Vol.2, No.5, 419-426 (2010) Natural Science
http://dx.doi.org/10.4236/ns.2010.25051
Research on the plasma dynamics in a magnetically
self-insulated ion diode with explosive emission
potential electrode
Alexander Pushkarev*, Yulia Isakova, Roman Sazonov
Tomsk Polytechnic University, Tomsk, Russia; *Corresponding Author:
Received 10 January 2010; revised 23 February 2010; accepted 10 March 2010.
ABSTRACT
The results of an experimental investigation of
the plasma dynamics in a magnetically insu-
lated ion diode in bipolar-pulse mode are pre-
sented. The experiments were done at the
pulsed TEMP-4M accelerator by formation of a
first negative pulse (100 ns, 150-200 kV) and a
second positive pulse (80 ns, 250-300 kV). The
voltage-current diode characteristics were used
to analyze the plasma behavior in the anode-
cathode gap. It is shown that, during the first
pulse, a discrete emissive surface is formed on
the graphite potential electrode and a plasma
forms by explosive-emission, which before the
second pulse comes, fills the whole working
surface of the electrode and spreads to the
anode-cathode gap. An analytical expression is
obtained for the total current in the cellular
structure approximation. It is shown that the
current build-up for a cathode surface with dis-
crete emitting centers is described satisfac-
torily by a modified Child-Langmuir formula wi-
th a form factor decreasing from F = 6 to 1. It is
found that, once plasma formation at the gra-
phite potential electrode is complete and until
the second positive pulse, the plasma speed is
constant and equals 1.3 ± 0.2 cm/μs.
Keywords: Ion Beams; Plasma Generation;
Graphite Cathodes; Plasma Speed; Magnetic
Insulation; Explosions
1. INTRODUCTION
Modernizing of engineering products is difficult without
application of new progressive technological processes,
which allow increasing the life and reliability of com-
ponents and connections under very severe operating
conditions. Powerful ion beam irradiation provides heat-
ing and cooling of boundary layers of a treated item at a
rate of more than 108 K/s. This allows compounds and
structures to be realized in surface layers which cannot
be made by traditional industrial methods. As a result,
the characteristics of materials change: solidity, strength,
wear resistance; the operational characteristics of items
made from these materials improve. For wide industrial
implementation of the modification methods of bound-
ary layers by high-power ion beams, a reliable and eco-
nomical powerful ion beam source with long operational
life is necessary.
The effective generation of powerful ion beams became
possible when two important problems were solved:
formation of dense plasma on the anode surface and
suppression of the electronic component of diode current.
The ion and electron generation and acceleration proc-
esses occur simultaneously when the voltage is applied
to the diode. As follows from the Child-Langmuir for-
mula [1], the proton current density is 2.3% of the elec-
tron current density. As for heavier ions, they are lower.
In 1973, Sudan and Lovelace [2] first suggested the con-
struction of an ion diode with external magnetic isolation
for the suppression of the electronic component of diode
current. The efficiency of such a construction was con-
firmed experimentally in 1976 by Dreike, Eichenberger,
Humphries, and Sudan [3]. In their article, the results of
experiments on proton beam generation in an ion diode
of coaxial construction with external magnetic isolation
were presented. The total diode current was described by
the Child-Langmuir ratio for proton current (subject to
diode geometry) by changing the accelerating voltage
from 120 to 200 kV, with pulse duration of 50 ns and a
magnetic induction of 1.03 T in the anode-cathode gap.
When the magnetic induction goes down to 0.52 T, the
total current exceeds the calculated value of proton cur-
rent by a factor of 2. In 1977, Humphries [4] first sho-
wed that it is possible to arrange magnetic self-insulation
using a special construction of ion diode. A transverse
magnetic field is formed in the anode-cathode gap by the
diode self current when the current flows in the elec-
trodes. In this case an additional magnetic field source is

