# Introduction

This section contains the details of design and testing of the resonator cavities and a short section on equipment verification.

# Equipment Verification

Before designing the resonating cavity and simulating, tests where done of the equipment bought off eBay, namely the circulator and waveguide to N transition. In figure 1, it shows how the circulator was tested and starts from the waveguide to N transition on the left, goes through the circulator into a WR340 to WR284 transition[1] into another waveguide to N converter. The tuning screws on the WR340 to WR284 transition were not used and left in neutral position. In order for the circulator to work properly, it was necessary to add water to the water load (via the yellow capped nozzles) and then it absorbed the reflected microwaves correctly. A calibrated HP 8753 Network Analyzer was used to measure the S1,2, S2,1 and S1,1 and S2,2 results as shown in figures 2 and 3.

The S1,2 and S2,1 plot shows the signal from port 1 to 2 through the circulator is -17dB, i.e. it is let through, but the signal from port 2 to 1, i.e. back through the circulator, is not.

# Resonating Cavity Design

One of the problems in using a simulation tool with an enclosed resonator with only one port is that the S1,1 results are all at or near zero. The reason is that there is a negligible load and the simulation only reports the steady state results, i.e. most of the power is reflected. In practice it means that the best method to determine if a resonator is holding the energy correctly is to check the field configuration.

In the Shawyer “demonstrator engine” where there is a magnetron putting energy into a cavity through a circulator, once the cavity has reached the maximum Volts per metre (V/m), most of the energy is reflected. The energy that is not reflected is used to make up for the energy lost as heat and, if the cavity does move, for movement as required by the conservation of energy.

An analogy is a water turbine, which, when under load, uses the kinetic energy of water to produce the current used by the load. When there is no load, all the available water is used to turn the free spinning turbine and create a little heat from friction. In the Shawyer cavity, the microwave energy is used in two ways, heat resulting from currents in the walls and to produce the force. The rest of the power is simply reflected and dumped into the water load of the circulator.

There are still two functions necessary to get a Shawyer cavity to work, the first is tuning, i.e. making sure the 2.45Ghz wave will resonate inside the cavity in the preferred mode. The second function is matching, which means placing a probe of correct length and diameter at the correct distance from the short within a waveguide to allow all the energy to enter the waveguide. With a bad match, most of the energy will not enter the waveguide and be reflected at the probe. Once a probe is matched and tuned, it is said to be “critically coupled”[2]

According to Shawyer[3], the critical factor in design of the cavity is the difference between the group velocity of the photons at either end of the tapered waveguide. Group velocity is define as follows:

The wavelength, $\lambda_g$ in a guided waveguide is determined by the “a” and “b” sides where the phase constant along the length (z direction) of the cavity is defined as:

$\beta_z=\left ( \frac{2\pi}{\lambda_g} \right)=\left ( \frac{2\pi f}{\vartheta_{ph}} \right)$

where $\vartheta_{ph}$ is the phase velocity.

Because $\vartheta_g*\vartheta_{ph}= c^2$, where $\vartheta_g$ is the group velocity, then
$\vartheta_g=\left ( \frac{c^2}{\vartheta_{ph}} \right)$

The phase velocities at either end of the waveguide can be determined by:
$\vartheta_{g1}=\beta_{z1}(a_1,b_1)$

and
$\vartheta_{g2}=\beta_{z2}(a_2,b_2)$.

The first version of the resonator will be an enclosed pyramid antenna used for the simulation confirmations.

As shown in figure 5, because of the wide mouth of the pyramid antenna, numerous “ghost” modes where being created on the sides and it was decided, as shown in figure 6, to narrow the cavity. It would also make it easier to build, although harder to solder the seams.

The group velocity, $\vartheta_{g2}=\beta_{z2}(a_2,b_2)$ , is dependent on the width and height of the cavity and using a different will test, for now, the difference in only one dimension. The flair was restricted to 8.6cm wide and 31.5cm high. The height was chosen because it produced the best field configuration inside the cavity as shown in figure 9. Once the general shape was determined, the cavity length was optimized by two factors, the highest Q and as close a match to a resonating condition as possible. The resonating match condition was visually determined by looking for field strengths propagating in a sine wave fashion down the length of the cavity.

Various cavities were tested as shown in figures 7 through 10:

The best results indicate that a cavity length of 180mm made out of copper would yield one complete wavelength inside the cavity and have a Q of 13000.

