Download Characteristics of Pulsed Virtual Cathode Oscillator for Nitrogen Gas

Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014
Characteristics of Pulsed Virtual Cathode Oscillator for Nitrogen Gas
H. A. El-tayeb
plasma physics and nuclear fusion department
Atomic Energy Authority, Cairo,Egypt
e-mail : [email protected]
Received: 29/1/2014
Accepted: 15/2/2014
ABSTRACT
The Pulsed Virtual Cathode Oscillator is considered as a high power
microwave source with transient characteristics dependant on the diode geometry
and the pulsed power system driving the vacuum diode. In this experiment, the
pulsed axially virtual Cathode Oscillator is designed and operated at working
nitrogen gas pressure 1 torr. The system consists of a copper solid disc cathode and
copper mesh anode . Both two electrodes have the same diameter 4cm, and a glass
ring of 0.4 cm thickness is fixed between the mesh anode and the cathode disk to
keep the distance between them. The electrical characteristics of pulsed axially
Virtual Cathode Oscillator showed that the inductance and resistance of system are
2.88µH and 21.4 mΩ respectively. Theoretically, the maximum discharge current
equals to 1.48 KA for 7.6KV charging voltage, while the measured experimental
discharge current equals to 1.27KA with plasma inductance of 13µH. The virtual
Cathode is formed at axial distance of 3 cm from the mesh anode and signal
waveform illuminated electromagnetic radiation at various charging voltage and
different distances.
Key Words: Glow Disharge ‫ ـ‬Pulsed Virtuel Cathode – Vircator
INTRODUCTION
The Virtual cathode oscillators (vircators) have been studied quite extensively over the last two
decades(1,2) In principle, a vircator employs an intense, mostly relativistic electron beam of density
greatly exceeding that in a space-charge-limited diode (3,4,5). This leads to the formation of an unstable
virtual cathode, which then generates relaxation oscillations when the current of an intense relativistic
electron beam exceeds the space charge limiting current (5).The oscillation mechanism in the vircator
can be explained by two dynamic mechanisms. One mechanism is an electron reflection due to the
virtual cathode, and the other is an oscillation of the virtual cathode itself, in which the electric
potential oscillates about its mean value because of the inherent instability of the electron cloud in
time and space (6). The vircator uses this phenomenon to generate high-power microwaves ranging
from a few tens of MW up to a few GW with an intense relativistic electron beam(7,8).
The virtual cathode oscillator appears to be one of the most promising high-power microwave
sources, due to its conceptual simplicity, high output - power capability, and tune ability. Two types
of vircators already exist. One type of vircator is an axially extracted vircator of conventional design,
and the other is a radially extracted vircator. Both types of vircator have an inherently low-power
conversion efficiency of less than 5%. In other words, less than 5% of the electron beam energy
converts into the microwave energy (9) . According to previous research, the microwave output power
depends strongly on the anode–cathode gap distance(10,11). The Virtual cathode restricts the
propagation of electron beam further downstream. Therefore, most of electrons are reflected back
toward the anode. Hence small fraction of the electron beam propagates forward. The forward current
increases as the diode gap increases, and it is often called the current leakage(12).
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The present work aims to study the plan electrode vircator, identify the circuit and plasma
parameters like inductance and resistance. It is also describing the effect of the charging voltage on
the plasma current which is measured at different radial positions.
VIRCATOR OPERATION FUNDAMENTALS
The massive short pulse of high voltage causes the cathode to emit an intense burst of
electrons by the field electron emission mechanism. The electrons are attracted to the anode. A large
proportion of the electrons passes through the anode and forms a cloud behind it, forming the virtual
cathode. However, the electrons are still attracted by the anode (and repulsed by each other), so they
change direction and fly back towards the anode, only to pass through again and be repulsed by the
cathode and attracted towards the anode. The rapidly accelerating and decelerating electrons, as they
oscillate back and forth between the real and virtual cathode through the mesh anode at microwave
frequencies, then produce a source of electromagnetic radiation(13) . The principle of process by a
vircator is illustrated in Figure (1).
