UHF-generation in a coaxial slowing down structure filled with plasma
Microwave generation by an electron beam in a coaxial transmission line in which the inner and outer conductors are both corrugated is studied theoretically. An annular electron beam propagates in a transport channel filled entirely with plasma. The results of nonlinear modeling of amplification o...
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| Zitieren: | UHF-generation in a coaxial slowing down structure filled with plasma / P.I. Markov, V.S. Antipov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2002. — № 5. — С. 86-88. — Бібліогр.: 4 назв. — англ. |
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irk-123456789-778902015-03-09T03:02:02Z UHF-generation in a coaxial slowing down structure filled with plasma Markov, P.I. Antipov, V.S. Onishchenko, I.N. Sotnikov, G.V. Plasma electronics Microwave generation by an electron beam in a coaxial transmission line in which the inner and outer conductors are both corrugated is studied theoretically. An annular electron beam propagates in a transport channel filled entirely with plasma. The results of nonlinear modeling of amplification of eigen waves in that structure are represented. The wave saturation amplitudes for various plasma densities are found. The influence of wave damping on the output power of this amplifier is studied. It is shown that the threshold current, at which one there is no amplification in whole wide passband. 2002 Article UHF-generation in a coaxial slowing down structure filled with plasma / P.I. Markov, V.S. Antipov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2002. — № 5. — С. 86-88. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 52.59.-f http://dspace.nbuv.gov.ua/handle/123456789/77890 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Plasma electronics Plasma electronics Markov, P.I. Antipov, V.S. Onishchenko, I.N. Sotnikov, G.V. UHF-generation in a coaxial slowing down structure filled with plasma Вопросы атомной науки и техники |
| description |
Microwave generation by an electron beam in a coaxial transmission line in which the inner and outer conductors
are both corrugated is studied theoretically. An annular electron beam propagates in a transport channel filled entirely
with plasma. The results of nonlinear modeling of amplification of eigen waves in that structure are represented. The
wave saturation amplitudes for various plasma densities are found. The influence of wave damping on the output power
of this amplifier is studied. It is shown that the threshold current, at which one there is no amplification in whole wide
passband. |
| format |
Article |
| author |
Markov, P.I. Antipov, V.S. Onishchenko, I.N. Sotnikov, G.V. |
| author_facet |
Markov, P.I. Antipov, V.S. Onishchenko, I.N. Sotnikov, G.V. |
| author_sort |
Markov, P.I. |
| title |
UHF-generation in a coaxial slowing down structure filled with plasma |
| title_short |
UHF-generation in a coaxial slowing down structure filled with plasma |
| title_full |
UHF-generation in a coaxial slowing down structure filled with plasma |
| title_fullStr |
UHF-generation in a coaxial slowing down structure filled with plasma |
| title_full_unstemmed |
UHF-generation in a coaxial slowing down structure filled with plasma |
| title_sort |
uhf-generation in a coaxial slowing down structure filled with plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2002 |
| topic_facet |
Plasma electronics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/77890 |
| citation_txt |
UHF-generation in a coaxial slowing down structure filled with plasma / P.I. Markov, V.S. Antipov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2002. — № 5. — С. 86-88. — Бібліогр.: 4 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT markovpi uhfgenerationinacoaxialslowingdownstructurefilledwithplasma AT antipovvs uhfgenerationinacoaxialslowingdownstructurefilledwithplasma AT onishchenkoin uhfgenerationinacoaxialslowingdownstructurefilledwithplasma AT sotnikovgv uhfgenerationinacoaxialslowingdownstructurefilledwithplasma |
| first_indexed |
2025-07-06T02:08:09Z |
| last_indexed |
2025-07-06T02:08:09Z |
| _version_ |
1836861556837580800 |
| fulltext |
PLASMA ELECTRONICS
UHF-GENERATION IN A COAXIAL SLOWING DOWN STRUCTURE
FILLED WITH PLASMA
P. I. Markov, V. S. Antipov, I. N. Onishchenko , G. V. Sotnikov
NSC “Kharkov Institute of Physics and Technology”, 61108, Akademicheskaya 1, Kharkov,
Ukraine, phone: (0572)356623, e-mail: sotnikov@kipt.kharkov.ua
Microwave generation by an electron beam in a coaxial transmission line in which the inner and outer conductors
are both corrugated is studied theoretically. An annular electron beam propagates in a transport channel filled entirely
with plasma. The results of nonlinear modeling of amplification of eigen waves in that structure are represented. The
wave saturation amplitudes for various plasma densities are found. The influence of wave damping on the output power
of this amplifier is studied. It is shown that the threshold current, at which one there is no amplification in whole wide
passband.
