the Sun

The reaction on the Sun producing the radiation is nuclear fusion.

This reaction is not likely to occur in the laboratory on the Earth, because a very high temperature (about 10^9 K) is required to initiate the process (i.e. to give sufficient kinetic energy to the molecules to overcome the electrostatic repulsion and fuse with each other.)

You may refer to the following for your reference...

The core of the Sun is considered to extend from the center to about 0.2 solar radii. It has a density of up to 150,000 kg/m3 (150 times the density of water on Earth) and a temperature of close to 13,600,000 kelvins (by contrast, the surface of the Sun is close to 5,785 kelvins (1/2350th of the core)). Through most of the Sun's life, energy is produced by nuclear fusion through a series of steps called the p-p (proton-proton) chain; this process converts hydrogen into helium. The core is the only location in the Sun that produces an appreciable amount of heat via fusion: the rest of the star is heated by energy that is transferred outward from the core. All of the energy produced by fusion in the core must travel through many successive layers to the solar photosphere before it escapes into space as sunlight or kinetic energy of particles.
About 3.4×1038 protons (hydrogen nuclei) are converted into helium nuclei every second (out of about ~8.9×1056 total amount of free protons in Sun), releasing energy at the matter-energy conversion rate of 4.26 million tonnes per second, 383 yottawatts (383×1024 W) or 9.15×1010 megatons of TNT per second. This corresponds to extremely low rate of energy production in the Sun's core - about 0.3 μW/cm³, or about 6 μW/kg. For comparison, ordinary candela produces heat at the rate 1 W/cm³, and human body - at the rate 1.2 W/kg. Use of plasma with similar parameters as solar interior plasma for energy production on Earth is completely impractical - as even modest 1 GW fusion power plant would require about 170 billion tonnes of plasma occupying almost one cubic mile. Thus all terrestrial fusion reactors require much higher plasma temperatures than those in Sun's interior to be viable.
The rate of nuclear fusion depends strongly on density (and particularly on temperature), so the fusion rate in the core is in a self-correcting equilibrium: a slightly higher rate of fusion would cause the core to heat up more and expand slightly against the weight of the outer layers, reducing the fusion rate and correcting the perturbation; and a slightly lower rate would cause the core to cool and shrink slightly, increasing the fusion rate and again reverting it to its present level.
The high-energy photons (gamma and X-rays) released in fusion reactions are absorbed in only few millimeters of solar plasma and then re-emitted again in random direction (and at slightly lower energy) - so it takes a long time for radiation to reach the Sun's surface. Estimates of the "photon travel time" range from as much as 50 million years[8] to as little as 17,000 years.[9] After a final trip through the convective outer layer to the transparent "surface" of the photosphere, the photons escape as visible light. Each gamma ray in the Sun's core is converted into several million visible light photons before escaping into space. Neutrinos are also released by the fusion reactions in the core, but unlike photons they very rarely interact with matter, so almost all are able to escape the Sun immediately. For many years measurements of the number of neutrinos produced in the Sun were lower than theories predicted by a factor of 3, a problem which was recently resolved through an introduction of the effects of neutrino oscillation between 3 species, out of which only one is detected.

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The Sun's diameter is about 110 times that of the Earth.

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Structure of the Sun