Plasma Devices and Operations
Vol. 14, No. 3, September 2006, 223–235
High-current large-area uniform electron beam generation by
a grid-controlled hollow anode with
multiple-ferroelectric-plasma-source ignition
J. Z. GLEIZER, D. YARMOLICH, V. VEKSELMAN, J. FELSTEINER and
YA. E. KRASIK*
Physics Department, Technion, 32000 Haifa, Israel
(Received 9 March 2006)
We report results on the generation of a large-cross-section (about 170 cm2 ) high-current (about 1000A)
uniform electron beam by a hollow anode (HA) plasma source at a pressure of approximately 8 × 10−5
Torr, in a diode with an accelerating pulse of 300 kV and approximately 300 ns duration. The HA
discharge was sustained for about 10 µs by seven Ba–Ti-based ferroelectric plasma sources. The
resistive decoupling of each plasma source produces a uniform plasma density distribution at the
HA output grid at a discharge current of not more than 1000 A. It was found that the HA plasma is
characterized by a density of about 1012 cm−3 , an electron temperature of approximately 8 eV and a
group of fast electrons with an energy of about 50 eV. It was shown that an increase in the HA output
grid potential allows the plasma prefilling of the accelerating gap to be reduced significantly.
Keywords: Plasma; Electron beam; Hollow anode; Ferroelectric plasma source
1.
Introduction
Electron beams with a current amplitude of several kiloamperes, an electron energy of
105 –106 eV, a cross-sectional area of 1–100 cm2 and a pulse duration of up to 10−7 –10−6 s
can be efficiently used for the generation of high-power microwaves in various slow-wave
structures [1, 2], for the pumping of gaseous lasers and for the surface modification of solids
[3]. In order to produce such electron beams, an electron source that yields a uniform electron
emission at accelerating fields of about 105 V cm−1 and should be compatible with a vacuum
of 10−5 –10−6 Torr is required.
Remarkable results on the reliable and reproducible generation of large-cross-section
(102 –103 cm2 ) long-duration (up to 50 µs) electron beams with an electron energy up to
400 keV were obtained in the experiments by Engelko [4]. It was shown that the original
design of uniformly distributed multipoint explosive emission sources allows critical problems of explosion sources (uniform plasma generation, fast explosion plasma expansion and
substantial outgassing) in the case when the extracted current density is je 1 A cm−2 to be
*Corresponding author. Email: fnkrasik@physics.technion.ac.il
Plasma Devices and Operations
ISSN 1051-9998 print/ISSN 1029-4929 online © 2006 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/10519990600777077
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solved. Using either ballistic or magnetic focusing, the density of the electron beam current
on the target was increased to 15 A cm−2 .
However, many applications require electron sources which by themselves (i.e. without any
focusing) can be used to generate electron beams with an extracted current density of up to
several tens of amperes per square centimetre, at a moderate electric field E 50 kV cm−1 .
The required current density is ten times higher than the current densities obtained by multipoint explosive emission sources [4]. Recent experimental research showed that carbon and
dielectric velvet cathodes can be successfully used at E 50 kV cm−1 for the generation of
electron beams of microsecond time duration with je 15 A cm−2 and cross-sectional area of
several tens of centimetres [2, 5, 6]. However, by the use of optical and X-ray diagnostics it was
shown that electron emission occurs from individual and non-uniformly distributed surface
plasma spots on the surface of these types of cathode. The latter leads to local non-uniformity
in the current density of the extracted electron beam [7]. Also, problems related to the lifetime
of these relatively high-current-density cathodes, namely the maximum achievable electron
current density without the formation of a rapidly expanding plasma, and vacuum compatibility at a high repetition rate of the accelerating pulse, have not been completely resolved.
Another approach to the development of electron sources for the generation of moderatecurrent-density electron beams is associated with sources that produce plasma prior to the
application of the accelerating pulse. Examples of such plasma sources are arc plasma sources
[3], ferroelectric plasma sources (FPSs) [8, 9], hollow-cathode sources [10] and hollow-anode
(HA) sources [11–18].
