Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma
Transition radiation of the modulated electron stream moving along the concentration gradient of the cold planarly stratified strongly inhomogeneous plasma is calculated for the case of strong external magnetic field parallel to the concentration gradient.
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2002 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma / I.O. Anisimov, T.V. Nychyporuk // Вопросы атомной науки и техники. — 2002. — № 5. — С. 104-106. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860261641977856000 |
|---|---|
| author | Anisimov, I.O. Nychyporuk, T.V. |
| author_facet | Anisimov, I.O. Nychyporuk, T.V. |
| citation_txt | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma / I.O. Anisimov, T.V. Nychyporuk // Вопросы атомной науки и техники. — 2002. — № 5. — С. 104-106. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Transition radiation of the modulated electron stream moving along the concentration gradient of the cold planarly stratified strongly inhomogeneous plasma is calculated for the case of strong external magnetic field parallel to the concentration gradient.
|
| first_indexed | 2025-12-07T18:56:03Z |
| format | Article |
| fulltext |
TRANSITION RADIATION OF THE MODULATED ELECTRON STREAM
IN THE STRONGLY INHOMOGENEOUS MAGNETIZED PLASMA
I.O.Anisimov1, T.V.Nychyporuk2
Taras Shevchenko Kyiv National University, Radio Physics Faculty,
64, Volodymyrs’ka St., 01033, Kyiv, Ukraine, 1ioa@rpd.univ.kiev.ua,2tvn@univ.kiev.ua
Transition radiation of the modulated electron stream moving along the concentration gradient of the cold planarly
stratified strongly inhomogeneous plasma is calculated for the case of strong external magnetic field parallel to the
concentration gradient
PACS: 52.40.Mj
1. INTRODUCTION
Transition radiation of the modulated electron
beams in the inhomogeneous plasma is particularly
interesting due to the possible construction of the beam-
plasma devices of direct radiation [1]. In the laboratory
experiments beam-plasma systems are usually placed into
the external magnetic field, that prevents the swelling of
the beam. Therefore plasma is anisotropic. The simplest
model of the anisotropic plasma corresponds to the
infinitely strong magnetic field. Transition radiation of
the modulated electron stream in the magnetized plasma
is studied, e.g., in [2-5]. It is shown that this process is
most effective in the local plasma resonance region
(LPRR), where the modulation frequency coincides with
the electron plasma frequency, and in the local Cherenkov
resonance region (LChRR), where the electron beam
velocity coincides with the phase velocity of
electromagnetic waves. In the LChRR predominantly the
wave co-directional with the beam is excited. In the
weakly inhomogeneous plasma the contribution from the
LPRR and LChRR can be calculated separately. In the
general case, when the distance between the LPRR and
the LChRR is arbitrary, it is impossible to make analytical
calculations. Therefore numerical methods are used. This
report contains the results of numerical computations for
the case when the characteristic length of the
inhomogeneity is less or of the order of the radiated wave.
2. MODEL DESCRIPTION AND BASIC
EQUATIONS
Cold planarly stratified plasma is considered.
Strong magnetic field is directed parallel to the
concentration gradient (Fig.1). Monoenergetic electron
stream moves along the magnetic field forming the
current density wave.
( ) ( )[ ] j r t e j i t rz m, exp= −ω κ , { }
κ κ κ= ⊥0; ; / / ,
κ ω/ / = v0 (1)
The direction of the wave vector of current
density wave makes the angle to the magnetic field
direction. The plasma concentration first linearly
increases from 0 to 2пс(ω), where пс(ω) is the critical
concentration at the modulation frequency ω, and then
remains constant (2).
( )
≥
<<−
+
−≤
=
,Lz,
e2
m
;LzL,
L
z1
e4
m
;Lz,0
zn
2
2
2
2
p
π
ω
π
ω
(2)
Transition radiation for such model was
calculated in the approximation of the given current.
Fig.1. Plasma concentration profile
The equation that describes the electromagnetic
wave excitation by the current wave has a form:
))(exp(
4
)( //
////
2
2
02
2
ztij
c
iHk
dz
Hd
mx
x κω
ε
π κ
ε
κ
−=−+ ⊥⊥
(3)
The method of Green's function was used for
calculating the values of the amplitudes of
electromagnetic waves.
H z z
z f z
W
dz z
z f z
W
dz
z
z
( ) ( )
( ) ( )
( )
( ) ( )
= +
− ∞
∞
∫ ∫Υ
Υ
Υ
Υ
1
2
2
1
(4)
Y1,2 - the solutions of the homogeneous wave
equation (3).
Contributions from the integrals (4) into the
radioemission magnitudes are given by the interval –
L<z<L with a non-zero concentration gradient and by the
points z=-L and z=L where concentration gradient jump
takes place. For large L the main contribution from the
interval –L<z<L is made by the vicinity of the resonant
points, i.e. LPRR and LChRR. Contribution from the
concentration gradient jumps forms the non-resonant
component of the radioemission. With increasing of the
104 Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 104-106
characteristic length of the inhomogeneity the
contribution from the resonance points grows and the
non-resonant component decreases.
