How does a hydrogen ion gas cool?

Question

Ok I understand that a hydrogen gas of non-ions at a temperature higher than its surroundings exists with many excited electrons. These electrons, either spontaneously or due to collisions, will return to a ground state and emit photons. Thus, the speed of the H atom will decrease and energy is transferred to the surrounding media.

But! What if I have a H+ gas (hydrogen ion gas)? Hypothetically lets say I have 10 H+ atoms, i.e. 10 protons. These protons are travelling at some high speed (v<< c) and thus have some high temperature.

Do these protons lose energy, are photons emitted? There are no electrons, so what mechanism causes them to lose energy?

If they can only lose energy via acceleration, does that mean a group of 10 protons will never lose energy (never cool down) since the mean free path is enormous and thus never accelerate?

Answer 1

You don't write which context this is in, so this answer may be inappropriate for you, but for an ionized gas of pure hydrogen (i.e. no heavier elements) in the interstellar medium (which contains also electrons, or else the protons would quickly repel each other), the main cooling mechanism above $T\sim10^6$ K is Bremsstrahlung, where the electron lose energy as they pass close to protons and are deflected from their path.

Below $\sim10^6$ K, a realistic gas cools via helium, and possibly also heavier elements if they are present, but if you had magically removed all helium, it would be really difficult for the gas to cool. Only when $T$ falls below $\sim10^{4.5}$ K, can recombinations of the protons and electron halp to cool it further.

This answer on astronomy.SE discusses the temperature of interstellar space, and shows how it cools at various temperatures.