Formation and properties of self-consistent Malmberg-Penning trap
In recent years a big attention is given to coherent structures at an explanation of phenomena of the fast convective carry from the scratch-off-layer in devices such as “tokamak” and “stellarator”. Coherent structures can appear at occurrence of the self-consistent electromagnetic traps (similar to...
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| Цитувати: | Formation and properties of self-consistent Malmberg-Penning trap / N.A. Azarenkov, A.A. Bizyukov, V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, I.K. Tarasov, M.I. Tarasov, E.D. Volkov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 140-142. — Бібліогр.: 5 назв. — англ. |
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Azarenkov, N.A. Bizyukov, A.A. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Tarasov, I.K. Tarasov, M.I. Volkov, E.D. 2015-03-24T08:01:31Z 2015-03-24T08:01:31Z 2005 Formation and properties of self-consistent Malmberg-Penning trap / N.A. Azarenkov, A.A. Bizyukov, V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, I.K. Tarasov, M.I. Tarasov, E.D. Volkov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 140-142. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.35.Mw https://nasplib.isofts.kiev.ua/handle/123456789/78944 In recent years a big attention is given to coherent structures at an explanation of phenomena of the fast convective carry from the scratch-off-layer in devices such as “tokamak” and “stellarator”. Coherent structures can appear at occurrence of the self-consistent electromagnetic traps (similar to Malmberg-Penning trap) with confinement and cooling of charged plasma in them. In this paper the results of researches of an opportunity of the self-consistent confinement configuration formation in the non-neutral plasma represented. Останнім часом багато уваги приділяється когерентним структурам у зв’язку з поясненням явища швидкого конвективного переносу з області обдирки в установках типу „токамак” та „стеларатор”. Когерентні структури можуть виникати у самоузгоджених електромагнітних пастках (подібних до пасток Малмберга-Пеннінга) при наявності утримання та охолодження в них зарядженної плазми. У работі представлено результати досліджень щодо можливості формування конфігурації самоузгодженного утримання у зарядженій плазмі. В последнее время большое внимание уделяется когерентным структурам в связи с объяснением явления быстрого конвективного переноса из области обдирки в установках типа «токамак» и «стелларатор». Когерентные структуры могут возникать в самосогласованных электромагнитных ловушках (подобных ловушкам Малмберга Пеннинга) при удержании и охлаждении заряженной плазмы в них. В работе представлены результаты исследования возможности формирования конфигурации самосогласованного удержания в заряженной плазме. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Formation and properties of self-consistent Malmberg-Penning trap Формування та властивості самоузгодженної пастки Малмберга-Пеннінга Формирование и свойства самосогласованной ловушки Малмберга-Пеннинга Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Formation and properties of self-consistent Malmberg-Penning trap |
| spellingShingle |
Formation and properties of self-consistent Malmberg-Penning trap Azarenkov, N.A. Bizyukov, A.A. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Tarasov, I.K. Tarasov, M.I. Volkov, E.D. Plasma electronics |
| title_short |
Formation and properties of self-consistent Malmberg-Penning trap |
| title_full |
Formation and properties of self-consistent Malmberg-Penning trap |
| title_fullStr |
Formation and properties of self-consistent Malmberg-Penning trap |
| title_full_unstemmed |
Formation and properties of self-consistent Malmberg-Penning trap |
| title_sort |
formation and properties of self-consistent malmberg-penning trap |
| author |
Azarenkov, N.A. Bizyukov, A.A. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Tarasov, I.K. Tarasov, M.I. Volkov, E.D. |
| author_facet |
Azarenkov, N.A. Bizyukov, A.A. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Tarasov, I.K. Tarasov, M.I. Volkov, E.D. |
| topic |
Plasma electronics |
| topic_facet |
Plasma electronics |
| publishDate |
2005 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Формування та властивості самоузгодженної пастки Малмберга-Пеннінга Формирование и свойства самосогласованной ловушки Малмберга-Пеннинга |
| description |
In recent years a big attention is given to coherent structures at an explanation of phenomena of the fast convective carry from the scratch-off-layer in devices such as “tokamak” and “stellarator”. Coherent structures can appear at occurrence of the self-consistent electromagnetic traps (similar to Malmberg-Penning trap) with confinement and cooling of charged plasma in them. In this paper the results of researches of an opportunity of the self-consistent confinement configuration formation in the non-neutral plasma represented.
