Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border
Transition radiation of the cylindrical electron bunch moving through the border between the vacuum and isotropic plasma semi-spaces is studied. Radiation patterns’ frequency dependencies, integrated radiated power and total radiated energy are calculated. Досліджено перехідне випромінювання циліндр...
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| Date: | 2003 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Cite this: | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border / O.I. Kelnyk, V.K. Tyazhemov // Вопросы атомной науки и техники. — 2003. — № 1. — С. 118-120. — Бібліогр.: 4 назв. — англ. |
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| citation_txt | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border / O.I. Kelnyk, V.K. Tyazhemov // Вопросы атомной науки и техники. — 2003. — № 1. — С. 118-120. — Бібліогр.: 4 назв. — англ. |
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| description | Transition radiation of the cylindrical electron bunch moving through the border between the vacuum and isotropic plasma semi-spaces is studied. Radiation patterns’ frequency dependencies, integrated radiated power and total radiated energy are calculated.
Досліджено перехідне випромінювання циліндричного електронного згустку, що проходить через межу поділу вакууму та ізотропної плазми. Розраховано залежність діаграми спрямованості випромінювання від його частоти, а також інтегральну потужність та повну енергію випромінювання.
Исследовано переходное излучение цилиндрического электронного сгустка, проходящего через границу раздела вакуума и изотропной плазмы. Рассчитана зависимость диаграммы направленности излучения от его частоты, а также интегральная мощность и полная энергия излучения.
|
| first_indexed | 2025-12-07T18:33:03Z |
| format | Article |
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TRANSITION RADIATION OF THE CYLINDRICAL ELECTRON BUNCH
AT THE SHARP VACUUM-PLASMA BORDER
O.I. Kelnyk1, V.K. Tyazhemov2
Taras Shevchenko Kyiv National University, Radio Physics Faculty,
64 Volodymyrs’ka St., 01033, Kyiv, Ukraine; 1oles@univ.kiev.ua, 2jet@univ.kiev.ua
Transition radiation of the cylindrical electron bunch moving through the border between the vacuum and isotropic
plasma semi-spaces is studied. Radiation patterns’ frequency dependencies, integrated radiated power and total radiated
energy are calculated.
PACS: 52.40.Mj
1. INTRODUCTION
Electromagnetic waves radiation excited by the electron
beam that is injected into the ionospheric or magnetospheric
plasma is one of the most interesting results of the space
beam-plasma experiments [1]. In such experiments, splashes
of electromagnetic radiation with the wideband frequency
spectrum were observed at the moments of electron beam’s
fronts injection [2]. Transition radiation is one of the possible
mechanisms of this radioemission. Particularly, the fronts of
electron beam have a wideband spectrum. Due the linear
transformation of the current density waves into electromag-
netic waves on the plasma inhomogeneity, these fronts can ex-
cite the splashes of electromagnetic waves. This radiation is
characterized by the frequencies’ spatial selection effect [3]
when each frequency is radiated mostly under its own angle.
Transition radiation of the cylindrical electron bunch on the
smooth plasma concentration profile was treated in [4], but
only the time dependence of the total radiated power was cal-
culated.
2. MODEL DESCRIPTION
The sharp border between the vacuum and isotropic
plasma semi-spaces is considered. The cylindrical elec-
tron bunch with current density
( )[ ]
>+−∉
≤+−∈−
=
)1(or]
v
2/,
v
2/[if,0
and]
v
2/,
v
2/[if,exp
00
00
000
arLzLzt
arLzLztztije
j
z χω
moves normally across such border (L, a, v0, j0, ω0 -
length, radius, velocity, magnitude and frequency of elec-
tron bunch correspondingly; χ0=ω0/v0; r,φ,z – cylindrical
coordinates, z is a perpendicular to border).
3. CALCULATION OF THE RADIATED
FIELD
One can expand expression (1) for the bunch current
density in the Fourier integral for time t (frequency ω) and in
the Fourier-Bessel integral for transversal coordinate r
(transversal wavenumber χ). So the temporal and spatial
spectrum of electron bunch current density will have the ap-
pearance of
( ) ( ) ( ) ],
v
exp[
v2
sin
)(
2,,
00
01
0
0 ziLaJajzj ωωωχ
χωω
χω −
−
−
= (2)
where J1(x) – first order Bessel function. Using this ex-
pression and Maxwell equations, one can obtain the spec-
trum of the eigen electromagnetic field of electron bunch:
),,,(
))
v
1(
v
(
4
2
2
0
2
0
2
22
)( zj
c
c
iE e
z χω
εωχ
ωπ
−+
−=
(3)
where ε - plasma dielectric permittivity. Equations set for
the radiation field components is formed according with
the expression (3) and electromagnetic boundary condi-
tions. So for the radiated field one can obtain:
2112
222
)(
22112
)(
1)(
1
)()(
εαεα
γαεεγεα
+
+++−
=
e
z
e
zw
z
EEE ;
2112
2121
)(
2111
)(
1)(
2
)()(
εαεα
εαγεγαε
+
−+−
=
e
z
e
zw
z
EEE , (4)
where Ez1
(w) and Ez2
(w) – z-components of the forward and
backward radiated electromagnetic wave field corre-
spondingly, and:
;
)1(
1
22
2,1
2
2,12,1
2,1
ck
k
z
z
ωε
α
−
=
;
)v1(
v
2
2
0
2,1
0
2,1
c
εω
γ
−
=
2
2,12
2
2,1 χεω −=
c
k z (5)
4. RADIATION PATTERNS IN DEPENDENCE
ON FREQUENCY
Expressions (4-5) can be integrated by the transversal
wavenumber χ so the radiated field dependence on radiation
angle θ and frequency ω will be obtained. This integration is
performed using stationary phase method. Corresponding den-
sity plots (darker color represents larger value, lighter - small-
er) are shown on Fig.1-3.
