High number harmonic exitation by oscillators in periodic media and in periodic potential
The some results of theoretic and experimental investigations about excitation high number harmonics by non-relativistic oscillators are represented in this report. Were shown that in media, which has even small periodic heterogeneity of dielectric permeability or potential, non-relativistic oscilla...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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irk-123456789-1110092017-01-08T03:03:52Z High number harmonic exitation by oscillators in periodic media and in periodic potential Buts, V.A. Kornilov, E.A. Нелинейные процессы The some results of theoretic and experimental investigations about excitation high number harmonics by non-relativistic oscillators are represented in this report. Were shown that in media, which has even small periodic heterogeneity of dielectric permeability or potential, non-relativistic oscillators can radiate as relativistic particles. They can efficiency radiate high number harmonics. The theory as one particle radiation as selfconsistent nonlinear theory radiation of oscillator ensemble was created. The experimental results confirm the main results of theory. In particularly, there was exited ultraviolet radiation in experiment, when on a crystal intense ten-centimetric radiation was acting. 2003 Article High number harmonic exitation by oscillators in periodic media and in periodic potential / V.A. Buts, E.A. Kornilov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 114-118. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.35.Mw http://dspace.nbuv.gov.ua/handle/123456789/111009 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Нелинейные процессы Нелинейные процессы |
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Нелинейные процессы Нелинейные процессы Buts, V.A. Kornilov, E.A. High number harmonic exitation by oscillators in periodic media and in periodic potential Вопросы атомной науки и техники |
| description |
The some results of theoretic and experimental investigations about excitation high number harmonics by non-relativistic oscillators are represented in this report. Were shown that in media, which has even small periodic heterogeneity of dielectric permeability or potential, non-relativistic oscillators can radiate as relativistic particles. They can efficiency radiate high number harmonics. The theory as one particle radiation as selfconsistent nonlinear theory radiation of oscillator ensemble was created. The experimental results confirm the main results of theory. In particularly, there was exited ultraviolet radiation in experiment, when on a crystal intense ten-centimetric radiation was acting. |
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Article |
| author |
Buts, V.A. Kornilov, E.A. |
| author_facet |
Buts, V.A. Kornilov, E.A. |
| author_sort |
Buts, V.A. |
| title |
High number harmonic exitation by oscillators in periodic media and in periodic potential |
| title_short |
High number harmonic exitation by oscillators in periodic media and in periodic potential |
| title_full |
High number harmonic exitation by oscillators in periodic media and in periodic potential |
| title_fullStr |
High number harmonic exitation by oscillators in periodic media and in periodic potential |
| title_full_unstemmed |
High number harmonic exitation by oscillators in periodic media and in periodic potential |
| title_sort |
high number harmonic exitation by oscillators in periodic media and in periodic potential |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2003 |
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Нелинейные процессы |
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http://dspace.nbuv.gov.ua/handle/123456789/111009 |
| citation_txt |
High number harmonic exitation by oscillators in periodic media and in periodic potential / V.A. Buts, E.A. Kornilov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 114-118. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT butsva highnumberharmonicexitationbyoscillatorsinperiodicmediaandinperiodicpotential AT kornilovea highnumberharmonicexitationbyoscillatorsinperiodicmediaandinperiodicpotential |
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2025-07-08T01:30:14Z |
| last_indexed |
2025-07-08T01:30:14Z |
| _version_ |
1837040366342111232 |
| fulltext |
HIGH NUMBER HARMONIC EXITATION BY OSCILLATORS
IN PERIODIC MEDIA AND IN PERIODIC POTENTIAL
V.A. Buts, E.A. Kornilov
National Scientific Center « Kharkov Institute of Physics and Technology», 61108,
Kharkov, Ukraine, vbuts@kipt.kharkov.ua
The some results of theoretic and experimental investigations about excitation high number harmonics by non-
relativistic oscillators are represented in this report. Were shown that in media, which has even small periodic het-
erogeneity of dielectric permeability or potential, non-relativistic oscillators can radiate as relativistic particles. They
can efficiency radiate high number harmonics. The theory as one particle radiation as selfconsistent nonlinear theo-
ry radiation of oscillator ensemble was created. The experimental results confirm the main results of theory. In par-
ticularly, there was exited ultraviolet radiation in experiment, when on a crystal intense ten-centimetric radiation
was acting.