# Experimental Setup

Because the pendulum is at the heart of this experiment, the source including the magnetron, circulator and waveguide to N transition pieces are to be attached at the top of the pendulum. The electromagnetic wave will then travel down a length of low loss LMR-400 cable and resonate inside a cavity as shown in figure 4. The separation of the source and DUT[4] allows for two things:

• Different iterations of the cavity can be switched out easily.
• If any force is present on the cavity, it will be more readily apparent because it has less mass to move.

## Hardware Setup

Based on the simulations, the cavity was built as shown in figures 5 and 6. The probe was taken from a commercial waveguide-to-N type transition, as used in the equipment verification tests (noted above). The magnetron was then mounted to a waveguide, bolted to the circulator with water load (figure 7) and mounted on a shelf above the hanging cavity (figure 8).

## Test Setup

Two methods were used to determine if the cavity moved:

• A visual method with a video camera. Because nobody was standing inside the Faraday cage when the experiment was operational, a video camera was used to tape the results.
• A laser was reflected off the cavity onto a white metal sheet which meant that any slight movement of the cavity would show up in a large movement of the reflected pattern.

The expected result, should the cavity move, is a slight deflection of the reflected pattern.

## Notes

• The LMR-400 cable has a very strong resistance to twisting meaning the cavity is restricted to a back and forth motion.

# Results – Test Run One

The results speak for themselves:

At first, the cavity moved, however, after a longer test run, it was apparent the movement was caused by a slowly heating (melting?) coax cable. During the last test run, shortly before the two minute mark, there was sharp twist and a puff of smoke. It turns out, not only was the coax heating, getting to 51deg C on the plastic casing, but the dielectric inside the N-Type connector to probe adapter melted causing the smoke. The video shows a number of interesting things, first the cavity is twisted off centre and continued to slowly do so over the numerous test runs. Second, there is the smoke which came from the dielectric melting around the probe.

There was one encouraging sign which is that in previous test runs, after the cavity was turned off, it did swing back towards neutral. Unfortunately because of the coax twisting due to heat, it is uncertain if the movement was our expected result or the coax cooling.

• Either the removal or upgrade of the coax – The trick is that the coax has to handle very high voltages and yet be flexible enough to allow free movement. Not having a coax means that the entire apparatus including the circulator, power supplies, fans, etc would have to be hung from the end of a pendulum.
• A better probe is required which has a dielectric that has a higher melting strength but the same 50 ohm impedance.

Overall, the test was a success because we learned a few things:

• The experiment requires a high melting point dielectric in the probe assembly (or better design) – Interestingly enough, the probe in the waveguide-to-N at the top of the pendulum did not have problems, maybe because the signals were attenuated by the coax(?)
• The coax has to be improved or removed. The problem with going with a higher power coax is that they start to have significant stiffness.
• Upon inspecting the probe after the test runs, there does not seem to be any arcing inside the cavity, i.e. between the probe and wall.
• The magnetron also got warm, 34c max at one point, but it was not as hot as during our simulation test runs which means the circulator is working great. The water used as the load in the circulator, even after all our test runs, which totalled probably four minutes, only got to 22c or three degrees over ambient. There is about four litres of water total in the cooling system.

## Possible Fixes

As shown in figure 9, one possible solution was to move the probe and it made a significant difference in the amount of voltage/metre the probe was subject to, dropping it from 21K to 14K. The Q also went up to 14,000 although, unfortunately, the mode changed to a vertical arrangement. It was decided that a probe with an air dielectric could be a possible solution.

# Results – Test Run Two

The coax was upgraded to half inch diameter air dielectric cable. As for the probe, what smoked was not the dielectric but the injected plastic which held the probe in place, as shown in figure 10. After taking the probe assembly apart it was apparent that the probe was held in place by plastic injected through holes (not shown) in the side of the metal mount, through the dielectric and around the probe top. The plastic was then allowed to harden. For our latest test runs, we just flipped the dielectric around, attached the coax and made sure the probe was pushed in far enough to seat on the N-type connector and then bolted the probe assembly into the cavity.

Figure 11 shows a picture of the video camera hooked up to an external monitor. With the camera’s IR remote, we can start and stop the recording from outside the Faraday cage, which means we can close the cage, watch until the pendulum stops moving and then start the experiment. We don’t have to enter the cage, except for temperature measurements.

The video below shows our last one minute and thirty second test run:

Before the last test, we ran 15, 30, 45 and 75 second test runs.

## Success?

The cavity does move, but it does it so slowly that when we watched it live, we thought it had not. However, there still seems to be a problem because the probe should swing back to a neutral position, which it doesn’t. Either the cable is heating causing the movement, or the cable stiffness is keeping it in position once it does move.

