Creating an exact model of the aurora is quite a difficult task in a small laboratory. You can simulate many of the individual physical processes in inexact ways, but each at a different scale such that they don't fit together as they would in nature, so you won't get the same result.
The major source of light emission from aurorae are jumps of electrons in oxygen atoms high in the atmosphere. One type of jump creates the green color which is the brightest and most familiar part of aurorae -- this is the so-called O(1S) -> O(1D) electronic transition. The red which is commonly seen at the top side of green auroral curtains is also produced by oxygen atoms making electronic jumps, though it's a different jump, starting at the excited state left over from the transition above, and ending up in the so-called "ground-state", oxygen's normal resting place. It's denoted O(1D) -> O(3P2).
Oxygen atoms get into these excited states by colliding with electrons (and to a lesser degree, protons) caught by the Earth's magnetic field from the solar wind, and funneled into the auroral regions where the magnetic field lines steer them into the atmosphere.
The electrons themselves can be used to excite gas very easily -- every neon sign does just this, using an easily produced (but also very dangerous!) high voltage to send electrons through a gas, kicking them into higher energy states.
The problem in simulating the auroral processes in the atmosphere is that the oxygen transitions that I mention above take much longer to complete than the neon transitions in a neon sign. The green transition I described takes about 1/3 of a second on average for the oxygen atom to fall from its more excited state to the lower excited state, and the red transition even longer -- about 104 seconds on average. And the atoms must be entirely undisturbed, because if they collide with other atoms while excited, they lose their excitation energy in the collision.
Because of this, the pressure must very low, so that there is not much chance of an oxygen atom encountering another oxygen atom in the period between when it gets excited by colliding with an energetic electron, and the time when it decays. Already for the green line, this pressure is quite small; for the red transition, the requirement is a vacuum difficult to obtain outside a relatively good laboratory (this is why red aurorae are seen at the tops of green auroral curtains, where the pressure is lower -- the red that sometimes fringes lower curtains of very bright aurorae is produced by an entirely different physical process).
And also because of this, the light produced in a small area is vanishingly small, because not many atoms participate. The aurora of nature are produced over many miles of gas. Even if a laboratory experiment duplicated these conditions, it would require sensitive detectors to record the very small amount of light produced in the small volume of gas simulating the upper atmosphere.
But in a small way, every neon sign or other gas discharge sign you see is a simulation in a small way of aurorae, only using gases which tumble down from their excited states in a much more rapid way, producing brilliant light in a small area. For the real thing, just step outside if you are lucky enough to live in the north, and enjoy nature's own laboratory.
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