Останнім часом багато уваги приділяється когерентним структурам у зв’язку з поясненням явища швидкого конвективного переносу з області обдирки в установках типу „токамак” та „стеларатор”. Когерентні структури можуть виникати у самоузгоджених електромагнітних пастках (подібних до пасток Малмберга-Пеннінга) при наявності утримання та охолодження в них зарядженної плазми. У работі представлено результати досліджень щодо можливості формування конфігурації самоузгодженного утримання у зарядженій плазмі.
В последнее время большое внимание уделяется когерентным структурам в связи с объяснением явления быстрого конвективного переноса из области обдирки в установках типа «токамак» и «стелларатор». Когерентные структуры могут возникать в самосогласованных электромагнитных ловушках (подобных ловушкам Малмберга Пеннинга) при удержании и охлаждении заряженной плазмы в них. В работе представлены результаты исследования возможности формирования конфигурации самосогласованного удержания в заряженной плазме.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/78944 |
| citation_txt |
Formation and properties of self-consistent Malmberg-Penning trap / N.A. Azarenkov, A.A. Bizyukov, V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, I.K. Tarasov, M.I. Tarasov, E.D. Volkov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 140-142. — Бібліогр.: 5 назв. — англ. |
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| fulltext |
FORMATION AND PROPERTIES OF SELF-CONSISTENT
MALMBERG-PENNING TRAP
N.A. Azarenkov*, A.A. Bizyukov*, V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, I.K. Tarasov,
M.I. Tarasov*, E.D. Volkov
NSC Kharkov Institute of Physics and Technology, Kharkov, 61108, Ukraine,
E-mail: itarasov@ipp.kharkov.ua;
*Karazin Kharkov National University, Kharkov, 61108, Ukraine
In recent years a big attention is given to coherent structures at an explanation of phenomena of the fast
convective carry from the scratch-off-layer in devices such as “tokamak” and “stellarator”. Coherent structures can
appear at occurrence of the self-consistent electromagnetic traps (similar to Malmberg-Penning trap) with confinement
and cooling of charged plasma in them. In this paper the results of researches of an opportunity of the self-consistent
confinement configuration formation in the non-neutral plasma represented.
PACS: 52.35.Mw
INTRODUCTION
The excitation and properties of electric trap for
beam’s electrons, which move through a metallic tube, are
investigated theoretically and experimentally in this paper.
The electron beam is shown to provide the instability
development. The instability leads to the formation of the
non-stationary electric barrier and the appearance of electric
potential trap. This phenomenon is observed in the central
region of the tube, where the hump of the electric potential
is formed [4]. On the end of the cylinder two dips of the
electric potential are formed. The trap confines electrons
during the barrier formation and keeps them inside the drift
tube. Trapped electrons have low temperature and are
unstable concerning the diocotron instability development.
During the diocotron instability development the spatial
charge redistribution takes place in the beam cross-section,
which is connected with the electron drift in longitudinal
magnetic and radial electric fields [1,2].
EXPERIMENTAL RESULTS
The experimental setup is shown in [3].
Fig.1.Oscillogrammes: 1 – impulse voltage on the cathode,
2 - current on the input grid, 3 - current on the output grid,
4 - currents on π - electrodes. UB = 30 V, scale - 2 µs/div,
sensitivity 1 - 5 mA/div, 2 - 1.2 mA/div, 3 - 0.25 mA/div, 4 -
4.5 µA/div
During the experiments a number of phenomena was
observed similar to the processes accompanying the well-
known phenomenon of current breakdown during the
propagation of a monopower electron beam in vacuum [3].
Fig. 1 represents the oscillogrammes: of the negative pulse
of the voltage on the cathode of the electron gun - 1; the
injected current Iin - 2; the current that passed through
the drift space Iout – 3; the radial currents -4. The
averaged by time (time of averaging - 20 s) distribution
function of the particles by the longitudinal speeds was
measured using of mobile electrostatic analyzer.