In previous papers [15–17], we described the parameters of the HA electron sources
with different plasma igniters which operated at a background gas pressure in the range
10−4 –10−5 Torr. For instance, in [15], six arc sources producing emission plasma placed on
the bottom of the HA cavity were used for the generation of high-current electron beams
with a cross-sectional area up to 100 cm2 . The drawback of this design is the large discharge
current amplitude (about 3 kA) which is four times the amplitude of the extracted electron
beam current; i.e. the efficiency of electron beam extraction is only approximately 33%.
Also, it was found [17] that a large-area FPS-assisted HA is a powerful and the most efficient
pulsed electron source of other previously investigated sources. Indeed, the efficiency of
electron beam extraction in this HA design is about 100%; i.e. the amplitudes of the discharge
and extracted electron beam currents are equal to each other. However, it was shown that prior
to the accelerating pulse the cross-sectional distribution of the ion plasma current outside the
HA output grid is not uniform, leading to a non-uniform cross-sectional distribution of the
electron beam current density during the accelerating pulse [17].
In this paper we report the development and study of the FPS-assisted HA which operates in
the pressure range 10−4 –10−5 Torr with reliable and reproducible generation of electron beams
having a current density of several amperes per square centimetre, a uniform cross-sectional
area of up to 200 cm2 , a pulse duration of about 4 × 10−7 s and an accelerating electric field
of up to 40 kV cm−1 . To provide efficient HA plasma formation compared with multiple-arc
sources and to improve the uniformity of the plasma density distribution in the vicinity of the
HA output grid, several FPSs arranged with azimuthal symmetry were used.
2.
Experimental set-up and diagnostics
The experimental set-up is shown in figure 1. The HA was made in the form of a stainless steel
cylinder of 24.6 cm diameter having an output diaphragm of 19 cm diameter. An HA output
stainless steel grid of 16 cm diameter was placed at a distance of 3 cm from the diaphragm.
A Plexiglas insulator 2 cm thick was used to support the HA output grid which was connected
Electron beam generation by a hollow anode
Figure 1.
225
Experimental set-up.
to the HA cavity either by a low-inductance resistance Rgr or by a parallel-connected resistance
Rgr and a capacitance Cgr . All experiments were carried out using a 55% transparency grid
with a grid cell of size 235 µm × 235 µm. The HA was placed inside a vacuum chamber of
50 cm diameter and 54 cm length. Two turbomolecular pumps (pumping rates of 500 l s−1 and
350 l s−1 ) were used to produce a pressure in the range 2 × 10−4 − 5 × 10−6 Torr inside the
chamber. Most experiments were carried out at a pressure of 8 × 10−5 Torr.
To ignite and sustain the HA discharge with a uniform plasma density in the vicinity of
the HA output grid, seven identical FPSs were used. Six FPSs were arranged with azimuthal
symmetry at the bottom of the HA at a radius of 65 mm and the seventh FPS was placed on the
HA axis. Each FPS was in the form of a disc (of 18 mm diameter and 2 mm thickness) made
from Ba–Ti solid solution with a high dielectric constant ε ≈ 3000. The front electrode of each
FPS was made of a stainless steel plate with six holes each of 3 mm diameter, and the rear
electrode was made from a solid copper disc. Both electrodes were glued to the FPS surface.
The distance between the FPSs and the HA output grid was 17.5 cm. This provided a relatively compact design; i.e. the length of the HA electron source was about 20 cm. Incomplete
discharges on the front surface of each FPS were generated by driving pulses applied to each
FPS rear electrode. These driving pulses were produced by a pulse transformer with a toroidal
ferrite core. The primary circuit of the transformer was made from seven coils connected in
parallel with two turns in each coil. The secondary circuit of the transformer consisted of
seven independent coils each of which had two turns and was connected to the rear and front
electrodes of its corresponding FPS. A high-voltage (HV) driving pulse with an amplitude in
the range 5–15 kV and a pulse duration of about 200 ns produced by a Blumlein generator was
supplied to the primary circuit of the pulse transformer.