PACS: 52.35.Mw
1. INTRODUCTION
The expression for radiation capacities of charge
particles, which are moving in media with dielectric
permeability cos( )0 q rε ε κ= + ⋅ ⋅r r
along the trajecto-
ry sin( )0 0r V t r t= + Ω ⋅
rr r
was found in previous in-
vestigations [2-4]. It necessary to mark, that the radia-
tion of relativistic particles in periodic inhomogeneous
were studied by many authors ( see, for example [5-9]
and quoted literatures there). This radiation is interest-
ing because using it open new opportunity to excite
short wave radiation λ γ~ /d 2 with high efficiency.
Such opportunity arises due Doppler effect. Such radia-
tion is already used in counters of the charged particles.
Moreover, it is supposed that this radiation can be useful
as sources of intense x-ray radiation [9].
2. RADIATION OF ONE CHARGED PAR-
TICLE
Below we shall be interested only radiation of the
non-relativistic particles β < < 1. The radiation features
of such particles, as it seems to us, are bigger interest
for using this radiation as sources of the intense short
wave radiation. It is necessary to say, that non-relativis-
tic particles radiate “long wave” radiation. The wave-
length λ of such radiation is large than the period het-
erogeneity of the media d , where the radiation take
place ( )λ β~ /d .
Let’s consider oscillator, which is rest ( V0 0= ).
Let’s assume, that vectors κr and 0r
r
are parallel to z
axis (
r rκ || ||r z0 ). In this case, such expression for capaci-
ties of radiation was received in the work [2]:
2
2 2 2 42 3 2 3( ) ( ) (sin )
3 2 1 0
W e q n J m dnt c mn
π∂ β θ θ
∂
⊥
∞Ω ⋅= ∑ ∫
=
(1)
where β ⊥ =
r
c
0Ω
, m r= ⋅
r rκ 0 .
It is useful to compare this expression with expres-
sion for capacities of a oscillator radiation in homoge-
neous media (in vacuum) (see, for example, [1]):
∂
∂
β θ θ θ θ
πW
t
e
c
n J n n d
n
= ⊥∫
=
∞
∑
2 2
2 2 2
01
Ω
( cos ) sin tan . (2)
Let's formulate more significant oscillator radiation
characteristics in heterogeneous media and compare
them to the same characteristics of radiation in homoge-
neous environment.
Spectrum. In a fig. 1 is submitted the dependence of
function
2
( , ) ( )n
nG n m J m
m
=
from harmonic numbers n
at m = 1000 ( )β γ= = = −01 1005 10 5. . , q . The function
G n m( , ) determines dependence of radiation capacity of
oscillator from number of the harmonic. It is visible,
that the radiation capacity grows with growth of har-
monic number. The radiation maximum is at the har-
monic number n m~ = 1000 . It is significant, that,
as it follow from the equation (2), it is necessary to have
energy of oscillator γ > 500 in vacuum for receiving
such radiation intensity on this harmonic. Thus, the
small dielectric permeability perturbation of media (
q = −10 5 ), where radiation take place, can result in
qualitative change of the radiation spectrum of the such
oscillator. The radiation spectrum of such oscillator be-
comes similar to a radiation spectrum of relativistic os-
cillator in homogeneous media.
The directivity diagram. As it follow from equa-
tion (1), the directivity radiation diagrams of non-rela-
tivistic oscillator for all harmonics are coincide with di-
rectivity diagram of a dipole. It necessary to mark, that a
directivity diagram of a relativistic oscillator is nestles
on a oscillator trajectory for high number harmonic.
