Space charge lens for focusing negative ion beams
The idea of space charge lens for focusing negative ion beam is set forth. With the use of this lens focusing of H– ion beam with 10 keV energy and 30 mA current is realized. Focal length value of ~ 12 cm is reached.
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Cite this: | Space charge lens for focusing negative ion beams / V.P. Goretsky, I.A. Soloshenko, A.I. Shchedrin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 121-123. — Бібліогр.: 6 назв. — англ. |
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Goretsky, V.P. Soloshenko, I.A. Shchedrin, A.I. 2015-03-18T18:42:59Z 2015-03-18T18:42:59Z 2000 Space charge lens for focusing negative ion beams / V.P. Goretsky, I.A. Soloshenko, A.I. Shchedrin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 121-123. — Бібліогр.: 6 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/78543 533.932 The idea of space charge lens for focusing negative ion beam is set forth. With the use of this lens focusing of H– ion beam with 10 keV energy and 30 mA current is realized. Focal length value of ~ 12 cm is reached. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Вeams and waves in plasma Space charge lens for focusing negative ion beams Article published earlier |
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Space charge lens for focusing negative ion beams |
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Space charge lens for focusing negative ion beams Goretsky, V.P. Soloshenko, I.A. Shchedrin, A.I. Вeams and waves in plasma |
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Space charge lens for focusing negative ion beams |
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Space charge lens for focusing negative ion beams |
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Space charge lens for focusing negative ion beams |
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Space charge lens for focusing negative ion beams |
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space charge lens for focusing negative ion beams |
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Goretsky, V.P. Soloshenko, I.A. Shchedrin, A.I. |
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Goretsky, V.P. Soloshenko, I.A. Shchedrin, A.I. |
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Вeams and waves in plasma |
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Вeams and waves in plasma |
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2000 |
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Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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The idea of space charge lens for focusing negative ion beam is set forth. With the use of this lens focusing of H– ion beam with 10 keV energy and 30 mA current is realized. Focal length value of ~ 12 cm is reached.
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1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/78543 |
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Space charge lens for focusing negative ion beams / V.P. Goretsky, I.A. Soloshenko, A.I. Shchedrin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 121-123. — Бібліогр.: 6 назв. — англ. |
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AT goretskyvp spacechargelensforfocusingnegativeionbeams AT soloshenkoia spacechargelensforfocusingnegativeionbeams AT shchedrinai spacechargelensforfocusingnegativeionbeams |
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2025-11-24T03:45:03Z |
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UDC 533.932
Problems of Atomic Science and Technology. 2000. № 6. Series: Plasma Physics (6). p. 121-123 121
SPACE CHARGE LENS FOR FOCUSING NEGATIVE ION BEAMS
V.P.Goretsky, I.A.Soloshenko, A.I.Shchedrin
Institute of Physics of National Academy of Sciences of Ukraine, Kiev, Ukraine,
e-mail: solosh@marion.iop.kiev.ua, fax: +38(044)2651589, phone: +38(044)2650925
The idea of space charge lens for focusing negative ion beam is set forth. With the use of this lens focusing of H–
ion beam with 10 keV energy and 30 mA current is realized. Focal length value of ∼ 12 cm is reached.
Introduction
The idea of the use of space charge fields for
focusing positive ion beams for the first time was
proposed by Gabor [1] and was further developed in
proceedings of A.I.Morozov [2]. Efficiency of such lens
has been confirmed in a number of experiments (e.g. in
[3]). Negative space charge of the lens is formed by
electrons, which are held by magnetic field. However, it
should be noted that any design of space charge lens for
positive ion beam cannot be used for negative ion beam
because in the last case positive ions should be used for
the focusing.
