# 2D Magnetron (magnetron2DT.pre)

Keywords:

magnetron, electromagnetic cavities, mode frequencies

## Problem description

This VSimMD example simulates a rising sun magnetron in two dimensions. The spectrum of the magnetron is first tuned through geometric properties, yielding the operating frequency. A load is then added to one cavity, representing a coupler to the magnetron through the quality factor, Q. Upon configuring an electrostatic voltage across the anode and cathode, particles are introduced to the simulation, exhibiting a five spoke pi-mode.

This simulation can be performed with a VSimMD or VSimPD license.

## Opening the Simulation

The 2D Magnetron example is accessed from within VSimComposer by the following actions:

• In the resulting Examples window expand the VSim for Microwave Devices option.
• Expand the Radiation Generation (text-based setup) option.
• Select “2D Magnetron (text-based setup)” and press the Choose button.
• In the resulting dialog, create a New Folder if desired, and press the Save button to create a copy of this example.

The basic variables of this problem should now be alterable via the text boxes in the left pane of the Setup Window, as shown in Fig. 398.

Fig. 398 Setup Window for the 2D Magnetron example.

## Input File Features

Fig. 399 Some exposed variables of the 2D Magnetron example.

As seen in Fig. 399 of the rising sun magnetron, the radius of the cathode is RCATHODE and the radius of the anode is RANODE. Long cavities have radius RCAVITY1 and opening angle ANGLECAVITY1. Short cavities have radius RCAVITY2 and opening angle ANGLECAVITY2. These geometrical properties control the spectrum and thus the operating frequency, which for the default parameters is approximately 960 MHz.

One long cavity is loaded with damping parameter NU_LOADING, which may be used to tune the quality factor Q of the magnetron, which is inversely proportional to NU_LOADING. Once the design of the magnetron is specified, electrons may be emitted from the cathode by setting INCLUDE_PARTICLES = 1.

The following are four run types accommodated in the magnetron2DT.pre file:

The Mode Spectrum

The magnetron is rung up with a magnetic field perpendicular to the plane of the magnetron, confined to one of the long cavities. The generated voltage spectrum can then be analyzed to anticipate the magnetron operating frequency.

Calibrating the Pi-Mode and Quality Factor

The magnetron is again rung up, but with a magnetic field profile with null lines part way up a long cavity arm at the approximate location required for a pi-mode. At this point, the magnetron geometry can be modified to yield the desired operating frequency. The load can also be tuned at this point to result in the appropriate cavity quality factor.

Calibrating the DC Voltage

A specific DC voltage between the anode and cathode is required to support a given operating mode for particles in the magnetron. Thus, in this run type, an electrostatic field generated between the cathode and anode is tuned using a combined source with feedback and drain, and a finite-difference divergence-free 1/r current profile.

Run with Particles

Finally, electrons are emitted into the magnetron from the cathode. The previous runs can be iterated to ensure that the electrons exhibit the desired mode.

The four basic run types may be configured as follows:

The Mode Spectrum

Set PI_MODE_PRIMING = 0, INCLUDE_DC_VOLTAGE = 0, INCLUDE_PARTICLES = 0, and IMPULSE_EXCITATION = 1.

Calibrating the Pi-Mode and Quality Factor

Set IMPULSE_EXCITATION = 0, INCLUDE_DC_VOLTAGE = 0, INCLUDE_PARTICLES = 0, and PI_MODE_PRIMING = 1.

Calibrating the DC Voltage

Set IMPULSE_EXCITATION = 0, PI_MODE_PRIMING = 0, INCLUDE_PARTICLES = 0, and INCLUDE_DC_VOLTAGE = 1.

Run with Particles

Set IMPULSE_EXCITATION = 0, PI_MODE_PRIMING = 0, INCLUDE_DC_VOLTAGE = 1, and INCLUDE_PARTICLES = 1.

## Running the simulation

For each of the setups described above, continue as follows:

• Proceed to the Run Window by pressing the Run button in the left column.
• To run the file, click on the Run button in the upper left corner of the right pane. You will see the output of the run in the right pane. The run has completed when you see the output, “Engine completed successfully.” This is shown in Fig. 400.

Fig. 400 The Run Window at the end of execution.

## Visualizing the results

After performing the above actions, continue as follows:

• Proceed to the Visualize Window by pressing the Visualize button in the left column.

Visualization of the four basic run types is described below.

The Mode Spectrum

Fig. 401 Fourier transform of voltage across rung up cavity as a function of frequency (in GHz).

In Fig. 401, the fourier transform of the voltage across the rung up cavity is plotted versus frequency (in GHz). This indicates that we should expect modes near 650 MHz and 960 MHz. To generate this plot, select History from the Data View pull-down menu at the top of the Visualization Controls pane. Choose the cavity1Voltage plot in the. Then in the Visualization Results pane, click FFT to the left of the cavity1Voltage plot, and zoom in to the relevant area.

Calibrating the Pi-Mode and Quality Factor

Fig. 402 Fourier transform of voltage across rung up cavity as a function of frequency (in GHz).

In Fig. 402, the fourier transform of the voltage across the rung up cavity is plotted versus frequency (in GHz). The 960 MHz mode is more pronounced than in the previous run, but the 650 MHz mode remains. If we instead seek another operating frequency, we could change the geometry of the magnetron to iteratively tune this spectrum.

Another quantity we may wish to tune is the magnetron quality factor, $$Q$$. We expect $$Q$$ to be inversely proportional to NU_LOADING, but it is possible to measure $$Q$$ using VSim. Using the decay of the cavity1Voltage history, $$Q$$ may be calculated as

$Q = \pi \ f \ \left(t_2 - t_1\right) \ \ln^{-1} \left[\frac{V\left(t_1\right)}{V\left(t_2\right)}\right]$

where $$f$$ is the operating frequency, $$V\left(t\right)$$ is measured as in Fig. 403. We calculate $$Q$$ to be 400 with f = 960 MHz.

Fig. 403 Decay of voltage across cavity 1 (in kV) as a function of time (in ns). The two indicated points could be used to calculate the quality factor.

Calibrating the DC Voltage

An electrostatic field is generated between the cathode and anode using a combined source with feedback and drain, and a finite-difference divergence-free $$1/r$$ current profile. In Fig. 404, the resulting voltage between the anode and cathode, the history cathodeAnodeVoltage (in kV), is plotted versus time (in ns). The user controls the average value of this voltage through the variable VOLTAGE_DC.

Fig. 404 Voltage between the anode and cathode (in kV) as a function of time (in ns), recorded through the history cathodeAnodeVoltage.

Run with Particles

Fig. 405 The five spoke pi-mode.

When electrons are emitted from the cathode, the four spoke, 650 MHz is present during startup. At approximately 250 ns, the five spoke begins to dominate and eventually appears as seen in Fig. 405.

## Further Experiments

Try varying RCATHODE and observing the effect on the spoke formation.