PACS: 52.59.-f
1. INTRODUCTION
It is well known that a vacuum slow-wave structure
acquires hybrid properties when the beam transport chan-
nel is filled by plasma [1]. In research on hybrid plasma
structures, the first experiments were carried out with vac-
uum slow-wave structures in the form of a chain of cou-
pled cavity resonators. In such hybrid plasma structures,
generation is most efficient when the frequency of the
synchronously excited microwaves is equal to the plasma
frequency. As a result, in a waveguide with a given plas-
ma density, the spectrum of the excited microwaves is
narrow (on the order of the instability growth rate). Ko-
rnilov et al. [2] suggested that filling a vacuum structure
in which a broadband cable wave can propagate with
plasma makes it possible to increase the amplification co-
efficient, while maintaining the broadband amplification.
Investigations of the electrodynamic parameters of a
coaxial plasma-filled slow-wave transmission line have
shown that it holds promise for creating high-power plas-
ma-based microwave devices [3]. The plasma waveguide,
like the vacuum one, is characterized by a broad frequen-
cy passband. Moreover, in a plasma waveguide, the am-
plification efficiency is higher and the frequency amplifi-
cation band is broader in comparison with the vacuum
case. In the first (lower frequency) passband, the amplifi-
cation coefficient depends linearly on the plasma density.
The electron beam interacts most strongly with the T-
wave. The generation efficiency of the plasma modes cor-
responding to the eigenmodes of an annular plasma col-
umn in which the electron beam propagates is low, and
the frequency band over which the plasma modes are am-
plified is narrow. In the first passband, the wave
impedance of the slow-wave structure is only weakly de-
pendent on frequency; in a plasma-filled structure, the fre-
quency interval over which the wave impedance is con-
stant is even broader than in a vacuum structure.
In this work we represent the results of nonlinear nu-
merical modeling of a plasma-filled slow-wave structure.
2. MAIN PART
The slow-wave structure under consideration is a
coaxial transmission line in which the inner and outer
cylindrical conductors (of radii ρ and b , respectively)
are both corrugated. The transport channel with an inner
radius σ and outer radius a is filled entirely with a plas-
ma of density pn . The microwaves in the transport chan-
nel are generated by a thin annular electron beam with ra-
dius br , velocity 0v , and current bI . The period of the
structure is D and the resonators have the same width
equal to d . The nonlinear stage of the interaction be-
tween an electron beam and eigen waves of a coaxial
slow-wave transmission line was investigated by using of
standard procedure of microwave electronics [4]. The full
set of equations for nonlinear analysis is: the equation for
the averaged (over the cross section of the transport chan-
nel) amplitude E of the longitudinal electric field
ie
2
0 0 2 0
e 0 0 b c 0
0
dE 1i( i )E ( ) I R d
dz 2
π
θβ β κ β θ
π
+ − − = т
and of the equations of motion of the beam electrons
( )
3 / 22
i
2
0
e
dv( z ) e v ( z )1 Re Ee ,
dz mv( z ) c
d 1 ,
dz v( z )
θ
νθ β
−цж
= − чзз ч
и ш
цж= − чз
и ш
where 0= / , e vβ ω 0
0β is the longitudinal wavenumber of
the eigenmode of the structure without beam, ω is wave
frequency, ( )0v v z 0= = , κ is wave damping coefficient,
0
cR is the of coupling impedance. The expression for 0
cR
of coaxial transmission line is adduced in [3]. Ibidem the
dependence of coupling impedance from plasma density
is studied.
