IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 26, NO. 1, FEBRUARY 1998
113
Analysis of the Nitrogen Ion Beam Generated in a
Low-Energy Plasma Focus Device by a Faraday Cup
Operating in the Secondary Electron Emission Mode
Héctor Kelly, Alejandro Lepone, Adriana Márquez, Marek J. Sadowski,
Jaroslaw Baranowski, and Elzbieta Skladnik-Sadowska
Abstract—The energy distribution and flux of fast nitrogen particles generated in a Mather-type plasma focus device operating
at 0.4 Torr of N2 pressure is reported. A Faraday Cup operating
in the secondary electron emission mode was employed. To
determine the total number of beam particles, multiple scattering
of the ions was taken into account. It has been possible to register
the ion energy up to a lower kinetic energy threshold of 50 keV,
which is a value much lower than that obtained with a Thomson
spectrometer in a previous work.
Index Terms—Faraday cup diagnostic, ion beams, ion energy
spectral analysis, plasma focus.
I. INTRODUCTION
P
LASMA FOCUS (PF) devices [1] are intense sources of
neutrons, X-ray radiation, ions, and electrons. In particular, attention has been focused on the use of the ion beam
generated in a PF to produce ion implantation [2], thermal
surface treatment [3], and/or ion-assisted coatings [4], [5]
on samples located in front of the coaxial electrodes of the
device. In this kind of applications, PF devices are usually
operated with N as the filling gas. In order to perform an
evaluation of these technological processes, it is necessary
to obtain reliable information on the nitrogen ion flux and
on the nitrogen ion kinetic energy spectrum. An important
difficulty in determining the PF ion spectrum is connected
with the recording of the ion energy in the low-energy region
of the spectrum, where most of the particles and beam energy
content are concentrated.
The first reported results concerning PF nitrogen ions were
presented by Mozer et al. [6] and Sadowski et al. [7]; however,
in these experiments, the nitrogen was present as an impurity.
An ion spectrum obtained from a nitrogen operated PF device
was reported by Rhee [8], but without deriving the value of
the ion flux. Later on, Kelly et al. [9] presented a nitrogen
spectrum derived from a Thomson spectrometer equipped
Manuscript received August 21, 1997; revised November 10, 1997. This
work was supported by the Argentine authorities of UBA and CONICET as
well as the Polish State Committee for Scientific Research for a financial
support of the bilateral scientific cooperation between INFIP and SINS.
H. Kelly, A. Lepone, and A. Márquez are with the Instituto de Fı́sica del
Plasma, Departmento de Fı́sica, Facultad de Ciencias Exactas y Naturales,
UBA, Ciudad Universitaria, Pab I, 1428, Buenos Aires, Argentina.
M. J. Sadowski, J. Baranowski, and E. Skladnik-Sadowska are with the
Soltan Institute for Nuclear Studies (SINS), 05-400 Otwock-Swierk, Poland.
Publisher Item Identifier S 0093-3813(98)01472-6.
with a CR-39 plastic nuclear track detector. By taking into
account multiple scattering of the ions and capture and loss
of electrons to the background gas, absolute values for the
ion flux were obtained in that work. However, due to the
unavoidable presence of impurities in the developed track
detector, a low-energy threshold of 170 keV was always
found in the detected ion energies.
A very simple and inexpensive diagnostic to register the PF
ion beam with temporal resolution is the Faraday Cup (FC)
technique [10], [11], which also has the attractive feature of
a fast processing time of the signal (as compared to the large
time-consuming Thomson spectrometer technique). FC has
been applied to several PF experiments to infer the deuteron
ion spectrum by time of flight (TOF) techniques [12]–[15].
Its main difficulties are: 1) a low signal-to-noise ratio and
2) the emission of secondary electrons (SEE) by the energetic
ions impinging on the collector. While the improvement of the
first point depends on each particular experimental situation
(for instance, it has been found [12] that the application of a
static transverse magnetic field across the region between the
FC collector and a shielding screen greatly suppress noise),
SEE effects have been minimized by using graphite collectors
[13] or by applying a strong transverse static magnetic field
in the vicinities of the collector [12] to capture the electrons.
