To actually fuse two nuclei together, incredibly high temperatures and pressures need to be reached. By incredibly high, I mean multiple million degrees Celsius high, around the temperature of the core of the sun. High density also needs to be maintained at this temperature for the fuel to fuse and release energy. The fuel used in this process is deuterium and tritium, both of which are isotopes of hydrogen, a very abundant element.
No fusion reactors have been fielded to any significant scale yet, but the theory behind them has been developed and multiple prototypes have been created. The most promising of these designs is the Russian "tokamak" style reactor. The way it works is that the fuel is injected into the reactor, and then heated to 100 million degrees Celsius. The heated plasma is thin and fragile, and many, many times denser than normal air. To prevent it from coming into contact with other sources that might disturb the temperature of the plasma, it can't touch the casing of the reactor. In tokamak reactors, this plasma is kept suspended in a circular container. When the fuel in the reactor fuses, it releases 10,000,000 times the amount of energy that would be released in a chemical reaction. Commercial reactors would use the energy carried by the neutrons given off in the process to harness the power released by the reaction.
Since this technology sounds so awesome and powerful, why isn't its use widespread yet? The biggest issue its the temperature required for it to operate. 100 million degrees Celsius translates to a very, very large amount of electrical power. Consider how many radiators it would take to make something reach the temperature of the sun. For a long time, containment was also a major blocking factor, as I'm certain you could imagine how difficult containing a miniature sun would be. Thankfully, more recent prototypes have been able to overcome that issue.
Now, what are the positives of this technology? Although not, strictly speaking, as renewable as something such as solar or wind power, fusion power gives off no carbon emissions, and unlike nuclear fission, the only by product is relatively harmless helium. The fuel is one of the most abundant elements in the universe, hydrogen, so it's not going to run out any time soon. Fusion power gives significantly more power per kilogram of fuel than fossil fuels do. A kilogram of fuel for a fusion reactor generates the same amount as 10 million kilograms of a fossil fuel. Since the reactors use relatively little fuel in operation, there is no risk of a large scale reactor meltdown, as there is in nuclear fission. Finally, and arguably most importantly, fusion power can provide a stable baseline of electricity on its own.
I would argue that fusion power is the best energy alternative to fossil fuels. While other renewable energy sources can replace fossil fuels, only a combination of all of them could do so, with solar power being the only possible exception, and each source has its own individual slew of problems. Fusion doesn't have that issue. While technically a similar energy source to solar power, it seems unnecessary to sacrifice the surface area that solar power needs when the possibility of creating a miniature sun almost anywhere on Earth exists. Our energy demands are only going to increase in the future, and we need a new source of energy that can not only replace fossil fuels, but produce more power than they can, while being certain that it won't run out any time soon. I would say that such a source of power can be found in nuclear fusion.
Sources -
http://www.pppl.gov/Tokamak%20Fusion%20Test%20Reactor
http://fusionforenergy.europa.eu/understandingfusion/
http://www.ccfe.ac.uk/introduction.aspx
http://www.extremetech.com/extreme/185649-the-new-dynomak-fusion-reactor-design-could-make-fusion-power-cheaper-than-coal
http://www.world-nuclear.org/info/Current-and-Future-Generation/Nuclear-Fusion-Power/
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