Plasma: the fourth state of matter

What is a plasma?

An atom is neutral: its electrons balance the positive charge of its nucleus. If an electron gets enough energy, it breaks free. The atom becomes a positive ion, and the electron becomes a free electron. This process is called ionisation. A hydrogen atom needs at least $13.6\ \text{eV}$ to lose its electron.

A plasma is quasi-neutral: in any large volume there is almost the same amount of positive and negative charge. But its charges can move, so a plasma conducts electricity and reacts strongly to magnetic fields. This is why it behaves so differently from a gas. Some scientists call it the fourth state of matter, after solid, liquid and gas.

Plasma in nature

Most of the ordinary matter that we can see in the universe is plasma, because stars are made of it. In the Sun's core the temperature is about $1.57 \cdot 10^{7}\ \text{K}$, and the matter is almost completely ionised.

On Earth, natural plasma is rare and short-lived. In a lightning flash a current of tens of kiloamperes heats a narrow channel of air to about $30\ 000\ ^\circ\text{C}$, and the air becomes a glowing plasma for a fraction of a second.

The northern lights (aurora borealis) start in space. The solar wind, a plasma that flows out from the Sun, disturbs the Earth's magnetic field. Electrons of a few kiloelectronvolts follow the field lines down towards the polar regions. At heights of about $100\text{–}150\ \text{km}$ they hit atoms and molecules of the air and ionise or excite them. Oxygen gives off green light ($557.7\ \text{nm}$) and, higher up, red light; nitrogen gives blue and violet light.

The aurora appears most often in a ring-shaped band around the magnetic pole, the auroral oval, about $2500\ \text{km}$ from the pole. Finnish Lapland lies under it: in the Kilpisjärvi–Utsjoki area northern lights can be seen on about three clear nights out of four, but in Helsinki only on about one night a month (Finnish Meteorological Institute).

Key idea

"Hotter than the Sun" is about temperature, not about pressure or power. The pressure of a plasma depends on both its temperature $T$ and the number of particles in each cubic metre, the number density $n$. The formula also contains the Boltzmann constant $k = 1.381 \cdot 10^{-23}\ \text{J/K}$.

$$p = n k T$$

In a plasma both the ions and the electrons push, so their densities are added.

The triple product

A fusion plasma loses energy all the time: hot particles escape and the plasma radiates. The energy confinement time $\tau_\text{E}$ is the energy stored in the plasma divided by the power it loses.

In 1955 the British engineer John Lawson worked out what a plasma needs to give out more energy than it loses. Today his result is a condition on the triple product of density, temperature and confinement time. For deuterium–tritium fuel, a plasma that keeps itself hot by its own fusion (ignition) needs the following, at a temperature near $T \approx 14\ \text{keV}$.

$$n T \tau_\text{E} \geq 3 \cdot 10^{21}\ \text{keV} \cdot \text{s/m}^3$$

Plasma physicists give temperatures as energies: $1\ \text{keV}$ corresponds to about $1.16 \cdot 10^{7}\ \text{K}$. The product means that a reactor can make up for a lower density with a longer confinement time, but it needs all three at the same time.

Worked example

Common misconception

"A fusion plasma is hotter than the Sun's core, so it must produce more power than the Sun's core, and it must melt any wall." Both parts are wrong. The Sun's core produces only about $280\ \text{W}$ in each cubic metre, because its reactions are very slow; it shines because it is enormous and old. ITER's plasma is planned to produce about $500\ \text{MW}$ in $830\ \text{m}^3$, about $0.6\ \text{MW/m}^3$. A reactor must be hotter than the Sun, because it cannot wait billions of years and it has no gravity to hold a dense plasma.

The plasma does not melt the wall because it is very thin and is kept away from the wall by magnetic fields. If the plasma touches the wall, the plasma cools at once. Its stored energy is still large enough to damage the wall surface when it is lost suddenly, so the plasma must be controlled carefully.

Summary

• Ionisation frees electrons from atoms. A plasma is a quasi-neutral mixture of ions and free electrons; it conducts electricity and reacts strongly to magnetic fields.
• Stars, lightning channels and the region where the northern lights form are plasmas. Finnish Lapland lies under the auroral oval.
• The pressure is $p = nkT$, with ions and electrons added. A fusion plasma is about ten times hotter than the Sun's core but extremely thin, so its pressure is only a few atmospheres.
• The energy confinement time $\tau_\text{E}$ tells how long the plasma keeps its energy.
• Lawson's idea: for ignition of deuterium–tritium fuel, $n T \tau_\text{E} \geq 3 \cdot 10^{21}\ \text{keV} \cdot \text{s/m}^3$ near $14\ \text{keV}$. Density, temperature and confinement are all needed at the same time.