An advanced relativistic magnetron operating with a split cathode and separated anode segments

The relativistic magnetron¹ (RM) is the most promising high-power microwave (HPM) source and many ideas were introduced to its design to improve its efficiency,² but there are two main problems that need to be solved to make it suitable for practical applications. First, HPM pulse shortening caused by the expanding explosive cathode plasma needs to be eliminated.³ To solve this problem, several ideas, such as transparent cathodes,⁴ the virtual cathode,⁵ the virtual cathode with a magnetic mirror,⁶ and so on,² were suggested. However, some of these are difficult to apply and other proposed solutions do not solve this problem completely because to some extent, the explosive emission plasma remains in the anode interaction space.

Recently, the split cathode consisting of a cathode placed upstream and outside a coaxial anode and connected by an axial rod to a reflector placed downstream from this anode was introduced and tested experimentally.^7,8 The split cathode is a simple way to realize a virtual cathode. The annular electron beam emitted by the cathode is trapped in the space between the cathode and the reflector. Also, the electron beam space charge screens the rod from explosive plasma formation. The operation of a split cathode in a RM was experimentally confirmed and revealed that, indeed, using a split cathode mitigates pulse shortening but in this research, no microwaves were radiated by design.⁸ 

The second problem needing solution is making the magnetic field producing system accompanying the RM compact and its operation repetitive. One way to reduce the size of the system is to replace the design of the microwave output from radial⁹ to axial.¹⁰ There are now many schemes attempting to improve the design of the axial output RM. We have chosen to follow the design of Xu et al.,¹¹ but our idea applies to any design chosen.

The problem of size, weight, and power requirements of the axial magnetic field producing system, typically a pulsed solenoid, is common to many other HPM sources needing magnetic insulation. Such pulsed solenoids operate on the millisecond timescale necessary for the magnetic field to diffuse through the conducting walls of the magnetron anode block. These long times require a high-power supply and limit the repetition rate of magnetron operation. Modern permanent magnets can provide such fields, but the magnetron system is still too large and too heavy to be considered compact and does not allow for variation of the magnetic field.^12,13 Permanent magnets can also be incorporated into the magnetron vanes and the cathode,¹⁴ but this compact arrangement is limited by the available magnetic field and the magnetic field cannot be varied.

Recently,¹⁵ we presented a hypothesis that by building the magnetron anode block and the tube containing it out of separate angular segments leaving longitudinal open slits between them, the magnetic field can rapidly penetrate into the interaction region. The result of this is that the power supplied to the solenoid can be on the microsecond timescale, which has dramatic implications. The pulsed power system required to power the solenoid of a segmented magnetron can be considerably smaller and lighter and can be rapidly recharged. In Ref. 15, we have shown by particle-in-cell (PIC) simulations that such slits between the segments have little effect on the operation of the RM.

In this paper, we present the results of the first experiment in which we successfully demonstrate the operation of a segmented relativistic magnetron fed by a split cathode. We compare these results with results obtained with the same magnetron operating with a common explosive emission solid cathode.

