Non-linear electron structures in high-current plasma lens
We describe the experimental investigations of the dispersion characteristics of the electron oscillations excited owing to drift instability in high-current plasma lens (PL). The experiments were carried out using the heavy ion beams of copper or carbon with energy up to 18 keV, beam current up to...
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Goncharov, A. Gubarev, S. Dobrovolskii, A. Litovko, I. Protsenko, I. 2015-05-19T08:49:59Z 2015-05-19T08:49:59Z 2000 Non-linear electron structures in high-current plasma lens / A. Goncharov, S. Gubarev, A. Dobrovolskii, I. Litovko, I. Protsenko // Вопросы атомной науки и техники. — 2000. — № 1. — С. 229-233. — Бібліогр.: 5 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/81679 We describe the experimental investigations of the dispersion characteristics of the electron oscillations excited owing to drift instability in high-current plasma lens (PL). The experiments were carried out using the heavy ion beams of copper or carbon with energy up to 18 keV, beam current up to 0,5 A, duration 100 mks produced by the MEVVA kind ion source. It is shown that the noise electrostatic potential oscillations arise in middle plane of the lens under passing ion beam through plasma lens. These noises in range of 0,25÷2 MHz have a regular structure with stationary amplitude depending on ion beam current value. On their background a comparable low-intensity high-frequencies noises in range 20÷50 MHz is also observed. We show that the regular structure is represented by waves that drift along azimuth and have a clear spatial localization on considerable radius from plasma lens axis. Experimental results are in accordance with theoretical analysis showing an appearance of nonlinear electron vortices structures for these conditions. This work was supported by the Ministry of Science and Technology of Ukraine (#2.4/705 and #2.5.2/10). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Нелинейные процессы Non-linear electron structures in high-current plasma lens Article published earlier |
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Non-linear electron structures in high-current plasma lens |
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Non-linear electron structures in high-current plasma lens Goncharov, A. Gubarev, S. Dobrovolskii, A. Litovko, I. Protsenko, I. Нелинейные процессы |
| title_short |
Non-linear electron structures in high-current plasma lens |
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Non-linear electron structures in high-current plasma lens |
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Non-linear electron structures in high-current plasma lens |
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Non-linear electron structures in high-current plasma lens |
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non-linear electron structures in high-current plasma lens |
| author |
Goncharov, A. Gubarev, S. Dobrovolskii, A. Litovko, I. Protsenko, I. |
| author_facet |
Goncharov, A. Gubarev, S. Dobrovolskii, A. Litovko, I. Protsenko, I. |
| topic |
Нелинейные процессы |
| topic_facet |
Нелинейные процессы |
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2000 |
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English |
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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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Article |
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We describe the experimental investigations of the dispersion characteristics of the electron oscillations excited owing to drift instability in high-current plasma lens (PL). The experiments were carried out using the heavy ion beams of copper or carbon with energy up to 18 keV, beam current up to 0,5 A, duration 100 mks produced by the MEVVA kind ion source. It is shown that the noise electrostatic potential oscillations arise in middle plane of the lens under passing ion beam through plasma lens. These noises in range of 0,25÷2 MHz have a regular structure with stationary amplitude depending on ion beam current value. On their background a comparable low-intensity high-frequencies noises in range 20÷50 MHz is also observed. We show that the regular structure is represented by waves that drift along azimuth and have a clear spatial localization on considerable radius from plasma lens axis. Experimental results are in accordance with theoretical analysis showing an appearance of nonlinear electron vortices structures for these conditions.
|
| issn |
1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/81679 |
| citation_txt |
Non-linear electron structures in high-current plasma lens / A. Goncharov, S. Gubarev, A. Dobrovolskii, I. Litovko, I. Protsenko // Вопросы атомной науки и техники. — 2000. — № 1. — С. 229-233. — Бібліогр.: 5 назв. — англ. |
| work_keys_str_mv |
AT goncharova nonlinearelectronstructuresinhighcurrentplasmalens AT gubarevs nonlinearelectronstructuresinhighcurrentplasmalens AT dobrovolskiia nonlinearelectronstructuresinhighcurrentplasmalens AT litovkoi nonlinearelectronstructuresinhighcurrentplasmalens AT protsenkoi nonlinearelectronstructuresinhighcurrentplasmalens |
| first_indexed |
2025-11-25T22:51:41Z |
| last_indexed |
2025-11-25T22:51:41Z |
| _version_ |
1850575188171685888 |
| fulltext |
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ 2000. №1.