A. Pushkarev et al. / Natural Science 2 (2010) 419-426
420
not required. It significantly simplifies the construction
of a powerful ion beam generator.
As for the problem of dense plasma formation on the
anode surface, in 1980 Logachev, Remnev and Usov
first suggested using the phenomenon of explosive elec-
tron emission [5]. They used a double pulse generator of
nanosecond duration (without any pause between pulses).
The first pulse had negative polarity and the second
pulse had positive polarity. During the first pulse, a
plasma forms by explosive emission on the potential
electrode. It contains ions with 1-4 degrees of ionization,
the plasma temperature is 4-5 eV and the density is more
than 1020 cm-3. During the second pulse, ions are pulled
out from the explosive emission plasma and accelerated.
A simple and robust construction of double pulse gen-
erator with an adjustable pause between pulses was first
suggested by Logachev, Remnev and Usov in 1983 [6].
We modernized this construction of the generator in
2009 [7], as a result the process of plasma formation on
the potential electrode surface has improved. This gen-
erator construction underlies the accelerator we use; it is
described in detail further in this text. For a more de-
tailed review of pulsed ion beam generation see [8,9].
In spite of much progress in powerful ion beam gen-
eration, many processes in an ion diode with magnetic
self insulation and with an explosive emission anode
have not been researched enough. In particular, there is
no experimental information about the duration of solid
emissive surface formation on anode and plasma expen-
sion velocity. This can be explained in the following way:
during the first 20-25 years, the main application of
powerful ion beams was in controlled thermonuclear
fusion investigations. The production of ion beams with
maximum current density and a pulse power of more
than 1012 W were mostly attempted. The relatively mod-
ern and broad application of high current ion beam ac-
celerators is in surface treatment or material modifica-
tion (i.e. smoothing and annealing of metal surfaces,
alloying, removal of coatings, thin film deposition, etc.).
One of the first attempts to use a high current ion accel-
erator for materials modification was made by Ham-
mer’s group at Cornell in collaboration with Hodgson’s
group at IBM in 1980 [10]. They used a pulsed 180 keV,
80 ns proton beam at several different ion current densi-
ties (40, 75 and 380 A/cm2) to anneal ion-implant-dam-
aged semiconductors. The first investigations into the
possibility of using powerful ion beams for metals alloy
materials modification were conducted by Didenko, Ku-
snetsov and Remnev in 1981 [11].
The conditions for the development and formation of
explosive emission plasma during pulsed ion beam gen-
eration in the first stage (negative polarity pulse) are
close to the conditions in an electron diode with an ex-
plosive emission cathode. Experimental data and theo-
retical models, describing a change of explosive emis-
sion plasma velocity during electron beam generation,
have a conflicting character. A review of the investiga-
tions into explosive emission plasma dynamics during
pulsed electron beam generation has been given in our
earlier article [12]. In 2006-2008 we conducted a com-
prehensive investigation of pulse electron beam genera-
tion in a diode with an explosive-emitting cathode of a
different configuration. For the first time it was shown
that, from the moment when the process of plasma for-
mation on the cathode is complete until the end of the
pulse (80-100 ns), the plasma velocity is constant and
equal to 2 ± 0.5 cm/μs for a graphite or carbon fiber
cathode, 3 ± 0.5 cm/μs for a tungsten cathode, and 4 ±
0.5 cm/μs for a cathode made from copper [12].
The first attempt at a systematic investigation of ex-
plosive emission plasma dynamics during pulsed ion
beam generation in a diode with self magnetic insulation
was made by Xin, Zhu and Lei in 2008 [13]. To deter-
mine the explosive emission plasma expansion velocity,
the voltage-current characteristics of the diode and the
Child-Langmuir ratio were used. That only applies when
a diode operates in a mode of space charge limitation.
They found that, during the first 29 ns after the voltage is
applied to the diode, the plasma velocity is equal to zero.
Then the plasma velocity increases up to a maximum
value of 4.5 cm/μs (t = 45 ns), subsequently it decreases
to 1.5 cm/μs at t = 70 ns. However, the authors did not
adduce proofs of the diode operation during the first 100
ns. Our investigations have shown that the duration of
solid plasma layer formation on the potential electrode
surface in a diode with a similar construction, exceeds
200 ns. During this period of time, the total diode current
is limited by the emissive ability of the potential elec-
trode. Thus, it is not correct to use the Child-Langmuir
ratio for the determination of the explosive emission
plasma velocity.
Also, the explosive emission plasma behavior from
the moment when separate emission centers form until
the solid plasma layer forms on the potential electrode
surface is not thoroughly investigated. In previous works
[14,15], numerical modeling was performed (tube of
current method) of the change of average electron cur-
rent density in a planar diode with the discrete emission
surface of the cathode during the evolution from forma-
tion on separate emission centers until the solid plasma
layer forms. The modeling conditions are a constant ve-
locity for the expansion of the plasma forming by explo-
sive emission and a rectangular pulse with constant am-
plitude. In our work [16], the first experimental investi-
gation of the voltage-current characteristics of a flat di-
ode with a graphite explosion emission cathode was de-
scribed. We show that the rise of electron current on the
discrete emission cathode surface is well described by
the Child-Langmuir ratio when the form-factor decreases
from 6 to 1. Results for plasma layer evolution without