In these experiments, we used a bipolar Marx generator consisting of 14 pulse forming network stages.⁸ With ±30 kV charging voltage, a negative polarity high voltage (HV) ∼250 ns long, ∼200 kV maximum amplitude pulse is produced on a matched resistive load of ∼120 Ω. The experimental setup is shown in Fig. 1. The six vane RM with axial output is placed inside a 400 mm long Perspex (PMMA) tube (with an inner radius of 60 mm and a wall thickness of 8 mm) as described schematically in our recent article (see Fig. 1 in Ref. 14). The magnetron anode manufactured from aluminum was 40 mm long (21 mm/42 mm inner/outer anode radii) surrounded by a cylindrical tube followed by a closed conical section separating it axially from the rest of the downstream region [see Fig. 1(a)]. The cylindrical part of this section has radial slots so that all six magnetron cavities are open [Fig. 1(c)]. Three vanes are continued radially into the space outside this tube and reach the outer radius of the system. The space outside the magnetron, which can be considered as a radiator, becomes divided into three sectors. Three 4° (2 mm wide) angular slits are cut radially at the center angle of three vanes [see Figs. 1(a) and 1(b)]. The slits cut the entire magnetron anode, the inner tube of the radiator (but not the cover of the conical section), and the edges of the outer tube (which are sufficiently far from the interaction region). The electron source of the split cathode consists of 5 mm long carbon capillary tubes (1/0.75 mm outer/inner diameters) placed in holes drilled in a 40 mm diameter cathode holder and symmetrically distributed along a 16 mm diameter circle. This emitter is connected to the 40 mm diameter downstream reflector by a 6.5 mm diameter rod. The cathode holder, rod, and reflector are covered with a 0.1 mm thick layer of aluminum oxide hard coating to suppress explosive plasma formation. The axial distance between the upstream edge of the anode and the edge of the carbon capillaries was 23 mm. The split cathode assembly was placed coaxially inside the anode with an accuracy of ±0.2 mm. The solid cathode tested was a common 20 mm long explosive emission cathode made of a 13 mm diameter carbon rod in which eight 1 mm deep longitudinal grooves, symmetrically distributed azimuthally, were drilled. This cathode was placed at the longitudinal center of the anode and connected by the rod between upstream and downstream reflectors, which were positioned at a distance of 35 mm from the anode edges. In Fig. 1(a), this magnetron system is drawn, attached at its upstream end to a vacuum chamber connecting it to the Marx generator and covered by a Perspex window at the downstream end that allows the microwaves to be radiated. The design of this magnetron follows that described in Ref. 11 with dimensions set by our PIC simulations.¹⁵ Some design features are to be noted. In Fig. 1(c), one can see that three of the magnetron vanes are continued radially, reaching the system's inner radius making up a three-segment structure that collects the radial magnetron output and transmits it in the axial direction. A cylindrical tube at the outer magnetron radius continues downstream where it ends in a closed conical tube. This conical structure helps transform the axial output to a TM₀₁ waveguide mode. This mode can be used as the input to a mode converter and antenna, which in these experiments have not been employed. Moreover, the closed conical tube collects any magnetron axial electron current from reaching and damaging the downstream Perspex window.

In Fig. 1(b), the azimuthal cross section of the magnetron structure is drawn where the position of the three symmetrically distributed thin slits, separating the system's anode parts into three segments, are pointed out. This entire structure was placed inside the Perspex tube and a vacuum level of 10⁻³ Pa was maintained by a turbo-molecular pump.

An external solenoid was used to magnetically insulate the electron beam. The solenoid was constructed from a single wire layer wound around the Perspex tube using a 6 × 1 mm² rectangular cross section copper wire. The solenoid is energized by a current pulse of 90 μs half-period, produced by a Silicon Controlled Rectifier (SCR) controlled discharge of a 25 μF capacitor charged to a voltage ranging from 2.5 to 5 kV, corresponding to total stored energy in the range of 78–312 J, which produced a magnetic field ranging from 0.125 to 0.25 T distributed axially as seen in Fig. 1(b). The total inductance of the discharge circuit was ∼32 μH and the maximal amplitude of the discharge current at 5 kV charging voltage was ∼4.2 kA. Because of the relatively short duration of the magnetic field, no special measures were taken to strengthen the solenoid that does not experience any vibrations, even for magnetic fields >0.3 T. The measured axial magnetic field was found to be almost constant and uniform within the magnetron's interaction region and gradually decreases by up to ∼25% from the magnetron anode edges to the location of the two reflectors (see Fig. 1). In this design, we did not seek to optimize the magnetic field producing electronics and one can, of course, do better, while we used equipment we already had in our laboratory.

The current of the magnetron was measured by a self-integrating Rogowski coil (RCO) at the output of the Marx generator in oil and a second coil (RCV) placed in the upstream vacuum tube connecting the exit from the generator to the Perspex tube. The waveforms obtained by the RCO and RCV showed similar temporal dependence and the same amplitudes. This indicates the absence of axial upstream electron flow. The voltage waveform was monitored by a resistive voltage divider (VD) located in the oil container at the output end of the Marx generator. The RCO, RCV, and VD are pointed out in Fig. 1. The microwave waveforms were measured by a calibrated D-dot electric field sensor SFE-10G (Montena) with a PRODYN Balun BIB-100G (250 kHz–10 GHz). The current, voltage, and microwave waveforms were acquired using an Agilent Infinium DSO 81204B digitizing oscilloscope (12 GHz, 20 GSa/s). The microwave pattern was obtained using a set of neon lamps placed at a distance of ∼10 cm from the output window.