Серия: Плазменная электроника и новые методы ускорения (2), с. 229-233.
229
NON-LINEAR ELECTRON STRUCTURES IN HIGH-CURRENT PLASMA
LENS
A. Goncharov, S. Gubarev, A. Dobrovolskii, I. Litovko, I. Protsenko
Institute of Physics NASU, pr. Nauki, 46, Kiev, 03650, Ukraine, phone/fax (38044)2657824,
E-mail: gonchar@iop.kiev.ua
We describe the experimental investigations of the dispersion characteristics of the electron oscillations excited
owing to drift instability in high-current plasma lens (PL). The experiments were carried out using the heavy ion beams
of copper or carbon with energy up to 18 keV, beam current up to 0,5 A, duration 100 mks produced by the MEVVA
kind ion source. It is shown that the noise electrostatic potential oscillations arise in middle plane of the lens under
passing ion beam through plasma lens. These noises in range of 0,25÷2 MHz have a regular structure with stationary
amplitude depending on ion beam current value. On their background a comparable low-intensity high-frequencies
noises in range 20÷50 MHz is also observed. We show that the regular structure is represented by waves that drift along
azimuth and have a clear spatial localization on considerable radius from plasma lens axis. Experimental results are in
accordance with theoretical analysis showing an appearance of nonlinear electron vortices structures for these
conditions.
1. Introduction
The trapped electron cloud in static electric and
magnetic fields is a very attractive subject for state-of-art
basic investigations in plasma physics, fluid dynamics and
atomic physics. This is very good confirmed by the paper
of T.M. O’Neil publicated not too long ago [1].
By origin the electrostatic plasma lens is modification
of Penning trap configuration with nonhomogeneous
magnetic field, B=B(r, z), for creation in the PL volume
over thermal electric fields for focusing high-current ion
beams. This mean that in the PL volume quasi-neutral
plasma medium is formed by fast ion beams with density
nb and compencated electrons with density ne. It is
obvious that ne≥nb because of formation the volume E-
field perpendicular to external magnetic field for focused
ion beam. Therefore, in the PL volume in focusing mode
we have some like nonneutral trapped electron plasma. In
this case, the presence of ion beam and the nonremovable
radial gradient Bz leads to growth of drift electron
instability even under ne=const. This instability is
modified diocotron-like instability of pure non-uniform
electron cloud.
This instability was observed firstly in the experiments
[2]. There was investigated also the theoretical linear
stage of this instability. In these experiments the high-
current electrostatic PL with a two-component quasi-
neutral plasma formed by the repetitively-pulsed wide-
aperture beam of hydrogen ions with a current up to 2 A,
energy up to 20 keV, duration 100 µs and the electrons of
secondary ion-electron emission was studied. It was
shown in the investigations that under passing ion beam
along the PL the noise small-scaled turbulence oscillations
arise in the range of frequencies 20÷50 MHz. The results
of analysis of linear dispersion equation of oscillations
could qualitatively explain the integral characteristics of
the noises observed in the experiments. At the same time,
in these experiments we could not obtain any data about
the increments, the excited frequencies, the wave numbers
of these oscillations and observed frequencies.
To understand further the mechanisms determining
evolution of the PL medium instability one need to study
nonlinear dynamics, first of all, the electron component
because of relatively small time the staying of fast beam
particles in the PL volume.
As linear theory predicts, the excited frequencies are
in range of Langmuir frequency of ion beam.
Therefore, use of more heavy ion beams in
experimental investigations is preferable.
Here are the results of our further experimental and
theoretical investigations of this instability with heavy
ion beams.
