IT ALL BEGAN with Project Matterhorn in 1951. The search for energy from thermonuclear fusion - clean, cheap and without limits, its supply of fuel nothing more than the deuterium found in the earth's seawater.

So optimistic were the scientists who started Matterhorn that they spoke of producing power in five years. Buzz words were: "Burnup by Christmas," meaning they hoped to demonstrate fusion's scientific feasibility by matching the temperature of the sun the first year.

So relaxed was the program in 1951 that its name was chosen because Princeton University's Dr. Lyman Spitzer Jr., the project's first director, was a mountain climber. A picture of the Matterhorn hung in his laboratory.

Two years later, the dream had dimmed but not by much. The scientists realized that the world of plasma physics where gas behaves like solids and liquids were more complex than they suspected but then they had built a machine at Princeton to test their understanding of the physics.

The machine was called the Stellerator and some of its builders fully expected to reach fusion temperatures of 100 million degrees centigrade the first time they turned it on. When the day came to test it, the lights were turned out in the Stellerator laboratory so everybody could get a good look at the superheated gas when it ignited and the Age of Fusion began.

Somebody pushed the button that started the machine. There was a sudden, blinding flash. Not from fusion, however. The magnetic coils built into the machine to insulate the hot gas and keep it away from the walls of the machine all burned up because of a massive short circuit.

It's taken them 27 years but the scientists who labor at fusion research are beginning to understand its physics and tame its special fury. It has not been easy. While there have been no more short circuit explosions like the one that struck Princeton 25 years ago, there have been countless small but embarrasing failures along the way. What began as a cakewalk up the Matterhorn has become what the Department of Energy's Dr. Edwin Kintner calls the "greatest technological challenge man has ever undertaken." A Turning Point

ON JULY 24, a piece of that challenge was met. On that day, a younger team of Princeton scientists than the group which started the charge up the Matterhorn reached a milestone which mark a turning point in technological history.

What the Princeton team did was achieve a temperature of at least 60 million degrees in a machine that might be described as a test-tube grandson of the old Stellerator. The temperature measurements which can be made on the Princeton device have a limit of 60 million degrees. Some scientists believe the real temperatures reached on July 24 at Princeton were upwards of 80 million degrees.

Even 60 million degrees is four times as hot as the interior of the sun. It's true the 60-million mark wasn't sustained for any longer than a 20th of a second, but sustainment time is beside the point. The highest temperature reached in a fusion device like the Princeton machine before July 24 was a paltry 26 million degrees.

"We'd been hoping to get up to 35 million degrees this time," said Dr. Melvin B. Gottlieb, director of Princeton's plasma physics laboratory, "but we went sailing right by it. We saw the temperatures go to 45 million, 50 million, 55 and then 60. It was amazing."

What's the importance of the Princeton achievement? Well, it's a little like breaking the sound barrier for the first time. The scientists have proven they can do it. There's nothing magic about 60 million degrees except that once a fusion device gets through 44 million degrees the heat is so high that the fusion reaction where light elements combine to form a heavier element begins to sustain itself.

The deuterium inside the machine is now so hot it has become a plasma, a gas whose electrons have been stripped away. When that happens, the gas is left with positive and negative charged particles moving at random. So rapid does that motion become that it's almost impossible to slow it down and cool the gas off again. It's like a runaway truck, moving down the steepest of hills. The Magic Numbers

PRINCETON'S Dr. Gottlieb insists that what took place in his laboratory July 24 is not a breakthrough and perhaps it isn't. Gottlieb says that fusion will not be demonstrated until a plasma reaches a confirmed temperature of 100 million degrees for at least one second. These are the magic numbers scientists have talked about the last 27 years. At those temperatures and for that span of time, more energy is pumping out of the fusion device than must be pumped in. Eureka!

The Princeton Large Torus, as Gottlieb's infernal machine is called, is the forerunner of a much bigger machine now being built at Princeton which will surely demonstrate sustained fusion for the first time. As intricate as fusion physics are, one thing about it is simple. Build a bigger machine and you go to higher temperatures and longer fusion times. It is an axiom of plasma physics.