Polarization. The analyze radiation field structure
of a non-relativistic oscillator in periodic inhomoge-
neous media show, that polarization of this radiation is
not differ from the radiation polarization of a oscillator
in homogeneous media. It is useful take in mind, that
energy of the oscillator must be more than the energy of
radiated quantum ( E mv= >2 2/ ω ), when analyze
of radiation take place.
mailto:vbuts@kipt.kharkov.ua
900 950 1000 1050
0
2000
4000
6000
G( ),n m
n
Fig.1. Efficiency of oscillator radiation
on high number harmonics
Radiation in periodic potential. Below we will be
interested with radiation of oscillators in crystals. In a
crystal there is a periodicity not only in dielectric per-
meability, but also periodicity of a crystal lattice poten-
tial. One more mechanism of radiation in this case is
possible which is very similar on described above and in
works [2-4]. We shall briefly describe this mechanism.
Let charged particle goes in external periodic in time an
electric field ( )E t E t( ) cos= ⋅ ⋅Ω and in a field of
periodic in space potential. ( )U U g z= + ⋅ ⋅0 cos κ .
For simplicity we shall consider, that the movement
occurs only along an z axis. Let's consider, that of in-
tensity of these fields are small enough, so it is possible
to consider movement of a particle in these fields as
non-relativistic. Besides we shall consider that
E g> > ⋅ κ . In this case it is possible to present func-
tion, which describes displacement of a particle along
an z axis, as the following line:
( )
( )
( ) ( ) 2 1
2 12
0
( ) cos
( ) sin 2 1 1
2 1
j
j
j
A cz t t
B cJ A j t
j
κ∞
+
+
=
⋅= − Ω −
Ω
⋅ ⋅ + ⋅ Ω ⋅ ⋅ − Ω+ ⋅ Ω
∑
(3)
where J j2 1+ - Bessel function - ( )2 1j + - order ,
( )A eE mc≡ =/ ( )Ω β , ( )B eg mc≡ κ / Ω .
Using the formula (3), it is easy to find radiation in-
tensity of the charged particle. We are interested with
radiation of high number harmonics. For high numbers (
j > > 1) the amplitudes of the Furies component of the
line (3) quickly decrease with growth number.
The exception is addend, in which the argument of
Bessel function is equal to number of Bessel function:
( )κcA j= +2 1 Ω . Taking into account only this com-
ponent, we shall receive the formula (2) for capacity of
radiation, in which it is necessary to put
r B c J mm0
2= ⋅ ⋅ ⋅Ω ( ) / ω , ( )m j m= + = ⋅2 1 , ω Ω .
Being limited in the formula (2) by dipole approxima-
tion, we shall receive the following expression for radia-
tion capacity:
)(mJB
c
e
t
W
m
22
3
22
⋅
⋅
Ω=
∂
∂
= e
c
eg
mc A
m J mm
2 2
3
1
2
2
2
2 2Ω
⋅
⋅ ( ) (4)
Thus, we see, that conditions for maximum radiation
in this case completely coincides with a condition of os-
cillator radiation in periodically non-uniform dielectric,
i.e. both in that and in the other case the maximum of
radiation corresponds to the same frequency. When
( ) ( )eg mc qA/ 2 2> the role of periodic potential on
radiation will be more significant.
Quantum consideration. The significant informa-
tion about radiation features of the charged particles in
periodic potential can be received at use quantum elec-
trodynamics methods. Using a perturbation method, it is
easy to receive the following expression for radiation
capacity of the charged particle:
2
,
0 0
( ) ( )sinf iP d d d W
π π
ϕ θ ω ρ ω θ= ⋅∫ ∫ ∫ h h
here
2
, ,
2 | | ( )f i f iW U Eπ δ ω= − ∆h
h
,
3 2 3
3(2 )
L n
c
ωρ
π
=
h
,
∫ ∑ ⋅+⋅⋅= + 12 2
13, N
wL
h
m
dhH Nif Ψ
λ
π
[ ] ( ) rdrkipeke ifif
rrrrrrr ⋅−⋅+ ∗∗ ∆ΨΨΨΨ exp)ˆ())(( λλ , (5)
n2 = ε -dielectric permeability of media, n − its pa-
rameter of refraction, ∆
r r r r
k k k ki f= − − λ
If particle goes in potential with weak periodic het-
erogeneity, its wave function is possible to present as:
( ), expi i m i
m
i k m rκ Ψ = Ψ + ⋅ ⋅ ∑
r r r
. ( 6)
where , ,0
m
i m igΨ ⋅ Ψ:
From (6) it is visible, that the wave function has ad-
dends, which can be identified with particles, which
speed are large than speed of a real particle. Such ad-
dends can be identified with fast virtual particles. In
themselves they do not exist. Analogy to virtual waves
in periodically non-uniform media is looked through.