A. Pushkarev et al. / Natural Science 2 (2010) 419-426
421
421
an external magnetic field were obtained. The results of
explosive emission plasma dynamics from formation on
separate emission centers until a solid plasma layer
forms on the potential electrode surface of the ion diode
(in a transverse magnetic field) have not been conducted
until the present time.
The purpose of this work is an investigation with high
temporal resolution of a magnetically insulated ion diode
in bipolar-pulse mode during the formation of the
plasma on the potential electrode surface.
2. EXPERIMENTAL INSTALLATION
Investigations were conducted at accelerator TEMP-4M
(modification of accelerator TEMP-4 [17,18]) with the
following parameters: the first impulse is negative (≈
100 ns, 100-150 kV) and the second one is positive (80
ns, 250-300 kV). Beam composition: ions of carbon and
protons, ion current density 10-150 A/cm2 (for different
types of diodes), pulse frequency 5-10 pulses per minute.
The accelerator contains a high-voltage pulse generator,
double forming line (Blumlein line), basic and prelimi-
nary gas dischargers, vacuum stripe diode, composed of
potential and grounded electrodes. The potential graphite
electrode of the diode is connected through a preliminary
gas discharger to the internal electrode of the double
forming line. The middle electrode of the double form-
ing line is connected to the high-voltage pulse generator.
In order to optimize the process of plasma formation by
explosive emission on the potential electrode, the nano-
second generator of the TEMP-4 accelerator was mod-
ernized. The positive voltage, which forms during the
delay between the first negative pulse and the second
positive pulse, was eliminated. This increases the effi-
ciency of plasma formation. Figure 1 shows a block
diagram of the diode connection of accelerator TEMP-
4M, the circuit for measuring voltage and current in the
stripe focusing diode with self-isolation.
For carbon, the electric field threshold, at which ex-
plosive emission of electrons begins, is lower than that
of copper and other metals. Moreover, in the space char-
ge limitation mode, the ion current density is inversely
proportional to the square root of the ion mass. The car-
bon ions in the materials of construction have the least
mass. Therefore, its use is much more practical for mea-
suring plasma expansion velocity.
We have investigated a focusing diode (4 cm × 25 cm)
and a planar diode (4 cm × 20 cm) each with a potential
electrode made from graphite. A grounded electrode of
the same dimensions is made from stainless steel and has
slits 0.5 cm × 5 cm, optical transparency of 60%.
To measure the total current consumed by the diode
connection a Rogowski coil with a reverse coil was used.
The voltage at the potential electrode was measured by a
resistive voltage divider. The recording of the electric
signals coming from sensors was performed on a Te-
ktronix 3052 B oscilloscope (500 MHz, 5·109 measure-
ments per second). The inaccuracy of electric signal
synchronization did not exceed 0.5 ns. The calibration of
the diagnostic equipment showed that it correctly refle-
cted the accelerator operation in short circuit mode (U =
50-60 kV), when operating with a resistive load up to 10
Ω (200-300 kV) and when operating with the diode.
Shown in Figure 2 is a typical oscilloscope trace of
the voltage on the potential electrode and of the load
impedance. These results were achieved using a 9.5
Ohm resistor during calibration. The voltage measure-
ment accuracy achieved by the resistive divider and of
the total electron beam current by the Faraday cup, as
well as their frequency performance allows to measure
the diode impedance with an accuracy better than ±10%.
The stripe diode with magnetic self-isolation performed
effectively at a vacuum of 10-3 Torr with a limit of more
than 106 pulses. The frequency of generation of these
powerful ion beam pulses was restricted only by the rate
of heating in the diode.
Figure 1. Diode connection of accelerator TEMP-
4M: 1-potential electrode of diode, 2-grounded
electrode, 3-Faraday cup, 4-Rogowski coil, 5-vol-
tage divider.
Figure 2. Oscilloscope trace of voltage (1) and cal-
culated values of impedance (2).

