The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics
Theoretical and the experimental results of studies of electrodynamics characteristics of the TWT on the basis of helical slow-wave structure (SWS) are presented. Представлені теоретичні та експериментальні результати дослідження електродинамічних характеристик ЛБХ на основі плазмонаповненої спіраль...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2008 |
| Автори: | , , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics / V.S. Antipov, I.A. Bez’yazychny, I.V. Berezhnaya, A.V. Borodkin, K.V. Galaydych, E.A. Kornilov, G.V. Sotnikov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 123-125. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859715760752951296 |
|---|---|
| author | Antipov, V.S. Bez’yazychny, I.A. Berezhnaya, I.V. Borodkin, A.V. Galaydych, K.V. Kornilov, E.A. Sotnikov, G.V. |
| author_facet | Antipov, V.S. Bez’yazychny, I.A. Berezhnaya, I.V. Borodkin, A.V. Galaydych, K.V. Kornilov, E.A. Sotnikov, G.V. |
| citation_txt | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics / V.S. Antipov, I.A. Bez’yazychny, I.V. Berezhnaya, A.V. Borodkin, K.V. Galaydych, E.A. Kornilov, G.V. Sotnikov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 123-125. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Theoretical and the experimental results of studies of electrodynamics characteristics of the TWT on the basis of helical slow-wave structure (SWS) are presented.
Представлені теоретичні та експериментальні результати дослідження електродинамічних характеристик ЛБХ на основі плазмонаповненої спіральної уповільнюючої структури.
Представлены теоретические и экспериментальные результаты исследования электродинамических характеристик ЛБВ на базе плазмонаполненной спиральной замедляющей структуры.
|
| first_indexed | 2025-12-01T08:10:05Z |
| format | Article |
| fulltext |
THE ANALYSIS OF OPERATION OF PLASMA-FILLED HELICAL TWT
TAKING INTO ACCOUNT SPATIAL HARMONICS
V.S. Antipov, I.A. Bez’yazychny, I.V. Berezhnaya,
A.V. Borodkin, K.V. Galaydych, E.A. Kornilov, G.V. Sotnikov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
Theoretical and the experimental results of studies of electrodynamics characteristics of the TWT on the basis of
helical slow-wave structure (SWS) are presented.
PASC: 52. 40.Mj
1. THEORETICAL ANALYSIS
Let's consider an amplification of multifrequency
signal in slow-wave structure which is a helix of radius a
with step of L and winding angle of θ surrounded with
metal waveguide of radius b. The helix has the form of a
tape with thickness . The inner region of a helix is
partially filled by plasma with density n
δ
p The structure is
in the strong external magnetic field Н directed along an
axis of system. The continuous annular electron bunch of
radius rb propagates inside of a plasma column.
Let's find at first eigen waves of plasmafilled helix
SWS. The dispersive equation for eigen waves can be
obtained by the method similar used at deriving of the
dispersive equation of a vacuum helix [1]. We shall note,
that the dispersive equation of plasmafilled helix in case
of full filling inner region of a helix and being in an
infinite magnetic field, it has been recently obtained by
authors of paper [2]. As a particular case, it transvers in
the equation earlier investigated by other authors. The
same authors considered a case of the helix which are
being in magnetoactive plasma and derived the dispersive
equations for noncoupled spatial harmonics [3]. In both
papers there is no numerical analysis of the dispersive
equations. For the first time the dispersive equation of the
helix which are being in magnetoactive plasma with
accounting only of zero spatial harmonic has been
received in paper [4].
The dispersive equation of the helix partially filled by
plasma with accounting of spatial harmonics of a field has
a form:
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 123
Series: Plasma Physics (14), p. 123-125.
sin( / ) 0,
/ n
n
n L D
n L
π δ
π δ
=∑ (1)
where:
2
20
2
'
2 ' 2
'
'
1 ( , )
( ) ( ) ( , )
2
( ) ( ) ( , )
2
( )( , ) ,
( )
(
n
n n n n n
n nn
n n n n n n n n n
n n n n n n n n n
n n
n n n
n n
n
n n
n
n nkD ctg ctg F a b
aa
J k d J a d F a d
J k d J b d F d b
J ak a b ctg
J b
k J k
β βθ κ θ κ κ
β βκ
πκ κ κ κ
πκ κ κ κ
κκ κ θ
κ
κ
⊥
⊥
⊥
⊥
⎛ ⎞⎛ ⎞⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜= + + ×⎟ ⎟⎜ ⎜⎟ ⎟⎟⎜⎟⎜⎜ ⎜⎟⎝ ⎠⎝ ⎠
− ⋅Ψ ⋅
× +
+ ⋅Ψ ⋅
+ Φ
Ψ = ') ( ) ( ) ( ).n n n n n n nd J d J k d J dκ κ⊥−
n nkκ β= − / 2tg L aθ π=
0n nk0β β= + ω
n
'
n
(2)
In (1),(2) the designations are
introduced: ,
,
, , , .