Only in the latter case we were interested with slow vir-
tual waves. For a case of particles we will be interested
with fast virtual particles. Substituting wave function (6)
in the formula (5), it is possible to receive the following
expression for radiation capacity of the charged particle,
which goes in periodic potential:
2 2
2
2 2( 1) (1 )q V cP g N d
c v
ω ω
ε
= ⋅ + ⋅ −∫ . (7 )
where 2 /( )iv eω κ= ⋅ ⋅r r
when i fv v> > ;
/( )iv eω κ= ⋅r r
when i fv v: ; ie - unit vector directed
along vector ivr .
If in periodic potential goes oscillator, we receive
the formula, which coincides with the formula (4).
3. RADIATION OF THE OSCILLATOR
FLOW
At a research of the elementary mechanism of the ra-
diation of the charged oscillator, which moves in a peri-
odically inhomogeneous medium the possibility of the
radiation high number harmonics by nonrelativistic os-
cillator was shown. In order the such a radiation to be
effective the following condition must be satisfied:
, / 2od r ndβ λ π≈ ≈ , here λ is the wave length of
the radiation, d - period of a heterogeneity, r0 is the
amplitude of a oscillator displacement from a position
of an equilibrium, β = < <v c/ ,1 v - velocity of the
oscillator, n is the number of radiated harmonic. In
present section we study self-consistence process of the
excitation of electromagnetic radiation by an ensemble
of charged oscillators both analytical and numerical
methods. The dispersion equation and the increments
for excited waves are obtained. The analytical results
are confirmed by computer simulation.
Basic equations. We consider excitation of an
electromagnetic wave by an ensemble of oscillators in a
periodically inhomogeneous medium which is described
by a dielectric permeability:
1 2 cos , 1q z qε κ= + < < . (8)
Most completely process of interaction of the
charged particles with excited fields is described by
self-consistent model, which consists of Maxwell equa-
tions for fields and motion equations for particles in
these fields.
∂
∂
∂
∂
π
r
r
r
r
r r r r r r
r
B
t
c E
D
t
c H j
dp
dt
eE
e
c
v B F t
dr
dt
v
= − = −
= + × + =
rot , rot
sin ,
4
0 Ω
. (9)
where
r r
D E= ⋅ε , Ω − oscillation frequency of oscilla-
tors, F0 - amplitude of a force which acts on oscillators.
Oscillations of oscillators happen along axes Z.
