The ten-sided faceted cathode geometry was chosen to minimize the current spike problem. Similar analysis was completed for this configuration. The model was simulated at the same reference parameters: Vca = -22.2 kV, B = 0.09 T, and J’e= 326 A/m. Figure
73 shows the RF Bz field and illustrates the π-mode for the ten-sided faceted cathode. Figure 74 shows the start up time for this device at approximately 110 ns; Figure 75 shows the FFT of the cavity voltage. The plot in Figure 75 indicates the π-mode operation at a frequency of 957 MHz; the 650 MHz peak is still present in this configuration. The linear power density at the loaded cavity was calculated to be 1.2 MW/m, which was the same as for the five-sided cathode.
Figure 73: Ten-sided faceted cathode model from VORPAL simulation showing the RF B-field and π-mode. This result corresponds to Vca = -
Figure 74: Ten-sided faceted cathode cavity voltage frequency versus time with moving window, showing the startup time of the device at 110 ns, showing the operating frequency (π-mode) at 957 MHz from VORPAL.
Figure 75: Ten-sided faceted cathode Fast Fourier Transform (FFT), over entire simulation time, of the loaded cavity voltage from VORPAL simulation. This plot indicates that the π-mode is dominant at the frequency of operation of 957 MHz.
Figure 76 shows the total emitter linear current density for the ten-sided faceted cathode. This simulation was performed with no applied B field. From the figure, it can be seen that the total emitted current averages to approximately 326 A/m, which matches the input current. Figure 77 shows the anode linear current density when the device is in operation. These results indicate a behavior very similar to the anode current for the cylindrical cathode geometry (see Figure 62), but the large current spikes are not present as in the five-sided cathode model. Instead there is a large spike at ≈ 110 ns, and then the oscillations are more stable. This result indicates that the ten-sided cathode geometry reduced the current instability.
Time (s) F re q u en cy (Hz) Startup Frequency (Hz) F F T Am p li tu d e 2.0x109
Figure 76: Ten-sided faceted cathode continuous total emitted linear
current density versus time with no applied magnetic field (B=0).
Figure 77: Ten-Sided faceted cathode continuous anode linear current density during device operation versus time.
The simulation for this case was also run for various emitted current densities, and the startup times were determined from the frequency versus time plots in VORPAL. Figure 64 shows the graph of startup time versus total emitted linear current density for various cathode geometries. From this graph, it can be seen that the ten-sided cathode geometry has a startup of 110 ns for the reference parameters. As can be seen, the startup time increases for lower current densities and decreases for higher current densities as expected. From this plot, the three cases: cylindrical, five-sided cathode, and ten-sided show very similar startup times for the reference parameters; however, as the linear current density is decreased (below 326 A/m), the startup times are not so similar
depending on cathode shape. It is also noticeable that the cylindrical cathode for the Vca =
Time (s) C u rr en t D en si ty ( A /m ) Time (s) C u rr en t D en si ty ( A /m )
-22.2 kV, B = 0.09 T, and J’e= 326 A/m parameters does not start for current density
values below 230 A/m. It was found that for this geometry, there is an increase in mode competition between the 650 MHz mode and the 957 MHz (π-mode); therefore, for values below 230 A/m, the device switches to the lower mode and does not start in π- mode. The nature of this behavior for this particular case needs further study and analysis.
The next step in the simulations is the study of the modulated, addressable, current sources at the operating frequency. This aspect of the work will be discussed in Chapter 7.
6.5 Summary of Results
This chapter studied the continuous current source model for the cylindrical and faceted cathodes. From the results, it is observed that all three models operated at the π- mode with frequencies of 960 MHz and 957MHz, respectively. A current instability was found in the five-sided faceted cathode. This current instability resulted in current spikes, which led to spokes disconnecting and collapsing. The ten-sided faceted cathode reduced this current instability and improved the overall startup time of the device from 200 ns (five-sided cathode) to 110 ns for the reference parameters; however, as the linear current density is decreased (below 326 A/m), the startup times are not so similar depending on cathode shape. Overall, the ten-sided cathode improved stability of the magnetron.
CHAPTER SEVEN: VORPAL SIMULATION RESULTS FOR THE MODULATED, ADDRESSABLE CATHODE
7.1 Overview
This chapter describes the results for the modulated, addressable cathode current source model. Two geometries were studied using this concept: a five-sided faceted cathode and a ten-sided faceted cathode. Work was completed for both cathodes; however, most of the analysis was performed on the ten-sided. Results showing the modulation technique and phase control will be presented in this chapter.