Naturally occurring fusion reactions (for example, the reactions that fuel the Sun) occur due to extreme gravitational forces. The minimal mass required to create such a large gravity in the core thus igniting hydrogen fusion, is 0.08 solar masses. This is roughly 75 times the mass of Jupiter.
Fusion happens when one hydrogen collides with another hydrogen and form He, one of the protons decays into a neutron (beta plus decay) you get a neutrino and a positron and a gamma ray (energy).
There is a probability that any two hydrogens will collide and fuse. This is quantum tunneling. In the sun with temperatures 15,000,000 K this is actually very rare. If it happened fast, the sun would have burned up a long time ago! This probability is exponential so that even though the core of of Jupiter is 10,000K and you might expect fusion to happen something like 150 times less since it is 150 times cooler it actually happens something like 10^150 times less often, which is to say maybe it can fuse one or two hydrogen atoms, not enough to detect.
The sun is much bigger and composed of hydrogen, and the gravitational pressure at the core is enough to set off fusion. Jupiter is composed of heavier elements, though I think mainly gaseous, which don't support fusion.
The core.
core and radiation
Actually, it is not. The Sun's core is about 28,000,000°F, but it needs to be at least 100 million to undergo nuclear fusion. There are some factors that fusion can occur there. One is density and pressure. The amount of pressure overturns the weak nuclear force which is the force that resists atoms from fusing. Another process known as quantum tunneling provides a sort of "barrier" that helps overcome the weak force and helps force the atoms to fuse.
The core
Fusion at the core of the sun is the process that gives the sun its energy. Fusion is the same process found in the explosion of a hydrogen bomb.
Fusion occurs in the core of the Sun
Fusion occurs in the core of the sun and other stars.
There is no fire in the sun, that is a chemical process. The process in the core is thermonuclear fusion.
High temp and pressure
Nuclear fusion occurs in the solar core.
Near the core (center).Near the core (center).Near the core (center).Near the core (center).
Although Jupiter is comprised of similar materials to the Sun - mainly hydrogen and helium, it does not have enough mass to heat the core of the planet to 10,000oK. This is a requirement for nuclear fusion to occur and without that, Jupiter is not a star, but a planet. For Jupiter to become a star, it would have to accumulate 75% more mass to achieve this.
The rest of the sun is too cold and too low pressure.
If you are asking where does solar nuclear fusion take place, then that would be at the core of stars.
Interior of the sun.
The Sun's core is hotter, and at a higher pressure, than the outer layers. I assume there is a very small amount of fusion in the outer layers, but not enough to make a real difference.
It has to be at hundreds of millions of degrees kelvin, before a fusion reaction between deuterium and tritium will start