Why did it take 27 years to prove the power of fusion? To begin with, the physics proved to be a lot more difficult than anybody imagined. Princeton's Gottlieb explains it this way: "People always ask me why we can't solve the fusion question if we put a man on the moon. And I always say that getting to the moon didn't involve any new principles, it was just a question of engineering the machinery to get there. In the fusion business, we're running up against new concepts every day and trying to put together the engineering at the same time."

Engineering the equipment to reach higher temperatures than the sun has turned out to be a task of backbreaking magnitude. Just one part of that job was developing magnets that had enough force to contain plasma at temperatures of millions of degrees. After all, those temperatures melt anything they touch so that any machine built to withstand those temperatures had to have a mechanism that kept the hot gas from touching the walls of the machine.

Magnets can do that because the plasma is electrically charged. The field built up by the magnets along the walls of the machine wrap around the plasma like a great big cloak keeping all but a tiny fraction of the gas from touching the walls. Put another way, the magnetic feilds act like the insulating layer in a thermost bottle and help to keep the heat from escaping.

It took 27 years for the scientists involved to learn what Gottlieb calls the "kitchen tricks" of the business that make fusion work. Start with the "heaters" that raise the temperatures of the gas to plasma-like heats. The heaters used in the Princeton experiment are what engineers call "neutral beams injectors," which are a brand new family of devices developed at the Oak Ridge National Laboratory for the purpose of lighting the fires fo fusion.

The neutral beams are ingenious "guns" that fire high energy charged particles right into the fusion machine. Along the way, the charged particles pass through a gas cell that strips half of them of their charge so that they're neutral when they enter the machine's magnetic field.

Charged particles would be trapped by a magnetic field. Neutral particles with no charge on them fly through magnetic fields as if they're not there. The result of a steady stream of high speed neutral particles striking a gas-like deuterium is that they collide with such force that they get charged again, heating the gas to enormous temperatures in fractions of a second.

The real "kitchen trick" that Gottlieb and his team used last month was to scrub the walls of the fusion machine and make them squeaky clean.

If that sounds oddly unscientific, consider this. It turns out that when an unheated gas first enters a fushion machine some of it escapes the magnetic field and clings to the walls of the machine. When the gas contained by the magnetic field is heated, the gas clinging to the walls tends to cool everything down and slow the fusion reaction. For years, scientists didn't understand this. And this response was to pump more gas into the machine to try to raise the temperature. This slowed down the reaction too, spoiling the experiment.

"It sounds so simple, except a lot of people have been struggling with it and after you've done it you say: 'Why didn't we do it a long time ago?'" Gottlieb said. "Now everybody will be doing it within the year or maybe less." An Errant Memo

AN ENDURING IRONY of the Princeton achievement of last month is that it does nothing to speed up the U.S. program to develop fusion as an energy source.

It proves that fusion is possible but it cuts not one month from the plan to generate electricity from fusion by 2005 and have a commercial network of fusion electric plants in place by 2025.

It doesn't save a penny of the money that's needed to develop fusion either. It's cost more than $2 billion already and it's going to take at least another $15 billion to make the first kilowatt of electricity from fusion.

"I keep on saying to people that if somebody invents a new energy system it will take at least 20 years before there's a 5 percent market effect," Gottlieb said. "You can't make changes in a hurry even if you know how to do it and we don't know how to do it yet."

The politics that followed the Princeton achievement are curious and deserve at least a mention. When the Department of Energy was notified of the 60-million-degree milestone, a mixed reaction ensued. The fusion people were ecstatic, drafting what the federal government calls an "early warning memorandum" for cabinet and agency heads to explain what had happened. Curiously, the memo never reached the White House, presumably the place such memos are aimed at.

There was discussion inside the Energy Department about whether to hold a press conference to announce the achievement. Top management did not want a press conference. They worried that Congress might demand an increase in the fusion budget request, anethema in this year of a forecast balanced budget.

There's another reason Energy Department sources say top management looked askance at the fusion achievement. Energy Secretary James R. Schlesinger believes in the "economics of scarcity," meaning he preaches energy economy because all our fuels are in scare supply.

Fusion? All fusion does is tell the world that we have all the energy we'll ever need.