The discharge between the front surfaces of the FPSs and the HA was ignited by a pulseforming network (PFN) generator (output voltage amplitude, up to 10 kV; pulse duration, about
10 µs; internal impedance, about 5.6 ). In order to decouple the operation of FPSs, limiting
resistors connected between the front electrodes of the FPSs and the output of the PFN were
used (see figure 1). In order to minimize the inductance of the feeding coaxial cable from the HA
to the PFN generator, the latter was placed inside a tank filled with transformer oil, at the output
of an HV pulse generator (output voltage amplitude, up to 300 kV; pulse duration, about 300 ns;
internal impedance, 84 ). To supply HV pulses from the Blumlein generator to the FPSs and a
dc HV to the PFN, a 500 µH decoupling inductance was used. This inductance and decoupling
capacitor (see figure 1) allow the 300 kV nanosecond-timescale-duration accelerating pulse to
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be decoupled from the 15 kV nanosecond-timescale-duration Blumlein pulse and the 10 kV
dc voltage supplied to the PFN [18]. The decoupling inductance was made from a coaxial
cable wound on two toroidal ferromagnetic cores connected in series.
The sequence of the experimental set-up operation is as follows. The driving pulse supplied
by the Blumlein generator causes the formation of an incomplete surface discharge plasma
on the front surface of each FPS. Further, the electron and ion flows emitted from the FPS
surface plasma initiate the HA main high-current discharge. The accelerating pulse from the
HV pulse generator ϕacc 300 kV was applied to the HA with a variable time delay with
respect to the beginning of the HA high-current discharge. The accelerating electric field
extracts electrons from the HA plasma and accelerates them towards a stainless steel grid
collector (see figure 1).
Various diagnostics were used to characterize the parameters of the HA discharge plasma
and the generated electron beam. The charged-plasma-particle flows outside the HA were
measured with an array of 12 biased collimated (1 mm collimator diameter) Faraday cups
(CFCs). A double floating probe was used for measurements of the bulk plasma electron
temperature Te and plasma density n. The double probe was placed at 9 cm distance from the
FPSs near the HA axis normal to the FPS surface. The distribution of the HA plasma electron
energies was determined by analysing the data obtained by a single floating probe. The single
probe was placed in the same position as the double probe was placed. The electron energy
distribution outside the HA was measured using a retarding-field electron energy analyser.
The latter consists of a collimator array, retarding grids and a collector. The collimator array
was made of a plate 3 mm thick with holes having entrance and output diameters of about 500
and about 150 µm, respectively. The total geometrical transparency of the collimator array
was approximately 25%. Two stainless steel grids (cell size, 50 µm × 50 µm; geometrical
transparency, 50%) were installed between the collimator array and the collector. The first
(ion) grid was supplied with a positive potential in order to cut off plasma ions and the second
grid was supplied with a negative retarding potential. The distances between the collector, the
retarding grid and ion grids were about 200 µm. The distance between the ion grid and the
collimator was about 300 µm. The entrance aperture of the analyser was 20 mm × 20 mm and
its overall dimensions were 60 mm × 40 mm × 8 mm.
The HA discharge voltage ϕd and the HA grid voltage ϕgr were measured with Tektronix
probes Tek P6015 and Tek P5100 respectively. The diode voltage ϕacc was measured with an
active voltage divider. Self-integrated Rogowsky coils (RCs) were used for current measurements which included the diode current, the FPS driving current, the HA discharge current
and the current distribution between individual FPSs (see figure 1). The light emission from
the HA was studied using a fast intensified framing camera 4Quik05A. The absence of explosive emission spots at the HA output grid during the accelerating pulse was checked with
the 4Quik05A camera. The uniformity of the electron beam current density was studied by
employing an array of ten CFCs placed behind the grid collector. In addition to the CFCs, the
uniformity of the electron beam was also checked by X-ray imaging of the collector. In this
case we used as an anode a molybdenum foil of 100 µm thickness and 15 cm diameter with a
fast plastic EJ-200 scintillator of 2 mm thickness attached to the back side.
3.
