Experimental investigation of peculiarities of the beam-plasma discharge initial stage
It was shown experimentally that beam-plasma discharge (BPD) in the system of electron beam plus plasma (created by the beam) does not “wait” the condition np>>nb, that connected with the instability increment usually used in that case (np and nb are electron concentrations of plasma and beam)...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2008 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/110792 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Experimental investigation of peculiarities of the beam-plasma discharge initial stage / B.I. Ivanov, V.I. Butenko, V.P. Prishchepov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 132-134. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860129639844806656 |
|---|---|
| author | Ivanov, B.I. Butenko, V.I. Prishchepov, V.P. |
| author_facet | Ivanov, B.I. Butenko, V.I. Prishchepov, V.P. |
| citation_txt | Experimental investigation of peculiarities of the beam-plasma discharge initial stage / B.I. Ivanov, V.I. Butenko, V.P. Prishchepov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 132-134. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | It was shown experimentally that beam-plasma discharge (BPD) in the system of electron beam plus plasma (created by the beam) does not “wait” the condition np>>nb, that connected with the instability increment usually used in that case (np and nb are electron concentrations of plasma and beam). Instead, BPD starts at np≈nb with another increment that was received in this work with help of the corresponding dispersion equation.
Результати наведених експериментів показують, що пучково-плазмовий розряд (ППР) в системі електронний пучок плюс плазма, що створюється пучком, не «чекає» виконання умови np>>nb (np и nb–густини плазми й пучка), пов’язаної з інкрементом нестійкості, що зазвичай використовується в даному випадку. Замість цього ППР починається при np≈nb з іншим інкрементом, значення якого отримано в даній роботі.
Результаты приведенных экспериментов показывают, что пучково-плазменный разряд (ППР) в системе электронный пучок плюс плазма, создаваемая пучком, не «ждет» выполнения условия np>>nb (np и nb–плотности плазмы и пучка), связанного с инкрементом неустойчивости, обычно используемом в данном случае. Вместо этого ППР начинается при np≈nb с другим инкрементом, значение которого получено в данной работе.
|
| first_indexed | 2025-12-07T17:43:49Z |
| format | Article |
| fulltext |
EXPERIMENTAL INVESTIGATION OF PECULIARITIES
OF THE BEAM-PLASMA DISCHARGE INITIAL STAGE
B.I. Ivanov, V.I. Butenko, V.P. Prishchepov
National Science Center "Kharkov Institute of Physics and Technology",
61108 Kharkov,Ukraine, e-mail: ivanovbi@kipt.kharkov.ua
It was shown experimentally that beam-plasma discharge (BPD) in the system of electron beam plus plasma
(created by the beam) does not “wait” the condition np>>nb, that connected with the instability increment usually used in
that case (np and nb are electron concentrations of plasma and beam). Instead, BPD starts at np≈nb with another
increment that was received in this work with help of the corresponding dispersion equation.
PACS: 52.40.Mj
As it is known, in case of electron beam propagating
through a rarefied gas of some critical pressure, the beam-
plasma instability starts and drives to the high-frequency
break-down of gas, that is, to the beam-plasma discharge
(BPD) (e.g., see [1] and references there). BPD used in
many fields of science and technology (plasma
electronics, plasma chemistry, plasma sources, etc.).
Practically all experimental and theoretical works
devoted to BPD (e.g., see references in [1]) do not deal
with collective effects at the initial stage of BPD where
plasma density (np) is less or equal to beam density (nb).
Usually, it was supposed that an electron beam firstly
prepared (by impact ionization of neutrals) the plasma
density that is much grater than the beam density.
Afterwards, the beam-plasma instability begins with the
increment [2-4]:
( ) 3/1/3/42
3
pnbnpω=γ (1)
and drives the beam-plasma discharge.
We have investigated the BPD initial stage (i. e., at
np~nb) in two experiments: 1) in case of pulse electron beam,
and 2) in case of CW (continuous in time) electron beam. In
both experiments the beams running along a uniform
magnetic field (with intensity up to 1 kOe) in air at pressure
p=10-6–10-3 Torr. Summary electron linear concentration
(electron number per cm) of the beam and plasma (Nb+Np)
was determined by measuring frequency shift (∆f) of an
UHF cavity of the 10-cm range: Nb+Np=∆f/A, where the
coefficient A was determined experimentally at p=10-6 Torr,
Np=0, Nb=6⋅1018 I/Vb, were I is electron beam current in
Amperes, V is beam electron velocity. (On increasing
accuracy of measuring small electron concentration see
[5,6]).
At р∼10-6 Torr the frequency shift was conditioned by
the beam electrons only (Nb=6⋅1018 I/Vb). In the interval
р=3⋅10-5–8⋅10-5 Torr the frequency shift slowly rose with
plasma electron concentration due to impact ionization of
neutrals. At р≈1⋅10-4 Torr the temp of plasma electron
concentration rising essentially increased.
