Plasma focusing devices in external programmed magnetic field
At present there is a significant requirement for the development of devices for focusing high-energy intense ion beams for the solution of actual scientific and technological problems (inertial thermonuclear fusion on heavy and light ions, radiotherapy, high energy investigations, research of radia...
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irk-123456789-815002015-05-18T03:02:01Z Plasma focusing devices in external programmed magnetic field Ivanov, B.I. At present there is a significant requirement for the development of devices for focusing high-energy intense ion beams for the solution of actual scientific and technological problems (inertial thermonuclear fusion on heavy and light ions, radiotherapy, high energy investigations, research of radiation resistance of materials, implantation metallurgy, etc.). 1999 Article Plasma focusing devices in external programmed magnetic field / B.I. Ivanov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 81-83. — Бібліогр.: 18 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/81500 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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At present there is a significant requirement for the development of devices for focusing high-energy intense ion beams for the solution of actual scientific and technological problems (inertial thermonuclear fusion on heavy and light ions, radiotherapy, high energy investigations, research of radiation resistance of materials, implantation metallurgy, etc.). |
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Ivanov, B.I. |
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Ivanov, B.I. Plasma focusing devices in external programmed magnetic field Вопросы атомной науки и техники |
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Ivanov, B.I. |
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Ivanov, B.I. |
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Plasma focusing devices in external programmed magnetic field |
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Plasma focusing devices in external programmed magnetic field |
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Plasma focusing devices in external programmed magnetic field |
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Plasma focusing devices in external programmed magnetic field |
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Plasma focusing devices in external programmed magnetic field |
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plasma focusing devices in external programmed magnetic field |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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1999 |
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http://dspace.nbuv.gov.ua/handle/123456789/81500 |
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Plasma focusing devices in external programmed magnetic field / B.I. Ivanov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 81-83. — Бібліогр.: 18 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT ivanovbi plasmafocusingdevicesinexternalprogrammedmagneticfield |
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2025-07-06T06:28:29Z |
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2025-07-06T06:28:29Z |
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1836877940655128576 |
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PLASMA FOCUSING DEVICES IN EXTERNAL PROGRAMMED
MAGNETIC FIELD
B.I. Ivanov
NSC KIPT, Kharkov, Ukraine
1. INTRODUCTION
At present there is a significant requirement for
the development of devices for focusing high-energy
intense ion beams for the solution of actual scientific
and technological problems (inertial thermonuclear
fusion on heavy and light ions, radiotherapy, high
energy investigations, research of radiation resistance of
materials, implantation metallurgy, etc. [1,2]). For this
purpose the quadrupole magnetic lenses are widely
used. Last time plasma lenses with essentially larger
focusing force are used. It is essential that the charge of
focused beam is compensated in these lenses. With
energy and current growth of accelerated beams plasma
lenses should replace the conventional ones.
Plasma lens investigation is performed in many
scientific centers such as Lawrence Berkeley
Laboratory, CERN, GSI (Darmstadt) and others (see,
e.g., one of the last reviews [3]). Nowadays three types
of lenses are usually used: Gabor electron (electrostatic)
lens, current (magnetic) plasma lens, Morozov
electrostatic plasma lens. As for historical approach, the
self-focusing of charged particles beams by own
magnetic field was considered in thirties by H.Alfven
and W.Bennet. In 1947 D.Gabor proposed the space
charge lens for electrostatic focusing of ion beams [4].
Gabor lens consists of cylindrical column of electron
plasma confined with magnetic field. Further
W.Panofsky and W.Baker performed experiments on
high-energy ion beams focusing by magnetic plasma
lens which represents itself the discharge in plasma [5].
In this case focusing is provided by the azimuthal
magnetic field produced by longitudinal current in
plasma column. Last years lenses of such type are
successfully elaborated and used in CERN and GSI. In
sixties A.Morozov proposed a plasma electrostatic lens
in which magnetic surfaces are the equipotentials of
electric field [6]. Further this direction was successfully
developed in experiments of A.Goncharov, i.e., for ion
beam focusing with the energy of tens kV [7, 8]. In
eighties for focusing ultra-high energy electron beams it
was proposed «passive» plasma lenses [9, 10] based on
conception of magnetic self-focusing. Later the
conception of «passive» plasma lenses was expanded on
more worth-while adiabatic plasma lenses [11].
