My reading is that "in the plane" literally means in the plane, +- a couple or tens of meters, depending. The paper is concerned with effects on the earth's sur

My reading is that "in the plane" literally means in the plane, +- a couple or tens of meters, depending. The paper is concerned with effects on the earth's surface, in an aircraft or orbit the duration of exposure and lack of stuff for neutrinos to run into probably means it's less of a concern. To put a number on it, they give examples of accelerators buried at 300 meters which would create a radiation hazard at a radius of 62 kilometers where the plane exits the surface (assuming earth is spherical). As far as the danger, the paper estimates up to a few mSv/year if you hung out in the wrong place all the time. You definitely wouldn't want to have a town in the way of that, but it's not an immediate danger on an individual level. The danger would be greater/more concentrated if there were straight segments in the accelerator, or if it was closer to the surface (smaller circle of intersection).