2. Experimental conditions and approach
The experiments were carried out on the set-up which
scheme is given in the [3]. For ion beam creation we use
two-chamber MEVVA-like ion source with grid anode
and three-electrode multi-aperture ion optical system
elaborated and proposed in [4]. Such ion source provides
repetitively pulsed wide-aperture (∅ 5.6 cm) low-
divergent metal ion beam with energy up to 18 keV,
current up to 500 mA and duration 100 µs. The ion source
is at the distance 31 cm from the middle plane of the PL.
The beam of copper or carbon ions passed through the
9-electrode plasma lens of diameter 7 cm and length 12
cm. The maximum potential on the lens electrodes could
be regulated up to 3,5 kV. The electrodes disposed
symmetrically around the central one were connected in
pairs. The strong of magnetic field on a lens axis could
vary up to 0,17 T. The experiments were conducted with
usage of radially and azimuthal movable capacitive probes
disposed in mean plane of the lens. The signals from them
were measured by memory oscilloscope with pass band
50MHz. In the experiments we used the optimum
configuration of the H-field found in [2]. The beam
current and density on-axis after lens were measured by an
axially movable sectioned collector. Before collector the
radially and axially movable Langmuir probe were placed.
The residual gas pressure in a vacuum chamber was at the
mailto:gubarev@iop.kiev.ua
2
level of 1÷2×10-5 Torr. This provided the plasma creation
in the PL volume by secondary ion-electron emission.
3. Experimental results
Experiments show that copper or carbon ion beam
passing through the PL leads to growth of regular
electrostatic potential waves rotated around the PL axis.
These waves with the frequency in the range of 0,2÷2
MHz have the nonharmonic shape. The values of these
frequencies are comparable with ion beam Langmuir
f
n
l
p
m
t
o
e
d
s
U
a
c
c
v
U
b
v
o
m
n
c
a
s
t
d
f
a)
b)
0,0 0,5 1,0
0,0
0,5
1,0
1,5
2,0
fpi, MHz
f,MHz
Fig. 1. Dependency of oscillation frequency on
Langmuir frequency of ion beam.
Cu,"O"-distribution, Ub=6 kV, UL=2,7 kV,
BL=75 mT, U-=-3 kV.
30
requency (fig. 1). As it is seen from fig.2,3 there are also
onregular of turbulent small-scale noises comparable
ow-intensity in range 20÷50 MHz. The azimuthal
otential waves are observed starting from the radius r=5
m and have a clear maximum amplitude up to 700 V at
he r≈20 mm from an axis of PL. These oscillations were
bserved under different potential distribution on fixing
lectrodes of the lens. The phase of these waves doesn’t
epend on radius. The oscillations rapidly arise and reach
tationary level for some (2÷4) periods of oscillations.
nder low ion beam currents (≈20 mA) the oscillations
re observed with mode m=1, then, with increasing of
urrent the modes increase (up to m=4 in experimental
onditions), as well as the frequency. The azimuthal phase
elocity also slightly grows. This can be seen on fig.4.
nder the same experimental conditions some modes can
e excited with adjacent different frequencies and phase
elocities. The photos of
scillograms of signals from capacitive probes, for modes
=1 and m=3 are exhibited in figures 2,3. It should be
oted that the direction of phase velocity changes with
hanging of the lens magnetic field direction. We note
lso that natural noises originate from MEVVA-like ion
ource can be enhanced under passing the ion beam
hrough lens plasma medium. The degree of current
ensity modulation on collector grows along radius of
ocused beam and can reach 20%.
Fig. 2. The typically oscillograms of signals from
capacitive probes for modes m=1 under some azimuthal
angles β between them:
Cu,"O"-distribution,Ub=6 kV,UL=2,5 kV,BL=60 mT, U-
=-3 kV, Ib=40 mA, scan duration = 10 µs, amplitude
oscillations 600 V, f=200kHz
a) β=0°, b) β=180°.
