Plasma accelerator with closed electron drift and open walls
We present the original approach to use plasma accelerators with closed electron drift and open walls for creating effective lens with positive space charge. In paper describes one-dimensional model and simplest analytical solutions following from it. The results of the numerical calculation and som...
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irk-123456789-1122402017-01-19T03:02:59Z Plasma accelerator with closed electron drift and open walls Goncharov, A. Dobrovolsky, A. Najko, L. Najko, I. Litovko, I. Нерелятивистская электроника We present the original approach to use plasma accelerators with closed electron drift and open walls for creating effective lens with positive space charge. In paper describes one-dimensional model and simplest analytical solutions following from it. The results of the numerical calculation and some experimental investigations data are presented also. Вперше описана одновимірна модель оригінального плазмового прискорювача з відкритими стінками, яка є плазмооптичним пристроєм нового покоління, для ефективного застосування в сучасних технологіях, зокрема, для створення плазмової лінзи з позитивним просторовим зарядом, а також малогабаритного ракетного двигуна. Отримані прості аналітичні розв’язки і представлені результати числового моделювання, які дозволяють з нових позицій розглядати фізику процесів у прискорювачах холлівського типу. Наведенo результати експериментальних досліджень. Впервые описана одномерная модель оригинального плазменного ускорителя с открытыми стенками, представляющая плазмооптическое устройство нового поколения, которое может быть использовано для современных технологий, в частности, для создания плазменной линзы с положительным объемным зарядом, а также малогабаритного ракетного движителя. Получены простейшие аналитические решения и представлены результаты численного моделирования, позволяющие с новых позиций рассматривать физику процессов в ускорителях холловского типа. Приведены результаты экспериментальных исследований. 2015 Article Plasma accelerator with closed electron drift and open walls / A. Goncharov, A. Dobrovolsky, L. Najko, I. Najko, I. Litovko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 26-31. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.65.-y http://dspace.nbuv.gov.ua/handle/123456789/112240 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Нерелятивистская электроника Нерелятивистская электроника |
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Нерелятивистская электроника Нерелятивистская электроника Goncharov, A. Dobrovolsky, A. Najko, L. Najko, I. Litovko, I. Plasma accelerator with closed electron drift and open walls Вопросы атомной науки и техники |
| description |
We present the original approach to use plasma accelerators with closed electron drift and open walls for creating effective lens with positive space charge. In paper describes one-dimensional model and simplest analytical solutions following from it. The results of the numerical calculation and some experimental investigations data are presented also. |
| format |
Article |
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Goncharov, A. Dobrovolsky, A. Najko, L. Najko, I. Litovko, I. |
| author_facet |
Goncharov, A. Dobrovolsky, A. Najko, L. Najko, I. Litovko, I. |
| author_sort |
Goncharov, A. |
| title |
Plasma accelerator with closed electron drift and open walls |
| title_short |
Plasma accelerator with closed electron drift and open walls |
| title_full |
Plasma accelerator with closed electron drift and open walls |
| title_fullStr |
Plasma accelerator with closed electron drift and open walls |
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Plasma accelerator with closed electron drift and open walls |
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plasma accelerator with closed electron drift and open walls |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Нерелятивистская электроника |
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| citation_txt |
Plasma accelerator with closed electron drift and open walls / A. Goncharov, A. Dobrovolsky, L. Najko, I. Najko, I. Litovko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 26-31. — Бібліогр.: 6 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-08T03:35:05Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №4(98) 26
PLASMA ACCELERATOR WITH CLOSED ELECTRON DRIFT
AND OPEN WALLS
A. Goncharov1, A. Dobrovolsky1, L. Najko1, I. Najko1, I. Litovko2
1Institute of Physics National Academy of Science of Ukraine, Kiev, Ukraine;
2Institute for Nuclear Research National Academy of Science of Ukraine, Kiev, Ukraine
E-mail: ilitovko@kinr.kiev.ua
We present the original approach to use plasma accelerators with closed electron drift and open walls for creat-
ing effective lens with positive space charge. In paper describes one-dimensional model and simplest analytical
solutions following from it. The results of the numerical calculation and some experimental investigations data are
presented also.