Typical waveforms of the voltage, the discharge current measured by the RCV, and that of the microwave measured by the D-dot probe for the magnetron fed by either a solid cathode or a split cathode are shown in Fig. 2. In these experiments, the D-dot probe was placed 5 cm from the output Perspex window, which is ∼16 cm from the cover of the conical anode section. This distance is close to the far-field, which starts at distances ≳19 cm. One can see in Fig. 2 that the voltage and current waveforms and amplitudes for both cathode types are similar with slightly larger current and smaller voltage amplitudes for the solid cathode. With the solid cathode, the microwave pulse duration is ∼90 ns [Fig. 2(a)] because of pulse shortening, whereas with the split cathode, the microwave generation continues for much longer until the voltage becomes ≲100 kV [Fig. 2(b)]. The maximum amplitude of the electric field's radial component reaches ∼460 kV/m for the solid cathode and ∼350 kV/m for the split cathode. For the solid cathode, the dominant frequency is 2.15 GHz (λ ∼ 14 cm) during ∼80 ns [Fig. 2(c)]. For the split cathode, a drift of the frequency of about ∼1 MHz/ns is observed between 2.18 and 2.12 GHz [Fig. 2(d)]. A similar drift was observed in our earlier RM research using regular cathodes.¹⁶ 

The pattern of the microwaves generated with the split cathode and registered by the luminescence of the neon lamps using a camera with open shutter is shown in Fig. 3. The same pattern was obtained with the solid cathode. One can see that the radial distribution of this luminescence strongly indicates the existence of the TM₀₁ mode retained close to the system window.

The total power of the microwave radiation was calculated by integration of the measured radial distribution of electric field (horizontal and vertical polarization) carried out at a distance of 30 cm from the Perspex output window. In Fig. 4, one can see the distribution of the power density calculated as $P(W/cm2)=(E(V/cm)/19)2$⁠.¹⁷ Here, for the split cathode experiment, the power density pattern is normalized to a power flux of 26.5 MW/m². At this distance, these measurements give a total average power of 25 MW, which corresponds to ∼10% efficiency of microwave generation. At a distance of 5 cm from the output Perspex window, a maximal electric field of ∼250 kV/m was measured. With the solid cathode, a similar power density distribution was obtained resulting in the total average power of ∼42 MW, which corresponds to ∼14% efficiency of microwave generation.

For the solid cathode, reproducible single frequency microwave generation at 2.15 GHz was obtained for magnetic fields in the range of 0.21–0.26 T. Decreasing the magnetic field below 0.2 T leads to a decrease of the microwave electric field amplitude and the appearance of additional frequencies at 1.9 and 2 GHz, indicating mode competition. For the split cathode, the highest electric field was obtained at ∼0.15 T, and decreasing the magnetic field also led to the appearance of additional frequencies and decrease in the electric field.

In the experiments described in this article, the energy stored in the 4 mF capacitor of the pulsed power generator feeding the solenoid was ≤312 J. For the longest microwave pulse obtained with the split cathode, the energy required to produce the magnetic field over a half-period of 90 μs was not more than 100 J. In our earlier experiments,⁸ we used magnetic fields that required stored energies up to 1 kJ over a half-period of 15 ms to produce magnetic fields of amplitudes of the same order as in the present experiment. It should be mentioned that one can use smaller capacitors by at least a factor of two (for instance 10 μF) for which even smaller stored energy will be required.

Let us note that in the present experiment, no mode converter or antenna was used. The present RM did not yet undergo sufficient optimization for best efficiency. The effect of varying the distances, such as the cathode and cathode holder diameters, the distances between the anode edges and the cathode and reflectors, and the effect of introducing a second downstream cathode need to be studied.

To summarize, we have demonstrated the success of two new ideas, namely, that the split cathode eliminates microwave pulse shortening and a segmented magnetron anode block with axial slits allows fast magnetic field penetration into the interaction region and operates as well as an ordinary magnetron. This increases considerably the total efficiency of the system because the magnetic field power supply requirements are drastically lowered. Such a RM is also suitable for repetitive operation.

At the Technion, this work was supported by Technion (Grant No. 2029541) and ONRG (Grant No. N62909-21-1-2006) and at the University of New Mexico by AFOSR (Grant No. FA9550-19-1-0225) and ONR (Grant No. N00014-19-1-2155).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.