A. Pushkarev et al. / Natural Science 2 (2010) 419-426
422
3. BASIC CALCULATION EQUATIONS
An analysis of plasma behavior in the anode-cathode gap
was performed based on the current-voltage characteris-
tics of the diode. The electron and ion current densities
flowing through the diode in the mode restricted by
space charge are determined by the following expres-
sions [1]:
Electron current:
2
0
3/2
6
2
0
3/2
e
0
e102.33
9
24ε
d
U
d
U
m
e
J  (1)
Ion current:
2
0
2/3
0
9
24
d
U
m
z
J
i
i
ion 

(2)
where U is the voltage applied to the diode; d0 is the
anode-cathode gap, me is electron mass; mi is ionic mass;
zi is ionic charge.
Taking into account the reduction of anode-cathode
gap due to expansion of plasma from the emissive sur-
face of the potential electrode, the electron current den-
sity is equal to:
2
0
3/2
6
e)(
102.33)( vtd
U
tJ    (3)
where v is plasma expansion velocity.
If the diode operates in the mode of space charge
limitation, then from correlation (3), we obtain the cath-
ode plasma expansion speed as:
63/2
0
0
e
2.33 10 1
() SU vt d
tI






(4)
where S0 is the surface area of potential electrode (cath-
ode during negative pulsed) of diode. This correlation is
used further down in the calculation of plasma expansion
speed.
The speed at which the cathode plasma spreads can be
correctly calculated from the current-voltage characteris-
tics of the diode only under operating conditions corre-
sponding to the mode of space charge limitation. The
mode operation of the diode can easily be determined by
comparing the experimental and calculated values of
diode impedance. Their coincidence corresponds to the
diode current being limited by space charge. In the initial
period (discrete emission surface mode) and in the satu-
ration mode, the diode current is limited by the electron
emission from cathode. This is why the experimental
values of impedance will be larger than the calculated
ones. It is evident from Eq.1 and Eq.2, that the ion cur-
rent amounts to only a small part of the total current
through the diode, therefore the impedance of the diode
can be calculated from the following:
1/26
0
2
0
e0
calc 102.33
)(
US
tvd
JS
U
R



 (5)
4. DISCRETE EMISSIVE SURFACE
MODE
Operation of the magnetic self-isolation diode at the first
(negative) pulse and during the pause between pulses is
analogous to the operation mode of a planar diode with
explosive emission cathode at electron beam generation.
In Figure 3, a typical oscilloscope trace of the voltage
on the potential graphite electrode and calculated values
of the diode impedance are displayed.
Two modes of operation can be singled out [12,19].
From the application of voltage until the formation of a
solid plasma surface at the potential electrode (discrete
emissive surface mode, 0 < t < 250 ns in Figure 3), the
diode current is limited by the emissive ability of the
cathode. After covering the potential electrode surface
with plasma, the total diode current is limited only by
the vacuum electron charge in the anode-cathode gap
(250 ns < t < 600 ns in Figure 3).
Reduction of impedance of the diode in discrete emis-
sive surface mode is connected with two processes. They
are the increase of emissive surface on the graphite elec-
trode and the reduction of anode-cathode gap through
movement of the explosive emission plasma towards the
grounded electrode (Eq.5). The origin of the reduction in
diode impedance in space charge limitation mode is the
reduction of anode-cathode gap only.
The diode changes to the space charge limitation
mode after formation of the solid emissive layer on the
cathode surface. Let us assume that: 1) the electron cur-
rent is limited by the space charge in the inter-electrode
gap from the first moment of voltage application to the
diode, and 2) electron beam current growth until saturation
Figure 3. Oscilloscope trace of voltage (1) and im-
pedance value (2-experiment, 3-calculation) of stripe fo-
cusing diode with self-isolation, anode-cathode gap 8
mm.