3. RESULTS AND DISCUSSION
For the modulated electron beams moving into
the plasma, emission both into plasma (Fig. 2a, 2b, 3a)
and into vacuum (Fig. 3b) monotonically increases with
the increasing of the characteristic length of the
inhomogeneity L and the beam velocity. For the case of
large L the radiated power dependence on the transversal
component of the wave vector κ⊥ of the current density
wave becomes non-monotonic. Emission into the vacuum
is considerably less. Depending on κ⊥ it has maximum,
which moves to smaller κ⊥ with the increasing of L.
a
b
Fig. 2. Emission into the dense plasma for the stream
moving into the plasma for β =0.1 (a) and for β =0.3 (b)
For the beams moving from plasma, emission
into the plasma (Fig. 4a) considerably decreases and
becomes approximately equal to the emission into the
vacuum (Fig. 4b). It should be noted that analytical
calculation for the weakly inhomogeneous plasma doesn’t
give any radiation into the plasma for this case. The
dependence of the emission power in both directions on
the parameters of model is approximately the same as for
the beam moving into plasma.
Thus, for the small L the dependence of emission
on the direction of the electron stream is less noticeable.
This is explained by appearing of the significant
nonresonant component, caused by the growth of the
concentration gradient of the plasma.
a
b
Fig.3. Emission into the dense plasma (a) and into the
vacuum (b) for the stream moving into the plasma (β
=0.5)
a
b
Fig.4. Emission into the dense plasma (a) and into the
105
vacuum (b) for the stream moving into the vacuum(β
=0.5)
The value of emission both into the vacuum and
into the plasma considerably depends on the velocity of
the modulated electronic stream (Fig. 2a, 2b) and
increases for the higher-energy beams in general.
The dependence of the amplitude of emission on
the parameter κ (κ=ω/v0) is shown on the Fig. 5. The sign
of k determines the direction of the electron stream (κ >0
– into the plasma, κ<0 – into the vacuum). This
dependence is approximately the same as in the case of
isotropic plasma.
Fig. 5. The normalized amplitude of emission versus κL
For the modulated electron beams moving into
the plasma the radiated power (the right side of the Fig.5)
increases with the growth of the parameter κ. This result
can be explained by increasing of the characteristic
dimension of the resonance region (Lν/ω), where
interaction of the modulated electron beam with the
electric field of the excited wave is most substantial (with
increasing of L) or by increasing of the holding time of
electrons in this region (with increasing of κ, i.e. with
decreasing of the stream velocity).
For the modulated electron beams moving from
the plasma the radiated power (the left side of the Fig.5) is
non-monotonic. This can be explained by the fact that,
when the direction of electron stream changes, the phase
correlation of the emission field, concerned with the jump
of the refraction index, and the radiation from the LPRR
and LChRR change to the opposite. For the modulated
electron stream moving into the plasma these fields are
co-phased, and for the stream moving from plasma they
are anti-phased, so they can compensate each other under
some conditions.
4. CONCLUSION
1. The most intensive transformation of the current
wave of the modulated electron stream into the
electromagnetic waves occurs in LChRR and
LPRR and in the vicinity of the reflection point.
2. For the modulated electron beams moving into
the plasma, electromagnetic waves are emitted
predominantly into the dense plasma. Emission
into the vacuum penetrates through the opacity
barrier.
3. For the modulated electron beams moving into
the vacuum, electromagnetic waves are emitted
both into the dense plasma and into the vacuum.
Emission into the plasma approximately equal to
the emission into the vacuum.
REFERENCES
1. A.N.Kondratenko, V.M.Kuklin. Fundamentals of
plasma electronics. Energoatomizdat, Moscow, 1988
(in Russian).
2. N.S.Erokhin, S.S.Moiseev. ZhETF, 65, 1431-1447
(1973) (in Russian).
3. S.S.Kalmykova. Fizika plazmy, 2, 643-653 (1976) (in
Russian).
4. I.A.Anisimov, D.G.Stefanovsky. Izvestija vuzov.
Radiofizika, 30, 643-647 (1987) (in Russian).
5. I.O.Anisimov, T.V.Nychyporuk. “Transitional
radiation of the modulated electron beam in the
weakly inhomogeneous magnetized plasma”. Proc. of
the 1st Intern. Young Scientists’ Conf. on Appl. Phys.
T. Shevchenko National University, Faculty of
Radiophysics, Kyiv, 2001, p.p.23-24.
106
I.O.Anisimov1, T.V.Nychyporuk2
Taras Shevchenko Kyiv National University, Radio Physics Faculty,
|
| id | nasplib_isofts_kiev_ua-123456789-78920 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:56:03Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Anisimov, I.O. Nychyporuk, T.V. 2015-03-23T09:31:47Z 2015-03-23T09:31:47Z 2002 Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma / I.O. Anisimov, T.V. Nychyporuk // Вопросы атомной науки и техники. — 2002. — № 5. — С. 104-106. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.40.Mj https://nasplib.isofts.kiev.ua/handle/123456789/78920 Transition radiation of the modulated electron stream moving along the concentration gradient of the cold planarly stratified strongly inhomogeneous plasma is calculated for the case of strong external magnetic field parallel to the concentration gradient. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma Article published earlier |
| spellingShingle | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma Anisimov, I.O. Nychyporuk, T.V. Plasma electronics |
| title | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma |
| title_full | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma |
| title_fullStr | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma |
| title_full_unstemmed | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma |
| title_short | Transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma |
| title_sort | transition radiation of the modulated electron stream in the strongly inhomogeneous magnetized plasma |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78920 |
| work_keys_str_mv | AT anisimovio transitionradiationofthemodulatedelectronstreaminthestronglyinhomogeneousmagnetizedplasma AT nychyporuktv transitionradiationofthemodulatedelectronstreaminthestronglyinhomogeneousmagnetizedplasma |