However, SEE was taken into account in the case of deuterium
ions by analyzing the FC grid signal [12]; in fact, by comparing
this signal to that corresponding to the collector, it was
possible to derive the number of secondary electrons ejected
per incident ion
as a function of the deuteron energy,
in reasonable agreement with the experimental values of
published in the literature. It must be noted that for ion kinetic
typical of PF experiments (several hundreds of
energies
keV), the values of
are very large (
for 100-keV
deuterons [12], and for heavy ions it can reach even larger
values), so an FC signal containing the SEE contribution in
a controlled way has the advantage of being a factor 5 (or
more) larger than that corresponding to a pure ion signal.
The purpose of this work is to report the energy distribution
and flux of fast nitrogen particles generated in a Mather-type
PF operating at 0.4 Torr of N pressure. Both quantities are
derived from an FC operating in the SEE mode. Multiple
scattering of the ions is taken into account to determine
the total number of beam particles. The obtained results are
0093–3813/98$10.00  1998 IEEE
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 26, NO. 1, FEBRUARY 1998
(a)
(b)
Fig. 1. (a) Scheme of the Faraday Cup; (b) scheme of the different charge
contributions to the grid and collector signals of the FC.
compared to those previously obtained employing a Thomson
spectrometer [9].
II. THE EXPERIMENT
The measurements were performed in our PF II device
(4.75 kJ, 30 kV) whose mechanical and electrical parameters
can be found elsewhere [16]. An FC located at 119.5 cm
far from the focus region (this large distance allowed us to
discriminate by time of flight the effects on the FC signals due
to electromagnetic radiation and to fast particles), a Rogowski
coil (to register the time derivative
where is the total
discharge current), and a PIN BPX 65 photodiode covered
with a 12- m Be filter (to register the temporal evolution of
medium-energy X rays,
) and located at 90 from the
electrode axis were employed. A scheme of the FC is shown in
Fig. 1(a). The FC consisted of a metallic solid grounded cage
on whose lower base was located a truncated cone hollow
Cu collector. Two ceramic posts (tied to the upper base of
the cage) held a circular Cu grid (25% of transparency). Two
small magnets [see Fig. 1(a)] generated a traverse magnetic
field in the space between grid an collector. Its intensity was
60 G at the center of symmetry, and reached 520 G at 2 mm
from the surface of the magnets. The FC entrance pinhole was
0.8 mm in diameter, and it was located at a distance of 10.5
cm from the focus region. A differential pumping ( 10
Torr) was applied to this system, while the pressure in the
discharge chamber was kept constant (within 10%) for 5
min. To register the signals (
FC collector,
and FC grid, ), a four-channel digitizing oscilloscope, with
a sampling rate of 250 Ms s and a frequency bandwidth
of 500 MHz, was employed. The delay time of the signals
was carefully measured so that the time correlation among the
four signals was better than 5 ns.
Fig. 2. Typical signals of
of the discharge.
dI =dt; dX=dt; Ic ;
and Ig during the focus stage
III. RESULTS
After a series of preliminary shots, it was found that the best
operating conditions for the FC in this experiment (concerning
the signal-to-noise ratio) corresponded to biasing voltages of
200 V for the grid and 700 V for the collector, respectively.
Under these conditions, secondary electrons emitted from the
collector should be partially collected by the grid.
In Fig. 2, typical signals of
, and
during the focus stage are shown, at a pressure
Torr.
The main pulse of the
trace is well correlated with
the corresponding dip in the
signal. The collector and
grid signals show a first peak (similar in shape to the
peak) lasting for 250 ns, followed by a second wider pulse
of 1.5 s duration. The first peak is not related to ions,
otherwise they would have kinetic energies in the range 2–10
MeV. In fact, when an Al filter 0.75 m thick) was employed
to register the FC signals, the first peak was absent from the
registers. As the Al filter was thin enough to allow the passage
of nitrogen ions with
MeV, it was concluded that the
first peak was due to X rays or ultraviolet radiation emitted
during the focus stage. The second pulse corresponded to nitrogen ions with kinetic energies ranging from 40 keV to 1 MeV.
In order to evaluate SEE effects on the collector signal,
the electron trajectories under the electric and magnetic fields
present in the experiment were evaluated. The electric field
was obtained by solving numerically Laplace’s equation in
the volume defined by the surfaces of the collector, the grid,
and a lateral cylinder joining both elements. The voltage
on this cylinder was assumed to vary linearly between the
collector and grid potentials. The magnetic field distribution
was measured in the whole volume between grid and collector
by using a Hall probe system. It was recorded one magnetic
field value every each 2 mm of spacing.