3.1
Experimental results
Operation of the ferroelectric plasma source and hollow anode
It was shown that the FPS array operates reliably and all seven FPSs produce plasma simultaneously. Typical images of the FPS light emission are shown in figure 2(a). It can be seen
Electron beam generation by a hollow anode
227
Figure 2. Fast framing photographs of the light emission from the front surface of the FPS: (a) prior to the beginning
of the HA discharge; (b) during the HA discharge but prior to the accelerating pulse; (c) during the accelerating pulse.
The frame duration is 400 ns, P = 8 × 10−5 Torr, Id ≈ 800 A and Ib ≈ 1000 A.
that the application of the driving pulse to FPSs caused the appearance of bright light plasma
spots on the front surfaces of all FPSs as a result of surface discharges. Also, it can be seen
that the structure of the surface light emission reproduces the front electrode design. Typical
dimensions of plasma spots were about 3 mm. It should be noted that the amplitude of the
driving pulse required for surface discharge was considerably smaller than the amplitude of
the driving pulses used in earlier work owing to a high value of the dielectric constant and
small thickness of the ferroelectric samples [17, 18]. As a result, the driving generator had a
stored energy that is a quarter of the previous stored energy, which is an important issue in
the case of the use of a battery supply [9]. Bright light emission from FPS surface spots was
observed, even at a driving voltage of 1.8 kV.
A PFN was connected between the HA and the resistor array without a gas spark switch in
the discharge circuit. Thus, the front electrode of the FPSs had a dc potential with respect to
the HA prior to the application of the driving pulse. The HA discharge began with a significant
delay, up to 15 µs, with respect to the beginning of the FPS surface discharges (figures 3 and
4(a)). During the HA discharge, light emission from all seven FPSs was observed with an
increased intensity in comparison with the light intensity obtained during the driving pulse
(see figures 2(a) and (b)). It was found that the increase in the amplitude of the HA discharge
voltage, up to about 10 kV, led to a decrease in the time delay of the HA discharge initiation
down to about 10 µs. In the experiments, an HA discharge voltage amplitude of approximately
9.5 kV was used and the amplitude of the FPS driving pulse was about 2.5 kV. The latter is
a quarter of that used in the case of the FPS sample 8 mm thick [17]. The generated surface
discharges produce plasma flows which ignite and sustain the HA discharge with a current of
up to 1 kA at a background gas pressure in the vacuum chamber of about 8 × 10−5 Torr (see
figure 4(a)). A distinctive feature of the present HA operation was the 200–250 V discharge
voltage which significantly exceeds the corresponding value for the HA discharge sustained by
a large-area FPS (about 120 V) [17]. This can be explained qualitatively as the high discharge
Figure 3. Dependence of the time delay of the beginning of the HA discharge on the charging voltage of the PFN.
Id ≈ 1000 A and P = 8 × 10−5 Torr.
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Figure 4. The general voltage and current parameters of the HA: (a) typical waveforms of the HA discharge current;
(b) HA output grid voltages (the HA output grid is loaded on the resistance Rgr = 100); (c) HA output grid voltages
(the HA output grid is loaded on the parallel connected resistance Rgr = 100 and capacitance Cgr = 990 nF).
P = 8 × 10−5 Torr and Id ≈ 1000 A.
voltage arises because it is necessary to have an increased potential drop inside the cathode
layer in order to extract electrons with a current density of hundreds of amperes per square
centimetre. Indeed, a rough estimate of the total surface area of the FPS bright spots gives an
approximate value of 2.5 cm2 , which corresponds to a current density of about 400 A cm−2
and a calculated cathode sheath width of about 40 µm.
3.2 Plasma parameters for the hollow anode
Using double floating probes (see section 2) the HA bulk plasma density n and electron
temperature Te were estimated to be n ≈ 1 × 1012 cm−3 and Te ≈ 8 eV respectively at an HA
discharge current amplitude Id ≈ 1000 A and a gas pressure P ≈ 8 × 10−5 Torr. Here, the
electron temperature was determined assuming a Maxwellian electron energy distribution.
In order to study the electron energy distribution function we used a retarding-field electron
energy analyser (section 2). In this experiment, the HA output grid was connected to the HA
and the analyser was placed outside the HA at a distance d = 5 cm from the HA output
grid. The ion grid and collector of the analyser were kept at 30 V and 65 V respectively.