Figure (1): Dynamic behavior of the Vircator parameters due to plasma expansion
The mechanism of modulated the beam current is illustrated in Figure (2). A uniform electron
beam is moving toward the virtual cathode, where there is an oscillating electric field which exists in
the background. Since the beam is uniform, the electrons distribute uniformly on the phase circle of
the field oscillation. However, the oscillating field modulates the electron energy, when the electrons
reflect at the virtual cathode, results in the electron density modulation. Therefore, as the electrons
move back toward the injection position, their distribution on the phase circle is no longer uniform but
with bunches. The oscillating electric field interacts with these electrons bunches which results in
beam–field energy exchange(14) .
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Figure (2): The mechanism of modulated electron beam
With this picture, a theoretical description of the virtual cathode and the beam-field interaction.
Based on the one dimensional analytical solutions, the important description of the virtual cathode
oscillator, were obtain.
The virtual cathode is formed by the space charge of the electron beam. The space charge of the
beam-electrons generates an electric field that decelerates the succeeding electrons. When this effect is
strong enough, some electrons are reflected by the electric field of the beam itself. It is consider this
steady state by assuming an electron beam with constant electric initial energy and beam current
density. The electric field generated by the beam space charge is related to the electron density by the
Poisson equation:
dE
ne

dx
0
(1)
where E, n, e, 0, and x are the electric field, the electron density, the elementary charge, the
free-space permittivity, and the coordinate, respectively. The electric potential (φ) , φ = zero at the
injection position. As the electrons move forward, their kinetic energy decreases while their potential
energy increases. If the initial electron kinetic energy is eV0 at the injection position, the electron's
kinetic energy diminishes to zero at the position where φ= -V0, which is called the virtual cathode. At
the virtual cathode, a certain fraction of the electron beam is reflected back toward the injection
position such that the potential minimum is kept at
φ= -V0 (at the virtual cathode). The electric field is obtained as a function of V.
E = - dV/ dx,
(2)
In order to improve the electron energy and the total current, the discharge parameters can be
optimized, which lead to the growth of oscillation between the real anode and the virtual cathode. The
maximum rate of growth of each oscillation occurs when the plasma frequency coincides with the
electron cyclotron frequency, so the vircator uses as the source of generate high-power microwaves
ranging from a few tens of MW up to a few GW with an intense relativistic electron beam.
EXPERIMENTAL SETUP
A pulsed vircators is shown in figure 3. It consists of two electrodes, a copper disk cathode (K)
and copper mesh anode (A) enclosed by discharge vessel, made from Pyrex glass 30 cm in length and
10 cm in diameter. It contains four parts at the middle for introducing the different diagnostic tools.
The Pyrex vessel is evacuated to a basic pressure of 10-2 Torr . The two electrodes have the same
diameter of 4cm and they can be moved freely in the axial direction (up and down) via vacuum-sealed
system. A glass ring of thickness 0.4 cm is fixed between the mesh anode and the disk cathode
keeping the distance between them constant. Figure (4) illustrates the device arrangements.
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.
Figure (3): The photograph of the virtual cathode oscillator
The condenser bank C = 0.22 µF is charged by a power supply in the range of 4 KV to 9KV.
Nitrogen gas is leaked through a needle valve keeping a constant working gas pressure at 1torr. The
cathode is connected to the negative of a pulsed power supply, while the anode is connected to the
earth.
Figure (4): The schematic diagram of the virtual cathode oscillator
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The pulsed voltage incoming from the shaping line is measured by using voltage divider. It
consists of tenth of resistance with 0.9K Ω and other small resistance with 12.75 Ω the voltage on the
small resistance will be recorded by oscilloscope. The air gap switch triggering system is used to
transfer the charge from the condenser to the plasma discharge chamber.
EXPERIMENTAL RESULT
Discharge Current and Voltage Measurement:
Rogowski coils with iťs "RC" integrator circuit is used to measure the total discharge current. It
has n = 67 turn , major radius rmax = 2.9 cm , minor radius rmin = 0.4 cm, cross sectional area A = 5 
10-5 m2, R = 10,8 K, and C = 1 nF.