Simultaneously, burning of the BPD could be visually
observed.
Parameters of our first installation (see Fig. 1) are: a
pulsed axial electron beam of 0-12 keV, 0-3 A, 10 mm
diameter; pulse duration 25 µs, a longitudinal magnetic
field up to 1 kOe. The electron beam was passed through
a multi-mode 10-cm cavity that was used for the electron
and plasma density measurements.
Fig. 1. 1-15 kV rectifier, 2-pulse forming line, 3-trigger
device, 4-400 V rectifier, 5–attenuator 10 dB, 6–power
distributor, 7–UHF oscillator, 8–delay line, 9–amplifier,
10–oscilloscopes, 11–frequency meter; 12, 13-cathode
and anode of electron gun, 14- electron beam collector,
15-quartz tube, 16-UHF cavity, 17–cutoff waveguides
In case of increasing gas pressure (air) up to 10-4 Torr,
the BPD starts, and the electron linear density quickly
rises from 2.3⋅109 cm-1 to 8.6⋅109 cm-1 (Fig. 2).
Fig. 2. Resonance frequency shift of the UHF cavity vs.
gas pressure in case of 2.3 A, 10 keV electron beam that
initiates the plasma-beam discharge at p≈1.5⋅10-4 Torr
and np~nb (here ∆f=1 MHz corresponds to electron beam
linear density Nb=2.3⋅109 cm-1)
It was determined that, in case of the pulse electron
beam, the BPD started at р≈1.5⋅10-4 Torr and Np/Nb ≈0.5
(but not Np>>Nb, as it was supposed in formula (1)). The
measuring accuracy of Nb/Np was less than 10 %.
In Fig.3 the second installation is presented. The
electron beam was created by a gun consisting of LaB6
cathode (11) and a mesh anode (12), with the following
parameters: DC beam voltage U=10-1000 V, current
I=1-100 mA, beam diameter 2a=10 mm, magnetic field H
132 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6.
Series: Plasma Physics (14), p. 132-134.
variable between 100 and 1 kOe , magnetic field
inhomogenity 1 %. The beam was shot down the axis of a
quartz tube 30 mm in diameter, which was evacuated
down to pressures of the order of 10-6 Torr.
Fig. 3. Setup of 2-nd installation. Main parts: electronic
equipment (1-10), electron gun (11, 12), magnetic
solenoid, cavity for electron density measurements (13),
spiral resonator for measurements of the electron
distribution function over axial velocities (15), beam
collector (17), multi-electrode probe to measure the
electron energy distribution by means of the retarding
potential method (18-20)
10-6 10-5 10-4
108
109
N
b+N
p, с
м
-1
P, Торр
Fig. 4. Measuring electron linear density versus gas
pressure in case of 10 mA, 300 eV electron beam that
initiates the plasma-beam discharge at p≈9⋅10-5 Torr
Magnetic field intensity H=1 kOe. The origin of
coordinates corresponds to N = Nb+Np = 2⋅107 cm-1,
p=10-6 Torr.
At p~10-6 Torr the plasma density Np=0, and the beam one
Nb=5.8⋅107 cm-1. In Fig. 4 a solid curve corresponds to
calculation of (Nb+Np) for case of impact ionization of
neutrals by the electron beam. In this experiment the BPD
started at р≈9⋅10-5 Torr and Np/Nb≈0.8, but not Np>>Nb,
as it was supposed in formula (1). The measuring
accuracy of Nb/Np was less than 10 %.
Both experiments show that the BPD in the system of
beam plus plasma (created by beam) do not “wait” the
condition np>>nb, connected with the increment (1).
Instead, the BPD starts at np≈nb with another increment
(see below). So, we made calculation of the instability
increment at the condition nb=np.
Firstly the two electron beam instability at equal
electron concentration nb1=nb2 had investigated
A.V. Haeff [7], theoretically and experimentally. In that
case, Haeff’s dispersion equation was as it follows:
12)2(
2
2)1(
2
=
−ω
ω
+
−ω
ω
Vzk
b
Vzk
b , (2)
where ωb is Langmuir frequency of each beam, kz is the
wave number, V1 and V2 are the beams’ velocities. By
method of successive substitutions, Haeff reduced (2) to
the biquadrate equation and solved the problem.
However, it was declared in [8] that Haeff’s results “were
vitiated by the omission of certain terms”. Actually, Haeff
neglected the difference of beam velocities in comparison
with their summary. That action is admissible to his two-
beam electron-wave tube but not right to the plasma-beam
instability at ωb=ωp, where beam velocity is much high
than plasma one (Vb>>Vp).
