About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations
The brief review of the most important results which have been gotten at study of the mechanism of the high numbers harmonics excitation by nonrelativistic oscillators, the mechanism of quantum whirligig effect and the mechanism of secondary resonances is given. These mechanisms give opportunity f...
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irk-123456789-907932016-01-05T03:02:12Z About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations Buts, V.A. Yegorov, A.M. Плазменная электроника The brief review of the most important results which have been gotten at study of the mechanism of the high numbers harmonics excitation by nonrelativistic oscillators, the mechanism of quantum whirligig effect and the mechanism of secondary resonances is given. These mechanisms give opportunity for transforming energy of low frequency oscillations to energy of high frequency oscillations. Коротко описано три фізичних механізми, що дозволяють використати низькочастотні коливання для збудження високочастотних хвиль. Цими трьома механізмами є: механізм збудження гармонік високих номерів нерелятивістськими осцилляторами, механізм квантової дзиґи й механізм вторинних резонансів. Кратко описаны три физических механизма, позволяющие использовать низкочастотные колебания для возбуждения высокочастотных волн. Этими тремя механизмами являются: механизм возбуждения гармоник высоких номеров нерелятивистскими осцилляторами, механизм квантовой юлы и механизм вторичных резонансов. 2011 Article About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations / V.A. Buts, A.M. Yegorov // Вопросы атомной науки и техники. — 2011. — № 1. — С. 74-76. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 03.65.Wj; 03.65.Yz; 41.60.-m http://dspace.nbuv.gov.ua/handle/123456789/90793 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Плазменная электроника Плазменная электроника |
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Плазменная электроника Плазменная электроника Buts, V.A. Yegorov, A.M. About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations Вопросы атомной науки и техники |
| description |
The brief review of the most important results which have been gotten at study of the mechanism of the high
numbers harmonics excitation by nonrelativistic oscillators, the mechanism of quantum whirligig effect and the
mechanism of secondary resonances is given. These mechanisms give opportunity for transforming energy of low
frequency oscillations to energy of high frequency oscillations. |
| format |
Article |
| author |
Buts, V.A. Yegorov, A.M. |
| author_facet |
Buts, V.A. Yegorov, A.M. |
| author_sort |
Buts, V.A. |
| title |
About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations |
| title_short |
About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations |
| title_full |
About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations |
| title_fullStr |
About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations |
| title_full_unstemmed |
About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations |
| title_sort |
about three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2011 |
| topic_facet |
Плазменная электроника |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/90793 |
| citation_txt |
About three mechanisms of transformation of lowfrequency energy of oscillations to the energy of highfrequency oscillations / V.A. Buts, A.M. Yegorov // Вопросы атомной науки и техники. — 2011. — № 1. — С. 74-76. — Бібліогр.: 12 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT butsva aboutthreemechanismsoftransformationoflowfrequencyenergyofoscillationstotheenergyofhighfrequencyoscillations AT yegorovam aboutthreemechanismsoftransformationoflowfrequencyenergyofoscillationstotheenergyofhighfrequencyoscillations |
| first_indexed |
2025-07-06T18:59:41Z |
| last_indexed |
2025-07-06T18:59:41Z |
| _version_ |
1836925199143927808 |
| fulltext |
PLASMA ELECTRONICS
74 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2011. № 1.
Series: Plasma Physics (17), p. 74-76.
r
ABOUT THREE MECHANISMS OF TRANSFORMATION OF LOW-
FREQUENCY ENERGY OF OSCILLATIONS TO THE ENERGY OF HIGH-
FREQUENCY OSCILLATIONS
V.A. Buts, A.M. Yegorov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: vbuts@kipt.kharkov.ua
The brief review of the most important results which have been gotten at study of the mechanism of the high
numbers harmonics excitation by nonrelativistic oscillators, the mechanism of quantum whirligig effect and the
mechanism of secondary resonances is given. These mechanisms give opportunity for transforming energy of low
frequency oscillations to energy of high frequency oscillations.
