A Ikonal equation integration -- source code request

[carlos-carlos]

Hi.
I would like a source code to integrate the ikonal equation. I would like to compute the ray path. Of course I am able to compute the phase refractive index n(x,y). Cartesian system is preferred. Can anybody give me a suggestion?

Bye,

Carlos

 

[jasonRF]

Carlos,

What physical situation are you trying to model and what exactly do you want to compute? Based on that, what equations (write them out for us!) are you solving? I think you will get more useful replies if you actually explain what you are doing. I suspect it is not too difficult to write your own code to do the ray tracing, but it depends on the details of your problem.

Jason

 

[carlos-carlos]

Thank you for your reply. Actually I am integrating the ray equation for HF radio frequency propagating in the ionosphere. The ionosphere is supposed without magnetic field and without neutral-electron collisions. Phase refractive index is n=(1-X)^0.5 where X=wp^2/w^2 (wp is plasma frequency, w frequency of the radiowave). Simple model of ionosphere is assumed (just a parabola having maximum at 300 km). But this is not relevant at this stage.
I integrated the ray equation. Then I obtained the ray path miinimizing the optical path,and I obtained slightly different results. Then I applied the Snell relation, and I obtained again slightly different results. I suppose the problem is approached correctly, but there are calculus mistakes or instabilities. I would like to get a reliable code so I can compare the results. Regards.

 

[jasonRF]

Simple model of ionosphere is assumed (just a parabola having maximum at 300 km). But this is not relevant at this stage.

Actually, it could be very relevant. Your ray tracing equations should have a vertical derivative of the electron density in them. This derivative will be discontinuous at the bottom of your ionosphere. It is easy to have numerical issues associated with such a discontinuity. I would not be at all surprised if this is your problem. Using some off-the-shelf black-box ray-tracing code will not necessarily fix this, although if it had adaptive stepsizes it may be able to reduce the error.

Edit: Since you know your problem you can easily write your own ray tracing routine that starts solving your differential equation(s) just above the base of the ionosphere, thereby avoiding this issue. Perhaps you already are doing this?

Of course, we still do not know what equations you are solving so the issue could be your problem formulation. I can probably help you more, but cannot without sufficient details from you. Good luck.

Jason