Is gravity a factor for sustaining fusion?

That's a great question, and it really depends on the type of fusion you are considering. Currently, the scientific community mostly works on two types of fusion - inertial confinement fusion and magnetic confinement fusion. I will mostly consider ICF as that is what I am working on.

In case of ICF the main problem lies in instabilities. Usually, a pellet of fuel is imploded by ablating the outer layer of a fuel capsule. As the outer material ablates, by the Newton's third law the centre of the fuel capsule is imploded and its density increases. It is in this phase that the denser fuel material inside is being imploded by a less dense outer material. Analogously to supernovaes, this leads to Rayleigh-Taylor instability that massively enhances any deviations from complete spherical symmetry of the fuel capsule and halts the fusion process.

In this sense gravity may be important - as it may slightly alter the shape of the fuel capsule away from spherical symmetry and lead to more pronounced instabilities. I believe I was even told once that it is taken into consideration during the design phase of the fuel capsules.

In magnetic confinement fusion I am fairly certain gravity is not an issue.

In gravitational confinement fusion (i.e. the Sun) gravity is the driving force that sustains fusion; however, this type of fusion is extremely inefficient in terms of energy generated per metre cubed of the reactor.

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Fusion

Experimental Physics

Newtonian Gravity

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