PACS: 03.65.Wj; 03.65.Yz; 41.60.-m
1. EXCITATION OF HIGH NUMBERS
HARMONICS BY NONRELATIVISTIC
OSCILLATORS
Earlier it was shown [1-5], that nonrelativistic
oscillators, which are moving in weak periodic
nonuniform medium or potential, can effectively radiate
high numbers of harmonics. At that the spectrum of
nonrelativistic oscillators radiation is similar to a
spectrum of relativistic ones. It means, that the maximum
of spectrum is in a vicinity of high numbers harmonics.
The mechanism of such radiation was found out. Has
appeared, that for radiation is responsible a slow
component (virtual wave) complex structure of a field,
which exists in periodically non-uniform medium. The
considered mechanism of radiation could be described
within the framework of classical electrodynamics.
The similar radiation takes place and at movement of
the charged particles in periodic potential [6]. However in
this case adequate theory should be the quantum theory.
Such theory was constructed. The main result of this
theory is the proof of high efficiency of harmonic
radiation by oscillators in such periodic potential:
. And for power of radiation it is
possible to get the following expression:
0( ) cos( )U r U g rκ= + ⋅ ⋅
rr
( )
2
2 3
3
0
( ) sin
4eff
dW e V ng d
dt c
πω θ θ⋅ ⋅ ⋅
= ⋅ ⋅∫ ,
where , - energy of particles before
radiation.
0/ 1effg eg E= < 0E
It is of interest to compare efficiency of the considered
radiation to efficiency of known radiation, for example
with Cherenkov radiation. The relation of this radiation
power to power of Cherenkov radiation can be estimated
by the following formula:
( ) ( ) ( )2
/ / / effHarm Cher
dW dt dW dt g β≈ ⋅ . (1)
At receiving (1) the power Cherenkov radiation we had
estimated by the formula: ( ) 2 2 2/ ~ ( ) /
Cher
dW dt e V cω⋅ ⋅ , it
means that we took Cherenkov radiation in frequency interval
~ω ωΔ and ( )1 / ~ 1c V εμ− . So, the power harmonic
radiation into narrow spectral line ( ) /cω ω κ βΔ << ⋅ )
close to the power Cherenkov radiation in wide spectral range
( ~ω ωΔ ). Schematically this relation is represented in Fig. 1
Let's formulate the most essential features of the
possible schemes of the X-ray laser, if as undulator to
take periodic potential of a crystal grate of an ideal
crystal: the period such undulator is the least of what can
be realized in a nature ( );density of emitters also
is greatest of what can be realized (electron density of a
solid state). Such density of emitters allows to realize
induce process of radiation in a X-ray range.
1310 .cm−
Let's explain a small period of undulator. The periodic
potential is created by nucleuses of a crystal lattice.
Distance between nucleuses is 10-8 cm. The sizes of
nucleuses about 10-13 cm. The number of components in
Fourier decomposition of such potential with
approximately identical amplitudes will be 105. The
minimal period of these components is 10-13
( rdingly, such source potentially can
excite radiation with wavelength
13
min 10d c−< m ). Acco
( )min min min~ / ~d dλ β .
Let's briefly describe the possible schema of
realization of such X-ray laser. On a crystalline target
falls the laser radiation with such parameters:
200L nmλ = , . During a
half-cycle of laser radiation all electrons of a target in
such a field become free. During the time about 100
periods the instability develops. As a result of this
instability the coherent X-ray radiation is excited. During
this time structure of undulator (the structure of a crystal
lattice) practically does not changed.
10 19 210 / 10 /E V cm W c≥ ⇒ m
2. SECONDARY RESONANCES
To explain the mechanism of the second opportunity
of transformation of low-frequency energy into energy
high-frequency oscillations easier of all on an example of
a children's toy - rotating button on thread (Fig. 2). In this
toy the energy of low-frequency movements of our hands
is transformed to energy of fast (high-frequency) rotations
of a button. The second simple example represents two
weakly - connected linear pendulums. It is known, that
the presence of the connection between these pendulums
results that the energy of oscillation of one pendulum a bit
later completely passes in energy of oscillation of the
second pendulum. The process of an energy exchange
between pendulums is periodic, which frequency is
defined (determined) by size of connection.