A. Pushkarev et al. / Natural Science 2 (2010) 419-426
423
423
is determined by an increase in the surface of discrete
emitting centers from zero to the total geometric area of
the cathode. This approach has been successfully veri-
fied [14,15] by modelling the variation of the average
electron beam current in a planar diode with a discrete
emitting surface. Using Eq.3 the total electron current of
the diode is:


2
0
3/2
6
e)(
)(
102.33 tvd
tSU
I

 
where S(t) - total area of plasma emissive surface on the
cathode.
In modelling the law of variation of the area of a dis-
crete emitting surface, we use the following assumptions
[16]: 1) the emitting centers are equidistant from each
other and form a uniform cellular structure on the cath-
ode surface; 2) the emitting centers are formed simulta-
neously and their number remains the same during the
entire period of electron beam generation. Thus, the total
emitting area on the cathode is:
 )sin(3π)()( 2
1ααtvNtS 
where N - number of emitting centers; v1 - speed of ex-
pansion of the explosive emission plasma across the gap,
α = 2arcos(b/v1·t), b - distance between adjoining emit-
ting centers.
The total number of emitting centers can be estimated
as the ratio of the cathode area to the area of a hexagonal
unit cell (0.865b2). Consequently, the total electron cur-
rent emitted by the discrete emissive surface is:

3/2
2
0
2
0
2
1
6
calc )(
)sin3(π)(102.7 U
tvdb
Sααtv
I




(6)
Figure 4 shows the current changing during plasma
formation by explosive emission on the potential elec-
trode of the focusing diode. Experimental data are com-
pared with calculated data based on the assumption that
emitting centers form and expand (Eq.6, v1 = 2 cm/μs, b
= 11 mm); within the presence of a solid plasma surface
when the voltage is applied (Eq.3). Calculations were
made of the total electron current of the diode with dis-
crete emissive surface based on the assumption that the
speed of expansion of the explosive emission plasma
across the anode-cathode gap is equal to the speed of
expansion of the graphite plasma without any magnetic
field. The minimum distance between individual emit-
ting centers was calculated from the electric field
screening around the center [20]:
cm,500 3/41/2
10

 UIdr
The radius of screening, r, is equal to 5-6 mm if the
electron current from one emitting center I1 = 90 A and
the average voltage applied to the diode, during emitting
center formation is 100-120 kV (see Figure 3).
Measurements taken of the spatial distribution of en-
ergy density in the electron beam formed by the diode
during the first pulse confirm the existence of a periodic
structure in the emitting surface on the potential elec-
trode.
The distribution of energy density of electrons over
the cross section was measured by using a special do-
simetric film. The method of measurement is described
in detail in our reference [21]. Figure 5 illustrates the
change of electron beam energy density across the diode.
The dosimetric film was placed in the outside of the
grounded electrode. To protect it from the effects of the
ion beam, the films were covered with aluminum foil
with a thickness of 15 microns. Due to the screening of
the dosimetric film by slits (0.5 cm × 5 cm) on the
grounded electrode, the density reduces to zero at x = 10
and 70 mm.
During the process in which the discrete emissive
surface spreads from separate emitting centers to a solid
plasma layer that covers the cathode, a form factor must
be incorporated in Eq.6 [19]. This form factor accounts
for the distortion of the electric field strength near emitting
Figure 4. The diode current changing during plasma
formation by explosive emission: (1) experimental
data, and calculation for (2) solid and (3) discrete
plasma surface on the cathode.
Figure 5. Distribution of energy density in the elec-
tron beam (cross section).