4. Discussion
The experiments presented here prove that use of
heavy copper ions instead of light hydrogen ions enables
to distinguish the low- and high-frequency oscillations,
which appear in the process of evolution of drift
instability on the big radii from the axis in the PL volume,
and thus, to distinguish regular low-frequency waves
propagating azimuthally. This can be understood as from
analysis of linear dispersion equation of small oscillations
for such system a development of instability on the
frequencies close to the beam ion Langmuir frequency
follows. It will be right to the point to present here a
dispersion equation of the linear oscillations of such
system (for more simplicity we consider it for the
Cartesian coordinates):
( ) ( ) 0
)(
1 2
2
2
2
2
2
2
2
=
−
−⋅
−
−
−
−
Pvkk
k
kvkvk Bidy
ybiz
dy
p
bz
bi ke
ωω
αω
ωω
ωω (1)
where ωbi and ωpe are the ion beam and electron Langmuir
frequency correspondingly, ωBi – an ion cyclotron
frequency, α= ne/nb (nb is the concentration of ion beam,
Vb- ion beam velocity.
w
v
w
a
b
v
g
c
e
d
t
o
i
w
a
e
s
a
[
e
f
{ } 0,)1( =∆+
∂
∂∆∇−
∂
∆∂ ϕϕ
ωω
ϕϕϕ
cece
y m
e
xm
e
t
0,0 0,1 0,20
1
2
3
4
m
Ib,A
a)
0,0 0,1 0,2
0,0
0,5
1,0
1,5
2,0
Ib,A
f,MHz
b)
75
100 V ph, *103m /s
a)
b)
Fig. 3. The typically oscillograms of signals from
capacitive probes for modes m=3 under some
azimuthal angles β between them:
Cu,"O"-distribution,Ub=6 kV,UL=2,5 kV,BL=60 mT,
U-=-3 kV, Ib=70 mA, scan duration = 5 µs,
amplitude oscillations 300 V, f=1MHz
a) β=0°, b) β=60°.
231
This equation describes both volume oscillations,
hich appear due to azimuthal electron stream with a
elocity BcEvd /= and gradient oscillations connected
ith space inhomogeneity of electron concentration ne(r)
nd axial component of the magnetic field Bz(r) describing
y function P.
An analysis and experimental data testify uniquely that
olume oscillations in the conditions of a curvilinear
eometry of a B-field will not take place. That is why one
an suggest that kz=0. With this approximation the
quation was solved in [2].
An analysis of dispersion equation enables to
etermine a space localization of oscillations, increment
imes, wave numbers and frequencies of excited
scillations. It follows from solutions that maximal
ncrements and frequencies are comparable, they are
ithin a range of the ion beam Langmuir frequency. With
help of the linear dispersion equation it is not possible to
xplain a high-frequency part of the excited noises
pectrum. This can be done with a help of a nonlinear
nalysis of a dynamics of excited electron oscillations. In
5] non-linear equation for the potential, describing
lectron dynamic had been received. It has the following
orm:
0 ,0 0,1 0,2
0
25
50
Ib, A
c)
Fig. 4. The dependency of mode, oscillation
frequency and phase velocity on beam current:
Cu, "O"-distribution, Ub=6 kV,
UL=2,7 kV, BL=75 mT, U-=-3 kV.
Numerical and analytical solutions of this equation
have shown existence of small-scaled electron vortex
structures that may lead to creation of high-frequencies
noises. For computer modeling of appearing and evolution
of large-scaled vortex structures we can represent this
equation in form:
ϕϕϕ
xyyx
yx
xH
cv
xH
cv
xH
c
y
v
x
v
t
∇=∇−=∆=Ω
=
∂
Ω∂+
∂
Ω∂+
∂
Ω∂
)(
,
)(
,
)(
0
which was solved on base of Lacks scheme for azimuth
perturbation type δφ=φ0sin(kуy)sin(ω0t). We take initial
values of all parameters so that they are close to
experimental conditions in order to compare further
232
numerical results with experimental data for ky=2π/3,
ω0=1MHz, φ0=10-5Ф0,on r=2/3R. Results of computer
simulations show that for a short period of time the
instability region in the plasma lens is covered by small-
scaled electron bunches, which create craters rotating
about their axes and moving along the axis y for the case
of stationary distribution of the electrostatic potential.
