When you hear someone talking about 'artificial sun' that is usually a reference to fusion, the process at the heart of stars which includes the sun.
You may be familiar with nuclear power. That is fission or taking atoms that contain large nuclei and breaking them down into atoms with smaller nuclei. That releases large amounts of energy and unfortunately radiation as well. Science has tried to make this tech cleaner and safer, which they have, but it still has a long ways to go. It is however still a viable tech. A lot of modern subs and ships use this tech without incident. It is postulated that these elements, the fuel for fission reactors, were formed originally at the heart stars, long before the planets in the solar system formed.
Fusion is the 'opposite' process; the process that drives stars. Smaller nuclei, usually hydrogen, are 'forced' into closer and closer proximity to one another. When a certain 'closeness' is passed, which is extremely difficult to achieve en mass, the nuclei combine to form larger nuclei, helium, etc.... This releases large amounts of energy. This tech is still a work in progress and currently not viable for energy production. Current test designs still requires more energy to start and sustains such a reaction, than they would get in the energy releases. So its not viable.
Current tech is using lasers and magnetic containment, which is very different than what is known about process stars use. Stars are so huge, that gravity drives the compression of the nuclei. I don't think the term 'artificial' sun is correct as it does not used the same mechanics. The terms are more for the sales pitch to attract investors and to get research grants. You'll also hear scary terms like 'hotter than the center of a star' or 'millions of degrees'. Get comfortable with the idea that temperature is and average kinetic energy of molecule, atom and particles. Take a million degrees. If one in a billion billion particles has high energy, it will not likely harm you. However, if it is one in three, it would vaporize you. It's likely just another dramatic selling point. I am still unclear as to how they intend to extract the energy release into a usable form. Heat water driving turbines? Induction to coils?
China has even made contradictory remarks as to what achievement they made. I thought they already surpassed the goal they have recently claimed.
Don't expect to see this in stores, anytime soon. Every decade as people have forgotten the last claim made. The empty hands a re thrust forth toward our pockets again for more money and another claim that in 10 to 20 years, we will be producing clean energy. The devil is always in the details though. Look at hydroelectric, geothermal, solar and wind energy. They all have their detractors with some serious concerns, but strangely not advertised.
You might also want to look into 'cold fusion' . They was a lot of hype many years ago. That seemed to have fizzled out.
Hope this provides a jumping point.