Probably the same sound as a bare fission reaction would make.
You only hear that which is registered by the temporal lobes in the brain. Usually those are receiving input from the auditory nerves, which are usually only excited when the tympanic membrane is vibrated by sound waves carried across molecules.
So, in the roughest manner, sound is perceived when longitudinal waves of energy travel through media — such as the air, the ground, your body, and the like — and vibrate your eardrums.
Nuclear fusion occurs when the distinct nuclei of two or more atoms approach near enough that it becomes easier for some of their neutrons and protons to fall into mutual nuclear “orbitals”. ‘Orbitals’ are, of course, a slightly antiquated name for the set of energy states which are considered to be stable for a certain set of conditions: why electrons stay near an atom, and why the nucleus of that same atom stays intact.
There are a few, and not too many, ways we know this could happen. In particle colliders at comparatively low energies, it is possible to bombard heavy nuclei with $\alpha$ particles, a.k.a. Helium nuclei, so as to synthesize heavier elements. This is how elements like Darmstadtium (a.k.a Ununnilium et al), for example, have been produced.
Lighter, smaller nuclei are less likely to collide at lower energies, so to make them stick you need an adequately dense and energetic — hot — plasma, where many of them are bouncing around.
If the energies of a stellar plasma get too dense, of course, then the nucleus ceases to exist, per se — but that's not relevant. (Neutron star.)
Then, of course, to perform a nuclear fusion at colder energies would require some other means of relaxing the repulsions between the electron shells of atoms — but you didn't ask about that.
When such fusion occurs, the energy is released in several forms:
- One of them is simply an imparting of additional kinetic energy to the resultant nuclei.
- A few neutrinos are emitted. These are largely hypothetical, as detecting them is difficult and indirect, but thus far the predicted characteristics haven't been counterindicated. They don't interact with much.
- $\gamma$ radiation — electromagnetic photons with a very short wavelengths.
- free neutrons, protons, or $\alpha$ particles a.k.a. Helium nuclei.
What manner of sound waves would these produce? Well, I suppose you could always see if the gamma rays, incident on the neurons in the brain or auditory nerve, would excite in a way that would either make them more likely (agonism) or less likely (antagonism) to fire off their neurotransmitters. Gamma radiation has a very small wavelength — well, what we call a wavelength — and isn't likely to interact with matter except on the nuclear scale. Mutogenic damage, sure. Perception of sound? The Hum, perhaps?
Not so likely, so far as I would expect.
Most of the sound would come from the resultant heat and thermal activity of the air. In rawest form, it would probably sound like an explosion: a rush of expanding gases.
However, depending on the nature of your containment, you would probably either hear nothing or you'd hear whatever passed through the containment. You don't explain enough about that for me to make accurate assessments.
Now, because you say that the reactions are contained and fed at a controlled rate, the only thing which you haven't adequately explained is the nature of the output beam.
Is it a beam of $\gamma$ radiation? A stream of $\alpha$ particles (Helium-4 nuclei)? Most of the sound from your reactor would probably come from this.
The size of the atomic nucleus with respect to the atom itself is quite remarkable. It has been compared to the distance between the sun and Pluto — i.e. the orbit of Pluto is the atom, and the sun is the nucleus. Tiny.
When nuclear fusion occurs, most of the emitted products are far too small to be sensed directly, more or less, by us. The only thing you could hear would be that which agitated the motion on the atomic or molecular scale.
Ergo: the heat of the fusion.
Note that I am ignoring the concommitant operational sounds coming from any equipment which are used nearby, or from the containment of the plasma itself, as your question doesn't ask for such things.