KELLY et al.: NITROGEN ION BEAM GENERATED IN LOW-ENERGY PLASMA FOCUS DEVICE
In calculating the electron trajectories, it was taken into
account that the energy of secondary electrons released by ions
with
of some tens of keV (or larger) is 50 eV (or less)
[17]. Although this value is somewhat uncertain, the results
were not sensitive to changes of this energy within the range
10–100 eV. It was also assumed that secondary electrons were
ejected in a direction normal to the surface, because different
angles would correspond to larger electron paths in the material
and hence to a larger absorption probability. As the presence
of the magnetic field breaks the azimuthal symmetry of the
problem, it was necessary to calculate the electron trajectories
for different angular positions of ejection. In all cases, it was
found that the electrons never returned to the collector and
always reached the grid plane.
For the analysis of the FC signals, the scheme shown
in Fig. 1(b) was followed. Let us consider an elementary
charge
associated to incident ions with energy in the range
which will contribute to the FC signals in the
time interval
The corresponding ion number,
will be given as
where is the electron
charge and
is the average charge of the beam with
energy [18] (it has been shown [9] that in these experimental
conditions, the nitrogen beam reaches an equilibrium charge
state due to capture and loss of electrons to the neutral gas).
The collector signal will be composed of a fraction
of
the ions which traverse the grid [where is the transparency of
the grid, and
is a nondimensional factor which takes into
account that the collector is hollow in our experiment; see
Fig. 1(a)] plus the SEE contribution
where
is the effective collector SEE coefficient. The grid
signal will have three contributions: the fraction
of primary ions collected by the grid, the SEE contribution
(where
is the effective grid SEE
coefficient), and the fraction of secondary electrons ejected
from the collector which trapped by the grid,
With
all of these considerations, the equations for the FC signals are
for the collector:
(1)
for the grid:
(2)
is the nitrogen mass and is the length between the
where
ion source and the grid. Note that in the above quoted analysis,
it is assumed that the fast particles are produced at the same
time and at the same point. This is a reasonable assumption,
since the typical ion time of flight
1 s is much larger
than the ion production time 0.1 s and also, the distance
between the ion source and the Faraday cup ( 1 m) is much
greater than those of the source. The ion transit time between
grid and collector is also considered negligible.
In order to obtain
from (1) or (2), the knowledge of
the SEE coefficient as a function of is required. According
to [19], can be expressed in terms of the electronic stopping
power
and the incidence angle
between the ion
115
Fig. 3. Final spectrum of the nitrogen (including elastic scattering effects)
calculated either from the FC grid signal or from the FC collector signal.
For comparison purposes, the nitrogen spectrum obtained with a Thomson
spectrometer in a previous work under the same PF operating conditions is
also shown.
and the normal to the surface of the target as
(3)
where
(dependent on the target material and independent
on the projectile) takes a value of 0.22 Å/eV for Cu [19].
Equation (3) was employed to calculate the functions
and
using the
values for a Cu target [20]. As
the grid is composed of circular wires with a semicircle facing
the ion incidence direction, an average value of
was
obtained in this case, resulting
To check the consistency of the above-described formulation, (1) and (2) were used to calculate the grid transparency.
By eliminating
from these equations, one can evaluate
in terms of the experimental quotient
and
and
This was done for the FC signals shown
in Fig. 2, and the resulting average value of for the whole
analyzed energy domain was 0.26, in good agreement with
the geometrical value of 0.25 obtained from a microscopic
observation of the FC grid.
To obtain the actual spectrum of the nitrogen fast particles
arriving per unit solid angle at the entrance pinhole of the
FC
, it was necessary to take into account
the elastic scattering of the particles in the neutral gas. Since
this procedure has been detailed elsewhere [9], [21], we will
present here only the main results.
can be related to
in the form
(4)
where
the collecting efficiency of the FC, is a nondimensional factor depending on the parameters of the experiment
(filling pressure, pinhole diameter, distance between focus
region and pinhole) and on the energy of the nitrogen ions. In
this case, it was calculated numerically following its definition
from [21].