2 2 2
2 2 2
3( )n nk k β ε⊥ = −
0 2 /k Lπ= /k cω= 2 2
3 1 /pε ω= −
, (3) ( , ) ( ) ( ) ( ) ( )n n n nF x y J x Y y Y x J y= −
, (4) '( , ) ( ) ( ) ( ) ( )n n n nx y J x Y y Y x J yΦ = −
' ( ) /n nJ x dJ dx= ' /n nY dY d= ' ( , ) /n nd x y dxΦ ≡ Φ
1
, , . x
Results of the solutions of the dispersive equation (1),
(2) are presented on Fig.1. Plasma frequency for the
calculations is equal . The dispersive
equations plasmafilled helix with accounting only of zero
spatial harmonics were investigated in papers [5,6].
94 10 secpω π −= ⋅
Fig.1. Dispersive curves plasma filled helix structure
The account of a backward spatial harmonic has led
to occurrence of backward plasma waves. At crossing
with a helix mode and direct plasma modes with n=0 they
form the cut-up spectrum of oscillations, typical for
hybrid plasma structures [7]. Unlike other hybrid
structures dispersive curves of plasma waves are not
symmetric concerning a point . The reason is
that in helix structure there is no translation symmetry.
Therefore displaced on longitudinal wave number on
the dispersive diagram will not coincide with the
initial diagram.
0 / Lβ π=
2 / Lπ
For investigation of a nonlinear stage of interaction
of electron bunch and eigen waves of a helix slow-wave
structure we shall start with the equation for the amplitude
of a longitudinal electric field average on cross-section
and the equations of movement for particles of bunch [8].
Coupling resistance is calculated according to the
following expression:
( )n
свR
2 2( ) 120 / (2 )j
c zj j
n
R Ohm E Sβ= ∑
124
n (5)
Here nS - the Poynting flux on n-th harmonic and
2
zjE - averaged on bunch cross-section longitudinal field
of j -th mode.
Below results of numerical calculation of axial
distribution of amplitude of a longitudinal electric field
are presented at the fixed current of bunch, but at different
values of electron bunch energy. Calculations for value of
plasma frequency is carry out. Coupling
resistance was calculated in impedance approximation i.e.
when in a microwave power stream the basic spatial
harmonic n=0 is considered only. The received values of
a longitudinal electric field were compared by the similar
distributions received at amplification of a multifrequency
signal in vacuum spiral slow-wave structure. The
objective of numerical calculations was a finding of
values of electron bunch energy, at which both waves
achieve characteristic maximal values at the same value
of longitudinal coordinate (variants of the best
amplification), (at comprehensible value of efficiency on
bunch losses, i.e. 15 - 30 %), and as character of influence
of partial plasma filling on changes of signal
amplification.
9 14 10 spω π −= ⋅
0 10 20 30 40 50 60
0
200
400
600
800
1000
E z ,
V
/c
m
z, cm
f = 1.9 GHz
f = 2.28 GHz
f = 2.28 GHz
f = 1.9 GHz
Fig.2. The axial electric field amplitudes for variants of
the best amplification of two waves for plasma-filled
helix structure (solid line) and for vacuum helix
structure (dashed line); bunch energy: 15 keV (without
plasma) and 17 keV (with plasma)
In Fig. 2 the results of numerical computations of the
best amplification simultaneously two waves. The current
of electron bunch was equal 0.8 A, that corresponds to
experimental conditions. From graphs results, that two
waves with essentially differing frequencies considerably
amplify along structure. Thus there is such length of
structure where both waves have great amplitude. I.e. the
amplifier can simultaneously operate on two frequencies
if to choose up corresponding energy of electron bunch.
From Fig.2 results, that plasma fillings leads to
significant growth of amplitudes of amplified waves in
comparison with a vacuum case, and as to change of a
amplitude-frequency spectrum of a output signal. The
length of SWS on which both waves achieve the
characteristic maximum values changes also. At that time
the coupling resistance of plasma-filled spiral structure is
greater, than vacuum spiral structure for the same
frequencies of amplified waves.
