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1.1 Occurrence of Plasmas in Nature
It is now believed that the universe is made of 69 % dark energy, 27 % dark matter, and 1 % normal matter. All that we can see in the sky is the part of normal matter that is in the plasma state, emitting radiation. Plasma in physics, not to be confused with blood plasma, is an “ionized” gas in which at least one of the electrons in an atom has been stripped free, leaving a positively charged nucleus, called an ion. Sometimes plasma is called the “fourth state of matter.” When a solid is heated, it becomes a liquid. Heating a liquid turns it into a gas. Upon further heating, the gas is ionized into a plasma. Since a plasma is made of ions and electrons, which are charged, electric fields are rampant everywhere, and particles “collide” not just when they bump into one another, but even at a distance where they can feel their electric fields. Hydrodynamics, which describes the flow of water through pipes, say, or the flow around boats in yacht races, or the behavior of airplane wings, is already a complicated subject. Adding the electric fields of a plasma greatly expands the range of possible motions, especially in the presence of magnetic fields.
Plasma usually exists only in a vacuum. Otherwise, air will cool the plasma so that the ions and electrons will recombine into normal neutral atoms. In the laboratory, we need to pump the air out of a vacuum chamber. In the vacuum of space, however, much of the gas is in the plasma state, and we can see it. Stellar interiors and atmospheres, gaseous nebulas, and entire galaxies can be seen because they are in the plasma state. On earth, however, our atmosphere limits our experi- ence with plasmas to a few examples: the flash of a lightning bolt, the soft glow of the Aurora Borealis, the light of a fluorescent tube, or the pixels of a plasma TV. We live in a small part of the universe where plasmas do not occur naturally; otherwise, we would not be alive.The reason for this can be seen from the Saha equation, which tells us the amount of ionization to be expected in a gas in thermal equilibrium:
ni nn

2:410
21 T3=2 U =KT
Here ni and nn are, respectively, the density (number per m3) of ionized atoms and of neutral atoms, T is the gas temperature in K, K is Boltzmann’s constant, and Ui is the ionization energy of the gas—that is, the number of joules required to remove the outermost electron from an atom. (The mks or International System of units will be used in this book.) For ordinary air at room temperature, we may take nn
3  1025 m3 (see Problem 1.1), T
300 K, and Ui 1⁄4 14.5 eV (for nitrogen), where 1 eV 1⁄4 1.6  1019 J. The fractional ionization ni/(nn + ni)
ni/nn predicted by Eq. (1.1) is ridiculously low:
ni
10122 nn
As the temperature is raised, the degree of ionization remains low until Ui is only a few times KT. Then ni/nn rises abruptly, and the gas is in a plasma state. Further increase in temperature makes nn less than ni, and the plasma eventually becomes fully ionized. This is the reason plasmas exist in astronomical bodies with temperatures of millions of degrees, but not on the earth. Life could not easily coexist with a plasma— at least, plasma of the type we are talking about. The natural occurrence of plasmas at high temperatures is the reason for the designation “the fourth state of matter.”
Although we do not intend to emphasize the Saha equation, we should point out its physical meaning. Atoms in a gas have a spread of thermal energies, and an atom is ionized when, by chance, it suffers a collision of high enough energy to knock out an electron. In a cold gas, such energetic collisions occur infrequently, since an atom must be accelerated to much higher than the average energy by a series of “favor- able” collisions. The exponential factor in Eq. (1.1) expresses the fact that the number of fast atoms falls exponentially with Ui /KT. Once an atom is ionized, it remains charged until it meets an electron; it then very likely recombines with the electron to become neutral again. The recombination rate clearly depends on the density of electrons, which we can take as equal to ni. The equilibrium ion fraction, therefore, should decrease with ni; and this is the reason for the factor ni1 on the right-hand side of Eq. (1.1). The plasma in the interstellar medium owes its existence to the low value of ni (about 1 per cm3), and hence the low recombination rate.