In Fig. 3, the final spectra of the nitrogen, calculated either
from the collector [(1)] or the grid signal [(2)], are shown. For
comparison purposes, the spectrum obtained with a Thomson
spectrometer in a previous work [9] under the same PF
operating conditions is also presented. It can be seen that the
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 26, NO. 1, FEBRUARY 1998
scaling law with the ion energy of both the FC and Thomson
spectra are similar, and the differences among the absolute
values of the ion flux can be attributed to the well-known
fluctuations from shot-to-shot in PF devices. It can also be
seen that the collector and grid FC spectra are almost the same,
which indicates the consistence of the adopted assumptions on
the SEE contributions to infer the spectrum. Note also that the
lower energy threshold in the FC case is 50 keV, a value
much lower than that previously obtained with the Thomson
spectrometer.
IV. FINAL REMARKS
By employing a Faraday Cup in an operating regime in
which SEE contributes to both the collector and grid signals,
the nitrogen ion spectrum obtained from a small PF device
has been derived. The main advantage of this operating
regime is that it allows us to register higher amplitude signals
5–10 times) than that obtained by suppressing secondary
electrons, which is a valuable point in experiments where the
electromagnetic noise is high. It has been possible to register
the ion energy up to a lower kinetic energy threshold of
50 keV, a value much lower than that previously obtained
with the Thomson spectrometer. Based on the presented data,
the total fast particle flux and its energy content (within
the energy range 50–1000 keV) reach 3.2 10 ions/sterad
and 0.74 J/sterad, respectively. Although several assumptions
concerning the behavior of the secondary electrons have been
adopted, the similarity between both signals supports the
accuracy of the assumptions.
Finally, it must be noted that Faraday Cup and Thomson
spectrometer ion analysis should be considered as complementary diagnostics, because the first allows a fast processing
time of the signals, while through the second the charge state
of the beam can be obtained.
REFERENCES
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studies of fast deuterons, impurity- and admixture-ions emitted from a
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55, pp. 1229–1234, 1984.
[9] H. Kelly, A. Lepone, and A. Márquez, “Nitrogen ion spectrum from a
low energy plasma focus device,” IEEE Trans. Plasma Sci., vol. 25, no.
3, pp. 455–459, 1997.
[10] Y. Kondoh, K. Shimoda, and K. Hirano, “Measurements of energetic
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[11] M. Zakaullah, I. Ahmad, A. Omar, G. Murtaza, and M. M. Beg, “Effects
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[15] J. Baranowski, M. Sadowski, E. Skladnik-Sadowska, J. Zebroski, H.
Kelly, A. Lepone, and A. Márquez, “Time resolved measurements of
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[19] R. J. Beuhler and L. Friedman, “A model of secondary electron yields
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[20] J. K. Ziegler, TRIM code version 90, IBM Research, 1990.
[21] H. Kelly and A. Márquez, “The influence of multiple scattering on the
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Héctor Kelly was born in Mendoza, Argentina, on
February 14, 1948. He received the M.S. degree in
1972, and the Ph.D. degree in physics in 1979, both
from Buenos Aires University.
Since 1973, he has worked as a researcher at the
Plasma Physics Laboratory of the Science Faculty
of Buenos Aires University. His current research
interests are in powerful electrical discharges and
plasma coatings based on electrical discharges.
Dr. Kelly is a member of the National Research
Council of Science of Argentina since 1980.
Alejandro Lepone was born in Buenos Aires, Argentina, on December 22, 1967. He received the
M.S. degree from Buenos Aires University in 1995.
He joined the Plasma Physics Laboratory of the
Science Faculty of Buenos Aires University in 1993.
His current research interest is in ion beam generation from electrical discharges.
Mr. Lepone is a Fellow of the Buenos Aires
University.
Adriana Márquez was born in Buenos Aires, Argentina, on August 4, 1964. She received the M.S.
degree in 1989, and the Ph.D. degree in physics in
1994, both from Buenos Aires University.
She joined the Plasma Physics Laboratory of
the Science Faculty of Buenos Aires University in
1987. Her current research interests are in powerful
electrical discharges and plasma coatings based on
electrical discharges.
Dr. Márquez is a fellow of the National Research
Council of Science of Argentina.
KELLY et al.: NITROGEN ION BEAM GENERATED IN LOW-ENERGY PLASMA FOCUS DEVICE
Marek J. Sadowski was born in Warsaw, Poland, on September 20, 1937.
He received the M.S. degree from Warsaw University in 1960, the Ph.D.
and Dr.Sc., both in plasma physics, from Soltan Institute in 1969 and 1976,
respectively.