# Results – Test Run Three

A number of improvements were made to the experimental setup, the largest of which was to move the microwave source assembly outside the Faraday cage. This improvement meant:

• The fan is outside the Faraday cage
• Any EM fields, including magnetic fields from the fan and magnetron magnets, are now farther away from the cavity.
• The coax cable is straight

Below is a gallery showing the new setup:

## Variables to Account For

There were a number of variables to be accounted for:

• Heated air escaping the cavity in a jet
• Measure the temperature of the cavity – The following temperature measurement were taken with a hand held IR sensor after each test, with the ambient temperature at 22 degree C. An average is noted:
• Coax Cable – Average 27c – because of the standing wave inside the cable, it varied from 24c to 30c along it’s length.
• Magnetron – Average 47c – The maximum measured was 50c
• Circulator and radiator – Average 25c
• Cavity – Average 23c – It rarely got over ambient temperature
• Fill the cavity with air or water and look for leaks
• With the probe hole covered, the cavity was first submerged in water, but no bubbles appeared. It was more productive to fill the cavity with water, and only one leak was found as shown in figure 15.
• Ion Wind
• In order for an ion wind to exist there must exist two oppositely and highly charged poles near enough to each other to create ions in the air. In the case of the Shawyer cavity, without a high DC voltage across the cavity, no ion wind is possible. As shown in Figure 16, a simple test with a volt meter shows the cavity is grounded, with one lead of the voltmeter on the cavity and the other on the copper mesh of the Faraday cage. With the cavity grounded there is no way a voltage difference could build up across the cavity, especially not the thousands of volts DC necessary to create ions.
• Buoyancy
• Even if the cavity was heating, there is not enough volume to lift the cavity.
• Magnetic or Static field attraction/repulsion
• The tests are done in a Faraday cage with the cavity at the end of a pendulum. The cavity is grounded and the closest magnets are in the electrical motor of the fan and the magnetron, some six feet away, outside the Faraday cage.

The last test, which is the most important, is to make sure a heating cable is not the cause of the movement and below are listed two tests:

• Put the cavity on a scale
• First, put the cavity on it’s side on the scale, zero the scale and then check if the EM fields inside the cavity have any effect on the scales measurement. We should measure nothing and that forms out baseline.
• Second, put the cavity facing downward, i.e. on it’s narrow end, then zero out the scale and we should see a weight gain,
• Three, put the cavity facing upward, i.e. on it’s large end, zero the scale again and we should see a weight loss
• Run four tests with the cavity rotated 90 degrees each time, but leave the cable the way it is.
• For the 1st 90 degree test, if the cavity moves sideways, it is the cable heating, if the cavity moves forward, toward the narrow end, it is the cavity.
• Repeat for the other 270 degrees and we should see movement toward the narrow end for each test.

## Cable Heating Caused Movement

Rotating the cavity 90 degrees was the simplest and for test runs of 75 seconds it produced the following results. The figures below are animated gifs which show the first frame just after power was applied and last frame, just after power was removed, for each test run. First and last frame comparisons were used as baseline measurements with the cavity powered off, done for each 90 degree rotation, over five minutes show that the cavity was not moving before the tests were done.

The results are clear that the cavity is first moving sideways, then after being rotated 90 degrees, moved back in the same direction. Because the cavity does not move toward the narrow end as expected but to the top left regardless of the direction of the cavity, it means that something, most likely cable heating, is causing the movement.

# Analysis

There are a number of reasons the pyramid cavity may not have moved:

• The shape is important in order to create the correct mode
• Because of slight changes in the cavity shape during fabrication, the Q may have been significantly lower and the EM fields may not have resonated. It is notable that in all the pictures of cavities published by Shawyer, with the exception of the superconducting cavity, they had tuning mechanisms.
• A “Q” sensitivity analysis was done on the CST model of the pyramid shaped resonator by changing the length slightly and checking to see if the Q change substantially, which it did not. Here are the results:

180mm length – Q of 13K
181mm length – Q of 12.7K
179mm length – Q of 13.4K
176mm length – Q of 13.9K
Note: The “length” in this case is the length of the pyramid’s flair, not the overall length.

# References

1. Jump up The transition piece was used because it is what we had on hand.
2. Jump up “Tuning and Matching the TM0,1 Cavity”, L.G. Matus et al., Department of Chemistry and Department of Electrical Engineering, North Carolina State University, August 1983
3. Jump up “A Theory of Microwave Propulsion for Spacecraft”,v9.4, Roger Shawyer, SPR Ltd., 2006
4. Jump up “DUT” or Device Under Test