Figure 1 shows how the amplitude of the longitudinal
electric field depends on the length of the slow-wave
structure without of wave damping account ( 0κ = ). Each
of the profiles was calculated for the frequency and wave
vector corresponding to the maximum amplification coef-
ficient in the linear regime. For a plasma density
11 3
pn 1.8 10 cm−= Ч , the longitudinal electric field satu-
rates at 1.42 kV/cm , the optimum length of a hybrid
structure being 43.6 cm . For a plasma density of
11 37.2 10pn cm−= Ч , the saturation level is 1.93 kV/cm
and the optimum length of the structure is 34.8 cm For
86 Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 86-88
the vacuum case, the relevant parameters are equal to
1.3 kV/cm and 48 cm .
Fig.1. The amplitude of electric field vs. structure length.
The experimental setup parameters were taken: ,b = 5.3
,a = 4.0 = 3.5,σ ,= 1.9ρ , D = 0.7 ,d = 0.5
( );br = 3.6 cm ,bI = 5.0A bW = 35keV
In practical experimental conditions the microwave
signal fed on an entrance, damps along slowing down
structure. It is conditioned by signal reflection from inho-
mogeneity, metal walls faultiness and particles collisions.
For numerical calculations of levels of microwave power
with account of a signal damping the dependence of sig-
nal damping vs. frequency obtained experimentally was
used.
2,0 2,2 2,4 2,6 2,8 3,0 3,2
0,00
0,02
0,04
0,06
0,08
0,10
κ , cm - 1
f, GHz
Fig. 2. Damping factor of a wave amplitude κ : points
obtained experimentally and an interpolation curve, used
in calculations
In Figure 2 the experimental points and used in calcu-
lations interpolation curve of the wave amplitudes re-
counted on a decay coefficient κ are adduced. The mea-
surements of decay coefficient κ were carried out for first
passband of vacuum slow-wave structure, i.e. for the ca-
ble wave.
For convenience of comparison of numerical calcula-
tions with outcomes of experimental measurements it is
useful to joint the longitudinal electrical field amplitude
E calculated according to (1)–(2) to the power distribu-
tion along of the amplifier P measured in the experi-
ment. As a result of not complicated transformations we
shall receive following relation:
[ ] b
b
2
2
z ,0
2
S *
r ,0 ,02
z ,0
S
E dS
E( kV / cm ) cP(W ) E H dS ,
240 8
E dS
ϕπ π
й щ
к ъ
к ъ
к ъл ы=
й щ
к ъ
к ъ
к ъл ы
т
т
т
%
% %
%
where z ,0E% , r ,0E% , ,0Hϕ
% are components of an electro-
magnetic field of eigen waves of slowing down structure
without beam.