For focusing of intense ion beams of high energy
the longitudinally homogeneous «active» magnetic
plasma lenses is applied with the greatest success (e.g.,
see [12, 13]). With the help of such lens the ions of gold
with energy 2 GeV were focused on the distance of
about 30 cm [12, 13]. For such focusing the discharge of
a capacity unit with current of about 10 kA was used at
time duration of beam focusing about 1 (sec. The
efficiency of such lens was (10-5 in the first work [12].
In the second work it was enhanced to (10-3 [13] but was
rather small yet. The beam was focused to possible
minimum radius 125 μm conditioned by initial
emittance. In the work [14] it was also proposed to use
adiabatic plasma lens for slow compression of ion beam
on the length of several betatron oscillations. These data
show good prospects of the focusing method in question
and the necessity of efficiency enhancement
investigation.
This work continues the investigations of plasma
lenses performed at the NSC KIPT in the frame of the
STCU Project No.298 [15,16]. In this work for the
enhancement of focusing efficiency by current
(magnetic) plasma focusing device (plasma focuser) it is
proposed to use the external magnetic field that changes
along the device length so that the focusing current
channel radius be close to the focused beam radius and
be decreasing with the beam radius decrease. (In this
consideration the fact is used that the current channel
radius is inversely proportional to the square root of
magnetic field strength). It will allow to reduce the
focusing current, to increase the efficiency, entrance
radius and pulse duration of the focused beam.
In this work the studies of non-uniform adiabatic
plasma lenses of different types (magnetic lens, Gabor
and Morozov lenses, charge-current lens) are
performed. It should be noted, that in [11, 14] the
criterium of adiabatic property is small changing of
plasma lens parameters over focusing length (slight
non-uniformity). In this work the another case will be
studied when that criterium is small changing of
focusing device parameters on much smaller «cyclotron
length» which is equal to the product of electron
cyclotron frequency by longitudinal velocity of plasma
electrons (the condition of drift approximation). In this
case the plasma parameters change mainly on the
focusing length (strong nonuniformity).
CALCULATIONS OF ION FOCUSING IN NON-
UNIFORM PLASMA LENSES
At first we study in detail the current (magnetic)
plasma lens, and then discuss the usefulness of these
results to Gabor and Morozov lenses of charge
(electrostatic) type. In conclusion, the charge-current
lens will be studied. Under the term «lens», the long
focusing channel will be understand in this paper (i.e.,
«plasma focuser» [11]).
2.1. Plasma current (magnetic) lens
Let us consider the problem of ion beam
focusing by an azimuth magnetic field of longitudinal
current in plasma. We investigate the case when the
current radius is determined by the external non-
uniform longitudinal magnetic field. The problem is
being solved at the paraxial approximation. In this case
the equation of the magnetic surfaces is as follows:
( ) ( ) ( )
( )a z
a B
B z
z
z
2
2 0 0
= , (1)
where a(z) is the variable radius of the magnetic surface,
Bz(z) is the longitudinal magnetic field on the axis, Bz(0)
and a(0) are determined by the boundary conditions at
are determined by the boundary conditions at z = 0. We
assume that in the case of the strong magnetic field the
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
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81
electrons which transport the current in plasma are
moving along cylindrical magnetic surfaces enclosed
one into another. The boundary conditions are defined
as follows: at z=0, a(0) = b, where b is the radius of an
electrode that supply the current in the plasma (e.g., it is
the inner electrode of the plasma gun). From Eq.(1) it
follows: if the equidistantness of the magnetic surfaces
is set in some cross-section, then it is conserved in any
other one. As a result, if the current density is
homogeneous in the electron emitter region, then it is
homogeneous in any other current channel cross-
section. It is necessary for focusing without spherical
aberration because the Lorenz force focusing an ion
toward the axis is proportional to the distance of the ion
from the axis:
( )F e
c
vB ev
c
I
cr
evI
c a z
rm = − = − = −ϕ
2 2
2 2 . (2)
As a result, the equation for the focusing ions
trajectories will take the form:
( )
( )′ ′ + =r k
B z
B
rz
z
2
0
0 , k I e
Mc vb
2
2 2
2= . (3)
In (2), (3), I is the current in plasma, e and M are the
charge and mass of the ion (i.e., the proton), c is the
light velocity, v is the ion velocity, Bz(0) is the magnetic
field induction in the region of the plasma gun output,
Bϕ is the azimuthal magnetic field of the current.
Under condition Bz(z) = const from Eq.(3) we have:
r r kz= 0 cos , and the focusing distance in the plasma:
L kf = π / 2 . For a lens of length l< L f we have:
)(klctgklL f
1−+= ,
where at kl <<1 it is easy to obtain the well-known
expression for focusing distance of a thin lens:
12 −= )( lkL f .