At a research of the elementary mechanism of a radi-
ation of an oscillator in a periodically inhomogeneous
medium was shown that the radiation of an oscillator is
mainly directed across its motion. Therefore we shall
search for a solution for the raised wave asr r
E A t z ikx= Re ( , ) exp( ) . (10)
It is known, that in periodic inhomogeneous medi-
ums it is possible to search for a solution as expansion
on spatial harmonics of a heterogeneity, therefore we
can write (10) as
r r
E E t ikx il zl
l
= +∑Re ( ) exp( )χ . (11)
Let's study temporal evolution of an electromagnetic
field (4) with distinct from of zero by components
E E Hx z y, , . Substituting expressions for fields (4) in
the system (2) and averaging over spatial phase of per-
turbation we receive the following set of equations for
fields and oscillators:
−+= ∑
l
lx
x ilxzikx
d
dp )exp(Re ,ε
τ
),(Re , ilxzikxexhv
l
lyz +− ∑
( ) τκ
ε
τ
ΩcosexpRe
)exp(Re
0,
,
fzilixhv
ilxzikx
d
dp
l
lyx
l
lz
z
+++
++=
∑
∑
2 2, , / 1 ,x z x y
dx dzv x v p p p
d dτ τ
= = = + +r r
,,,
,
lxlz
ly ilxi
d
dh
εε
τ
− (12)
oox
b
ly
lxlxlx
dxzdxilxzixvwilxh
qq
d
d
)exp(
)2(
2
)(
2
0
2
0
2
2
,
1,1,,
−−−−=
=++
∫ ∫
+−
π π
π
εεε
τ
oox
b
ly
lzlzlz
dxzdxilxzixvwih
qq
d
d
)exp(
)2(
2
)(
2
0
2
0
2
2
,
1,1,,
−−−−=
=++
∫ ∫
+−
π π
π
εεε
τ
.
The integration on the right-hand sides of equations
for fields is over the initial values of the oscillator coor-
dinates. The set of equations (12) are written in dimen-
sionless variables:
2
20
0 2
, , ,
, , ,
4, ,
( )
b
b
pkct kr r p
mc
eE
k kc mckc
F e neHh f
mckc mckc m kc
τ
κ κ ε
πω
→ → →
Ω→ → Ω =
= = =
r
r r r
r
r
rr
where m e, - mass and charge of an electron, nb – den-
sity of oscillators.
The analysis of linearized set of equations. The
dispersion equation. Let's research the set of equations
(12) on a stability in linear approximation on fields. For
this purpose we shall present a dependence of fields
from time proportional to exp( )− i tω and shall neglect
by terms of second order of perturbation. Also we shall
consider non relativistic oscillators and we shall leave
only main wave E0 (own wave of the system) and the
wave E1 which corresponds to the first order of a
diffraction, i.e. we shall choose the field in following
form
0
1
Re exp( )
Re exp( )
E E ikx i t
E ikx i z i t
ω
κ ω
= − +
+ + −
r r
r
Fulfilling necessary transformations we receive the
system of linear algebraic equation for amplitudes of
fields. To have non-zero solution the determinant of this
system must be equal to zero. It is dispersion equation.
It is tremendous large. That is why we shall represent
this equation in most interesting case when the condi-
tions kκ > > , β < < 1 , ω ωb kc< < ≈ are satisfied. It
is natural, that the maximum increment of instability is
reached in the case when frequencies of excited waves
lie near to the resonance frequencies, therefore we can
leave in infinite sums only one resonance term
ω ≈ nΩ . The magnitude of this term depends on
Bessel function of order n. At large numbers n Bessel
function fast decreases and has maximal value only
then, when its argument is equal to its number, in this
case Bessel function has asymptotic dependence
J n nn ( ) ( )≈ − 1
3 . Therefore we assume that condition
n = µ (i.e. n cκ βΩ = ) is satisfied also. In this case
dispersion equation takes form
1 1
2 2
2
2
2
2 2
2
2− −
−
−
=
k c J
n
qb b n
ω
ω
ω
ω µ
ω
( )
( )Ω
. (13)
In Fig.2 the dispersion curves of the considered sys-
tem, obtained from the equation (13), are presented
k
ω
n Jb nΩ − ω
n Jb nΩ + ω
ω ω= +k c b
2 2 2
С
Fig.2.
In the region of intersection of branches of electro-
magnetic oscillations (point C) the dispersing equation
(13) has the complex roots. To determine them we
rewrite (13) as
( )( )( ) ( )ω ω ω ω ω ω ω ω2
0
2
1 2
2 2 2− − − = −q nΩ ; (14)
ω ω ω ω ω ω0
2 2 2
1 2= + = − = +k c n J n Jb b n b n, ,Ω Ω
.