A. Pushkarev et al. / Natural Science 2 (2010) 419-426
424
centers [20]. The dependence of planar diode current
with a discrete emissive cathode is:

FU
tvdb
Stv
Icalc 




2/3
2
0
2
0
2
1
6
)(
)sin(3)(107.2 
It has been demonstrated [22,23] that the current-
voltage characteristic of a planar diode with flat elec-
trodes (U = 20-40 kV) and a single emitter arising at an
artificial micro-protrusion on the cathode surface (d =
0.3-1 mm) in the initial stage of emitter evolution (v·t <
d/3) is well described (to within 10%) by the following
relation:
2
0
3/26
1044.4 







 
d
tv
UI
Note that this expression is obtained from correlation
(1) for a cathode with an emitting area of π(v·t)2 and F =
6. Figure 6 shows the ratio of experimental values of
diode current divided by calculated values based on the
correlation (6).
This ratio reflects the change in form factor during
explosive emission plasma formation. There are 4 typi-
cal ranges for the form factor. During the initial period
of time (t < 80 ns) the value of the form factor exceeds 6,
which fits with an increase in the number of emitting
centers and a simultaneous increase in their sizes. Dur-
ing the time that the ratio of distance between adjacent
emitting centers to their radius decreases from 7 to 5 (80
< t < 100 ns, see Figure 6) the formation of additional
emitting centers is suppressed by screening effects. The
value of the form factor is constant (within the meas-
urement accuracy) and is equal to 6. Furthermore, with
the size of the emitting center increasing as neighboring
centers overlap, the value of F decreases to 1. Thus, a
continuous emission surface forms on the graphite cath-
ode to generate the second pulse, F = 1.
Previous research has shown that the duration of solid
emissive layer formation on the cathode surface (only
when congruent with the duration of the pulse edge)
depends on the area and material of the cathode [16].
Figure 7 gives a comparison of the duration of explosive
emission plasma formation on the graphite cathode sur-
face of an electron diode (400 kV, 10 kA, 80 ns).
This was done with both 45 and 60 mm diameter
cathodes. The values of the duration of solid emissive
surface formation on the potential graphite electrode of
the ion diode (flat and focusing geometries) in the
self-magnetic insulation mode (first pulse) are illustrated
in Figure 7. It was shown that, in the discrete emissive
surface mode, the influence of the magnetic field on the
dynamics of the cathode plasma in a magnetically insu-
lated diode is negligible.
5. SPACE СHARGE LIMITATION MODE
After covering the potential electrode surface with
plasma, the total diode current is limited only by the
electron charge in the anode-cathode gap (250 ns < t <
600 ns in Figure 3). Experimental values of the diode
impedance are well described by correlation (5). Figure
8 shows the values of cathode plasma expansion speed
calculated from Eq.4.
Through these experiments we have found that the
rate of expansion of a graphite plasma (across the anode-
cathode gap) in a magnetically insulated diode is sig-
nificantly lower than the plasma rate of expansion in an
electron diode with graphite explosive emission cathode
[12]. This indicates the significant influence of the mag-
netic field in the gap on the expansion dynamics of an
explosive emission plasma. In the generation of power-
ful ion beams, the reduction of the rate of expansion of
the explosive emission plasma is a useful effect which
decreases the possibility of the anode-cathode gap being
bridged by the plasma.
Figure 6. Oscilloscope trace of voltage (1) and
form-factor for the formation of the plasma surface
on the cathode (2).
Figure 7. Dependence of the duration of solid emis-
sive surface formation on graphite cathode surface
area.