PACS: 52.65.-y
INTRODUCTION
Plasma accelerators with anode layer are well known
and widely used devices. The theory of the physical
processes in such kind accelerators with metal walls is
well developed due to long time history of their investi-
gations. The same could be related to accelerators with
closed electron drift and dielectric walls. However ac-
celerators with closed electron drift and open (gas) walls
were not research till now. This type accelerator could
be interested for manipulating high-current flow of
charge particle. For example, it could be used for elabo-
ration of the low-cost, effective and low maintenance
plasma lens with positive space charge cloud. As was
shown in our preliminary works [2 - 5] the dynamical
positive space charge plasma lens with magnetic elec-
tron insulation and non-magnetized ions is effectively
focusing and manipulating by high-current beams of
negatively charged particles (electrons and negative
ions). Another attractive and perspective way using such
kind accelerators is the creation of cost-effective, small
rocket engines and enhancment ion-plasma technology
also that open up novel attractive possibility for effec-
tive high-tech practical applications.
In this paper we firstly present and describe model
of accelerator with closed electron drift and open (gas)
walls. Based on the idea of continuity of total current
transferring in the system obtained exact analytical
solutions describining potential distribution in accelera-
tion gap. The solution was got for the case of zero elec-
tron temperature, as well as in case finite electron tem-
perature, which magnetized electrons acquire in a cross-
heating electron field. It is shown that in case when all
electrons originated from the gap only by impact ioniza-
tion, and then go out at the anode due to classical trans-
verse mobility the condition complete potential drop in
the gap correspond to equality of the gap length to the
anode layer thickness in boundary mode.
1. THEORETICAL MODEL
AND SOME SOLUTIONS
For creation an effective lens of positive space
charge could be used plasma accelerators with closed
electron drift and open walls. The simplified scheme of
device is shown in Fig. 1. To analyze the properties of
such kind an accelerator we use a one-dimensional hy-
drodynamic model.
Fig. 1. The simplified scheme of device:
1 – anode; 2 – cathode; 3 − magnetic system
The base equations describe kind system includes
Poisson equation:
ϕ
π
′′=−
e
nn ie 4
1 , (1)
here for ion density we could write:
∫ −
=
x
ie
i sx
dssn
e
Mxn
0 )()(
)(
2
)(
ϕϕ
ν
. (2)
Will assume that the current density in gap volume
is the sum of the ion and electron components:
die jjj =+ , (3)
where ji, je − are ion and electron current density conse-
quently:
∫=
x
eii dxxnexj
0
)()( ν , (4)
( )
−= ⊥ eeee Tn
dx
dxEnexj )()( µ , (5)
iν − is the ionization frequency;
2
eH
e
m
e
ω
νµ =⊥
–
electron transverse mobility;
dx
dxE ϕ
−=)( − electric
field; φ − potential; νe is the frequency of elastic colli-
sions with neutrals and ions and ωeH is the electron
cyclotron frequency; Te – electron temperature that
could write in form:
∫=
x
e
e
e ds
ds
dj
xj
xT
0)(
)( ϕβ
. (6)
Thus, taking into account the said above, from (3)
we obtain expression:
mailto:ilitovko@kinr.kiev.ua
ISSN 1562-6016. ВАНТ. 2015. №4(98) 27
d
x
eeeei jTn
xx
nedxxne =
∂
∂
+
∂
∂
−∫ ⊥
0
)()( ϕµν . (7)
For simplicity in first approximation neglect the dif-
fusion and could consider that ne is constant along gap,
with given the fact that ion current is equals dj on the
cathode from (7) we get:
0)1( 2 =
∂
∂
−−
x
en
m
exen e
eH
e
ie
ϕ
ω
νν . (8)
Substitute ne, using the Poisson equation (1) where
ne >> ni., we can obtain from (8) the differential
equation of second order and representing this equation
in dimensionless form we have:
( ) 0)1( =′−−′′ ϕαϕ x , (9)
Here we have introduced the notation
2di
a
ν
ϕµα ⊥= ,
where φа − anode potential, d – gap length. Omitted
trivial solution ϕ′′=0 and taking into account boundary
condition 1
0
=
=x
ϕ we obtain potential distribution
within gap in form:
( ) 11)1( 2 +−−= xaϕ , (10)
here a=1/2α.