75
Fig. 1. The relation of our power radiation to power
of Cherenkov radiation
Fig. 2. Children toy. Illustration of secondary
resonances
Fig. 3. Two unmutually conjugated resonators
Fig. 4. Interaction of two x-ray waves in crystal
Fig. 5. The scheme of the energetic levels.
1ω -the frequency of the stabilized perturbation
The less connection, the less this frequency. Thus,
two connected identical pendulums at presence of
connection get the low frequency in their dynamics. The
presence of this low frequency allows to organize
resonant connection of high-frequency pendulums with a
low-frequency source of energy. We have considered
various variants of such systems [7-10]. Most interesting
are two connected resonators (Fig. 3). The low-frequency
generator is included in the connection channel. It was
shown, that if connection between resonators is not
mutual, the energy of the low-frequency external
generator can be transformed to energy of high-frequency
oscillations of the resonators. Let's note, that the necessity
in unmutual connection arises only in systems with two
degree of freedom. In systems with the large number of
degrees of freedom this requirement is not obligatory.
For example, for three identical, one after another
connected linear oscillators the presence of unmutuallity
is not required. It is explained by that that the central
oscillator is connected with two oscillators but others two
are connected only with it (only with one). By the second
interesting example is an opportunity of X-ray
amplification at its distribution in crystals. At that the role
of pendulums are play two X-ray waves (falling wave
and wave a minus of the first order of diffraction), the
connection between which is carried out through a crystal
(Fig. 4).
3. THE MECHANISM OF SUPPRESSION
OF QUANTUM TRANSITIONS (QUANTUM
WHIRLIGIG)
Let’s consider quantum system, which is described by
Hamiltonian:
0 1 ( )H H H t= +
) ) )
. (2)
Second summand in the right part describes
perturbation. The wave function of system (2) satisfies
Schrödinger equation which solution we shall search as a
row of own functions of the not perturbed system:
( ) ( ) exp( )n n n
n
t A t i tψ ϕ ω= ⋅ ⋅∑ , (3)
where /n nEω = h ; 0/n ni t H En nϕ ϕ ϕ⋅∂ ∂ = = ⋅
)
h .
In simplest case it’s enough to study three-level
quantum system with two periodic
perturbations: 1 0 0 1( ) exp( ) exp( )1H t U i t U i tω ω= +
) ) )
(Fig.5).
In this case the system equations for determination of the
amplitudes iA takes the form:
0 01 1Ai A V⋅ ⋅ =&h 1 10 0 12i A V A V A⋅ ⋅ = +&h 2 21 1i A V A⋅ ⋅ =&h; ; (4) 2
Besides we shall consider the case when the matrix
elements of direct and return transitions are equal
(V V12 21= ,V10 01V= ). Let's consider also, that the matrix
elements of transitions between the first and second levels
are much more, than matrix elements of transitions
between zero and first levels (V V12 10/ 1μ≡ >> ). Let at the
initial moment of time ( 0t = ) the considered quantum
system is on first, excited level. Then, as it is easy to see,
the solution of system (4) will be functions:
( )0
1 sinA t
i
μ
μ
= ⋅
⋅
; ( )1 cosA tμ= ⋅ ; ( )2 sin .A i μ= − ⋅ t (5)
From the solution (5) follows, that the large
parameter μ , the less will be probability that the system
from the excited state will pass in nonexcited, stationary
state [11, 12]. Similarly it is possible to s how, that occur
stabilize and initially not exited states, i.e. the zero level is
stabilized too. It is necessary to say some words about
parameter μ . Physically this parameter defines the ratio
of number of quanta of low-frequency perturbation which
is responsible for transitions between the first and second
levels to number of quanta of high-frequency
Z
L ext.
L ext.
CR YS T AL F ell ing. wa ve
M inus ferst orde r
O f dif fr . w ave
76
perturbation, which determines transitions between the
first and zero levels.
The mechanism of quantum whirligig allows to create
the dense ensemble of high excited quantum systems, i.e.
allows to increase essentially the lifetime of the excited,
inverted states.
CONCLUSION
Thus, the considered three mechanisms allow to use
the low-frequency perturbations for excitation of high-
frequency radiation.
