ULTRAHIGH-POWER CYCLOTRON MASERS/LASERS
10.3 VIRCATOR IMPULSE SOURCE
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main solenoid to produce electron velocity components parallel and perpendicular to the magnetic axis. Thus, electrons have axial and orbital components leading to a helical path around the axis (Section 10.2.1). Electrons move into growingBfield and are adiabatically compressed, causing orbital momentum to increase. In the uniform Bfield, electrons interact with the eigenmodes of the electromagnetic microwaves in the cavity and some of the kinetic energy transforms to microwave energy. The spent beam exits from the axially open cavity, is decompressed in the decreasing magnetic field, and settles on the collector. The generated microwave passes through the output window.
VIRCATOR IMPULSE SOURCE 185
(a) (b)
(c) (d)
Insulator Anode Window
Cathode Virtual cathode
Window
Insulator Anode
Cathode
Virtual cathode
Window Insulator
Anode Cathode Virtual cathode Insulator Anode
Window
Cathode Virtual cathode
FIGURE 10.6 Virtual cathode oscillator: (a) basic vircator, (b) transverse extracted, (c) red- itron, and (d) reflex triode removes chirp.
The vircator operates by forming a virtual cathode, hence name virtual cathode oscillator (vircator). The virtual cathode arises when the cathode generated current exceeds the maximum current that can pass through the drift space of the tube. This current is called the space charge current and is of the order of 10 kA. If the injected beam current is greater than the space charge current and the radius of the drift space region is sufficient, the excess space charge forms a strong potential barrier at the head of the beam. This is the virtual cathode that reflects electrons to form an oscillating cavity. The cavity reinforces microwave radiation by bremsstrahlung radiation. The cavity can be designed to radiate at a frequency suitable for airborne mine detection (say less than 10 GHz). In the structures shown in Figure 10.6a and b [9], the virtual cathode oscillates axially, but in Figure 10.6b the direction of the microwave output beam is transverse to the axis.
When the drive voltage is switched off at the end of a pulse, the amplitude of the virtual cathode oscillation decays and the frequency increases as the cavity length reduces. This chirp significantly increases bandwidth that may be useful in some applications.
Some variations of the vircator are aimed at removing the chirp to maintain a constant frequency (narrowband), in order to maximize peak power. Figure 10.6c shows a reditron [27] that uses a thick anode plate with holes to remove virtual cathode oscillation and hence the chirp. The peak power of an experimental unit was 1.6 GW. Figure 10.6d shows a reflex triode that also eliminates the oscillation of the
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virtual cathode and hence the chirp. This is the configuration that was selected for the tabletop demonstration unit described in Section 10.3.5. By switching the frequency through a sequence of frequency steps such as 8.5, 9.5, 10.5, and 11.5 GHz, we can design a matched filter.
10.3.3 Selecting Frequency of Microwave Emission from a Vircator In short pulse operation, the maximum level of radiated power is restricted by the microwave breakdown near the structure walls [40]. The breakdown restricts the maximum electric field according to
Ebr=0.8×103
f (10.12)
From Newton’s equation, the maximum frequency of oscillation near a positively charged electrode is provided from
d2z dt2 = eEz
mγ3 (10.13)
whereeEzis the force on a particle with chargeeand rest massmnear a positively charged electrode,Ezis the electric field along the axis of the vircator, andγis the relativistic factor. For a time harmonic, single angular frequencyω0, (d2z)/(dt2)= ω20Lwith amplitude of oscillationL=V/Ez. Hence,
ω20= eEz
mγ3L = eEz2
mγ3V (10.14)
At breakdown,Ez=Ebr, whereEbris the dielectric breakdown strength. Substituting equation (10.12) into equation (10.14) gives
ω20=(2πf)2=e(0.8×103)2f
mγ3V (10.15)
or
f = 1 (2π)2
e(0.8×103)2
mγ3V ≈3×1015V−1 (10.16) Therefore, at 300 kV, the frequency is 10 GHz.
10.3.4 Marx Generator
The vircator needs a power supply of 300 kV and current greater than 10 kA with a rise time less than 100 ns. A cost-effective power supply can be constructed with a Marx generator. The Marx generator was patented in 1924 and is used to simulate
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0 V
0 V
(a) (b)
30 kV 120 kV
C4 G3
C3
C2 G1
C1 30 kV
G2
C4
G3
C3
C2 G1
C1 G2
FIGURE 10.7 Marx generator structure: (a) showing charging and (b) discharge.
lightning, generate X-rays, and ignite a thermonuclear device. It charges a number of capacitors in parallel and then discharges them in series. We would like the output impedance of the Marx generator to match the input impedance of the vircator for maximum transfer of energy to the vircator load. This avoids large and expensive impedance matching components.
Figure 10.7a shows the structure of a four-stage Marx generator in which a 30 kV DC source charges four capacitors in parallel. For a system with N stages, the Vcharge=30 kV power supply source charges allN capacitors of valueCstage,C1
toCN, in parallel up to 30 kV through boxes containing resistors. TheNcapacitors in parallel give an equivalent capacitance for charging ofCset=NCstage(Figure 10.7a).
Inductors may be used in place of charging resistors for more efficiency and speed.
To generate a high-voltage pulse at the right-hand side of Figure 10.7b, a spark gap G1is triggered to form a short circuit between the two dark circles atG1. This now doubles the voltage acrossG2, causing it to trigger into a short circuit. This repeats rapidly until all the capacitors are discharged in series as shown in Figure 10.7b, where the peak voltage is 4×30 kV=120 kV. In general, on discharge, a pulse is generated at the right-hand side of Figure 10.7b of peak approximatelyVpeak=NVcharge. For discharging, theN capacitors in series have a capacitance ofCset=Cstage/N and inductanceLset=NLstage. Therefore, the Marx output impedance may be written as
ZMarx=
Lset Cset =N
Lstage
Cstage (10.17)
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FIGURE 10.8 Photograph of combined Marx generator with vircator demonstration.
10.3.5 Demonstration Unit of Marx Generator Driving a Vircator A vircator driven by a Marx generator appears to be capable of producing 200 MW impulses suitable for airborne applications such as ground penetration radar [123].
Figure 10.8 [123] shows a photograph of a tabletop demonstration unit in which a 25- stage Marx generator drives a reflex triode vircator to provide a high-power microwave impulse source suitable for airborne mine detection. The 18output impedance of the Marx generator is similar to the input impedance of the vircator, so large and lossy impedance matching components such as transmission lines, transformers, or tapered waveguides are avoided. This simplifies the system, reducing cost and weight and improving reliability. The maximum voltage that can be delivered to the matched load is (1/2)N×Vcharge. So for a charging voltage ofVcharge=20 kV and 25 stages, the maximum voltage is 250 kV.
FIGURE 10.9 Photograph of Marx generator used in demonstration.