The VOC frequencies depend on the diode gap distance and the applied diode voltage and
current. A high speed digital oscilloscope is used to record the waveform of the diode voltage and
current as shown in figure (5). This figure shows that the discharge current increases from zero with
fast rise rate until it reach a maximum value with rise time of 1.25 s which is a constant for different
gas pressure. On the other hand, the discharge voltage has a large value at zero time, and then begins
to decrease. Theoretically, the peak of the discharge current is given by the relation:
I Dis 
2CchVch
(3)

where τ is the time period of the signal = 7µsec , Cch =0.22 µF, is the capacitance of the charged
condenser bank and Vch is the charging voltage. According this equation, the maximum discharge
current value calculated equals to1.48 KA for Vch =7.6KV, while the experimental discharge current
at any time is
calculated by the following relation (15).
Idis = 2π r max × R × C V out
µ0 nA
I dis  0.5  10 7
(4)
rmax  R  C
nA
Vout
(5)
where n = 76 turns, is the number of turns of the Rogowiski coils, with cross sectional area for each
turn, A = πr² and r is the radius of each turn = 0.4cm, r max =2.8 cm is the major of coil, µ0 is the
permeability of space, R is the integrator resistance = 10.8KΩ , and C = 1nF is the integrator
capacitance. Then the previous equation becomes:
Iexp (KA)= 0.21Vout (V)
(6)
where Vout is the output signal measured by the oscilloscope.
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Figure (5): signal waveform for both the discharge current and discharge voltage
Electrical Characteristics of the System:
The electric circuit of pulsed virtual cathode oscillator experiment has constant inductance and
resistance for all charging voltages. The total circuit resistance RT could be calculated according to the
current decay relation (16):
I p  I o sin( t ) exp  RT t 2LT 
(7)
Cosidering the position of the current peak, sinωt = 1, so the total system resistance could be
calculated by drawing the relation between ln (Ip / I0) and discharge time, hence calculating the line
slope which equals to RT/2LT. The calculated resistance of system equals to 21.4mΩ for 7.6 kV
charging voltages and 1torr gas pressure.This indicates that the total ohmic resistance of the system is
very small, and hence, the consideration of the system as L-C one is valid.
The total inductance of the circuit LT could be calculated by considering the resonance circuit
equation, hence (17) :
LT 
2
4 2 C
(8)
Where LT is the total circuit inductance, C is the capacitance of the main capacitor bank which equals
to 0.22 µF. The calculated total inductance of system equals to 2.88 µH.
Inductance of Vircator system:
The voltage drop across the plasma V (t) consists of two parts, the first one, equals to that across
the plasma Lp which is varying with time, and the other across the plasma resistance Rp. Therefore,
the voltage drop V (t) can be given by (16, 18, 19) ;
V (t ) 
d ( L p I (t ))
d
 I (t ) R p 
 I (t ) R p
dt
dt
(9)
Where Ф is the magnetic flux, hence, neglecting the voltage drop across the plasma resistance
compared to that across the plasma inductance, so that (20,21) ,
t
L p (t ) 
  V (t ) dt
0
I (t )
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Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014
So, the variation of plasma inductance with the discharge time could be calculated by
integrating the discharge voltage numerically and dividing by the current. The variation of the plasma
inductance with the discharge time is shown in Fig. (6). The maximum inductance occurs at minimum
radius. The system inductance has constant value at starting current discharge around 13µH.
14
Lp
inductance ( H)
12
10
8
6
4
2
0
-2
0
2
4
6
8
(Discharge Time ( sec))
Figure (6): plasma inductance as a function of discharge time.
Plasma Current measurement:
The plasma medium is accompanied by current which generates the magnetic field. The plasma
current inside plasma medium is calculated by a miniature Rogowiski coil which inserted inside the
plasma bulk. Simply Rogowiski coil is a belt of wound wire inserted inside a quartz tube encircling
the current path. The two ends connected by integration circuit, which will act as current transformer,
where the plasma current flow through it and this is considered as simple primary loop while the
miniature Rogowiski coil is considered secondary loop. Figure 8 shows signal waveform for both the
discharge current and plasma current.