This created bunches merge together into one stable
vortex. It has practically unchanged amplitudes and is
shifted along the axis у with a velocity u~0,4vd. Rotation
speed of this structure may be estimated by the formula
vвр~eφmax/mωher0, where r0 is a calculated radius of a
structure, which is equal approximately to 0,2R. Then vвр
~1,2 vd, and from this fact the conclusion follows that
such kind structure is a stable vortex which has spin
velocity much higher then shift velocity along the y-
direction. The spin rate can be estimated as ωвр=
vвр/r0~20ω0, so if ω0~1МHz, that means ωвр~20МHz.
30 60 90 120
Ln(Fi/Fi0)
Time intervals
Fig. 5. Potential (ln scale) vs time for different initial
perturbations. Upper case- φ0=0.005Ф0 , middle case-
φ0=0.001Ф0 , lower- φ0=0.0005Ф0 (single time interval ~
0.28•10-7 с)
On the Fig. 5 the logarithmic dependency of the
potential amplitude on time is shown for different initial
amplitudes of perturbations φ0 (calculations were made for
the mode 3/2). One can see at first the amplitude is
growing rapidly, changing its value by orders during a
very small period of time, and then it reaches a saturation
value during the time of about 1-2 periods of oscillations
(10-6 sec). The higher is the amplitude of initial
perturbation, the faster the saturation value is reached; the
saturation value does not depend practically on initial
values of perturbation amplitudes.
Fig. 6 presents results of simulation appearance and
evolution vortex structure (ky=2π/3, ω0=1Мгц, φ0=10-5Ф0,
r=2/3R.) Using this mode 3 is because of the only
possibility to compare the numerical results to
experiments. One can see that vortex structure appears
just after 90 intervals. Its amplitude has fast growing and
reaches saturation.
T=0 T=30
T=40
T=50
T=65 T=80
T=100 T=140
*105
T=240
*105
T=180
Fig.6. Modeling of arising process for a vortex
structure (y-fraction, x = 0, time interval ~ 0.28•10-7s,
φ0=10-5Ф0)
It is very difficult to distinguish evolution of a separate
mode in the conditions of the presented experiment where
modes are excited spontaneously and the multi-mode
regime is realized in fact. At the same time, one can
suppose that observed high-frequency bursts of turbulent
noises appearing most frequently in the regions of variable
potential minimums may be connected with passing of
vortexes in the place of probes allocation.
233
Conclusion
Thus, it is shown in the paper that low-frequency
electron-wave structures have increment times and
frequencies corresponding to the linear theory of a drift
instability of electrons that take place in the presence of
fast particles of the ion beam and non-removable radial
gradient of the axial component of a magnetic field.
Observed bursts of high-frequency noises may be
connected with creation of non-linear electron vortex
structures, which were predicted theoretically.
Acknowledgements
This work was supported by the Ministry of Science
and Technology of Ukraine (#2.4/705 and #2.5.2/10).
References
1. Thomas M. O’Neil. Trapped Plasmas with a Single
Sign of Charge// Physics Today, Febr. 1999, p. 24.
2. Goncharov A., Dobrovolskiy A., Protsenko I., Zatuagan
A. High-current plasma lens// IEEE Trans. Plasma Sci.
21, 1993, p. 573.
3. Goncharov A., Gubarev S., Dobrovolskiy A., Litovko
I., Protsenko I., and Brown I. Moderate Energy Metal
Ion Beam Focusing by a High-Current Plasma Lens//
IEEE Trans. Plasma Sci. v 27, N4, 1999, p. 1068.
4. I.Brown, Vacuum Arc ion sources// Rev.Sci.Instr. v.
65, N7, 1994, p. 3061
5. Goncharov A., Litovko I. Electron Vortexes in High-
current Plasma Lens// IEEE Trans. Plasma Sci. 27,
1999, p. 1073.
Conclusion
Acknowledgements
References
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