Seems that we are on the same conceptual page finally.

You just don't listen. If the "conceptual page" you refer to is that atmosphere is lost to space, then I am pleased that we are on the same page. It is well documented and everyone around here with any scientific chops know it. We have said so many times. No one has disagreed with this. If you've been paying attention to the space boards, or mars exploration in general, there's a puzzle about mars' atmosphere. It deals with how much deuterium (heavy H) is in the air there. Deuterium is not statistically as likely to be lost from an atmosphere as lighter H. Assuming that the H on mars started out with the same approximate ratio of deuterium to lighter H as the rest of our neighborhood, then the current ratio of deuterium to lighter H can give you a means to calculate how much H it started with and how much H it lost. You can also make statements about how much water could have been on mars based on this ratio.

You say that the cause is the solar wind; I do not disagree with that, but you seem to imply that the quantity is extremely small...

Yes. Study by satellites has shown it to be small.

...and the solar wind is the only cause (or reason) for atmospheric loss.

Certainly the primary cause. There's an awful lot of energy from the sun hitting our atmosphere. There's comparitively very little else doing so. Maybe cosmic rays account for .001% or something like that. You'd need someone who worked in the field to come up with a reasonable number.

I’m sure that you agree that the planets gravitational field... sure ...and the atmospheres temperature also have a large bearing on the magnitude of the atmospheric loss. temperature? maybe. A wildly vibrating molecule is certainly not any lighter than a cold one. In any case, in the far upper reaches of the atmosphere it is very hot.

If we can agree on these basic assumptions, then we can study the phenomenon further. There are people who do study this. None of them are you or me, though.

For instance, we can figure out why the planet Mars has less atmosphere than Earth or Venus. There are people doing a very good job of this. We have a whole fleet of orbiters that are working on the question. A lot has been published. If you want to help then you should study what's been determined. Read some papers. Go to a conference.

Also we can investigate questions of why the moon has so little atmosphere and why the comets leave a trail of gas behind their path. Nothing much to investigate. Theories have been around for hmmm... less than a century that have been confirmed over the years (Raoul? I'm not doing any research for this. Just in case you know off the top of your head). The investigations are done.

Why does Earth have a thermosphere? Because we have looked at the properties of different layers of the atmosphere and decided we needed a name for the part above what we decided to call the mesosphere and below what we decided to call the exosphere. We thought Thermo might be a good quickie description of the region, and a bit of nomenclature was born.

Or do you mean why the gasses become ionized there? Or why the few atoms that are up there are so hot? Or why there are only lighter gasses there? There's no mystery. Look it up if you want to know.

After that, we can continue further and find out how fast the molecules in the thermosphere move and IF radioactive molecules exist in that area and IF such molecules can impart kinetic energy to the surrounding molecules. Crazy theory time. Yes, it is very well explored by sounding rockets and satellites (and the space stations that orbit through it). No, they have not discovered any Pu or U or whatever you expect to be there.

If we come to a mutual understanding of all that information, then we can start asking the real hard questions. You need to come to an understanding of what has been studied, what "hard questions" have already been asked, and what the answers were.