In general case, the trajectories of focused
particles are calculated with the help of a computer [16].
For some cases the Eq.(3) has an analytic solution, e.g.,
for the «bell-liked» distribution of the magnetic field
( ) ( ) ( )[ ]B z B z dz z= +
−
0 1 2 2
/ . (4)
In this case Eq.(3) takes the form:
( )[ ]′ ′ + + =
−
r k r z d2 2 2
1 0/ . (5)
The solution of Eq.(5) that is known from the electron
optics [18] can be written as it follows:
( )
( )r
r
k
k z d
z d
=
+
+
0
2
2
1
1sin arcctg
sin arcctg
. (6)
The coordinate of the ion beam focus
corresponds to the condition r=0, and is defined by the
expression:
z d
k
f =
+
ctg π
1 2 . (7)
The calculations based on the above formulae
show: due to compression of the current channel by the
external magnetic field, the one -order decrease of the
focusing current can be reached. In this case the
focusing of intense proton beams (of MeV range
energy) in steady state regime can be realized.
During the ion focusing and compression of the
current channel by the magnetic field of a solenoid,
some ions (with large injection radius) can move partly
out of the current channel. They also deflected to the
axis but not get to the common focus. The moving
equation for them has the form:
′ ′ + =r
r
κ 0 , where κ = 2
2
ZeI
c Mv
. (8)
To put together all ions in the focus, it is
necessary to optimization the external magnetic field
distribution. For this aim we can determine the form of
the magnetic surface that limits the current channel.
Then we can calculate the parameters of the solenoid
(for producing such magnetic surface) and determine
the focusing ion trajectories (see [16,17]). The
calculation can be carried out for paraxial ion
trajectories and paraxial magnetic surfaces where
particles and magnetic force lines go through input and
output butt-endes (faces) of a cylindrical lens.
The limit magnetic surface is determined from
the condition that its radius (R) coincides with the
current channel radius (a) and the radius of the focused
beam. The functions ( )R z and B zz ( ) are determined
from the equation similar to (8):
′ ′ + =R
R
κ 0 , κ = 2
2
ZeI
c Mv
. (9)
The solution of the Eq.(9) (with initial conditions:
R R R R= ′ = ′0 0, at z=0) has the form:
z
dr
R R RR
R
= ±
′ −∫
0
2
02
0
κ ln /
. (10)
Using the substitution:
t
R R
R
2 0
2
0
2=
′
−
κ
ln (11)
and the definition of the tabulated function (the
probability integral):
( )Φ R e dt
t
R
=
−∫2 1
2
0
2
π
, (12)
we reduce the solution (10) to the form:
z R
R
R R
R
R
= ±
′
×
′
−
−
′
π
κ κ
κ κ
2 2
2
0
0
2
0
2
0
0
exp
lnΦ Φ
. (13)
In the case of the parallel ion beam injection, at z=0 we
have ′ =R0 0 , besides, in the focusing region z > 0. As
a result, the Eq.(13) takes the form:
z R
R
R
=
π
κ2
20 0
0Φ ln . (14)
In the real experiment the current channel
compression leads to the certain value Rg (not equal to
zero) that corresponds to the coordinate zg . At this
place the current channel is finished (by a wire mesh or
metallic foil). Later on the inertial ion focusing in the
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 81-83.
81
focal spot takes the place. This point’s coordinate is
defined as follows:
z R
R
R
R
R
R
f
g
g
g
=
+π
κ
κ
2
2
2
0 0
0
0
Φ ln
ln
. (15)
The numerical calculations of the Eq.(8) by PC (see
[16], Fig.2) give the result for z f coinciding with the
(15).
2.2. The long Gabor lens
For the uniform Gabor lens the expression for the
focusing electrostatic force have the form:
F ne re = − 2 2π , where n is the electron density.
The equation for ions’ movement has the form:
′ ′ + =r k rG
2 0, k ne
MvG
2
2
2
2= π
, (16)
the equation of ions trajectories and focusing distance
are defined by the expressions:
r r k zG= 0 cos , L
k
v
e
M
nf
G
= =π π
π2 2 2
. (17).
For a lens of length l: )( lkctgklL GGf
1−+= ,
where at k lG <<1 it is easy to obtain the known
expression for focusing distance of a thin lens [3, 4].
2.3. The long Morozov lens
In the Morozov lens the electric potentials are
inserted into plasma by the concentric ring electrodes.