The idea of space charge lens for negative ion beam
is based on the use of positive ions formed at gas
ionization by the beam itself. That is, here the use of
process, which is undesirable in case of focusing
positive ion beams, is proposed. Since in ionization
process the electrons are also formed, required positive
space charge can be created only at condition of
withdrawal these electrons by electric field. Large
lifetime of positive ions in the system is ensured at that
by their inertia. Particularly, the simplest focusing
system may be represented by metal cylinder, which
coaxially embraces the beam, and two electrodes at the
ends of the cylinder. The last must be transparent for the
beam, that is, should be grid or ring ones. In internal
space of the cylinder required positive space charge will
be created, if one will ensure withdrawal of the
electrons by supplying positive potential to periphery
electrodes with respect to central electrode. It should be
noted that for efficient withdrawal of the electrons the
potential should be applied at which extension of space
charge layer is comparable with longitudinal dimension
of the system. Such extended space charge layers in the
system under study can be created already at potential
difference between the lens electrodes of 100÷1000 V
due to relatively low concentration of the beam plasma
(∼ 108 cm-3).
By supplying the gas immediately into the cylinder
space required conditions for ionization may be created
without essential increase of the pressure outside the
lens.
Estimation of focal power of space charge lens
Obviously, proposed principle of the focusing can be
realized only at condition when space charge of positive
ions formed in result of gas ionization exceeds space
charge of the beam ions. It applies limitation on low
bound for the pressure of associated gas. The value of
required gas concentration can be determined from the
balance equation for positive ions formation and
leaving, and is given by formula:
0i
a rσv
2v
n
−
+≥ (1)
where na is gas concentration; σi is cross section of
ionization of the gas particles by the beam ions; v+,v- are
velocities of leaving ions and the beam particles,
respectively; r0 is the beam radius [4]. In regime of free
propagation of the beam, at fulfilling the condition (1),
the beam potential with respect to periphery is positive,
and its value is determined by average thermal energy
of the plasma electrons which, in turn, is defined by
Coulomb collisions with the beam ions. Focusing fields,
which arise at that in the beam with concentration of
∼ 108 cm-3, possess strength just several V/cm and thus
can be used just for improvement of transportation of
weakly divergent beams.
Usually for focusing the beams extracted from the
single aperture the lenses with focal length∼ 10-20 cm
are necessary which requires radial fields ∼ 100 V/cm.
Such fields in the system under study may be achieved
only at condition of practically total withdrawal of the
electrons from the focusing region. At fulfilling this
condition the electrons space charge may be neglected,
and focusing features of the lens can be estimated
comparatively easily.
As initial equations for calculation of focusing field
we use the continuity equation for positive ions, Poisson
equation for the potential and the equation for positive
particle motion in radial electric field:
i
ia λ
j
Vσnenrj
rr
1 −
−−+ ==
∂
∂
(2)
)ne(n4
r
r
rr
1
−+ −−=
∂
∂
∂
∂ πϕ (3)
+
+
−
=
m
(r)))(r2e(
r),(rV i
i
ϕϕ (4)
Here λi is path length of the beam particle till gas
ionization; V+(ri,r) is velocity of positive particle formed
at ri point and reached r point.
From (2) and (4) in assumption of uniform
distribution of positive ions concentration along the
radius one can determine (in regime of strong
overcompensation of the beam space charge) that radial
fall of the potential is the following:
3
2
i
0
a
m2eλ
rI
≈
+
−ϕ . (5)
122
In opposite case, which is achieved by the beam current
increase and corresponds to quasineutral regime, the
potential fall is given by:
−
−
+≈ U
mλ
mr
2
i
2
0
aϕ . (6)
Here I – and U– are current and energy of negative ion
beam. It follows from equations (5) and (6) that at the
increase of beam current radial fall of the potential ϕ a
grows up at first, and after that reaches its maximum
value which is independent on the beam current value.
It follows from the expressions given above that for
the beam of hydrogen negative ions with energy
∼ 10 kEv in the lens with dimensions ∼ 10 cm at gas
(argon, krypton, xenon) pressure ∼ 10-3 Torr actually
achievable radial fields exceed 100 V/cm.