The velocity distribution function f (Ve ) is proportional to dIcoll /dϕ, where Ve is the electron
velocity, Icoll is the collector current and ϕ is the retarding potential which is numerically equal
to the electron energy E. Electrons with velocities between Ve and Ve + dVe , and a density dN
produce a current density dIcoll = e dN (e/m)f (Ve ) d(mVe2 /2) = (e2 /m)f (Ve ) dϕ, where m
and e are the electronic mass and charge respectively. Thus, the first derivative of the collector
current, dIcoll /d(ϕ) ∝ f (Ve ), allows the plasma electron velocity distribution to be obtained
and also the plasma electron energy distribution. The electron energy distribution function
f (E) for the plasma flow propagating outwards from the HA is shown in figure 5. This
distribution can be fitted using two Maxwellian distributions which are typical for discharges
with a flow of fast electrons. In this case, the first Maxwellian distribution, which peaks
at approximately 8 ± 2 eV, is responsible for the bulk plasma electron energy distribution
and the second Maxwellian distribution, which peaks at 45–50 eV, is responsible for the
fast electron energy distribution. It can be considered that the low-temperature Maxwellian
distribution describes the HA bulk plasma electrons and the high-temperature Maxwellian
distribution describes the fast electron flow which is typical for gaseous discharges.
In addition to the retarding analyser, measurements of the energy distribution of the plasma
electrons inside the HA cavity were carried out using a single floating probe (see section 2).
The obtained dependences of the probe current versus the bias voltage Ipr = f (ϕpr ) were
analysed using the Druyvesteyn technique [19] which allows the plasma electron velocity
Electron beam generation by a hollow anode
229
Figure 5. Distribution function of the plasma electron energy obtained with the electron retarding analyser at
a distance of 5 cm from the HA output grid (a.u., arbitrary units). The HA output grid is connected to HA.
P = 8 × 10−5 Torr and Id ≈ 900 A.
distribution to be obtained as f (Ve ) = (m2 /2Sπ e3 ) d2 Ipr /d 2 ϕpr , where S is the probe area.
It was found that the electron energy distribution inside the HA cavity is also characterized by
slow electrons with an average energy of 6 ± 1 eV and fast electrons with an energy of 50 eV
or greater. The uncertainty in the energy of fast electrons is related to parasitic discharges,
which appeared at a higher bias voltage of the probe. Nevertheless, single-probe data also
showed the presence of fast electrons in the HA discharge.
3.3 The autobias output grid of the hollow anode
The formation of the HA discharge is accompanied by plasma penetration inside the accelerating gap prior to the application of the accelerating pulse. This phenomenon leads to a plasma
prefilled mode [1] of the diode operation, which significantly changes the characteristics of
the diode and the generated electron beam and may prevent coupling of this source to most
high-power microwave tubes. In order to avoid this apparent disadvantage, the plasma penetration through the HA output grid should be reduced. The latter can be achieved by the use
of a negatively biased HA output grid (see figure 1).
In previous experiments, an autobiased HA output grid was used. The autobias potential
was produced by the electron plasma current passing through the resistance Rgr connecting
the grid to the HA [14–18]. The maximum negative autobias grid potential ϕgr does not exceed
70 V. All efforts to increase the autobias potential by an increase in the value of Rgr surprisingly
caused a decrease in the value of ϕgr to 40 V [17]. An additional study of this phenomenon
carried out in the present work showed that fast high-energy (up to several kiloelectronvolts)
electrons existing during the transient phase of the HA discharge formation should be taken
into account. Some of these electrons are collected by the HA output grid and, consequently,
these electrons develop a high (a few kilovolts) negative potential. It was shown that, when
this transient grid potential exceeds a threshold of –1.5 kV, which corresponds to an Rgr value
greater than 200 , a parasitic vacuum discharge develops between the HA diaphragm and the
HA output grid. This vacuum discharge reduces the value of ϕgr to about 40 V during the main
HA discharge (see figure 4(b)). To avoid this parasitic vacuum discharge, a capacitance Cgr
was connected parallel to Rgr (see figure 1). The use of this capacitance allows the HA output
grid potential to be significntly decreased during the transient stage of the HA discharge and
to avoid vacuum discharge initiation (see figure 4(c)).