2. EXPERIMENTAL RESULTS
As it’s demonstrated [9], investigations with the help of
video pulses permit to detect dispersion characteristics of
waveguide systems. The registering and processing of the
probe pulse and the pulse passed through the structure are
necessary. The measuring system operating on the time
scale performs the following principal functions: detecting
of the slow-wave structure dispersion over a wide frequency
range, processing of signals with various algorithms -
including the interpretation of the results on the frequency
scale, presentation of the experimental results in the form
convenient for the further application, and heightening of the
precision of signal measurements.
As a probe signal for measurements, the pulse formed
by the generator is applied (the duration is 1 ns). For the
measurement of the bearing signal, the conducting
segments of the coaxial lines are connected together (with
the exception of the measuring unit). The probe- and at
output pulses are registered with the oscillograph C7-19.
Then - through the videocameras - they are introduced
into the PC memory.
In Fig. 3, the input pulse 1 and the output pulse 2,
which, has transmitted over the whole of helical structure,
are depicted. As one can see, the output pulse retardation
with respect to the input pulse is 2.9 ns, and the pulse
shape is almost the same. This reveals that, in the
frequency band determined by the initial pulse, the phase
velocity variations are inessential. The output signal
amplitude decrease is conditioned by the reflection in the
helical structure input.
Fig. 3. The oscillograms of the video probe pulse 1 and
the video probe pulse 2 transmitted through structure
Fig. 4. The measured dispersion (3) in comparison with
those calculated (1,2) the system. The line (1) is
calculated at the account in dispersion equation only
single harmonics n=0, the line (2) is calculated at the
account seven harmonics n = -3 … 3
125
Applying the fast Fourier transform, one can
determine the values of the transmission coefficients in
the given frequency band. With the known frequency of
the phase shift, it’s not difficult to determine the
coefficient of slowing-down in the structure examined
and, correspondingly, the dispersion characteristic of the
helical slow-wave structure.
In Fig. 4, for the frequency band 10 − 2000 MHz, the
results of experimental investigations of the structure are
given. The data calculated by the dispersion equation (1)
are presented as well.
CONCLUSIONS
An amplification of a multifrequency signal in
plasma-filled helix SWS is investigated experimentally
and theoretically. For the first time the numerical analysis
is carried out with the accounting of coupling between
spatial harmonics of an electromagnetic field. The
spectrum of eigen frequencies of plasma-filled helix SWS
consists of the modified electromagnetic branches of the
oscillations, the modified vacuum helix oscillation mode
and spatial harmonics (forward and backward) radial
modes of plasma oscillations. In the frequency region that
is below plasma frequency all of them form a well-known
"dense" spectrum [7]. Unlike other plasma hybrid
structures the dispersion of helix plasma-filled structure
has no translation symmetry.
Plasma filling leads to an increase in phase velocity
of helix oscillation mode, and a coupling resistance.
Numerical simulation of amplification of a two-
frequency signal in plasma-filled helix SWS is carried
out. As well as in vacuum structure, in plasma-filled
structure the simultaneous amplification of two waves at
high enough efficiency is possible. At that time the output
amplitudes of gained waves in plasma-filled structure are
significantly greater.
With the application of the fast Fourier transform, the
software is elaborated for the numerical calculation of the
experimental data: it permits exactly to determine the
dispersion characteristics of helical structure.
REFERENCES
1. E.V Anisimov, N.M. Sovetov. Rasprostranenie
electromagnitnyh voln vdol’ lentoshnoy spirali//J. Tech.
Fiz. 1955, v.25, № 11, р.1965-1971(in Russian).
2. Xie Hong-Quan, Liu Pu-Kun. Dispersion equation of a
tape helix slow wave structure filled with plasma //
Acta Physica Sinica. 2006, v.55, № 7, p.3514-3518.
3. Xie Hong-Quan, Liu Pu-Kun. Dispersion equation of a
tape helix slow wave structure filled with magnetized
plasma // Acta Physica Sinica. 2006, v.55, №5, p.2397-
2402.
4. B.М. Bulgakov, V.P. Shestopalov, L.A. Shishkin,
I.P. Yakimenko. Medlennye volny v spiral’nom
volnovode s plazmoy // J. Tech. Fiz. 1960, v.30, №.7,
p.840-850 (in Russian).
5. V.A. Buts, I.K. Kovalchuk, I.N. Onishchenko,
A.P. Tolstoluzhsky. Elektrodinamika neravnovesnyh
spiral’no-plazmennyh sistem. Sh. 1 // Problems of
Atomic Science and Technology. Series “Plasma
electronics and advanced acceleration methods” (2),
2000, № 1, p.174-178.