Using methods described in [5] it is easy to obtain
expression for focal power of the lens:
2
0
a
L
0
2
0
a
rU
L
(z)Ur
dz
(0)U
1
f
1
−−−
≈= ∫
ϕϕ
. (7)
Substituting ϕ a in (7) by expressions from (5) and (6)
we obtain for large current regime (quasineutral
regime):
−
+=
mλ
Lm
f
1
2
i
, (8)
and for small current regime:
−
+
−
−
+
==
U
L
m
2eλ
πj
)r(λ
L)
m
m
()
9π
П(
f
1
3
2
i3
2
2
0i
3
1
3
2
. (9)
It follows from (8) that at lens parameters given above
required focal length value ∼ 10 cm is achieved, and the
losses of negative ions at the beam current density
> 45 mA/cm2 are less than 10%.
EXPERIMENTAL STUDY OF H– ION BEAM
FOCUSING BY SPACE CHARGE LENS
The researches have been performed at the setup
shown schematically on Fig.1. The beam of H– negative
ions with current ∼ 10÷30 mA and energy ∼ 10 kEv was
extracted from the source of surface-plasma type 1.
Beam formation and turn were accomplished by
magnetic field ∼ 2 kGs by means of magnets 2. The
beam current was measured by collector 7 with diameter
∼ 10 cm, current density was measured by collector 6
with 2 cm diameter. Space charge lens was placed at
distance ∼ 20 cm from emission slit of the source.
Distance from output plane of the lens till the collector
comprised ∼ 30 cm. With such geometry of the system
minimum beam radius should be observed at distance
12 cm. Lens design was the following: inside grounded
cylindrical cabinet 3 made from stainless steel with
10 cm external diameter, 13 cm length, input and output
apertures with 5 cm diameter, metal cylinder 5 with
7 cm diameter and 10 cm length was placed. Presence
of the last unit allowed maintenance of uniform
distribution of the gas pressure inside the lens. Its
potential was hold either at ground level, or at level of
electrode 4 potential (it had no essential influence on
focusing features of the lens). Cylindrical electrode 4
made from stainless steel grid with 5 cm diameter and
10 cm length was mounted inside electrode 5 by means
of dielectric rings at the ends. During the experiment the
potential of electrode 4 could be varied in range from 0
down to –1500 V. At outer side of the cabinet two
sockets were placed; one of those served for supply of
working gas, and another was used for measurement of
the pressure in lens region. Pressure in the lens section
and in the beam drift chamber differed at that for more
than one order of magnitude. Argon, krypton and xenon
were used as working gases. Choice of those gases was
due to, at first, comparatively high values of ionization
cross sections and, at second, comparatively large
inertia of positive ions formed in result of ionization.
Both factors facilitated creation of the conditions
required for efficient focusing of negative ion beam.
Fig.1. Schematic drawing of the experiment
Before proceeding to description of the experimental
results, let us estimate critical pressure, in excess of
which the charge formed due to positive ions created
during the gas ionization starts to overcome essentially
negative space charge of negative ion beam. For the
estimation let us suggest that average energy of ions
created in result of the gas ionization by the beam
comprises ∼ 1 eV. Then from expression (1) and known
from proceeding [6] values of ionization cross section
for the beam with parameters given above we obtain:
Po ∼ 1.5⋅10-4 Torr for argon, Po ∼ 4⋅10-5 Torr for krypton,
Po ∼ 6⋅10-5 Torr for xenon. At pressure above Po the rate
of positive ions creation is proportional to the pressure,
however, density of positive ions charge grows up at
that slightly slower due to the increase of the rate of
their leaving along the radius at the expense of radial
potential fall growth.