Figure (7): signal waveform for both the discharge current and plasma current
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The plasma current is calculated by equation (5) where the coil has these properties, R = 10.8
kΩ, C = 10 nF, "n = 70 turns" is the number of turns, "A= πr 2 = 3.14 × (0.1×10-2)2 m2" is the crosssection of area for every turns of coil, "rmax =0,4cm" is the main radius of coil. The above equation
becomes:
I p (kA)  9.8 Vout (V )
(11)
Figure (8): shows the axial distribution of plasma current measured at distance 1 cm from the
center for different discharge voltage. This figure that the plasma current increases by increasing the
charging voltage. It is also clear that the plasma current has the same distribution behavior along the
axial distance. The first region is at 2cm beyond the anode mash represented the electron beam is
injected from the cathode and a accelerated toward the mesh anode then it passes through mesh and
forms a stream of electron beam of definite potential. The second regions is at 3cm from the anode
mesh ,this is the field of virtual cathode oscillator . In this region the electrons kinetic energy
diminishes to zero at the certain position the beam current is higher than the space- charge limited
current of this area. In this region the current have the lowest value may be due to the current
leakage. The third regions at 5cm from the anode mesh represented the electromagnetic radiation.
Vdis=7.6Kv
Vdis=6.6Kv
4.0
Vdis=5.6Kv
at R = 1 cm
from the center
KA
3.5
3.0
Plasma Current
2.5
2.0
1.5
1.0
0.5
0.0
2.0
2.5
3.0
3.5
Axial Distance
4.0
4.5
5.0
cm
Figure (8): Axial Distribution of Plasma Current at Different Discharge Voltage
Figure 9 shows that the radial distribution of plasma current at three different axial positions
measured from the mesh anode. It is clear that the plasma current has the same radial distribution,
they have a maximum value at 1cm from center and lower values elsewhere near the center and the
wall. It clear that the plasma current have very low value at the wall resulting in the kinetic pressure
and low value at the axial of the tube since it is have a maximum density. The figure shows that the
virtual cathode is formed at axial distance equal to 3 cm from the mesh anode. The virtual cathode
reflected a certain part of electron beam and the reflected electron beam velocities are modulated by
the electric field of the virtual cathode. The electron densities increases duo to the variation of
electrons velocities, this lead to increases of the energetic electron beam which interacts with the same
field of VCO to emit a high electromagnetic wave. Then this region of electromagnetic radiation have
the largest current.
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Vdis=6.6KV atX=5cm
Vdis=6.6KV atX=2cm
40
Vdis=6.6KV atX=3cm
39
38
37
KA
36
35
Plasma current
34
33
32
31
30
29
28
27
26
25
0.0
0.5
1.0
1.5
2.0
Radial Distance
2.5
3.0
cm
Figure (9): Radial Distribution of Plasma Current at Different Axial Distance
(a) At Vdis = 5.6 KV
(b) At Vdis = 6.6 KV
(c) At Vdis = 7.6 KV
Figure (10): Signal Waveform of electromagnetic Radiation at Various Charging Voltage.
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Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014
Figure 10 shows that the propagation of electromagnetic radiation along the discharge tube at
various charging voltage. The intensity of the radiation increases by increasing the discharge voltage,
then the charging voltage is essential factor for the electromagnetic emission.
It is noticed that, there are points have sharply intense energetic current and its harmonics, and anthers
having the radiation intensity nearly diminishes to zero. This is duo to the constructive and destructive
interference between the electron beam and the virtual cathode field.
CONCLUSION
In this experiment, the pulsed axially virtual Cathode Oscillator is designed and operating at
working nitrogen gas pressure 1 torr. The discharge takes place between the two electrodes and
formed the virtual cathode .The electrical characteristics of pulsed axially Virtual Cathode Oscillator
has been studied. The inductance and resistance of system are calculated and their values of 2.88µH
and 21.4 mΩ respectively, also the inductance of plasma are13µH. Theoretically maximum discharge
current value equals to 1.48 KA for Vch =7.6KV,while the experimental discharge current
measurements for the same discharge voltage equals to 1.27KV. The distributions of the plasma
current are measured in the radial direction inside the chamber, at certain axial distances, and charging
voltage, using a miniature Rogowiski coil. It is found that the decreasing of current with the
decreasing of the charging voltage. The axially distribution of the plasma current was indicated that
the virtual Cathode is formed at axial distance of 3 cm from the mesh anode. The recorded plasma
current signals waveform illuminated electromagnetic radiation at various charging voltage at
different distances.
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