Look at gaussian beam profile

[MatthewGrim]

This issue documents some final work that has been carried out to put the Lunar SPS project to the test and see if there are any missing holes in the analysis.

[MatthewGrim]

Gaussian beam divergence

One issue that has to be tested is to see if the receiver has enough information to generate a closed loop control system for pointing and tracking to the satellite. This is essential if we are going to be able to achieve sub-microradian pointing accuracies. An open loop system will not be able to achieve this, I am told.

[MatthewGrim]

Results of initial designs

From the initial results in studies/012, the AMALIA and Sorato designs were specified. These designs are what I am considering for determining whether the intensity of the Gaussian beam is too uniform for the target to acquire real information about the satellite.

Sub-microradian Results

These results show that the beam still has some significant gradients in intensity compared across the target radius. This was unexpected for me. The reason being that I thought the target beam would be uniform, as my initial assessment showed.

Microradian results

The microradian results show more what I was expecting. The beam diverges significantly. I think there may have been some drift in this assumption since we first began the project...

[MatthewGrim]

Implications

For me, this implies that tracking the target with sensors becomes a lot easier. However, at the same time, the power delivered and thermal management constraints become more transient. We are delivering lower than solar irradiance on average, and we are delivering variable power to the control system with these designs. This needs to be addressed.

So essentially, I don't think the sensors will have trouble. But this throws up some issues elsewhere.

[MatthewGrim]

Review of results

Something is strange about these results. In the updated results, I have added the target radius and the pointing error onto the plot. These values are much smaller than the beam radius observed. Have we actually optimised the transmitters to the ideal transmitter size?

It can be seen also that the power in the centre of the beam is much higher than the power needed. Why is this?

Causes:

1. The uniform beam assumption is not reasonable for these transmitter sizes, making the intensity at the centre of the beam more than it needs to be. This is certainly true to some degree.
2. ... I don't really know yet.

With the intensity being so high, and the accuracy meaning the intensity does not drop off so much, we could in principle lower the power of the laser. This is a good thing for the design but confusing for me. I need to understand why the intensity is higher than I anticipated.

New Tasks:

• Figure out whether the transmitter size optimisation actually works.
• Figure out why the intensities being delivered are actually so high compared to what is needed by the target.

[MatthewGrim]

One thing to note is that the values I am using were optimised for a 859nm laser. If I switch to a 1070nm the results are going to shift. I need to take this into account.

[MatthewGrim]

Testing whether the code works, assuming a uniform beam

Right now, the code is spitting out the following results for AMALIA and Sorato.

For AMALIA: Number of SPS: 1 Optimal orbit altitudes --> Perigee: 1200.0 km, Apogee: 1400.0 km Orbital period --> 250.28 minutes Total active time (blackout reduction) --> 6.04 % Total blackout time --> 43.72 % Max active period duration --> 0.94 hours Max blackout period duration --> 13.31 hours Min range to target --> 2183.26 km Max range to target --> 2531.95 km ------------------------------ LASER TRANSMITTER ------------------------------ Minimum allowable transmitter power --> 2.98 kW Transmitter aperture radius: 88.44 cm --------------------------- RECEIVER CHARACTERISTICS --------------------------- Receiver Area --> 0.365764447695684 $m^2$

For Sorato: ------------------------------- SATELLITE ORBIT ------------------------------- Number of SPS: 1 Optimal orbit altitudes --> Perigee: 2300.0 km, Apogee: 2300.0 km Orbital period --> 383.57 minutes Total active time (blackout reduction) --> 10.42 % Total blackout time --> 39.34 % Max active period duration --> 1.91 hours Max blackout period duration --> 5.5 hours Min range to target --> 3065.15 km Max range to target --> 3644.01 km ------------------------------ LASER TRANSMITTER ------------------------------ Minimum allowable transmitter power --> 4.29 kW Transmitter aperture radius: 105.62 cm --------------------------- RECEIVER CHARACTERISTICS --------------------------- Receiver Area --> 0.07863935625457205 $m^2$

[MatthewGrim]

Let's test the above results with the range analysis I did in 012/range_analysis.py ... just to make sure that the results still make sense.

[MatthewGrim]

Results of range analysis

These results show that the analysis works, subject to a uniform beam. The AMALIA rover varies slightly because the orbit the code spits out is slightly off the 1300km circular I'm using to get the range.

[MatthewGrim]

Looking at the results with the adjustments made from the optimiser. The intensities are much the same. Much higher than I expected, and the beam radius needn't be so large.

This is the main thing I need to understand now. Why is the beam larger than I think it should be?

After that I need to figure out if the code is really optimising the transmitter size.

[MatthewGrim]

Explanation for larger beam

I've now completed an analysis of the minimum beam spot size. For a diverging gaussian beam, this spot size. The plots below show that for the AMALIA and Sorato rover case, the code does find the optimum beam aperture (or very close to it anyway).

So the code works - why is the beam so much larger than the target + pointing errors? Because this is the best possible beam size we can achieve without focusing. If we could go smaller we would, up to the pointing accuracy, but the plots above show we physically can't subject to constraints. For this reason, there is a conservative margin in the results that we have unwittingly introduced.

The pointing accuracy does not need to be 0.1microradian for this design. It can be more. Alternatively, the power of the laser can also be reduced. I need to quantify by how much.

[MatthewGrim]

I think I've gotten as much as I need out of the gaussian profiles. There are a few follow on things to explore:

• How much could I reduce the power of the laser by? If I remained at 1 microradian?
• The code as it stands chooses one transmitter radius to optimise for all orbits. Following this analysis, it is clear the optimum transmitter for a particular orbit will be different. To really assess the optimum orbit, we should give each orbit its ideal transmitter radius and compare these. Maybe this will reveal better designs (or at least I do not have a proof that it will not).

Both of these issue are high priority and deserve separate issues.