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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). 146 Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014 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) . 147 Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014 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. 148 Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014 . 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 149 Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014 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 2CchVch (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. 150 Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014 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 ) 151 (10) 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 152 Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014 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. 153 Arab Journal of Nuclear Science and Applications, 47(2), (146-156) 2014 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. 154 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. REFRENCES (1) V. L. Granatstein and I. Alexeff, High-Power Microwave Sources. Norwood, MA: Artech House, 1987, ch. 13, 14. (2) R. J. Barker and E. Schamiloglu, High-Power Micowave Sources and Technologies, ser. 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