Assuming that
ω ω δ ω ω δ ω= + = < <0 0 1, , b nJ we obtain from
(11) the following increment of instability:
Im , ,δ ω ω ω ω ω ω= = + = +
q
J k c n Jb n b b n2 0 0
2 2 2
0Ω .
(15)
Thus the self-consistent set of equations (12) has un-
stable solution with an increment (15).
The set of equations (12) were studied by numerical-
ly. The numerical results are in good agreements with
analytical ones.
4. THE SDUDING OF GENERATION HAR-
MONICS MECHANIZM IN EXPERIMENT
A.N Antonov, O.F. Kovpik and E.A. Kornilov exe-
cuted the experimental researches. First of all, the mech-
anism of harmonics excitation was investigated in a mi-
crowave range. In this series of experiments the plasma
electrons, which oscillate in a field of an external elec-
tromagnetic, were as oscillator ensemble. The artificial
lattice was as periodic inhomogeneous media. The exci-
tation of the third harmonic of a falling wave frequency
was studied in experiment. The frequency of this wave
was 2.7 Gh. As a whole, the results of the carried out
experimental researches are in the good qualitative con-
sent with the theory. The excitation of electromagnetic
wave on the third harmonic (8,1 Gh) was observed only
at simultaneous presence of plasma and lattice, shipped
in it. If the lattice left, the radiation on harmonics was
absent. If the plasma left, the radiation also was absent.
Moreover, the plasma could be deleted from a lattice on
various distances. Thus there is some critical distance
(~2mm), since which the signal on harmonics vanishes.
The polarization of radiation on character corresponds
to dipole radiation. It is in the consent with the theory.
The directivity diagram of radiation also is in the con-
sent with the theory: the intensity of radiation in a direc-
tion that is perpendicular to lattice considerably surpass-
es radiation intensity in a direction that is parallel to a
surface of a lattice.
Excitation of harmonics under acting of electro-
magnetic radiation on a crystal. If as periodic struc-
ture to use a crystal, it is possible to expect to excite op-
tical, UV and X-ray radiation in the same experimental
conditions. For check of such opportunity, the same ex-
perimental installation was slightly changed. Namely,
the resonator was as a load of a high-frequency path
(waveguide). The crystal plates of semi-conductor were
located in the resonator. The electronic multiplier fixed
the optic radiation from the resonator. The photo - mul-
tiplier with the converter (UV into optic) for registration
UV. The main result of the carried out experiments con-
sists that in all cases the radiation was observed. The
origin of this radiation is possible to explain by the
mechanism, investigated by us. As an example on Fig. 3
the characteristic results of experiments are represented.
The oscillogram of a high-frequency pulse in the res-
onator on frequency 2,7 Gh and registered radiation
from a crystal ( λ ~ 10 5− sm ) in this figure are repre-
sented. The strength of electric field was 20 kV/sm. Ex-
citation of radiation on a million harmonics thus was
observed.
5. DISCUSSION OF RESULTS AND
CONCLUSIONS
The main interest represents the results of experi-
mental researches. Therefore, we shall below discuss
these results. The results of the carried out experiments,
as a whole, are in the good agreement with our repre-
sentations about the mechanism of high numbers har-
monics radiation by non-relativistic oscillators. In many
cases there is a good enough quantitative consent of the
theory with experiment. It is necessary to note that the
results of experiments in a centimetric range are com-
plete enough for unequivocal interpretation. The charac-
teristics of radiation in this range are clear practically in
all details. As to a ultra-violet range ( λ ~ 10 5− sm ) -
situation less clear.
Fig.3. The microwave signal amplitude (the up-
per ray) and the radiation signal from the crys-
tal (the lower ray)
Unfortunately, we have no sufficient experimental
opportunities for more detailed research of this range.
Now it is not clear, what role play electrons, taking
place near to a surface of a crystal and in its volume.Not
clearly also the ratio of the contributions in radiation pe-
riodicity of potential and periodicity of dielectric perme-
ability.
