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the density of the axion field
φ
a
Lagrangian, and a summand allowing for
these fields interaction.
The density of the field Lagrangian written with regard to the electromag-
netic field interaction with the pseudoscalar boson field is written as
follows:
=
=
−
1
4
F
μν
F
μν
+
1
2
(
∂
μ
φ
a
∂
μ
φ
a
−
m
2
a
φ
2
a
)
−
1
2
gφ
a
F
μν
˜
F
μν
.
(8)
Here
F
μν
, F
μν
are electromagnetic field tensors;
˜
F
μν
= (1
/
2)
ε
μνλρ
F
λρ
;
φ
0
is the wave function of the pseudoscalar field;
g
is the corresponding
constant of the fields interaction. We will further use the unit system where
the fundamental constants
с
и
~
are equal to one.
Proceeding from (8), the equations of motion for the corresponding
fields will be written in the following form:
∂
μ
F
μν
=
g∂
μ
(
φ
a
˜
F
μν
); (
∂
μ
∂
μ
+
m
a
)
φ
a
=
gB
0
E.
(9)
The solution (8) for a pseudoscalar field
φ
a
is
φ
±
a
(
~r, t
) =
e
−
iωt
Z
d
3
r
0
1
4
π
exp(
±
i~k
a
(
~r
−
~r
0
)
|
~r
−
~r
0
|
g ~B
0
~E.
(10)
In the one-dimensional case, the decision (10) can be written as follows:
φ
+
a
(
r, t
) =
iE
0
(
gB
0
l/
2
k
a
)
F
(
q
)
e
i
(
k
a
x
−
ωt
)
.
Here
q
= (
ω
−
k
a
)
is the momentum transferred to the magnetic field;
F
(
q
) =
sin(
ql/
2)
ql/
2
,
i.e.
F
(0) = 1
.
The probability of pseudoscalar boson occurrence
N
a
as a result of
conversion
N
γ
of stimulating radiation quanta (photons) into pseudoscalar
bosons is specified by the relation
P
γ
→
a
=
N
a
N
γ
=
1
4
ω
k
a
(
gB
0
l
)
2
F
2
(
q
)
.
If
g
≈
10
−
10
GeV
−
1
,
В
= 10
Т,
l
= 1
m [4–7], then
P
γ
→
a
≈
10
−
18
.
In [9], Fabri – Perot matched interferometers were proposed to be used
for increasing the probability of conversion (Fig. 1). If the cavity
Q
factor
is
Q
≈
10
4
, the conversion process probability increases as follows:
P
γ
→
a
=
1
4
Q
π
ω
k
a
(
gB
0
l
)
2
F
2
(
q
)
≈
10
−
14
.
ISSN 1812-3368. Herald of the BMSTU. Series “Natural Sciences”. 2014. No. 6
9