Let us get back to the BPD. Firstly, at the very initial
stage of the BPD, where np<<nb, the increment of the
beam-plasma instability, in accordance with a remark in
[9, §1.5], can take the following form:
( ) 3/1/3/42
3
bnpnbω=γ , (3)
where np and nb change over. In case of increasing plasma
density up to beam density, np=nb, the dispersion equation
takes the form of (2), where V1≡Vb, V2≡Vp (Vp<<Vb).
Now we change the laboratory coordinate system to
another one, moving with (non relativistic) velocity
Vm=(V1+V2)/2 (4)
In this system the beam velocity is Vbm≡
V1m=(V1-V2)/2, and the plasma velocity (or 2-nd beam
one) is Vpm≡V2m= – (V1-V2)/2. Then, the dispersion
equation takes the form:
1
)21(
2
1
2
)21(
2
1
2
22 =
−+ω
ω
+
−−ω
ω
VVzk
b
VVzk
b
(5)
The solution of this biquadrate equation concerning to the
complex frequency ω takes the form:
( ) ( ) 2/12
21
222
21
2
4
122
−+ωω±−+ω=ω VVzkbbVVzkb (6)
Instability will take place at 02 <ω , that, as it
appears from (6), at the choice of sign of “–” before a
square root, and kz<kz1, where:
( )21/221 VVbzk −ω= . (7)
From (6) we will find also, that at an optimum value
of the wave number:
( )21/32 VVbzk −ω= (8)
the maximum value of increment of instability takes place
bω=ω≡Γ 5.0Immax (9)
(in this case 0Re =ω ). At the transition to the laboratory
coordinate system the oscillation frequency, having
greatest increment, in accordance with Doppler
transformation, takes on a value:
21
21
2
3
2Remax.Re
VV
VV
bmVzklab −
+
ω=+ω=ω . (10)
133
In our experiments V1>>V2 and
Re blab ω=ω
2
3
max. . (11)
Thus, accordingly to the formulas (6-11) the branches
of oscillations in the plasma-beam system in case of np=nb
look like the following (Fig. 5).
Fig. 5. The branches of oscillations in the plasma-beam
system at Nb=Np
In Fig. 5 the relative instability increment Imω/ωb is
presented by the bottom curve. Upper branches present
dispersion of waves Reω(kz) in this system.
At further growth of the plasma density and
fulfillment of the condition np>>nb the evolution of BPD
is possible accordingly to the increment (1).
REFERENCES
1. A.K. Berezin, E.V. Livshits, Ya.B. Fainberg et al.
Collective interactions of intense pulse electron beams
with plasma. Formation and evolution of beam-plasma
discharge, I and II // Physics of Plasma. 1995, v. 21, N 3,
p. 226-256 (about 90 references).
2. A.I. Akhiezer, Ya.B. Fainberg. On interaction of
charged plasma beam with electron plasma // Doklady AN
SSSR. 1949, v.64, N 4, p.555-556.
3. A.I. Akhiezer, Ya.B. Fainberg. On high frequency
oscillations of electron plasma // J. Exp. Theor. Phys.
1951, v.21. N 11, p.1262-1269.
4. A.I. Akhiezer, I.A. Akhiezer, R.V. Polovin,
A.G. Sitenko, K.N. Stepanov. Electrodynamics of
Plasma. Moscow: “Nauka”, 1974, Chapter 6.
5. B.I. Ivanov. Method of measuring small frequency shift
of UHF cavity // Pribory and Tekhnika Experimenta.
1969. No.1, p. 93-95.
6.B .I. Ivanov. Development of electron concentration
measuring by UHF cavity // J. Techn. Physics. 1970,
v. 40. N3, p. 489-495.
7. A.V. Haeff. The electron-wave tube – a novel method
of generation and amplification of microwave energy //
Proc. IRE, 1949, v.37, N 1, p. 4-10.
8. J. Feinstein, H.K. Sen. Radio wave generation by
multistream charge interaction // Phys. Rev. 1951, v. 83,
N 2, p. 405-412.
9. A.B. Mikhailovskii. Theory of plasma instabilities. //
Moscow: “Atomizdat”, 1970, v.1, Chapter 1.
Article received 22.09.08.
ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ ОСОБЕННОСТЕЙ НАЧАЛЬНОЙ СТАДИИ
ПУЧКОВО-ПЛАЗМЕННОГО РАЗРЯДА
Б.И. Иванов, В.И. Бутенко, В.П. Прищепов
Результаты приведенных экспериментов показывают, что пучково-плазменный разряд (ППР) в системе
электронный пучок плюс плазма, создаваемая пучком, не «ждет» выполнения условия np>>nb (np и nb–плотности
плазмы и пучка), связанного с инкрементом неустойчивости, обычно используемом в данном случае. Вместо
этого ППР начинается при np≈nb с другим инкрементом, значение которого получено в данной работе.
