We're in the control room of JET, the 30-year-old Joint European Torus tucked behind the thatched houses and winding country lanes of Oxfordshire, which holds the world record for coming the closest to proving fusion's commercial viability.

Engineers and physicists tap at their computers and gaze up at a dark video screen.

There is a countdown, then a pause.

A ghostly, rosy halo flickers into existence on the monitor, illuminating the inside of a hollow, airless metal "doughnut".

The doughnut would fit into half a basketball court, though you can't tell from here, on the other side of three-metre concrete walls and a verging-on-paranoid security cordon.

The glow fills the tunnel, hugging the walls, and its base thickens into a bright stream that seems to pour along the bottom of the device in a river of light.

Inside that halo, trapped by an intense magnetic field that saps 1 per cent of Britain's national electricity grid to switch on, is a swirling plasma that is, at this moment, the hottest place in the solar system. Then, seconds later, with a last flourish,the glow sputters and vanishes. The plasma has escaped its bonds. Show over.

And that's it, until the next try an hour later, and over and over again, as scientists chase the dream of igniting a tiny star that could power human civilisation for a million years.

"We are trying to do something that nobody else has ever done before," says Professor Steven Cowley, chief executive of the UK Atomic Energy Authority, with infectious enthusiasm. "[If fusion is proven to work] it's one of those historic moments in science, like the Wright brothers taking off."

In a way, fusion has already been proven to work. Just look up – it's what makes the sun shine. Here on Earth, fusion (hot, not the discredited cold variety) is – on paper – the ideal way to generate power.

The fuel is a bit of seawater, which contains a trace element called deuterium, plus a bit of lithium. And I mean a bit: the lithium in one laptop battery and the deuterium in a barrel of seawater could power a typical Western household for a decade.

The exhaust is helium, an inert, lighter-than-air gas. There's also eventually a little radioactive waste but it has a short half-life and is safe to handle after a couple of decades.

And – unlike nuclear fission – there's no risk of a meltdown. Due to the tiny quantity of fuel and the difficulty keeping a reaction going, if there were a major incident at a fusion reactor you'd be perfectly safe a few hundred metres away (at least, safe from the reactor).

Just thinking about how this could change the world is a mind-blowing exercise. No greenhouse gas emissions. No Fukushimas or Chernobyls. Practically limitless desalinated water for the parched throats of the Third World. An end to the geopolitics of oil: the wars and invasions and standover tactics. No more need for "ugly", endangered-bird-killing wind turbines, if that's your beef.

The problem is, the basic principles have been known since the heroic age of physics a century ago but no one has yet figured out how to make it commercially viable. There is a whole category of wry fusion "jokes", such as "fusion is the power source of the future, and it always will be".

In his new book A Piece of the Sun, Science magazine journalist Daniel Clery describes how it was the insight of two Australians last century that laid down the path to harnessing fusion power.

In the early 20th century, lightning – a form of plasma – hit the chimney of the Hartley Vale kerosene refinery near Lithgow in NSW. G. H. Clark, a worker at the refinery, noticed something odd had happened to the sturdy copper pipe that served as the chimney's lightning conductor: it had been crushed by some massive force "like a toothpaste tube".

This was dubbed the "pinch effect" and considered a mere scientific curiosity for 40 years until a University of Sydney postgraduate, Peter Thonemann, realised it might be used to contain and compress plasma – hydrogen or deuterium stripped of its electrons – enough to ignite a fusion reaction – a straitjacket of pure force able to withstand heat beyond the limits of any physical material.

Thonemann left Sydney for Oxford University, arriving in 1946. He figured that if you put plasma into a doughnut-shaped ring and applied an electric current, you'd get fusion. He presented his idea to the lab director, an old confidant of Winston Churchill, and was given the green light for a series of experiments that earned him the title of Britain's "father of fusion".

They were heady days. Teams of pipe-smoking, white-lab-coat-wearing professors pushed the boundaries of science during the day and drank beer in the evenings.

They barely understood what they were achieving. Even today, a lot of what goes on inside a fusion reactor is beyond the power of the smartest minds or the fastest computers to predict. It's a case of suck it and see: tweak your machine, turn it on and see what happens.

In those days, it was like playing with the fire of an unhappy god. They soon hit trouble. Magnetically imprisoned plasma is turbulent stuff. It strains and stresses and bubbles inside its shackles, in a bewildering array of instabilities that still plague JET 30 years after it was first switched on, and after significant modifications.