6. S. Kobayashi, T.M. Antonsen, G.S. Nusinovich. Linear
Theory of a Plasma Loaded, Helix Type Slow Wave
Amplifier //IEEE Trans. on Plasma Science. 1998,
v.26, issue 3, p. 669-679.
7. G.V. Sotnikov. Amplification of oscillations in a
plasma coaxial transmission line // Phizika Plazmy.
2001, v.27, № 6, p. 509-518.
8. K.V. Galaydych, P.I. Markov, G.V. Sotnikov.
Amplification of a multifrequency signal in coaxial
slow-wave structure // Radiophysics and Electronics.
2006, v.11, № 3, p. 353-359 (in Russian).
9. V.S. Antipov, I.V. Berezhnaya, E.A. Kornilov.
Investigation of dispersion in the hybrid coaxial
slowing down structure with the help of videopulse
probing //Problems of Atomic Science and Technology.
Series “Plasma Physics” 3(3), 4(4). 1999, p.295-297.
Article received 30.09.08.
АНАЛИЗ РАБОТЫ ПЛАЗМОНАПОЛНЕННОЙ СПИРАЛЬНОЙ ЛБВ
С УЧЕТОМ ПРОСТРАНСТВЕННЫХ ГАРМОНИК
В.С. Антипов, И.А. Безъязычный, И.В. Бережная,
А.В. Бородкин, К.В. Галайдыч, Е.А. Корнилов, Г.В. Сотников
Представлены теоретические и экспериментальные результаты исследования электродинамических
характеристик ЛБВ на базе плазмонаполненной спиральной замедляющей структуры.
АНАЛІЗ РОБОТИ ПЛАЗМОНАПОВНЕННОЇ СПІРАЛЬНОЇ ЛБХ
З УРАХУВАННЯМ ПРОСТОРОВИХ ГАРМОНІК
В.С. Антіпов, І.А. Без’язичний, І.В. Бережна,
О.В. Бородкін, К.В. Галайдич, Є.О. Корнілов, Г.В. Сотніков
Представлено теоретичні та експериментальні результати дослідження електродинамічних характеристик
ЛБХ на основі плазмонаповненої спіральної уповільнюючої структури.
|
| id | nasplib_isofts_kiev_ua-123456789-110794 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T08:10:05Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Antipov, V.S. Bez’yazychny, I.A. Berezhnaya, I.V. Borodkin, A.V. Galaydych, K.V. Kornilov, E.A. Sotnikov, G.V. 2017-01-06T12:55:22Z 2017-01-06T12:55:22Z 2008 The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics / V.S. Antipov, I.A. Bez’yazychny, I.V. Berezhnaya, A.V. Borodkin, K.V. Galaydych, E.A. Kornilov, G.V. Sotnikov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 123-125. — Бібліогр.: 9 назв. — англ. 1562-6016 PASC: 52. 40.Mj https://nasplib.isofts.kiev.ua/handle/123456789/110794 Theoretical and the experimental results of studies of electrodynamics characteristics of the TWT on the basis of helical slow-wave structure (SWS) are presented. Представлені теоретичні та експериментальні результати дослідження електродинамічних характеристик ЛБХ на основі плазмонаповненої спіральної уповільнюючої структури. Представлены теоретические и экспериментальные результаты исследования электродинамических характеристик ЛБВ на базе плазмонаполненной спиральной замедляющей структуры. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics Аналіз роботи плазмонаповненної спіральної ЛБХ з урахуванням просторових гармонік Анализ работы плазмонаполненной спиральной ЛБВ с учетом пространственных гармоник Article published earlier |
| spellingShingle | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics Antipov, V.S. Bez’yazychny, I.A. Berezhnaya, I.V. Borodkin, A.V. Galaydych, K.V. Kornilov, E.A. Sotnikov, G.V. Plasma electronics |
| title | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics |
| title_alt | Аналіз роботи плазмонаповненної спіральної ЛБХ з урахуванням просторових гармонік Анализ работы плазмонаполненной спиральной ЛБВ с учетом пространственных гармоник |
| title_full | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics |
| title_fullStr | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics |
| title_full_unstemmed | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics |
| title_short | The analysis of operation of plasma-filled helical TWT taking into account spatial harmonics |
| title_sort | analysis of operation of plasma-filled helical twt taking into account spatial harmonics |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110794 |
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