Potential distribution (10) for different values of pa-
rameter a is shown in Fig. 2. One can see that under
a=1 the total applied potential falling down inside of the
accelerating gap. In this optimal case
i
Ad
ν
ϕµ⊥=
2 . (11)
Fig. 2. Potential distribution for different parameters a
Suggested that all electrons originated from the gap
only by impact ionization, and then go out at the anode
due to classical transverse mobility this expression can
represent in form:
( )
i
e
Ae ν
ν
ϕρδ
2
= . (12)
This expression coincides with one for classical an-
ode layer (see [6]) accurate within √2.
Note, in case when parameter a < 1 (the gap length
less than δ) potential drop is not completed. For case
a > 1, when the gap length d > δ potential drop exceed
applied potential. This can be due to electron space
charge dominated at the accelerator exit.
Extend our description and take into consideration
that ne changes along gap. As before will study case
Te = 0, than for dimensionless equations (7) is true:
1)()(
0
=
∂
∂
−∫
x
ee x
xbndssnc ϕ , (13)
where we introduce notices:
dj
en
b
d
a 0ϕµ⊥= ,
d
i
j
den
c 0ν
= . (14)
Will consider quasi-neutral plasma ne ≈ ni for sim-
plicity, so substitute dimensionless equality (2) in (13)
get:
∫ ∫ =
−
⋅
∂
∂
⋅⋅−
x x
e
e sx
dssn
x
fbdssnс
0 0
1
)()(
)()(
ϕϕ
ϕ
, (15)
here
a
i e
Mdf
ϕ
ν
2
= .
After some transformations and subject to the fact
that ion current is (first term in left part (13)) equals dj
on the cathode, equality (15) could rewrite in form:
( )∫ ∫ ⋅=−
∂
∂1 1
)()()(2)(
x x
ee csndssxbf
x
snds ϕϕ . (16)
Equality integrand gives:
( ) csxbf
x
=−
∂
∂ )()(2 ϕϕ ,
or for potential distribution taking into account bounda-
ry condition we have :
( )22
2
2
2
1
44
1)( −+−= x
f
a
f
axϕ , (17)
where bca /= , note it is corresponding to parameter
α/1 introduced above. From (17) could note the behav-
ior of potential distribution depends on ratio
2
2
4 f
ap = .
Here parameter f describes impact of ion density. Poten-
tial distribution for this case is shown in Figs. 3 and 4.
Fig. 3. Potential distribution for quasi-neutral plasma
for different parameter α
If we now derived (13) we could obtain equation for
electron density:
ϕ
ϕ
′
′′−
=
∂
∂ a
x
n
n
e
e
1 . (18)
ISSN 1562-6016. ВАНТ. 2015. №4(98) 28
Fig. 4. Potential distribution in gap for quasi-neutral
plasma for different values of parameter f
Solution (18) with given (17) has form:
12 2
)1()(
−
−⋅= a
f
e xCxn , (19)
where C – some constant. Note that if a = 2f2 the elec-
tron density doesn’t change along the gap and solution
(17) is reduced to (10) and C=jd/eν id. The condition
above could rewrites in form:
i
id
ed ν
τ
τ 22 = or 12 22 == iidied ντντ , (20)
where
E
d
ed
⊥
=
µ
τ – electron lifetime, idτ =d/vid – ion
living time. Indeed (20) is some generalization condi-
tion of self-sustained discharge in crossed EH fields
taking into consideration both electron and ion dynamic
peculiarity.
All these solutions were got under condition Te=0.
For clarification temperature effect on the acceleration
layer characteristics assume that electrons get energy
from electric field E, then (6) could be presented as:
ϕβ ⋅=eT , (21)
where 10 ≤< β . In this case from (7) instead of (8)
we have:
( ) 0)1()1( =′+−−′′ ϕβαϕ x (22)
and get solution in form:
1)2(
)1(
+−
+
= xxa
β
ϕ . (23)
Similarly to the above for gap length receive:
i
Ad
ν
βϕµ )1(2 +
= ⊥ . (24)
Note, that it differs from the previous one (11) by
factor β+1 only, that describes temperature effect.
Potential distribution for different value parameters a
and β is shown in Fig. 5. One can see that with increas-
ing temperature the gap length where potential drop is
completed is grows.