From 1960 until 1968, he was a member of the scientific staff of the
Department of Nuclear Physics and Department of Plasma Physics and
Technology at SINS in Swierk n. Warsaw, performing experimental studies of
various plasma injectors and open-ended magnetic traps. He discovered the
Spherical Multipole magnetic configuration, and after that he designed and
studied Kactus SM-facility, which led to the known multipole Q-machines.
From September 1968 until July 1969, he worked in Princeton Plasma Physics
Lab., USA, performing experiments with Spherator. From 1970 until 1973,
he worked as an Assistant Professor in Lab. Hot Plasma Physics at SINS,
developing laser interferometers and particle analyzers for dense plasma
studies. From 1973 until 1980, he was Associate Professor in the Department
of High-Temperature Plasma at SINS, working with different Plasma Focus
(PF) facilities. In 1980–1981, as a Fellow of the Humboldt Foundation, he
worked with Nessi PF facility at IPF in Stuttgart, Germany. From 1983
until 1988, he was Associate Professor in the Department of Thermonuclear
Research at SINS, working on development of plasma diagnostic methods and
studies of PF discharges. Since 1988, he has been Head of the Thermonuclear
Research Department. He is the author or main coauthor of more than 160
scientific papers on plasma physics and CFR, which have been published
in recognized scientific journals or proceedings of international conferences.
He has been a Visiting Professor at IPF in Stuttgart, at Kurchatov Institute
in Moscow, and recently at the Universities of Buenos Aires and Tandil,
Argentina.
Dr. Sadowski is a member of the Polish Physical Society, European Physical
Society, and Polish Society for Applied Electromagnetism.
Jaroslaw Baranowski was born in Warsaw, Poland, on February 8, 1948.
He received the M.S. degree from Warsaw University in 1969, and the Ph.D
degree in plasma physics from Soltan Institute in 1996.
Since 1970, he has been working as a member of the scientific staff at the
Department of Thermonuclear Research, and since 1980, at the Department
Plasma Physics and Technology at SINS in Swierk n. Warsaw. He has
been engaged in experimental studies with corpuscular diagnostic methods
in plasma focus and ionotron-type facilities. He is author or coauthor of
more than 60 scientific papers on plasma physics and CFR, which have been
published in scientific journals or proceedings of international conferences.
He has also been engaged in a scientific collaboration with the Institute of
Plasma Physics at the National Science Center Kharkov Institute of Physics
and Technology (Ukraine), the Czech Technical University in Prague (Czech
Republik), and the Universities of Buenos Aires and Tandil, Argentina.
Dr. Baranowski is a Member of the Polish Nuclear Society.
117
Elzbieta Skladnik-Sadowska was born in Paprotnia n. Warsaw, Poland, on
August 25, 1938. She received the M.S. degree from Warsaw University in
1961, and the Ph.D. degree in plasma physics from Soltan Institute in 1976.
From 1959 until 1961, she worked as a Junior Assistant in the Institute
of Experimental Physics at Warsaw University. In 1962, she was nominated
Research Assistant in the Department of Plasma Physics and Technology,
and she concentrated on experimental studies of so-called multi-rod plasma
injectors. In 1966, she was nominated Senior Assistant at the same department.
In 1970, she moved to the Laboratory of Hot Plasma Physics, where she
started research on corpuscular plasma diagnostics. In 1976, she spent six
months at Physico-Technical Institute in Kharkov, Ukraine. In 1976, she
became Assistant Professor in the Department of High-Temperature Plasma
Physics at SINS. In that year, she was appointed the leader of a group engaged
in studies of plasma interactions with magnetic fields. She also developed
Thomson-type spectrometers adapted for studies of plasma streams. In 1983,
she was nominated Assistant Professor in the Department of Thermonuclear
Research in Swierk. Acting as a head of the Plasma Diagnostic Group, she
performed studies of mass- and energy-spectra of ions emitted from different
plasma facilities. Since 1988, she has been engaged in research on Plasma
Focus (PF) facilities. In 1992 she spent two months at IPF in Stuttgart,
Germany, participating in experimental studies of high-current PF discharges.
In 1993, she stayed another six weeks in Stuttgart to carry out time-resolved
measurements of gas-puffed PF discharges, and in 1995 she spent four weeks
at Universities of Buenos Aires and Tandil, Argentina.
Dr. Skladnik-Sadowska is a Member of the Plasma Physics Section at the
Polish Academy of Sciences.