American scientists have successfully turned on a machine that is expected to help harness the process that powers the hydrogen bomb to make safe, peaceful and limitless electric power in the future.

Physicists at Princeton University's Plasma Physics Laboratory disclosed yesterday that at 3:06 a.m. on Friday they produced the first burst of plasma, or hot, electrified gas, in a $314 million test vessel financed by the Department of Energy.

The burst lasted only a 20th of a second, and it took more power to produce than it created.

But by 1986 it is expected to lead to a "break-even" burst that creates at least as much energy as it consumes. That should point the way to commercial nuclear fusion machines that generate electricity for homes and industries in the 21st century.

What happened Friday "means a tremendous amount of hope for fusion power . . . . The Princeton machine is our major new fusion facility, our flagship and probably the most single important facility in the next generation of energy technology," said Dr. George Keyworth, President Reagan's science adviser.

Fusion power--heat and electricity made by joining hydrogen atoms--is the goal. It is how energy is made in the H-bomb and the sun. It is the very opposite of the atom-splitting, or fission, process that creates heat and energy in the fission reactors that now generate nuclear power.

A fusion reactor, proponents say, would join two forms of hydrogen atoms, the main one distilled from seawater, which is plentiful, to produce power with far less radioactivity and dangerous waste matter than fission reactors.

The 25-foot-across, ring-shaped Princeton machine, seven years in the building, is called the Tokamak Fusion Test Reactor. "Tokamak" is a Russian acronym for words meaning "current in a doughnut-shaped device."

The Soviet Union made the first Tokamak and is building a larger one, as are Japan and Britain.

But Princeton's is the first of this new generation to operate. By 1986, said Dr. Harold Furth, director of the Princeton laboratory, "we are confident" it will produce a plasma with at least as much heat and energy as it devours in the fierce reaction that should convert the mass in the two forms of hydrogen, deuterium and tritium, into useful energy.

Friday's burst, Keyworth said, was "an essential milestone." It created a plasma of just 100,000 degrees centigrade, which is cool by fusion standards. The hoped-for 1986 break-even burst should be 100 million degrees, survive "on the order of seconds" and "have desired pressure and density," said Dr. Mary Shoaf, assistant director.

What Friday's burst showed, she said, is that the machine works, and works so well "the event occurred the first time we tried it."

"It's like Columbus finding the New World," Furth said. "It's not how big it is, but that they found land."

Making a burst of atoms so hot and dense that they become a completely ionized or electrified gas is only part of the task. Keeping them from spreading and melting the walls of their stainless steel vessel is an even larger part.

It is done by containing them in a doughnut-shaped magnetic field, in effect a magnetic bottle, with the magnetism coming from massive coils around the whole vessel.

In Keyworth's view, fusion power won't come until "well into the 21st century -- it's probably the most difficult technology man has ever attempted to develop."

It is nonetheless one the usually tight-fisted Reagan administration has supported well. The Energy Department also funds research at the University of California's Lawrence Livermore Laboratory, the Massachusetts Institute of Technology, Gulf Technologies and Oak Ridge and Los Alamos National Laboratories.

The fusion power program will cost $454 million this year, the same as last year, up from $316 million in 1977.

The Princeton laboratory currently gets $120 million a year. It has stayed level, which means absorbing inflation, for the last two years. Compared with many other programs, said Dr. Shoaf, "one congressional aide told me we stand like a mountain in a devastated plain."