Fig. 2. The function of electron beam distribution on
speeds in three points along a magnetic field. UB = 30
B, IB = 17mA, H = 1 kOe. 1 - Z = 10 cm, 2 - Z = 40 cm,
3 - Z = 70 cm, IB = 17 мА
On Fig. 2 the distribution functions f(U) are presented
for the injected beam that past in the drift interval are
submitted: curve 1 - 10 cm, curve 2 - 40 cm, curve 3 -
70 cm. The figure shows us, that in space of drift
strongly dim on speeds electron beam have disorder on
longitudinal speed V, comparable with drift speed Vdr is
injected . The division V / Vdr, is measured on halfheigh
of ordinate f (U) for curve 1 is V / Vdr = 0.8. The beam
that has passed through the drift interval remains
scattering and the amount of particles with low
velocities increases. A reorganization of function of
distribution takes place, when the electron beam passes
through the drift space. With two maxima-shape in the
initial area of the drift space, the distribution function
gets one-maximum shape when moving from the
injection plane to the central intermediate region of the
drift space. It is necessary to note, that after being
injected into the drift channel the electron beam loses its
energy at about 10-20 eV. The distribution function of
the particles by velocity has a two-maxima shape when
the emission current reaches 10 mA. The distribution of
140 Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 140-142
the electric potential in the drift space during the impulse of
injection was obtained by measuring the floating potential
in the axial direction with electrostatic probe.
Fig.3. Distribution of the potential in the axial direction of
the drift space. UB = 30 V, H = 1 kOe, 1 – IB = 17 mA, 2 –
IB = 10 mA
In Fig.3 the dependences of the distribution of plasma
potential in the drift space along the magnetic field are
given. The curve 1 corresponds to the intensity of the
magnetic field 1 kOe and the duration of the pulse of
injection - 5 µs. The current of injection of the electron
beam was 17 mA. The curve 2 corresponds to the intensity
of the magnetic field 1 kOe, and the current of injection 10
mA The behaviour of the curves in Fig. 3. demonstrates that
in the central part of the drift space, depending on the
current of injection, there exist regions with the increased
potential. The spatial distribution of the potential depends
on the energy of injection Ui (the potential increases with
the energy increase) and on the intensity of magnetic field.
The injection current being changed, the form of the spatial
distribution changes as well, instead of one maximum it gets
two maxima with 70-90 cm between them. It takes no more
than 10 ms for the system to make such transition.
DIOCOTRON INSTABILITY DEVELOPMENT
AT FINITE LONGITUDINAL WAVEVECTOR
Let's consider the development of the diocotron
instability at a finite longitudinal wave vector k z of the
cylindrical electron beam with the internal Ro and
external R p radiuses, moving with velocity V o inside
the magnetized metal cylinder with radius Rc and length
L . We take into account members not more senior than
the first degree k z . Also we neglect cross members
k z
ωc
.
We take into account members not more senior than the first
degree on
ω p
ωc
. Here ω p , ωc are the electron plasma
and cyclotron frequencies. We use the following equations
[5]
r−1 ∂r r ∂ rϕ−
ℓ2
r2 ϕ=0 , r≠Ro , R p (1)
Here ϕ is the electric potential.
ϕ 1=βr ℓ χ
r ℓ , RorR p
ϕ 2= β χ
Ro
2ℓ r ℓ
, 0rRo (2)
ϕ 3= βRp
2ℓ χ Rc
2ℓ−r2ℓ
Rc
2ℓ−R p
2ℓ
1
r ℓ , R prRc
r−1 ∂r r ∂ rϕ−
ℓ2
r2 ϕ=− ℓ
ωc r
ϕ ∂r ω p
2
ω−ℓωe−k z V o
(3)
From (3) for r=Ro , R p we derive
R p ϕ 3−ϕ 2∣r=R p
= ℓ
ωc
ϕ∣r=Rp
ω p
2
ω−ℓωe Rp−k z V o
Ro ϕ 2−ϕ 1∣r=Ro
=− ℓ
ωc
ϕ∣r=Ro
ω p
2
ω− ℓωe Ro−k zV o
(4)
Here ωeR p=ωd1 −
Ro
2
R p
2 , ωeRo =0 ,
ωd=
ω p
2
2ωc
, ω is the perturbation frequency. From
(2)-(4) it follows
ω−k z V o
2
ωd
2 −α1
ω−k z V o
ωd
α2=0 (5)
Here α1=ℓ1 −
Ro
2
Rp
2 R p
2ℓ
Rc
2ℓ−
Ro
2ℓ
Rc
2ℓ ,
α2=ℓ 1 −
Ro
2
R p
2 1 −
Ro
2ℓ
Rc
2ℓ −1 −
Ro
2ℓ
R p
2ℓ 1 −
R p
2ℓ
Rc
2ℓ
. The solution (5) looks like ω=Re ωi Im ω
Re ω=k z V o
α1ωd
2
,
Im ω=
ωd
2 4α 2−α1
2 (6)
If k z=−
α1ωd
2Vo
, the perturbation does not move in
the longitudinal direction. The comparison with the
experimental data shows, that λ=2π
k z
=
4πVo
α1 ωd
≈L
the length of the perturbation is approximately equal to
the system length.