There is "kink instability". There are "disruptions" when the plasma current suddenly collapses, unleashing hundreds of tonnes of mechanical force that literally rocks the reactor on its foundations. There are "ELMs", tendrils similar to the flares that erupt from the surface of the sun, curling out of the plasma and melting the reactor walls.

At JET they deliberately trigger disruptions to try to understand them. Fairfax witnessed one: only moments after the rosy glow appeared on the monitors it swirled as if hit by a stiff breeze and snuffed out. A loud "bang" came over the speakers from the reactor room. It was just a small one, we were told: 50 tonnes to 60 tonnes of rogue force.

"A pattern began to emerge in fusion research," Clery writes. "Scientists would build a new machine: when it was working they would make progress towards fusion conditions but not quite as much as they had predicted.

"This could be because the machine underperformed or they encountered some new, unforeseen type of instability. The way forward was to build another bigger and better machine, and so on. Fusion got a reputation for promising a lot but never delivering."

JET's moment of glory was in 1997. Its best shot produced 16 megawatts. It was only 70 per cent of the power pumped in to heat the plasma and it lasted just a couple of seconds. No fusion reactor has ever done better.

Paul-Henri Rebut, the flamboyant, now-retired French physicist who designed and built JET, admits he's disappointed.

"I would prefer to have a better result," he says. "Fission didn't take very long and we expected [fusion] would not take long. I thought it would take 30 years or so. But the physics is much more complicated. It's almost an impossible problem."

So the cycle goes round again. Europe and a syndicate of other countries including Japan, Russia and the US, are now building JET's successor, the International Thermonuclear Experimental Reactor, or ITER, in the south of France.

Twice the diameter of JET and powered by superconducting magnets, it should put out 500 megawatts of power, 10 times what was put in, for minutes at a time. This would prove the viability of fusion power. This is the moment that Cowley is waiting for.

"In late 2020 it will reach fusion burn, pouring out energy like a little star," Professor Cowley confidently predicts.

David Campbell, a bearded, plain-spoken Scot who will direct plasma operations at ITER, admits there are a lot of risks and unknowns in the ITER, some of which JET can model but many of which will be faced only once the machine is switched on.

For example, the force of disruptions in such a machine is going to be "pretty meaty", he says. Another of the problems is the prosaic matter of dust – the neutrons shot out by the plasma will erode the reactor's inside and leave deposits inside the tube. It's already been seen in miniature in JET."We really don't know how this extrapolates to ITER," he says.

But the biggest concern is, quite simply, cost. The ITER will be the most expensive scientific experiment on Earth, at a currently estimated $14 billion just to build.

As each of the member countries is providing key components; any one of them could delay the entire project. In the US, Congress has put increased scrutiny on the country's contribution to ITER. And its own major fusion experiment at the National Ignition Facility, which is trying a different technique using lasers, is being told that if it doesn't produce results soon it may have to go back to its original focus on nuclear weapons research.

Some predict only China has the combined money, size and determination to push all the way to commercial fusion.

"The past few years haven't been very comfortable for us," says Niek Lopes Cardozo, chairman of the European Fusion Education Network governing board.

In a Europe concerned about austerity and debt, there is serious debate over big capital investments at the expense of social welfare.

"Fusion just sounds too good to be true," one EU bureaucrat told Fairfax. "It always seems a little too far away."

In a way, Europe is already showing the best way to harvest energy generated from fusion: in solar power cells, in the wind and tides, whose ultimate motivating power is the sun.

But fusion experts disagree. Dr Francesco Romanelli, head of the European Fusion Development Agreement, says the world needs a portfolio of energy solutions and fusion can play a specific role within a realistic time frame.

"We are not looking for perfection, for the ultimate technological solution, but for something that works. We don't need to build a Rolls-Royce."

Late in the evening, after the experiments are done, we go inside the reactor room itself, through an airlock and a concrete tunnel. The reactor core, that metal doughnut, is hidden behind a mass of laser detectors, ion heaters, electromagnetic generators, sensors, cooling systems and gas injectors. There is a loud roar of machine exhaust.

It's impressive – storeys high, bulging with power. It feels industrial. It feels real.

"This is terra incognita," our guide says. "This is what scientists do. It's our duty."