0 10 20 30 40 50 60 70 80
0
1
2
3
4
5
6
7
8
9
10
11
12
10
9
87
6
5
4
3
2
1
P,
k
W
Z, cm
0 10 20 30 40 50 60 70 80
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0 54
10
9
8
765432 1
P,
k
W
Z, cm
0 10 20 30 40 50 60 70 80
0
10
20
30
40
50
60
70
80
90
100 10987654321
ρ = 1.7cm; σ = 3.5cm; a = 4cm; b = 5.3cm; D = 0.7cm; d = 0.5cm; l = 0;
Wb = 23kV; Ib = 3A; P0 = 8W; Zmin = 56.96cm; fzmin
= 2.716 HHz
P,
W
Z, cm
Curve
number 1 2 3 4 5
Frequen-
cy f, GHz
2.81
5
2.76
6
2.71
6
2.66
7
2.61
7
Curve
number 6 7 8 9 10
Frequen-
cy f, GHz
2.56
8
2.51
9
2.46
9
2.42
0
2.37
0
Fig. 3. Distribution of microwave - power along slow-
ing down structure for beam current bI 3A= and elec-
trons energy 23keV without of wave attenuation ac-
count; ,= 1.9cmρ other parameters are same as in Fig.1
In Figs 3 and 4 are adduced the distribution of mi-
crowave power along slowing down structure for a beam
87
current bI 3A= and electrons energy 23keV without ac-
count (fig. 3) and with account (fig. 4) of wave attenua-
tion. The calculations are made for various eigen frequen-
cies of a cable mode of vacuum coaxial structure. The
value of an input power P 8W= corresponded to the
power of a driving generator used in experiment. The ver-
tical straight line demonstrates the length of slowing
down structure used in the experiment, that is equal to
38 cm . The attenuation account results in decreasing of
maximum output power in 1,5 times, and on the structure
length L 38 cm= the decreasing of output power caused
by damping is yet more. The microwave power drops
down from 0.9 kW to 0.4 kW . For more clear represen-
tation of microwave power dependence vs. a signal fre-
quency hereinafter charts are shown in three different
scales.
0 10 20 30 40 50 60 70 80
0
1
2
3
4
5
6
7
8
10
9
87
6
5
4
2
3
1
P,
k
W
Z, cm
0 10 20 30 40 50 60 70 80
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
10
9
8
5342
7
65432 1
P,
k
W
Z, cm
0 10 20 30 40 50 60 70 80
0
10
20
30
40
50
60
70
80
90
100 31098765432 1
ρ = 1.7cm; σ = 3.5cm; a = 4cm; b = 5.3cm; D = 0.7cm; d = 0.5cm; l = 0;
Wb = 23kV; Ib = 3A; P0 = 8W; Zmin = 59.84cm; fzmin
= 2.716 HHz
P,
W
Z, cm
Fig. 4. The same as on fig. 3, but with wave attenuation
account
For definition of a threshold electron beam current
necessary to obtaining the microwave signal amplifica-
tion, the similar calculations for different electron beam
currents were carried out. The input power at the same
time was fixed. The numerical analysis outcomes have
shown following. The decreasing of an electron beam cur-
rent results in narrowing of enhanced frequencies band.
Threshold current, at which one there is no amplification
in whole passband, corresponds to a case, when the maxi-
mum gain factor of an eigen wave is equal to a damping
factor. The value of beam current bI 0,5 A= is close to
this threshold current. The minimum signal amplification
is observed in a very narrow bandwidth, approximately
f 2,67 2,77 GHz= ё . At further current decreasing the
input signal of any frequency in the first pass band will
not amplify.
This work is supported by the STCU grant № 1569.
REFERENCES
[1] Ya. B. Fainberg, Yu. P. Bliokh., P. I. Markov, M. G.
Lyubarsky, I. N. Onishchenko, G.V.Sotnikov.The
electrodynamics of hybrid plasma wave-guiding sys-
tem // Dokl. Akad. Nauk Ukr. SSR, Fiz.-Mat. Tekh.
Nauki. 1990, No. 11, p.55-58(in Rusian).
[2] E. O. Kornilov, O.M.Korostelyov, O.V.Lodygin,
I. N. Onishchenko, G.V.Sotnikov. The electrodynam-
ics hybrid slowing down structures kind of diaphrag-
matic coaxial line filled with a plasma // Ukrainian
Fiz. Zh. 1995, v.40, N.4, p.312-317
[3] G. V. Sotnikov. Microwave amplification in coaxial
slow-wave plasma transmission line// Plasma Physics
Report. 2001, v.27, N.6, p.480-489.
[4] L. A. Vainshtein and V. A. Solntsev. Lectures on Mi-
crowave Electronics (Sov. Radio, Moscow, 1973).
88
UHF-GENERATION IN A COAXIAL SLOWING DOWN STRUCTURE FILLED WITH PLASMA
1. Introduction
2. Main PART
references
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