The HA plasma flow penetration through the output grid was studied using a CFC placed
at a distance of 1 cm from the grid. The experiments were carried out with either a positively
biased or a zero-biased CFC. In the latter case the difference jpl = je − ji between the plasma
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Figure 6. Parameters of the plasma flow: (a) dependence of the plasma flow current density jpl on the HA grid bias
voltage ϕgr (the CFC bias voltage is zero); (b) dependence of the ion plasma flow current density ji on ϕgr (the CFC
bias voltage is −90 V). P = 8 × 10−5 Torr, Cgr = 990 nF, Rgr = 100 and Id ≈ 900 A.
electron current density je and the ion current density ji was measured. The output grid autobias
potential was varied by using different values of Rgr in the range 3–1500 , keeping Cgr at a
constant value of about 990 nF. The dependences of jpl and ji on the autobias grid voltage ϕgr
are shown in figure 6. It can be seen that the use of Cgr = 990 nF allows the value of ϕgr to
be increased up to about 300 V compared with ϕgr 70 V in the absence of this capacitance.
It was shown that the increase in the value of ϕgr up to about 300 V leads to a decrease in
the value of jpl by a factor of 120, namely from about 120 mA cm−2 to about 1 mA cm−2
(see figure 6(a)). In fact, a sharp decrease in the plasma flow already occurs at ϕgr −100 V.
Thus, the use of an additional capacitance, which is charged by high-energy electrons at the
beginning of the HA discharge up to −300 V, allows an efficient cut-off of plasma electrons
having energies not more than 100 eV during the main HA discharge (see section 3.2).
It should be note that a fourfold decrease in the value of ji , from about 12 mA cm−2 down
to about 3 mA cm−2 , was also obtained (see figure 6(b)). The latter cannot be explained by the
plasma ion cut-off by the negatively autobiased grid of the HA. Two effects can be used to
explain the decrease in the ion flow. Firstly, it is reasonable to consider that a large autobias
grid potential leads to the formation of a sheath in the vicinity of the HA grid, where the ion
flow extracted from the HA plasma boundary prevails. This ion flow is accelerated towards
the grid, penetrates through it and forms a virtual anode similar to the electron reflex triode
operation [1]. Thus, a significant decrease in the plasma ion current density can be explained
by ion oscillations around the grid. Secondly, the fast expansion of ion flow due to the Coulomb
repulsion forces in the absence of neutralizing electrons can be used to explain the fast decrease
in the ion current density.
3.4
The spatial plasma density distribution of the hollow anode
The cross-sectional uniformity of the distribution of the electron beam current density is one
of the key issues in applications related to high-power microwave generation and gaseous
laser pumping. The uniformity of the extracted electron beam depends on the plasma density
distribution in the vicinity of the HA output grid. In a recent study [15], an HA operation ignited
and sustained by six arc plasma sources was described. A uniform arc current distribution
among these sources, achieved by decoupling inductances, allowed electron beam generation
with a satisfactory uniform cross-sectional current density distribution within about 8 cm
diameter. The main disadvantage of this HA design was a high arc discharge current of about
3 kA compared with an extracted electron beam current of about 1 kA.
Electron beam generation by a hollow anode
231
In the present work, seven FPSs were used to initiate and sustain an HA discharge. The
amplitude of the current via each of these sources could be adjusted using limiting resistors
connecting the front electrode of each FPS and the PFN output (see figure 1). The experimental
results presented in this work were obtained with limiting resistances Rl = 10 for each of
six symmetrically distributed FPSs and Rl = 20 for the central FPS. The latter required a
lower current in order to achieve a uniform plasma distribution in the vicinity of the HA output
grid 5. The current distribution between six FPSs measured by RCs is shown in figure 7(a).