Within the framework of the carried out experi-
ments, the displacement formed by an external field os-
cillation should exceed 10 104 5− of atom distances in
a crystal. In this case essential role on dynamics of elec-
trons, which are moving in volume of a crystal should
be played collisions. The collisions, certainly, will pre-
vent to coherent radiation. If the laser radiation will be
use as a wave that forming oscillators, than the neces-
sary displacement of electrons will be only some hun-
dreds atom distances. The role of collisions in this case
will be essential smaller. Besides the crystal can be
cooled. It is possible to expect, that during formation of
radiation, the crystal will not essentially heated.
Now, we don’t know other mechanisms (except for
researched by us) which could result in radiation, ob-
servable by us. Really, such radiation could be caused
by discharge. We specially create conditions, in which
the discharge is absent. Such radiation could arise as a
result of excitation any admixture centers in the semi-
conductor. However relaxation of the admixture centers
carries absolutely other character. It is necessary to no-
tice that when the conditions for existence discharge on
a surface of a crystal were created, the intensity of radi-
ation, observable by us, considerably grew. It is possible
to explain it both radiation of plasma, and that fact, that
the number of the electrons near to a surface of a crys-
tal, in these conditions, was considerably increased. Last
fact can result in essential increase of efficiency of the
radiation mechanism, considered by us. However, these
facts require the further study.
It is necessary to note that the formula (4) for radia-
tion capacity was received in the assumption, that the
field of spatially periodic potential is less than a field of
an external wave. In many cases it not so. However, as
show our preliminary investigation, and in that case,
when the return inequality is executed, the spectrum of
radiation of the charged particle will have a maximum
on the same frequency ω κ≈ v . Thus, general feature
of the radiation mechanism in periodic media and in pe-
riodic potentials is that fact that the particle during
quanta radiation can get or give a part of a pulse to peri-
odic structure. It is possible, apparently, to consider that
for electrons placed near to a crystal surface fairly to use
inequalities, which we used for derivation of the equa-
tion (4). For the electrons inside crystal the crystal field
considerably exceeds field of an external wave. The
special interest represents collective process of radia-
tion. In a centimetric range of lengths of waves we, cer-
tainly, observed collective radiation. In optical and ul-
tra-violet ranges we only hope on an opportunity of
such radiation. The available experimental results do not
give us opportunities to make any conclusion in this oc-
casion.
The authors thank Stepanov K.N., Fineberg Ya.B.
and Yakovenko V.M. for useful discussions of results.
REFERENCES
1. А.А. Sokolov, I.M. Ternov. Relativistic electron
// Moskow. Science. 1974, 392 p.
2. V.A.Buts. Extitation of the harmonics by the os-
cillators flux in periodically heterogeneous medi-
um //Intense Microwave Pulses V. 1997, San
Diego, California, v. 31158, p. 202-208.
3. V.A.Buts “Longwave” radiation of charged parti-
cles in a media with periodic inhomogeneous //
«Radiotechnic». 1997, №9, p. 9-12.
4. V.A.Buts. Shortwave radiation nonrelativistic
charged particles // Journal Tech. Phys. 1999, v.
69, № 5, p. 132-134.
5. V.L. Ginzburg, V.N.Tsitovich. Transition radia-
tion and transition scattering // Moskow, Science,
1983.
6. V.A.Buts, А.V.Schagin. Investigation of the para-
metric cherenkov radiation // Ukraine Phys. Jour-
nal. 1998, v. 43, №9, p.1172-1174.
7. V.G. Barishevskii, I.Ya. Dubovkaya. Results of a
science and engineering. Series: Beams of the
charged particles and solid body. 1992, №4.
8. V.L. Ginzburg // Progress of Phys. Science,
1996. v. 166, №10.
9. М.A. Piestrup, P.P. Finman .// IEEE Journal of
Quantum Electronics. 1983, v. QE-19, № 3.
HIGH NUMBER HARMONIC EXITATION BY OSCILLATORS
IN PERIODIC MEDIA AND IN PERIODIC POTENTIAL
V.A. Buts, E.A. Kornilov
PACS: 52.35.Mw
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