ЭКСПЕРИМЕНТАЛЬНЕ ДОСЛІДЖЕННЯ ОСОБЛИВОСТЕЙ ПОЧАТКОВОЇ СТАДІЇ
ПУЧКОВО-ПЛАЗМОВОГО РОЗРЯДУ
Б.І. Іванов, В.І. Бутенко, В.П. Прищепов
Результати наведених експериментів показують, що пучково-плазмовий розряд (ППР) в системі
електронний пучок плюс плазма, що створюється пучком, не «чекає» виконання умови np>>nb (np и nb–густини
плазми й пучка), пов’язаної з інкрементом нестійкості, що зазвичай використовується в даному випадку.
Замість цього ППР починається при np≈nb з іншим інкрементом, значення якого отримано в даній роботі.
134
Im(ω)/ωb
kzV/ωb
Re(ω)/ωb
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-110792 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:43:49Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Ivanov, B.I. Butenko, V.I. Prishchepov, V.P. 2017-01-06T12:53:36Z 2017-01-06T12:53:36Z 2008 Experimental investigation of peculiarities of the beam-plasma discharge initial stage / B.I. Ivanov, V.I. Butenko, V.P. Prishchepov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 132-134. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.40.Mj https://nasplib.isofts.kiev.ua/handle/123456789/110792 It was shown experimentally that beam-plasma discharge (BPD) in the system of electron beam plus plasma (created by the beam) does not “wait” the condition np>>nb, that connected with the instability increment usually used in that case (np and nb are electron concentrations of plasma and beam). Instead, BPD starts at np≈nb with another increment that was received in this work with help of the corresponding dispersion equation. Результати наведених експериментів показують, що пучково-плазмовий розряд (ППР) в системі електронний пучок плюс плазма, що створюється пучком, не «чекає» виконання умови np>>nb (np и nb–густини плазми й пучка), пов’язаної з інкрементом нестійкості, що зазвичай використовується в даному випадку. Замість цього ППР починається при np≈nb з іншим інкрементом, значення якого отримано в даній роботі. Результаты приведенных экспериментов показывают, что пучково-плазменный разряд (ППР) в системе электронный пучок плюс плазма, создаваемая пучком, не «ждет» выполнения условия np>>nb (np и nb–плотности плазмы и пучка), связанного с инкрементом неустойчивости, обычно используемом в данном случае. Вместо этого ППР начинается при np≈nb с другим инкрементом, значение которого получено в данной работе. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Experimental investigation of peculiarities of the beam-plasma discharge initial stage Экспериментальне дослідження особливостей початкової стадії пучково-плазмового розряду Экспериментальное исследование особенностей начальной стадии пучково-плазменного разряда Article published earlier |
| spellingShingle | Experimental investigation of peculiarities of the beam-plasma discharge initial stage Ivanov, B.I. Butenko, V.I. Prishchepov, V.P. Plasma electronics |
| title | Experimental investigation of peculiarities of the beam-plasma discharge initial stage |
| title_alt | Экспериментальне дослідження особливостей початкової стадії пучково-плазмового розряду Экспериментальное исследование особенностей начальной стадии пучково-плазменного разряда |
| title_full | Experimental investigation of peculiarities of the beam-plasma discharge initial stage |
| title_fullStr | Experimental investigation of peculiarities of the beam-plasma discharge initial stage |
| title_full_unstemmed | Experimental investigation of peculiarities of the beam-plasma discharge initial stage |
| title_short | Experimental investigation of peculiarities of the beam-plasma discharge initial stage |
| title_sort | experimental investigation of peculiarities of the beam-plasma discharge initial stage |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110792 |
| work_keys_str_mv | AT ivanovbi experimentalinvestigationofpeculiaritiesofthebeamplasmadischargeinitialstage AT butenkovi experimentalinvestigationofpeculiaritiesofthebeamplasmadischargeinitialstage AT prishchepovvp experimentalinvestigationofpeculiaritiesofthebeamplasmadischargeinitialstage AT ivanovbi éksperimentalʹnedoslídžennâosoblivosteipočatkovoístadíípučkovoplazmovogorozrâdu AT butenkovi éksperimentalʹnedoslídžennâosoblivosteipočatkovoístadíípučkovoplazmovogorozrâdu AT prishchepovvp éksperimentalʹnedoslídžennâosoblivosteipočatkovoístadíípučkovoplazmovogorozrâdu AT ivanovbi éksperimentalʹnoeissledovanieosobennosteinačalʹnoistadiipučkovoplazmennogorazrâda AT butenkovi éksperimentalʹnoeissledovanieosobennosteinačalʹnoistadiipučkovoplazmennogorazrâda AT prishchepovvp éksperimentalʹnoeissledovanieosobennosteinačalʹnoistadiipučkovoplazmennogorazrâda |