What's in the neighborhood?

The content of the interstellar medium in the solar neighborhood is surprisingly poorly understood. It is thought that the Sun in in a Local Bubble of higher temperature and lower density than elsewhere nearby in the Galaxy. The bubble is the result of supernovae going off in the last few million years, or perhaps recent star formation. One recent article suggests that most of the Local Bubble is filled with about 40,000 m^-3ionized atoms with an admixture of 10,000 m^-3 on non-ionized material. To first order we can just assume that this material is all hydrogen. If so that means each for each square meter of cross-section of our ship we'll have about

    s = D ρ = 1017 x 50,000 m-2 = 5x1021atoms m-2

This isn't very much. A single meter of air has about 10²⁷ atoms, so over the entire journey we'll only run through the equivalent of about 5 microns of atmosphere....

It also seems likely to be a bad assumption that the interstellar medium is uniform on any particular scale. We know of lots of small bubbles with a bit more neutral gas and higher densities, but we should probably be visualizing this as a chaotic environment with lots of fluctuations on all scales.

That lack of intervening matter good news and bad news. Friction won't be much of a problem: if our cross section of the main ship is a few hundred meters we're not goring to run into more than a gram or so of matter on the way. If we are hoping to use interstellar material for fuel or reaction mass we need to look over a large area. E.g., how large an area do we need to collect over to get a mass comparable to our ship. One gram of hydrogen is about 6 x 10²³ atoms and our ship masses 1000 tons or a billion grams. So the area we need to collect over is

    A = 6x1032 / 5x1021 = 1011 m2 = 105km2

If we collect in an area of a circle then

    π r2 = 105km2

So we need to collect all of the material within a radius of about 200 km of the center of the ship. Here the fact that most of the matter is ionized could be a big help. In principle at least, we can use magnetic fields to interact with the medium and move it around.