Over two billion degrees!
The article by Malcolm Haines
Published on February 24, 2006, in Physical Review Letters
Updated on July 16, 2006 (data at the bottom of the curve showing current rise in the Z-machine)
Update of March 18, 2008. Following an article published in Science and Avenir
For non-scientists:
Readers are asking whether these ion temperatures exceeding two billion degrees have actually been measured. The answer is yes. However, a puzzling phenomenon had already been observed as early as 1998 in plasma compression experiments conducted with the Z-machine. These experiments involved various configurations. For example, when the "birdcage" imploded, a "gas puff"—a burst of gas—was injected precisely at the center, which then became compressed. X-ray emission allowed measurement of the electron temperature. A plasma is a mixture of two species: heavy ions and light electrons. In an "iron plasma," or ionized iron, the iron nuclei (56 nucleons, 26 protons) are 100,000 times heavier than the electrons (nuclei consist of "nucleons" of nearly identical mass: protons and neutrons. An electron is 1,850 times lighter than a proton).
A neon tube also contains "these two species": electrons and neon ions (although in this case, they haven't been completely stripped of their electron shells). When the tube is operating, it contains a "bitemperature" mixture: the gas made of atoms and neon ions remains cold (you can touch the tube with your hand), but the "electron gas" is much hotter, reaching 10,000°C. Why don’t you feel this heat on your hand? Because the electrons, poor things, are too stingy to transfer energy—or heat—to you. However, they have enough energy to excite, via collisions, the fluorescent coating lining the inside of the tube. This is why they are called fluorescent tubes. Fluorescence is the ability to absorb radiation and re-emit it at a different frequency. For example, fluorescein absorbs solar radiation and re-emits it in green. Nylon shirts can absorb ultraviolet radiation and re-emit it in the visible range (this is the "black light" effect in trendy nightclubs), etc. The white coating inside the neon tube is bombarded by electrons with energies corresponding to the ultraviolet range, but when they strike the materials making up the coating, they trigger re-emission in the visible spectrum. The coating is formulated so that the re-emitted light is as close as possible to visible light. But it's not quite perfect. That’s why the light from neon tubes seems so "strange" to you.
What’s important to remember is that bitemperature environments can exist. The reason for this situation is that the electric field present in the tube—due to the voltage applied to the electrodes—transfers energy primarily to the electrons, which then transfer it to the ions through collisions. However, because the energy transfer between the electron gas and the ion gas is inefficient, a large temperature difference can arise. This is especially due to the rarefied nature of the medium. If the tube leaks and pressure increases, this "nonequilibrium state" disappears immediately. The electron gas, now strongly coupled to the ions, cools down very rapidly. The electrons, less agitated (absolute temperature in a gas corresponds to the thermal agitation motion), calmly return to atoms, which then recombine and become neutral again.
The Z-machine experiment led to a very curious situation. Two species were present:
- The electron gas
- The ion gas (in stainless steel, mainly iron nuclei, positively charged)
Since 1998, when researchers tried to interpret their measurements, they had access only to electron temperature, by measuring the emitted X-rays. Why is the electron gas the main source of this radiation in these experiments? Because surrounding the plasma is a very strong magnetic field. When electrons, traveling at 40,000 km/s, enter this region of intense magnetic field, they spiral. Then they "scream"—they emit "bremsstrahlung radiation." It was by measuring these emitted X-rays that the experimenters determined the temperature of the electron gas: 35 million degrees in the experiments reported in this paper.
But using formulas (the "Bennett relation"), when they attempted to estimate the temperature that the iron ions must have in order to balance the enormous "magnetic pressure" outside the plasma, they found that it had to be significantly higher. Since 1998, regardless of the experiments conducted, this temperature difference between the two species was an undeniable fact. Such high values were necessary to prevent the plasma from being instantly crushed by magnetic pressure. This suggests a nonequilibrium state (at thermodynamic equilibrium, all species in a gaseous mixture have equal temperatures)—a bitemperature condition opposite to that in a neon tube, where this time it was the ion gas that was hotter than the electron gas.
A simple note: What creates this "thermodynamic equilibrium"? It's the exchange of energy between particles through collisions. Energy, for example, is kinetic energy: 1/2 m_i <v_i²>. Why the subscript i? Because a plasma is a mixture of different species. v_i is the thermal agitation velocity, and <v_i²> is the "mean square velocity." Thus, 1/2 m_i <v_i²> is the average kinetic energy in the species under consideration. This is precisely the definition of absolute temperature, which quantifies the average kinetic energy (of thermal agitation) of a given species, according to the relation:
(3/2) k T_i = 1/2 m_i <v_i²>
where k is Boltzmann's constant, equal to 1.38 × 10⁻²³.
In collisions, particles exchange energy. This process tends toward energy equipartition. When dealing purely with kinetic energy, different species tend to acquire equal thermal kinetic energies. Therefore, their absolute temperatures become equal:
T_i = T_j
Consider two particles of different masses, m_i and m_j, with i being the lighter one. Kinetic theory of gases tells us that the rate of kinetic energy transfer in a collision is proportional to the ratio 2 m_i / m_j. When masses are very different, the return to thermodynamic equilibrium becomes... laborious. This is why in a fluorescent tube, a pronounced nonequilibrium state can exist (electron temperature: 10,000 K, ion and neutral atom temperature: 300 K, ratio 33). The electric field re-accelerates electrons between collisions (ions, being too heavy, are hardly affected). This maintains the nonequilibrium state. If the field is switched off, the electron gas cools down extremely rapidly, at a...