Today I am following DuPont-Murphy's work. (In the meantime I've been downloading and installing VS 2022 Community, since that is Official Release now.) Again, this is all on the unstated assumption that Mars' crustal microteslae are of negligible help shielding the planet at a high altitude.
They work in Earth units until they can get around to putting this stuff into S.I. units. As long as they are working in proportions, they don't ... care about units. They are on the cm/g/s plan, as can be seen in figure 1 where ρv2 is B(r)2 / 8π. That denominator if S.I. should be 2μ0 where μ0 is the vacuum permeability. Be nice if they'd told us . . .
I wasted a heap o' time figuring out what "B(r)" meant. I can make sense of it only if B is a function of r. Apparently B(rs) = B(r🜨) × (r🜨 / rs)3. I don't know how they came up with that, but - whatever. My problem again is how they didn't tell us.
Moving along to the ram-pressure, here they show their work better - toward an inaccurate result. We all want a function of B(r) at a Standoff Radius which, confusingly, they call B0 rather than B(r's) or even just B'. So - I'll do it. Their equation is B' = B🜨 × [Earth distance in Mars' units] × [Earth radius in Mars' radius]3 × (r's / rs)3.
That [Earth distance in Mars' units] would be the ram-pressure factor. It is, in effect, the square root of [Solar irradiation at 1 AU in Mars' units].
Earth distance in Mars units is 2/3, for them - which is more than it should be, since we want the worst-case scenario which is Mars' perihelion. That is not 1.5 of Earth AU; it's 1.38. Earth in Mars' radius is indeed more like 2 although, we'll take 1.88. All said and done, they use the fraction 16/3 which is 5.333; pretty sure Math.Pow(6371.0/3389.5, 3.0) / 1.38 = 4.81 would be better. Good news: their errors cancel out, so they hit the high-side!
16/3 of B🜨 × (r's / rs)3, then. For them r's / rs is 1/6. So they got 1/40 B🜨; where I have the slightly lower 2/90 B🜨. Given B🜨 = 50 that's 1.25 microtesla for them. I'd been given to understand that Earth's field ranges: 25 to 65 μT. Again, they're hitting the high side.
All in all, they err on the side of caution - by accident, and until they get to mass-density. But we'll take it.
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