REFERENCES
1. V.A. Buts. Excitation of the harmonics by the
oscillators flux in periodically heterogeneous medium //
Intense Microwave Pulses. 31 July-1August. San-
Diego, California, 1997, v. 31158, p. 202-208.
2. V.A. Buts Short-wave radiation of nonrelativistic
charged particles. // Journal Technical Physics. 1999,
N 5, v. 69, p. 132-134.
3. А.N. Antonov, V.A. Buts, O.F. Kovpik, E.A. Kornilov,
V.G. Svichensky. Excitation of high number harmonics
by nonrelativistic oscillators // Electromagnetic Waves
and Electron Systems. 2005, № 4, v. 10, p. 39-44.
4. V.A. Buts, А.М. Egorov. Lasers with nonrelativistic
electrons // Progress in Modern Radioelectronics.
2006, N 7, p. 3-17.
5. V.A. Buts, A.M. Egorov, A.P. Tolstoluzhsky. Excitation
of harmonics by flows of the charged particles in the
magnetic field // Problems of Atomic Science and
Technology. Sеries “Plasma Physics”(15)., 2009, N 1,
p.107-109.
6. V.A. Buts. Quantum theory of radiation by
nonrelativistic oscillators in periodic potential //
Electromagnetic Waves and Electron Systems. 2009,
N 9, v. 14, p. 73-80.
7. V.A. Buts. The Dynamics of the Systems at secondary
resonances with low-frequency perturbation // 6-th
Intergovernmental Seminar «Plasma Electronics and
NEW Methods of Acceleration». Problems Of Atomic
Science and Technology. 2000, N 1(2). P. 209-211.
8. V.A. Buts. Peculiar properties of systems under
secondary resonances with an external perturbation //
Problems of Atomic Science and Technology. Special
issue dedicated to the 90-th birthday anniversary of
A.I. Akhiezer. 2001, N 6, p. 329-333.
9. V.A. Buts. The Dynamics of the Systems at secondary
resonances with low-frequency perturbation //
Electromagnetic Waves and Electron Systems. 2004,
N 1, v. 9, p. 59-68.
10. V.A. Buts. Using Secondary Resonances for
Amplification 0f Short-Wave Radiation // 8th
International Conference on Transparent Optical
Networks. Nottingham, United Kingdom, June 18-22,
2006, ICTON, p. 193-196.
11. V.A. Buts. Modification of the Quantum Zeno’s
Effect – Quantum Whirligig // Electromagnetic Waves
and Electron Systems. 2010, N 1, v. 15, p. 58-65.
12. V.A. Buts. Stabilization of the excited states //
Problems of Atomic Science and Technology. Sеries
“Nuclear-physical researchers”. 2010, N 3, p. 90-93.
Article received 13.09.10
О ТРЕХ МЕХАНИЗМАХ ПРЕОБРАЗОВАНИЯ ЭНЕРГИИ НИЗКОЧАСТОТНЫХ КОЛЕБАНИЙ
В ЭНЕРГИЮ ВЫСОКОЧАСТОТНЫХ КОЛЕБАНИЙ
В.А. Буц, A.M. Егоров
Кратко описаны три физических механизма, позволяющие использовать низкочастотные колебания для возбу-
ждения высокочастотных волн. Этими тремя механизмами являются: механизм возбуждения гармоник высоких
номеров нерелятивистскими осцилляторами, механизм квантовой юлы и механизм вторичных резонансов.
ПРО ТРИ МЕХАНІЗМИ ПЕРЕТВОРЕННЯ ЕНЕРГІЇ НИЗЬКОЧАСТОТНИХ КОЛИВАНЬ
В ЕНЕРГІЮ ВИСОКОЧАСТОТНИХ КОЛИВАНЬ
В.О. Буц, О.M. Єгоров
Коротко описано три фізичних механізми, що дозволяють використати низькочастотні коливання для
збудження високочастотних хвиль. Цими трьома механізмами є: механізм збудження гармонік високих номерів
нерелятивістськими осцилляторами, механізм квантової дзиґи й механізм вторинних резонансів.
|