Fig.1. Radiation patterns into vacuum as a function of
frequency
Plot on Fig.1 represents the transition radiation into vacuum.
Radiation patterns in this case are strongly different on the
frequencies above and below the Langmuir frequency of the
plasma semi-space (ωp). There is a sharp maximum in the
band above ωp that corresponds to the excitation of the bor-
118 Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 118-120
der’s quasi-eigen mode (Such a mode exists near the border,
can not propagate in one of the semi-spaces, and emanates
into another semi-space at the angle of the total reflection).
Below the ωp, radiation patterns have less sharp maximum
that is formed as a result of the interference between the
waves with different transversal wavenumbers.
Fig.2. Radiation patterns into plasma as a function of
frequency
Fig.2 shows the similar dependence for the radiation into
plasma. This radiation takes place only in the frequency band
above ωp. Radiation patterns in this case have only the inter-
ference maximum that is relatively smooth.
Fig.3. Radiation patterns into plasma in the wide
frequency band
For wider frequency band, radiation patterns into plasma are
shown on Fig.3. On high frequencies, these patterns contain the
additional maxima due the interference effects. If the width of
the bunch grows, corresponding frequencies become smaller.
The number of the interference maxima grows when the ratio of
the bunch radius to the radiated wavelength increases.
In all cases, angle of the most efficient radiation vary de-
pending on frequency due the effect of spatial selection of the
transition radiation [3].
5. TOTAL RADIATED POWER AND ENERGY
The energy flux of the transition radiation can be obtained
via the integration of the dependencies that are shown above.
This integration is performed numerically.
Form of the radiated pulse on different radiation angles for
the radiation into vacuum is shown on Fig.4. This pulse keeps
its form during the propagation. Sharp splashes on this figure
correspond to the moments when the bunch fronts move
through the border. Non-zero level of the radioemission be-
tween these splashes can be explained similarly to the radiation
of the collapsing dipole in the case of the vacuum-metal border.
Fig.5 shows the similar dependencies for the case of
the radiation into plasma. In this case the sharp splashes
that correspond the bunch fronts are also present. Contrary
the previous, these pulses are blurring during the propagation
as a result of plasma dispersion.
a
b
Fig.4. Energy flux of the integrated transitional radiation
into vacuum as a function of time and angle (distance
from border in case b is larger than in case a)
Level of the radiated power between the front splashes is
smaller in comparison with the vacuum case (at the time when
blurring is not yet sufficient) because most of the power of
collapsing dipole-type radiation lies in the spectral band below
the Langmuir frequency ωp.
a
b
Fig.5. Energy flux of the integrated transitional radiation
into plasma as a function of time and angle (distance
from border in case b is larger than in case a)
To obtain the total radiated energy, the integral of radiat-
ed power over all angles and time was calculated. Fig. 6-8
119
show the dependencies of this total energy upon the model
parameters.
The dependence of the total energy upon the bunch length
is shown on Fig.6. For the case of the radiation into vacuum
(Fig.6a) this energy grows when the length increases.
a b
Fig.6. Total radiated energy as a function of bunch length
(a – radiation into vacuum, b - into plasma)
That fact can be explained as the integral of the collapsing
dipole-type radiation between the front splashes. Contrary, for
the radiation into plasma (Fig.6b) most of the radiated power
is contained in the front pulses so average level of the radiated
energy remains almost constant. Both dependencies have non-
monotonic component that can be explained as the interfer-
ence between the radiation from bunch fronts. This effect is
more efficient for the radiation into plasma because in that
case more spectral components are superposable.
a b
c d
Fig.7. Total radiated energy into vacuum as a function of
bunch velocity
The dependence of the total energy of the transition radia-
tion into vacuum upon the bunch velocity is shown on Fig. 7.
Particularly, Fig. 7a shows this dependence in the wide band
of velocities. Total radiated energy grows when the bunch ve-
locity increases. Partial plots (Fig. 7b-d) represent this depen-
dence in more narrow bands. At the relatively small velocities
(Fig. 7b) the non-monotonic component of that dependence
has a small and short pulsations. The length and magnitude of
these pulsations increases at the average bunch velocities (Fig.
