What causes the sharp borderline at the bottom of northern lights? The northern lights are caused by cosmic charged particles interacting with the earth's upper atmoshphere. The particles can be trapped by the Lorentz force, so that we can see them where the magnetic field is nearly perpendicular to the earth's surface.
Now, if one looks more closely one can see that the colors seem to dissappear continously into space but have a more or less sharp border at the bottom. At least it seems like there is a discontinuity of northern lights at their bottom.

Is it because the particles cannot enter the lower athmosphere? Or is the transition region not so narrow anyway and only appears so? What is the real reason it looks like this?
 A: You have picked a very striking picture to illustrate your question, although the northern lights do not always have such a sharp lower border to them.
However, let me advance a plausible explanation. The green northern lights are formed high up ($\geq 100$ km) in the Earth's atmosphere, largely by photons at 557.7 nm emitted from excited oxygen atoms. This is an example of a forbidden transition with a long radiative lifetime (a second or so).
Forbidden lines get "quenched" by collisions if the density is high enough - i.e. the atoms are de-excited by a collision rather than by emitting a "forbidden line" photon. At lower heights the densities increase and the forbidden emission is quenched, thus we may not expect to see any green light emitted lower down in the atmosphere. This may well be the explanation of what you see, rather than the penetration depth of the high energy charged particles. This also accounts for the stripes of different colours that are sometime seen, caused by transitions with different radiative lifetimes that quench at different densities and hence heights.
