Where there is fire, there is always smoke. So why there isn't any smoke near the Sun?
The sun isn't on fire. Fire is actually very rare in the solar system. It requires chemical potential energy, which happens on earth because of life. Photosynthesis uses solar energy to build things out of carbon, oxygen, nitrogen and hydrogen (and some other elements). It's these carbon chain structures that are ultimately flammable, and pretty much, only in an Oxygen atmosphere. Oxygen atmosphere is produced by the same photosynthesis.
The sun's heat comes from nuclear fusion which doesn't make smoke. Also, the nuclear fusion only happens deep the inside of the sun, the outside is just a thick blanket of molecules - mostly hydrogen. The sun also isn't transparent. The light we see from the sun is like the light we see from a red hot piece of metal or lava. Red hot metal doesn't smoke (unless you drop water on it - which is actually steam.) The sun, like red hot metal or lava, glows bright because of temperature.
In a certain sense, the tail of a comet is kind of like steam being made by the heat of the sun.
The sun is not undergoing an oxidation reaction, so it's not producing particulates that one might refer to as smoke.
The process the sun is undergoing is nuclear fusion, where hydrogen are combined and create helium. This reaction is very energetic and releases heat, visible radiation, and other radiation along a wide swath of the electromagnetic spectrum. The reaction is self-sustaining - as long as there is fuel, the emissions of fusion reactions cause nearby fuel to react as well. No oxygen or oxidizing agent is required.
Further, the resulting helium is comparatively heavy, and the sun being a huge mass keeps both the hydrogen that is the fuel and the helium that is the product nearby - they don't leave like hot smoke does from a fire.
So there is no smoke as we might consider it - just helium gas (plasma), and even if there were it would simply drop into the sun, there is no such thing as "rising" from it as one might consider smoke does on earth-borne fires.
You might find this music video provides further instruction on composition and reaction of the sun.
Even if an entire volcano worth of smoke and dust particles, like 1000000 tons, and you detonated it near the Sun's surface, it would probably go red and fall into the sun in 5 seconds.
The sun has turbulent whisps of high energy particles escaping its huge gravity, except that it's invisible and it's called solar wind. If you could see a slice of it, it might look similar to smoke on a large format.
Carbon based smoke ignites at around 400 degrees, and all other smokes decompose into atomic vapor and ion blasted by intense ionic forces at the sun's surface temperature, and some miles form the surface. If you breathed a cigarette at 1 mile from the sun, the smoke would change states into ions because the temperature would excite the molecules and atoms of smoke that they would be a plasma.
The sun weighs 333,000 times more than here... so the gravity is probably at least 10,000 times as strong at the surface of the sun.
Atmosphere is heavy, and if air is compressed 10,000 times it is closer to being a fluid than something that can handle gas.
So, the Sun doesn't have any atmosphere, because it's too liquid, it bubbles. If the sun were cold, it would perhaps have a bizarre kind of atmosphere, perhaps someone here can say what kind, perhaps only a few meters high, and perhaps 1mm. A human on a cold sun would become a puddle and sink, his bones would flatten under their own weight, to something very fine.
The temps are too high for visible molecules, and the movement is too violent for smoke, smoke can't exist in a fire, and the Sun is a kind of fire multiplied by 1000.
The question is, what molecules at all can exist at Sun temperatures? Molecules decompose in microseconds and there is perhaps some literature about any kinds of couplets and triads of atoms that can exist near the surface.