An almost uniform distribution of the FPSs discharge current with an amplitude of 140 ± 7 A
can be seen. This uniform current distribution was achieved because of the high value of Rl in
comparison with the impedance of the discharge circuit, approximately 0.2 . The amplitude
of the discharge current from the central FPS was about 70 A. Typical waveforms of three FPS
discharge currents are shown in figure 7(b). It can be seen that a significant difference, up to
40%, between individual FPS currents is obtained only during the phase of the HA formation.
During the main HA discharge the current non-uniformity is about 5%.
The radial distribution of the HA plasma density was studied using an array of 12 negatively
biased (−100 V) CFCs placed at 1 cm distance behind the HA output grid. In these experiments,
an autobias grid capacitance Cgr = 990 nF and a resistance Rgr = 100 were used. The
distance between the FPSs and the HA output grid was varied in the range 10–19 cm. A
satisfactory uniform radial distribution of the ion plasma current density (ji ≈ 3 mA cm−2 )
was obtained within a diameter of 13.5 cm at a distance of 17 cm (figure 8(a)). At shorter
distances the ion plasma current density distribution was non-uniform.
3.5
High-voltage diode operation
In most experiments with electron beam generation in the HV diode the accelerating pulse was
applied with a delay of about 17 µs with respect to the beginning of the HA discharge current.
Figure 7. Parameters of the FPSs: (a) the HA discharge current distribution for six symmetrically distributed FPSs;
(b) typical discharge current waveforms of three different FPSs. P = 8 × 10−5 Torr.
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Figure 8. (a) Radial distribution of the ion current density ji in the accelerating gap dacc prior to the beginning of the
accelerating pulse at a distance of 1 cm from the HA output grid. (b) Radial distribution of the electron beam current
density. P = 8 × 10−5 Torr, dacc = 5 cm, ϕac ≈ 165 kV, Ib ≈ 1000 A, Id ≈ 800 A, Cgr = 990 nF and Rgr = 100 .
Typical framing images of the light emission from the FPS array are shown in figure 2(c).
These images show that there is no significant change in the light intensity of the plasma
spots during the accelerating pulse in comparison with the light intensity of the plasma spots
prior to the accelerating pulse (see figure 2(b)). Thus, it can also be assumed that there are
no significant changes in the surface plasma density and temperature during the accelerating
pulse. In addition, framing images of the HA output grid showed an absence of explosive
plasma spots at the HA output grid during the accelerating pulse at an average electric field of
about 60 kV cm−1 . The latter agrees with recent results, which showed formation of plasma
spots on the HA output grid only at an electric field of about 160 kV cm−1 [17].
Typical waveforms of the diode voltage ϕacc , diode current Ib and calculated space-charge3/2
2
limited current Isc = 2.33 × 10−6 Sc ϕacc /dacc
, where ϕacc is the accelerating voltage, dacc is
the accelerating gap and Sc is the effective area of the plasma emission surface, are shown
in figure 9. A diode current amplitude Ib ≈ 1000 A at ϕacc ≈ 165 kV and dacc = 5 cm was
obtained. The effective emission area Sc ≈ 165 cm2 can be found by equating the spacecharge-limited current Isc and the measured current Ib . At these values of Ib and Sc the diode
current density jb 6.5 A cm−2 . In addition, it can be seen that, at the beginning of the
accelerating pulse, Ib is greater than Isc , which is typical for the plasma prefilled mode of the
diode operation [1]. The latter agrees with the plasma measurements showing the presence of
Figure 9. Typical waveforms of the diode voltage, diode current and the calculated space-charge-limited current.
P = 8 × 10−5 Torr, Cgr = 990 nF, Rgr = 100 , dacc = 5 cm and Id ≈ 800 A.
Electron beam generation by a hollow anode
233
Figure 10. (a) Typical X-ray image of the electron beam; (b) radial distribution of the intensity of the X-ray image
(a.u., arbitrary units). The frame duration is 400 ns, P = 8 × 10−5 Torr, dacc = 5 cm, ϕacc ≈ 170 kV and Ib ≈ 1000 A.
tenuous plasma inside the accelerating gap prior to application of the accelerating pulse (see
section 3.3). The plasma prefilled mode of the diode operation is characterized by a diode
current amplitude exceeding Isc owing to compensation of the electron beam space charge
by plasma ions with further fast plasma erosion towards the collector. The process of plasma
erosion leads to an increase in the effective accelerating gap between the plasma boundary
and the collector. Plasma ions leave the accelerating gap during the first 100–150 ns of the
accelerating pulse. When the plasma boundary reaches the collector, Ib becomes equal to Isc .
