true and the
nuclear georeactor exists.
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