Now consider more general model description, as-
suming that heating losing occurs mostly by different
kind of collisions. Introducing characteristic time of
temperature loss by collision − τ0 could write for tem-
perature definition:
Fig. 5. Potential distribution for different parameters
a and β
e
d
e en
EjT 0τ= . (25)
Thus equation (7) rewritten in form:
12
2
0 =+− ∫⊥
⊥ dxn
j
de
dx
dn
j
e
dx
d
e
d
i
e
d
νϕµϕτµ . (26)
Dimensionless this equation and Poisson’s equation
and introducing dimensionless parameters, obtain sys-
tem:
1)()(
0
=+′−′′ ∫
x
dssncxbna ϕϕ ,
ϕ
ϕϕ
′′=
−
− ∫ g
sx
dssnfxn
x
0 )()(
)()( , (27)
where introduced dimensionless parameters
2
0
d
a aϕτµ⊥= ,
0
24 end
g a
π
ϕ
= , (28)
parameters b, c, f – are corresponds to entered above.
In general case this system hasn’t analytical solu-
tions and requires numerical calculations. At firstly
consider solution under next boundary conditions:
0,1
10
==
== xx
ϕϕ . (29)
The results computer simulations are shown in
Fig. 6. One can see that for α<0.5 possible potential
drop below zero, that could correspond accumulating
electron density.
Fig. 6. Potential distribution (numerical simulations)
under boundary condition (29)
ISSN 1562-6016. ВАНТ. 2015. №4(98) 29
If we will suggest zero electric field on the cathode
layer and change boundary condition (29) on next:
0,1
10
==
== xx
Eϕ (30)
got solutions similar to those obtained above (Fig. 7).
Fig. 7. Potential (up) and electron density (down)
distribution (numerical simulations) under boundary
condition (30)
As ones can see from Fig. 7 electron density is a lit-
tle change along the gap. Note, also if we assume that
edττ =0 then (25) will be reduced to form:
e
d
e en
djT
⊥
=
µ
, consequently in (5) the temperature term
escapes. Therefore we come back to case (8) and poten-
tial distribution (10).
2. EXPERIMENTAL SETUP AND RESULTS
The experimental setup of plasma accelerator, form-
ing ion flow converging towards the axis system had
been made for theory testing purpose. It is shown in the
Fig. 8.
Fig. 8. Experimental setup: 1 – cathode; 2 – anode;
3 – permanent magnets system
Anode diameter is 6.7 cm, cathode is 3.2 cm, distance
between anode and cathode is 1.75 cm. Magnetic field
Н=650…750 Oe, voltage less 2 kV. The working gas is
argon. The current-voltage characteristics were obtained
in a low-current and high-voltage discharge condition
(current about 100 mA, voltage discharge of a few kV).
Under such condition experimental current-voltage
characteristics must be linear that ones can see in Fig. 9.
Fig. 9. The current-voltage characteristic
From experimental data can be found electron densi-
ty, which in our case is equal to 5·1010 cm-3, that is typi-
cal for related system. The current is a little depends on
gas pressure in the system since anode layer is inde-
pendent from neutrals concentration (Fig. 10).
Fig. 10. Current dependence vs gas pressure
Fig. 11 is shown the photo of plasma jet that is ob-
served in high-current mode of accelerator operation.
Fig. 11. Plasma jet in high-current mode
ISSN 1562-6016. ВАНТ. 2015. №4(98) 30
It was measured the floating potential and ion cur-
rent downstream 6 cm from plasma device.
In Fig. 12 is shown dependence floating potential on
the system axis vs pressure of working gas in chamber.
Anode potential is 1.5 kV.
Fig. 12. Floating potential dependence vs working gas
pressure (up – at the system exit, down – at the axes)
Ones can (see Fig. 12) the formed potential drop that
could be used for ion beam accelerating. In the Fig. 13
is shown ion beam current density dependence on cur-
rent discharge on the jet axes. The power flow increase
with current grows. Note also, the ion current density at
torch axes can consist up to 2…3% total discharge cur-
rent. That opens up too novel attractive possibility for
using this kind devices as rocket engines.
Fig. 13. Dependence current density vs discharge
current density
CONCLUSIONS
First, the original approach to use plasma accelera-
tors with closed electron drift and open walls for crea-
tion cost effective low maintenance plasma device for
production converging towards axis accelerating ion
beam was described. Based on the idea of continuity of
current transferring in the system are found exact ana-
lytical solutions describing electric potential distribution
along acceleration gap. It was shown that potential dis-
tribution is parabolic for different operation modes as in
low-current mode well as in high current quasi neutral
plasma mode and can’t depend on electron temperature.