7c) because the wavelength on given frequency also increases.
In the relativistic band these pulsations become insignificant
relatively to the fast growth of average radiated energy (Fig.
7d).
a b
c d
Fig.8. Total radiated energy into plasma as a function of
bunch velocity
Similar dependencies for the case of the radiation into
plasma are shown on Fig. 8, where average radiated ener-
gy and length of pulsations also increases with velocity
growth. Pulsations’ magnitude in this case is larger in
comparison with the radiation into vacuum because the
interference between the radiation from bunch fronts is
more efficient in plasma.
6. CONCLUSIONS
The transition radiation of the electron bunch on the
sharp vacuum-plasma border has the radiation patterns
those are strongly dependent on frequency. The character
of these patterns is significantly different above and be-
low the Langmuir frequency of plasma that can be useful
for this plasma diagnostics. There is the collapsing dipole-
type radiation into vacuum between the front splashes.
The total radiated energy dependence upon the parameters
has the non-monotonic component that is related to the in-
terference between the transition radiation of bunch
fronts.
REFERENCES
1. J.R.Winckler // Rev. Geophys. And Space Phys., (18),
1980, No3, p.659-682.
2. K.I.Gringauz, N.I.Izhovkina, S.A.Pulinets, V.A.Fe-
dorov, N.M.Shjutte // Geomagnetizm i aeronomija,
(29), 1989, No4, p.659-661 (In Russian).
3. O.I.Kelnyk, V.K.Tyazhemov. // Proc. of the 1st In-
tern. Young Scientists’ Conf. on Appl. Phys. T.
Shevchenko National University, Faculty of Radio-
physics, Kyiv, 2001, p.p.36-37.
4. I.O.Anisimov, O.I.Kelnyk. // Kyiv University Bul-
letin. Physics&Mathematics. 1991, No4, p. 69-73 (in
Ukrainian).
ПЕРЕХІДНЕ ВИПРОМІНЮВАННЯ ЦИЛІНДРИЧНОГО ЕЛЕКТРОННОГО ЗГУСТКУ НА МЕЖІ
ПОДІЛУ ВАКУУМ-ПЛАЗМА
О.І. Кельник, В.К. Тяжемов
Досліджено перехідне випромінювання циліндричного електронного згустку, що проходить через межу поділу вакууму
та ізотропної плазми. Розраховано залежність діаграми спрямованості випромінювання від його частоти, а також
інтегральну потужність та повну енергію випромінювання
120
ПЕРЕХОДНОЕ ИЗЛУЧЕНИЕ ЦИЛИНДРИЧЕСКОГО ЭЛЕКТРОННОГО СГУСТКА НА ГРАНИЦЕ
РАЗДЕЛА ВАКУУМ-ПЛАЗМА
О.І. Кельник, В.К. Тяжемов
Исследовано переходное излучение цилиндрического электронного сгустка, проходящего через границу раздела вакуу-
ма и изотропной плазмы. Рассчитана зависимость диаграммы направленности излучения от его частоты, а также инте-
гральная мощность и полная энергия излучения.
121
O.I. Kelnyk1, V.K. Tyazhemov2
Taras Shevchenko Kyiv National University, Radio Physics Faculty,
|
| id | nasplib_isofts_kiev_ua-123456789-110540 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:33:03Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kelnyk, O.I. Tyazhemov, V.K. 2017-01-04T18:49:02Z 2017-01-04T18:49:02Z 2003 Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border / O.I. Kelnyk, V.K. Tyazhemov // Вопросы атомной науки и техники. — 2003. — № 1. — С. 118-120. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 52.40.Mj https://nasplib.isofts.kiev.ua/handle/123456789/110540 Transition radiation of the cylindrical electron bunch moving through the border between the vacuum and isotropic plasma semi-spaces is studied. Radiation patterns’ frequency dependencies, integrated radiated power and total radiated energy are calculated. Досліджено перехідне випромінювання циліндричного електронного згустку, що проходить через межу поділу вакууму та ізотропної плазми. Розраховано залежність діаграми спрямованості випромінювання від його частоти, а також інтегральну потужність та повну енергію випромінювання. Исследовано переходное излучение цилиндрического электронного сгустка, проходящего через границу раздела вакуума и изотропной плазмы. Рассчитана зависимость диаграммы направленности излучения от его частоты, а также интегральная мощность и полная энергия излучения. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border Article published earlier |
| spellingShingle | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border Kelnyk, O.I. Tyazhemov, V.K. Plasma electronics |
| title | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border |
| title_full | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border |
| title_fullStr | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border |
| title_full_unstemmed | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border |
| title_short | Transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border |
| title_sort | transition radiation of the cylindrical electron bunch at the sharp vacuum-plasma border |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110540 |
| work_keys_str_mv | AT kelnykoi transitionradiationofthecylindricalelectronbunchatthesharpvacuumplasmaborder AT tyazhemovvk transitionradiationofthecylindricalelectronbunchatthesharpvacuumplasmaborder |