A. Pushkarev et al. / Natural Science 2 (2010) 419-426
425
425
Figure 8. Change of explosive emission plasma
speed during beam generation in electron diode
with graphite cathode (1) and in planar ion (2) and
focusing ion (3) diodes with graphite potential
electrode.
6. DISCUSSION OF EXPERIMENTAL
RESULTS
To provide magnetic insulation to the electrons in the di-
ode, the grounded electrode is connected to a camera
only from one side. Electrons, which compose the major
part of charge carriers in the diode, generate a magnetic
field as they move through the electrode (or along the
surface).
The magnetic field vector is perpendicular to the elec-
tric field vector in the anode-cathode gap. Figure 9
shows the change in magnetic induction in the diode
during the formation of the explosive-emission plasma
and the generation of the ion beam (according to the
Biot-Savart law). The calculation of magnetic field using
the ratio, based on diode geometry [13], gives results in
close agreement.
We consider an electron, emitted from the explosive
emission plasma on the potential electrode at the start of
the first pulse. Under the influence of the electric field, it
is accelerated towards the grounded electrode. In crossed
electric and magnetic fields under the influence of the
Lorentz force, the electron begins to change its direction
of motion from a transverse one to a longitudinal one,
along the grounded electrode. The Lorentz force does no
work and does not change the energy (or velocity) of the
electron, but changes only the direction of motion. Elec-
tron motion in crossed electric and magnetic fields can
be represented as a rotation over the cyclotron circum-
ference with the center of the circumference drifting in
the direction perpendicular to vectors E and B. The drift
velocity is equal to the ratio of electric field strength to
magnetic induction.
At the first pulse, the electrons are emitted from the
plasma surface on the potential electrode and move to-
wards the grounded electrode, which is a current-car-
rying conductor. The magnetic induction in the anode-
cathode gap increases towards the grounded electrode.
When the electron approaches the distance to the groun-
ded electrode, at which the magnetic induction exceeds
Вcr, the electron fails to reach its surface because it is in
cycloidal motion in the diode gap along the grounded
electrode. However, the electron motion in vacuum in
the diode gap comprises the current of the grounded
electrode and generates a self-magnetic field.
The change of critical magnetic induction during for-
mation of the plasma on the cathode by explosive emis-
sion is shown in Figure 9.
It is obvious that during the first 200-300 ns (discrete
emissive surface mode) the magnetic field induction in
the whole anode-cathode gap exceeds Вcr. This points to
the fact that at the first pulse, electrons move into the
anode-cathode gap near the potential electrode surface.
It is evident that the influence of the magnetic field on
the value of electron current (magnetic cut-off) is sig-
nificant when the duration of electron drift in crossed
magnetic and electric fields is comparable to the dura-
tion of the voltage pulse applied to the diode. The aver-
age drift velocity is equal to 12 cm/ns, and the elec-
trons reach the end of the diode (electrode length of 25
cm) within 2 ns. Therefore the effect of magnetic insula-
tion at the first pulse is insignificant. It is important to
note that, at the first pulse, only a small portion of elec-
trons reach the surface of the grounded electrode, which
restricts the process of plasma creation near the anode
surface.
7. CONCLUSIONS
An analysis of the pulsed ion diode with a passive anode
in the double-pulse mode, with matching of the diode
impedance to the output resistance of the nanosecond
generator has shown that the effect of magnetic self-
isolation is significant only during ion beam generation
(second pulse). In the initial period, at the stage of
forming explosive centres and developing the potential
electrode emission surface of the diode, the plasma dy-
namics are similar to the processes in the electronic diode
Figure 9. (1) the change of the accelerating voltage; (2)
the magnetic induction close to the potential electrode;
(3) critical magnetic induction.

A. Pushkarev et al. / Natural Science 2 (2010) 419-426
426
of a pulsed electron accelerator. After the solid plasma
forms on the surface of the passive anode, the effect of
magnetic insulation manifests itself only in a reduction
of the rate of explosive emission plasma expansion
across the gap. The value of electron current amounts to
more than 90% of the total diode current. It is well de-
scribed by the model of space charge limitation. The
electron drift duration in the crossed magnetic and elec-
tric fields during plasma formation in the passive anode
does not exceed a few nanoseconds, and the height of
the Trochoid of drift motion is close to the value of the
anode-cathode gap.
The results of our investigations show that the experi-
mental current-voltage characteristics of a magnetically
insulated ion diode with a graphite explosive emission
cathode in the initial stage (featuring a discrete emitting
surface) is satisfactorily described by a modified Child-
Langmuir formula, assuming that all discrete emitters
are formed simultaneously, their number is constant, and
the emitter radius increases at a constant rate. In the ini-
tial period of time, when the emitter radius is much
smaller than the distance between adjacent emitters, the
form factor in the modified Child-Langmuir formula cor-
responds to the experimental value F = 6, obtained for a
diode with a single emitting center. As the emitter area
increases, the form factor decreases from F = 6 to 1,
which corresponds to the current-voltage characteristic
of a planar diode with a continuous emitting surface on
the graphite cathode.
8. ACKNOWLEDGMENTS
This work was supported by the Russian Foundation for Basic Re-
search under project No. 08-08-12086.
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