From the given parameters:
ωp=2/3×108radn/sec, ωc=2×109radn/sec, R0=12mm.,
Rp=15mm., Rc=20mm., V0=0,5×107cm/sec.we obtain:
α1=0.5625, ωd=1/9×107Hz.
Then we find λ=113.04сm. Which has same order with
the device length L=150сm.
141
CONCLUSIONS
The results obtained lead to the following conclusions.
Upon the injection of an electron beam with a broad
velocity distribution into the drift space with a longitudinal
magnetic field the majority of the particles experiences a
reorganization of their movement: they start moving in the
azimuthal direction, having lost their axial velocity Such
reorganization promotes the occurrence of sagging of the
spatial potential and a virtual cathode as a consequence,
thus changing the dynamics of particles particles in drift
space. An inverse flow of the electrons takes place and a
certain part of particles leave in a radial direction.The
inverse flow performs a transformation of the function of
distribution, so it gets the second maximum, and the loss of
the electrons in the radial direction causes a non-stationarity
of the virtual cathode and following increase of passing
current. As a result, during the time corresponding to the
front of increase of the current of injection, between two
saggings of the potential a dynamic trap is formed that can
capture 'slow' electrons that are situated in the drift space
upon the occurrence of double sagging.
REFERENCES
1. V.A. Bashko, S.M. Krivoruchko, and I.K.
Tarasov // Proc. 16 th Europ. Conf. on Contr.
Fusion and Plasma Phys., vol.13B, part IV,
Venice, 1989, p. 1587.
2. V.R. Bursian, B.I. Pavlov. On one special case
of influence of the space charge on the transfer
of electron beam in vacuum // Journal of
Russian Society of Physics and Chemistry,
1923, 55(1), p.71.
3. A.A. Buzyukov, E.D. Volkov, I.K. Tarasov //
Problems of atomic science and technology.
Series: Plasma physics (5). 2000, N.3, p.120-
122.
4. N.A. Azarenkov, A.A. Bizukov, D.Yu. Frolova,
V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, I.K.
Tarasov, E.D. Volkov // 30th EPS Conference on
Contr. Fusion and Plasma Phys., St. Petersburg,
7-11 July 2003 / ECA Vol. 27A, P – 4. 109.
5. R.C. Davidson. Theory of nonneutral plasmas.
London-Amsterdam. 1974.
ФОРМИРОВАНИЕ И СВОЙСТВА САМОСОГЛАСОВАННОЙ ЛОВУШКИ МАЛМБЕРГА-
ПЕННИНГА
Н.А. Азаренков, A.A. Бизюков, В.И. Лапшин, В.И. Маслов, И.Н. Онищенко, И.К. Tарасов,
M.И. Tарасов, Е.Д. Волков
В последнее время большое внимание уделяется когерентным структурам в связи с объяснением явления
быстрого конвективного переноса из области обдирки в установках типа «токамак» и «стелларатор».
Когерентные структуры могут возникать в самосогласованных электромагнитных ловушках (подобных
ловушкам Малмберга Пеннинга) при удержании и охлаждении заряженной плазмы в них. В работе
представлены результаты исследования возможности формирования конфигурации самосогласованного
удержания в заряженной плазме.
ФОРМУВАННЯ ТА ВЛАСТИВОСТІ САМОУЗГОДЖЕННОЇ ПАСТКИ МАЛМБЕРГА-
ПЕННІНГА
М.А. Азарєнков, А.А. Бізюков, В.І. Лапшин, В.І. Маслов, І.М. Онищенко, І.К. Тарасов,
М.І. Тарасов, Є.Д. Волков
Останнім часом багато уваги приділяється когерентним структурам у зв’язку з поясненням явища швидкого
конвективного переносу з області обдирки в установках типу „токамак” та „стеларатор”. Когерентні структури
можуть виникати у самоузгоджених електромагнітних пастках (подібних до пасток Малмберга-Пеннінга) при
наявності утримання та охолодження в них зарядженної плазми. У работі представлено результати досліджень
щодо можливості формування конфігурації самоузгодженного утримання у зарядженій плазмі.
142
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