In this case, the system of the «charged» magnetic
surfaces are created in the plasma. It is supposed that in
the applied strong magnetic field the transverse current
is absent. For the long Morozov lens, it is worth-while
to place the concentric ring electrodes on the lens faces
(or near by them at lateral surface), i.e. at the input and
output of the focused beam. In these conditions, the
expression for the focusing force of electric field has the
form:
( )
r
zreeEF re ∂
∂ ϕ=−= ,
. (18)
With the given distribution of potential along the radius:
2
0
2
0 ar /ϕ=ϕ , (were 0a is the radius of the external
magnetic surface at z=0, and 0ϕ is its potential), one
can have:
( ) ( ) r
za
ezrFe 2
02ϕ
=, . (19)
With taking into account Eq.(1), the equation for
movement of focused ions is:
0
0
2 =+′′ rk
B
zB
r M
z
z
)(
)(
, where 2
0
2
02 2
aMv
e
kM
ϕ
= (20)
In the uniform case the focusing distance is equal to:
0
01
22
2
ϕ
π
=π= −
e
Mva
kL Mf )( . (21)
In the non-uniform case, the external magnetic
field can increase from the input to the output of the
lens in such a manner, that the limiting magnetic surface
can coincide with the focusing beam radius.
Simultaneously the focusing electric field is increasing
that results in the enhancement of the lens efficiency
and focusing distance decreasing. The solution of this
problem is similar to the case of the non-uniform
magnetic lens (see above).
2.4. The charge-current lens
In conclusion, we study briefly the case of ion
beam focusing by the counter-stream intense electron
beam. As it is known, the electron concentration in such
beams can reach to 1012 – 1013 cm-3, therefore its using
for ion beam focusing can have good prospects.
The expression for the focusing force has the
form:
F F F ne r ejvc rr e m= + = − − −2 22 2π π , (22)
where n is the electron concentration, j is the current
density. Let us express n and j by the current I, radius a
and velocity ve of the electron beam:
( ) ( )n z I
ev a ze
=
π 2 , ( ) ( )j z I
a z
=
π 2 . (23)
The expression for the focusing force takes the
form:
( )F eI
a z v
vv
cr
e
e= − +
2 12 2 . (24)
The equation for focused ion trajectories (with
taking into account Eq.(1)):
0
0
2 =+′′ rk
B
zB
r e
z
z
)(
)(
,
( )
2
0
2
2
2 12
avMv
cvveIk
e
e
e
−+= . (25)
In the uniform or non-uniform cases one can use
similar methods and formulae (with the own ke ) as in
the above-mentioned case of magnetic lens.
The author would like to thank I.N. Onishchenko
and V.I. Butenko for help and fruitful discussions.
References:
1 Proc. CERN Accelerator School: Cyclotrons, Linacs and
Their Applications. Ed. S.Turner. Geneva, 1996.
2. Hofmann I. Application of RF Linacs to Heavy-Ion Fusion,
ibid, p. 267.
3. Hairapetian G., AIP Conf. Proc. 335, P.174 (1995).
4. Gabor D., Nature, V.160, P.89 (1947).
5. Panofsky W.K.H., Baker W.R., Rev. Sci. Instr., V.21, P.445
(1950).
6. Morozov A.I., DAN USSR, V.163, P.1363 (1965).
7. Goncharov A.A. e.a., RSI., V.65, P.1428 (1994).
8. Goncharov A.A. RSI, V.69(2), P.1150 (1998).
9. Katsouleas T., Phys. Rev., V.A33, P.2056 (1986).
10. Chen P., Part. Accel., V.20, P.171 (1987).
11. Chen P., Oide K., Sessler A.M., Yu S.S., Phys. Rev., Lett.,
V.64, P.1231 (1990).
12. Boggasch E., Jacoby J. e.a. Phys. Rev. Lett., V.66, P.1705
(1991).
13. Boggasch E., Tauschwitz A. e.a. Appl. Phys. Lett., V.60,
P. 2475 (1992).
14. Tauschwitz A., Yu S.S. e.a. Proc. of the Conf. «Beams-
96» (Prague, 1996), V.1, P.91.
15. Belan V.N. e.a., RSI, V.69(2), P.1110 (1998).
16. Belan V.N. e.a. // Problems of Atomic Science and Techn.
1999. v. 3. Issue: Nuclear Physics Researches. (34),
P. 79.
17. Butenko V.I., Ivanov B.I. // Ibid, P. 23.
18. Glaser W. Principles of electron optics, M., 1957.
B.I. Ivanov
(E-mail: ivanovbi@kipt.kharkov.ua)
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 81-83.
81
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