PLAINSBORO, N.J.— ON a grassy site here surrounded by cornfields and dense woods, not far from Princeton University, scientists want to build a machine of vast complexity and cost that they hope will lead to a powerful new source of energy half a century from now.

Their proposal is confronting the Bush Administration with a difficult choice as it tries to develop new sources of energy while cutting an enormous budget deficit.

The machine, the Compact Ignition Tokamak, would be the next stage of development in what is turning into a century-long quest to harness the kind of thermonuclear fire, or fusion energy, that lights the sun and produces the awesome blast of the hydrogen bomb.

Scientists here at the Princeton University Plasma Physics Laboratory say the new machine could be a major step toward ushering in a future age of relatively safe, cheap, clean and nearly inexhaustible energy.

But the device, meant to be switched on in 1998, would cost nearly $1 billion, a huge sum in an era of tight Federal budgets. Moreover, skeptics say the machine, even if successful, offers no guarantee that the field could advance in the 21st century to produce electrical power that would be economically competitive. They say that fusion advocates, long noted for promising more than they deliver, are engaging in another of their periodic bouts of hyperbole meant to promote Federal financing of yet another costly project.

The new machine would be based on traditional ''hot'' fusion principles rather than the low-temperature or ''cold'' fusion that was proposed with great fanfare last year. The allure of cold fusion was that it seemed to promise enormous energy from simple devices that worked at room temperature, in contrast to hot fusion machines, which must operate at temperatures above those on the sun, and are vastly complicated and expensive. But after a year of intense investigation, most experts have dismissed the notion that cold fusion, if it exists, will ever be a significant energy source.

Controlled fusion, which seeks to fuse hydrogen atoms to generate bursts of usable energy, has long been one of the most risky, daunting, contested and costly aspects of big science ever undertaken by the Federal Government. Billions of dollars have already been spent but, even amid reports of progress, the goal of practical fusion energy always seems to recede into the distance. Today experts estimate that the payoff, if it comes at all, will represent an investment of tens of billions of dollars as well as roughly a century of hard work by generations of scientists. The pursuit got under way in the 1940's and, in optimistic Government scenarios, could culminate in the 2040's with the operation of the first commercial power plant.

Fusion produces energy by fusing, or welding, the atoms of light elements together. In contrast, the nuclear fission reactors now in operation generate energy by breaking apart the atoms of heavy elements like uranium.

In the interior of the sun, where temperatures are 14 million degrees centigrade and gravitational pressures are crushing, nuclear particles are driven so close together that they fuse and release vast energy. In a fusion reactor, the temperature must be even higher, around 100 million degrees centigrade, since the fusion fuel undergoes far less compression than materials at the center of the sun. The main fuel for fusion experiments is a heavy form of hydrogen known as deuterium, which is found in endless quantities in water.

For years, the main path to achieving controlled fusion has been to heat fusion fuel so it breaks into a cloud of electrically charged particles known as a plasma, which can be contained by magnetic fields. No earthly vessel would be up to the task. Any kind of metal, ceramic or glass would melt. So magnetism has been used to build increasingly powerful magnetic ''bottles,'' which today are usually housed in building-size machines that have a doughnut shape.

The job has not been easy. Edward Teller, a founder of the field, once said that confining the plasma with lines of magnetic force was ''like trying to confine jelly with rubber bands.'' The hot plasma would heat water to rotate turbines and generate electricity.

A Vast Supply of Energy

Despite the challenge, scientists here say the practical payoffs are so great that forging ahead is worth the risk and expense. In theory, they say, the process could extract far more energy from the top two inches of Lake Erie than exists in all the earth's known oil reserves. And they say the alternatives of relying on coal supplies that pose a threat of global warming, or on nuclear fission reactors that raise safety concerns and generate mountains of high-level radioactive waste, or on oil from politically unstable parts of the world, are likely to grow increasingly disagreeable in the 21st century.

''The fight over oil at $100 a barrel is going to make the fight at $30 look pretty trivial,'' said Dr. Rob J. Goldston, the scientific head of the proposed machine. ''The question is whether there will be a new energy source to keep us at a high level of civilization.''