As it was shown by the experiments, in agreement
with the estimation for the pressures higher than critical
one the effect of negative ion beam focusing is
observed. The most clear demonstration of focusing
features of the lens is exhibited in Fig.2 which presents
the dependencies of the beam compression degree on
potential difference between the lens electrodes
(grounded cabinet 3 and grid electrode 4) obtained at
various pressures of argon. The beam compression
-U
1
2 3 4 5
6
7
H–
Working
gas
To vacuummeter
123
degree means here the ratio of maximum current density
with optimal potentials applied to the electrodes to that
without applying the potentials. Behavior of the curves
is in agreement with qualitative considerations given
above. At first the beam is compressed with the growth
of potential difference, but starting from V ∼ 200 V all
curves reach the saturation. It is explained by the fact
that at V > 200 V electrons density in the beam becomes
inessential and radial fall of the potential is mainly due
to positive ions and beam ions. At the pressure increase
the rate of compression degree growth increases which
is due to the growth of positive space charge. At that
maximum compression degree increases at first (curves
1-3), and decreases in subsequent (curves 4-6) which
can be explained by the beam overfocusing. The last
circumstance was confirmed by special experiments in
which metal plate with two holes was placed at 4 cm
distance from the lens output aperture, and at distance of
22 cm luminescent screen was situated which served for
observation of images of the holes. At optimal potential
difference at the lens electrodes xenon pressure increase
results at first to converging of the holes images, and at
high enough pressure these images join together, and
after that diverge in direction opposite to initial one with
respect to the center thus giving unambiguous evidence
of the beam overfocusing.
-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6
1,0
1,5
2,0
2,5
3,0
3,5
j/j
0
UBR, kV
1
2
3
4
5
6
Fig.2. Dependence of hydrogen negative ion beam compression j/j0 on negative potential of braking cylinder UBR.
Argon pressure (Torr) in the lens is: 3⋅10-4(1), 7.6⋅10-4(2), 1.5⋅10-3(3), 2.2⋅10-3(4), 3.6⋅10-3(5), 6.4⋅10-3(6)
And, finally, the fact that maximum compression
degree at given system geometry corresponds to focal
length ∼ 12 cm can be used for comparison of the
experimental results with the calculations. Let us choose
for the comparison the case of argon use in which
optimal pressure comprises ∼ 3⋅10-3 Torr. Accordingly
to (9), at beam current of 15 mA calculated value of
focal length is ∼ 20 cm. This value is close enough to
actually measured one (f ∼ 12 cm).
Thus, in current proceeding the method of negative
ion beam focusing by means of space charge lens is
proposed and realized. This method possesses practical
interest for the beams with comparatively large current
density in which acquirement of big enough positive
space charge can be reached without significant losses
of the beam ions due to overcharging.
References
1. D.Gabor. Space Charge Lense for Focusing Ions
Beams. // Nature. 1947, 160, p.89-90.
2. A.I.Morozov. Focusing of cold quasineutral beams in
electromagnetic fields. // Reports of Acad. of Sciences of
the USSR. 1965, 163, p.1363-1368.
3. A.A.Goncharov, A.N.Dobrovolsky, A.N.Kotsarenko,
A.I.Morozov, I.M.Protsenko. Static and dynamic
properties of high-current plasma lens. // Fiz. Plasmy.
1994, 20, N.5, p.499-505.
4. M.D.Gabovich, L.S.Simonenko, I.A.Soloshenko.
Compensation of the space charge of intensive negative
ion beam. // Zh.Tekh.Fiz. 1978, 48, N.7, p.1389-1393.
5. V.M.Kelman, S.Ya.Yavor. Electron Optics. Moscow:
USSR Academy of Science Publishing, 1959.
6. Ya.M.Fogel, A.G.Koval, Yu.Z.Levchenko. Gas
ionization by negative ions. // Zh.Eksp.Teor.Fiz. 1960,
38, N.4, p.1053-1060.
SPACE CHARGE LENS FOR FOCUSING NEGATIVE ION BEAMS
V.P.Goretsky, I.A.Soloshenko, A.I.Shchedrin
Introduction
Estimation of focal power of space charge lens
EXPERIMENTAL STUDY OF H– ION BEAM FOCUSING BY SPACE CHARGE LENS
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