It is found under conditions that everything electrons
originated within the gap by impact ionization only, and
go out at the anode due to mobility in transverse mag-
netic field, the condition full potential drop in the accel-
erating gap corresponds to equality gap length to the
anode layer thickness. In case when the gap length less
than anode layer thickness potential drop is not com-
pleted. For case when the gap length more than anode
layer potential drop exceed applied potential.
Experimental model of accelerator that formed ion
flow converging towards the axis system was created.
The current-voltage characteristic of the accelerator in
different operating mode was defined. In high-current
mode of accelerator operation is observed plasma jet. It
is shown at the jet axis forms potential drop that could
be used for ion beam accelerating. The experimental
results are in good accordance with theory data.
Note also that the presented plasma device is attrac-
tive for many different high-tech practical applications,
for example, like plasma lens with positive space cloud
for focusing negative intense charge particles beams
(electrons and negative ions) and for potential devises
small rocket engines.
The work is supported by the grant of 34-08-14
(Ukr) and 14-08-90400 (Rus).
REFERENCES
1. A.A. Goncharov and I.G. Brown. Plasma Devices
Based on the Plasma Lens-A Review of Results and
Applications // IEEE Trans. Plasma Sci. 2007, v. 35,
№ 4, p. 986-991.
2. A. Goncharov, A. Dobrovolskiy, S. Dunets,
A. Evsyukov, I. Litovko, V. Gushenets, E. Oks. Pos-
itive-Space-Charge Lens for Focusing and Manipu-
lating High-Current Beams of Negatively Charged
Particles // IEEE Trans. Plasma Sci. 2011, v. 39,
№ 6, p. 1408-1411.
3. V. Gushenets, A. Goncharov, A. Dobrovolskiy,
S. Dunets, I. Litovko, E. Oks, A. Bugaev. Electro-
static plasma lens focusing of an intense electron
beam in an electron source with a vacuum arc plas-
ma cathode // IEEE Trans. Plasma Sci. 2013, v. 41,
№ 4, Part 3, p. 2171-2174.
4. Potter D. Methods of Calculations in Physics. Mos-
cow: “Mir”, 1975 (in Russian).
5. A.A. Goncharov, A.M. Dobrovolskiy, S.P. Dunets,
I.V. Litovko, V.I. Gushenets, E.M. Oks // Rev. Sci.
Instrum. 2012, v. 83, p. 02B.
6. S.D. Grishin, L.V. Leskov. Plasma Accelerators.
Moscow: "Mashinostroenie”, 1983 (in Russian).
Article received 08.05.2015
ISSN 1562-6016. ВАНТ. 2015. №4(98) 31
ПЛАЗМЕННЫЙ УСКОРИТЕЛЬ С ГАЗОВЫМИ СТЕНКАМИ
И ЗАМКНУТЫМ ДРЕЙФОМ ЭЛЕКТРОНОВ
A. Гончаров, A. Добровольский, Л. Найко, И. Найко, И. Литовко
Впервые описана одномерная модель оригинального плазменного ускорителя с открытыми стенка-
ми, представляющая плазмооптическое устройство нового поколения, которое может быть использова-
но для современных технологий, в частности, для создания плазменной линзы с положительным объем-
ным зарядом, а также малогабаритного ракетного движителя. Получены простейшие аналитические
решения и представлены результаты численного моделирования, позволяющие с новых позиций рас-
сматривать физику процессов в ускорителях холловского типа. Приведены результаты эксперименталь-
ных исследований.
ПЛАЗМОВИЙ ПРИСКОРЮВАЧ З ГАЗОВИМИ СТІНКАМИ
ТА ЗАМКНУТИМ ДРЕЙФОМ ЕЛЕКТРОНІВ
O. Гончаров, A. Добровольський, Л. Найко, I. Найко, I. Лiтовко
Вперше описана одновимірна модель оригінального плазмового прискорювача з відкритими стінка-
ми, яка є плазмооптичним пристроєм нового покоління, для ефективного застосування в сучасних тех-
нологіях, зокрема, для створення плазмової лінзи з позитивним просторовим зарядом, а також малога-
баритного ракетного двигуна. Отримані прості аналітичні розв’язки і представлені результати числово-
го моделювання, які дозволяють з нових позицій розглядати фізику процесів у прискорювачах холлів-
ського типу. Наведенo результати експериментальних досліджень.
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