At this point, we should define what “hot” means. When a gas like air or steam has a temperature, it means that the velocities of the molecules are spread out in a particular way, known as a Maxwellian distribution. This is the same bell-shaped curve, called a Gaussian, that teachers use to grade exams. Gaussian and Maxwellian mean the same thing. Physicists tend to use Maxwellian while mathematicians use Gaussian. Figure 4.4 shows such a curve representing the relative number of hydrogen ions having different velocities in a gas at about 10,000 K.2 When a material is in thermal equilibrium, it has such a “Maxwellian” distribution. The temperature is proportional to the width of this curve, so the velocities are higher at higher temperature. By raising the temperature, we can assure that there will be enough D and T ions in the “tail” of the distribution with enough energy to fuse. The “tail” is either end of the Gaussian curve, far from the center, where there are few particles of very high velocity. The ones that collide without fusing go back into the body of the distribution. In our billiard ball analogy, those would be the balls that go up a hill and come down again without falling into the hole. Multiple collisions

automatically maintain the shape of this most probable distribution. That means that the energetic particles in the tail which are lost in fusion reactions are replen­ished by successive favorable collisions. The collisions are random, so a particle can gain or lose energy each time. Only a fortuitous sequence of energy-gaining collisions can get a particle to high energy; that is why there are so few of them in the tail. Fusion reactors will require gas temperatures over 100,000,000 K!

At these temperatures, or even at 20,000 K, which is the temperature of the electrons inside a fluorescent light bulb, the gas no longer resembles the gases that we are familiar with, like air, helium, or CO2. Molecules become dissociated, and atoms become ionized. An oxygen molecule O2, for instance, first becomes dissoci­ated into two O atoms, and then each O is ionized into an ion (O+) and an electron (e-). Normally, an oxygen nucleus with charge +8 is surrounded by eight electrons, so that the atom as a whole is neutral. When one of the electrons is stripped off by colliding with a free electron, it becomes free, and the nucleus is left with an excess charge of +1. The gas is now a gas of ions thoroughly mixed with a gas of electrons, the way NaCl molecules are mixed with H2O molecules in a saline solution. But there is a big difference: this gas mixture is electrically charged. The ion fluid is positive, and the electron fluid is negative, so there can be electric fields inside the mixture. This type of electrically charged fluid is called a plasma. A plasma as a whole is neutral, with the same number of positive and negative charges. It is not exactly neutral, however, because there are electric fields inside a plasma. These fields are created by a very small charge imbalance of the order of one part in a million. If these fields were not there, nuclear fusion would not be a problem. So we call these gases “quasineutral” plasmas. Figure 4.5 shows what this new kind of gas is like. The ions are the small (blue) dots. They are given tails to show that they are moving in random directions. The big, fuzzy objects are the electrons, which provide the negative charges to make the plasma quasineutral. They are fuzzy

because you can never tell exactly where a given electron is. These particles move around at their thermal velocities and bump into one another, preserving the Maxwellian distribution. At the temperatures we are dealing with, the electrons and ions move too fast to stick to each other and recombine into an atom.

Often called the fourth state of matter, plasma is what you get when you heat a solid into a liquid, then into a gas, and finally into an ionized gas. Plasma emits light when electrons collide with atoms, kicking one of the orbiting electrons into a higher orbit. Light is emitted when that bound electron goes back to its original orbit. Although 85% of the matter in the universe is believed to be dark matter, the part that we see can be seen because it is in the plasma state. That includes all the stars, galaxies, and nebulae. On earth, plasmas cannot survive in our dense atmo­sphere, but we can see them in the Aurora Borealis and in fluorescent lights. You may have encountered plasmas without knowing it. Sparks are plasmas at atmo­spheric pressure. When there is a high voltage, electrons can jump across and make a transient plasma. This happens when you touch a doorknob on a cold day or plug in the power brick of a laptop computer. Lightning is a huge spark between a cloud and the earth or another cloud. These breakdowns are uncontrolled; but the steady, voluminous plasmas that we create on purpose are well behaved. They cannot spark because they are already completely broken down!

Plasma behavior is extremely complicated, and a whole new science of plasma physics has grown up from the effort to produce fusion energy. This science has now permeated into other fields. Computer chips cannot be made without plasmas. Plasma TVs are commonplace. Chaos theory and supercomputers were spawned by plasma research. How did we get to this subject? We found that particle beams cannot create fusion with a net energy gain. We had to heat a whole gas up to an extreme temperature so that, in a thermal equilibrium with a Gaussian velocity distribution, there are ions in the tail of the distribution with enough energy to fuse together. This is, then, a thermally generated nuclear reaction or thermonuclear reaction. This word has bad connotations and is no longer used by fusion researchers. Nonetheless, this clever method underlies the hydrogen bomb.

It is obvious that no solid material can withstand temperatures of millions of degrees, so we cannot hold the plasma with walls. We can hope to hold it with invisible forces, such as gravity, electricity, or magnetism. The sun produces fusion energy by holding plasma in its core with a large gravitational field. We cannot do this on earth because our gravity is much too weak, and we cannot shape it. That leaves electricity and magnetism. We can make strong electric fields, but these would not do it. The real proof is subtle, but basically you can see that an electric field will pull ions one way and push electrons the other way. The field will pull a plasma apart rather than confine it. That leaves magnetic fields. The name of the game is to make a magnetic bottle to hold plasma. That is the main subject of this book. All magnetic bottles leak. It is like holding Jello(R) with rubber bands. A plasma has a mind of its own. Fixing one leak reveals another one that you didn’t see before. Nobel Laureate Irving Langmuir chose the unfortunate name plasma, which had already been adopted by the blood people. It means something that can be shaped or molded. Nothing can be further from the truth! But the problem has been solved, and the end is in sight.