Therefore, in the main part of the accelerating pulse, the diode operates in a space-chargelimited mode (see figure 9).
The radial distribution of the electron beam current density was studied using an array
of ten CFCs placed behind holes drilled in the grid collector. The measured waveforms of
the electron microbeam current density showed a smooth form without sporadic spikes in
the current amplitude, which are typical of electron emission from explosive emission or
flashover plasmas. The radial distribution of the diode current density at the instant of the
maximum accelerating pulse is shown in figure 8(b). A satisfactory uniformity of the radial
distribution of the electron beam current density can be seen within a diameter of about 13.5 cm
with an average diode current density jb ≈ 5.8 A cm−2 . The latter agrees with estimates of
the average diode current density. A space- and time-resolved pattern of the distribution of
the electron beam current density obtained using X-ray imaging of the electron beam (see
section 2) shows a beam about 15 cm in diameter (figure 10). The absence of an X-ray image
at the anode segment is due to a smaller scintillator dimension in comparison with the anode
molybdenum foil (see figure 10(a)). It should be noted that the area of the X-ray pattern
at the anode is approximately 176 cm2 , which is larger than the estimated effective cathode
area Sc ≈ 165 cm2 . Thus, a weakly divergent electron flow can be assumed, which suggests
the absence of an ion flow inside the accelerating gap. Finally, placing the seventh FPS in
the centre of the FPS array prevents an almost 30% decrease in the electron beam current
density at the HA axis, which was always obtained in the case of just six symmetrically
distributed FPSs.
4.
Summary
The design and operation of the HA plasma source with seven incorporated FPSs were
presented. The use of an HA as an electron source in a high-current diode showed its applicability for the generation of electron beams with an amplitude of about 1 kA, a cross-sectional
area of about 170 cm2 and a uniform cross-sectional current density at an accelerating field of
234
J. Z. Gleizer et al.
not less than 30 kV cm−1 . The diode operation was characterized by a space-charge-limited
mode during the major part of the accelerating pulse.
It was demonstrated that the use of seven small-area identical FPSs allows an HA discharge
of approximately 10 µs duration with a current up to 1 kA at a background pressure as low as
10−5 Torr to be reliably and reproducibly ignited and sustained. Also, it was shown that the use
of decoupling resistors permits the HA discharge current distribution between the FPSs to be
controlled. An extremely high HA discharge current density, up to 400 A cm−2 , was observed
from the surface plasma of FPSs. However, no visible damage was obtained on the surface of
the FPSs, which indicates a low rate of erosion of the Ba–Ti-based ferroelectric samples. It
was also found that, for an HA discharge current amplitude Id ≈ 1000 A, the plasma density
is about 1012 cm−3 and the electron temperature is about 8 eV. Investigation of the plasma
electron energy distribution showed the existence of a group of fast electrons with directed
energy in the range 40–50 eV.
In spite of the point-like form of the FPSs, the radial distribution of the plasma density within
an emission area of about 170 cm2 in the vicinity of the HA output grid and also the radial
distribution of the electron beam current density were found to be satisfactorily uniform. The
latter can be explained by the expanding and overlapping plasma flows generated by individual
FPSs. Also, it can be assumed that the partial pressure of neutrals desorbed from the FPSs
surface is higher at the peripheries of the HA cavity. In this case a non-uniform radial potential
distribution inside the HA cavity and an increased ionization rate of ion production at larger
radii, which leads to ion acceleration not only towards the HA walls but also towards the
axis, may be obtained [20]. It is understood that additional research is required in order to
understand the obtained uniform cross-sectional plasma distribution.
Finally, it was found that the use of an additional capacitance Cgr allows a vacuum discharge
between the HA output grid and the diaphragm to be avoided, and the HA operation with an
autobias grid potential to be studied in the range up to –300 V.
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