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What does "At an ion temperature of about 40 million degrees" mean? How does "ion temperature" relate to "regular" temperature? Is it similar to how we can co

What does "At an ion temperature of about 40 million degrees" mean? How does "ion temperature" relate to "regular" temperature? Is it similar to how we can cool down things to fractions above absolute zero, by using lasers to reduce the movement of atoms? i.e. is the "ion temperature" a measure of how fast are they moving, as opposed to the every-day meaning of temperature as "how hot something is"? I realize that "how hot something is" depends on how fast the atoms of said "something" are moving, but since they specify "ion temperature" I'm guessing it has a very specific meaning. I searched for "ion temperature" but only found about Electron temperature [0]. Could someone explain it to me in lay terms? :) [0] https://en.wikipedia.org/wiki/Electron_temperature https://en.wikipedia.org/wiki/Electron_temperature

Certhas 8y ago
In a plasma electrons and ions can have very different temperatures: "[...] the ion temperature may be very different from (usually lower than) the electron temperature" https://en.wikipedia.org/wiki/Plasma_(physics)#Temperature https://en.wikipedia.org/wiki/Plasma_(physics)#Temperature
- saganus 8y ago
  Oh, that's interesting. From that Wikipedia article: "For this reason, the ion temperature may be very different from (usually lower than) the electron temperature." So if the ion temperature of the plasma in the Wendelstein 7-X is about 40 million degrees...the electron temperature could be even higher? What does it even mean to have a temperature of 40 million degrees? AFAIU, the Sun has temperatures much lower than that. That's utterly mind blowing...
  - wolf550e 8y ago
    The core of the sun is 15 million Kelvin [1]. The surface temperature of the sun is approximately 5,778 K (5,505 °C, 9,941 °F) [2]. I can guess what the insane pressure means ("estimated at 265 billion bar (3.84 trillion psi or 26.5 petapascals (PPa))"), but I don't know what millions Kelvin means. It should be kinetic energy. So maybe it means the ions vibrate very fast? 1 - https://en.wikipedia.org/wiki/Solar_core https://en.wikipedia.org/wiki/Solar_core 2 - https://en.wikipedia.org/wiki/Sun#Sunlight https://en.wikipedia.org/wiki/Sun#Sunlight
    - wolfram74 8y ago
      if it were a solid, vibration would be a reasonable guess, but unbound particles, the primary form of kinetic energy is basic translational movement, like a baseball's got most of it's kinetic energy in moving from the mound to the batter and a bit of it in how it's spinning.
      - sounds 8y ago
        Keep in mind the mean free path of translational movement, even at those very high pressures, is quite large relative to the size of a proton (even more so an electron).
    - contact_fusion 8y ago
      High energy density systems are quite hard to develop an intuition for. While average kinetic energy is one way to think about temperature, think about it instead in terms of the Maxwellian particle distribution [1]. In this sense, the Maxwellian is a parameter of this distribution, and as it increases, the location of the distribution changes. A high temperature corresponds to, in this hypothetical system, more particles with higher velocities in the system. (This technically only applies to certain systems in which the assumptions hold. For example, in systems in which other degrees of freedom matter, such as vibration/rotation of molecules, the interpretation is harder. At high temperatures, these degrees of freedom are destroyed, though others, like ionization, can matter significantly.) Of course, these systems are highly collisional, in the sense that each particle will probably go only a short distance before Coulomb scattering off another particle. So the particles are not really vibrating; the energy is in translational motion, but in the mean, there is no real directionality to it, so the particles won't typically stream out of the plasma. This can be readily understood in the context of achieving controlled fusion. Nuclei are positively charged, and therefore exert forces that tend to repel them away from other nuclei. The nuclear scale, at which nuclear reactions must occur, is very small, and the 1/r* Coulomb potential is quite large at those distances. As a result, it is to be expected that an individual fusion reaction should only occur when the kinetic energy of an incoming nucleus is sufficiently strong to overcome the Coulomb barrier. (Practically, quantum mechanics effectively reduces the barrier through tunneling, but nevertheless it is quite high.) As a result, you need a sufficiently large number of nuclei with high speed to have an appreciable fusion rate, i.e. your temperature must be high enough. (Hence, "thermonuclear" fusion.) This has to be contrasted with your confinement quality, in the sense that you have to keep your fuel at that temperature and at a sufficient density (so that your collision rate is high enough) long enough for fusion burn to consume an appreciable fraction of your fuel. In context, the temperature seems a simpler quantity to discuss rather than the pressure. It is easier to conceive of this pressure as a momentum flux, and in stars, gravitational confinement demands that the plasma pressure balance the crushing momentum flux of the weight of the star. Such static pressures are simply outside of our ability to intuit, and result in quite counterintuitive properties of matter. [1] https://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution https://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution *edit: inverse square is the force, the potential goes as 1/r... update for clarity.
Obi_Juan_Kenobi 8y ago
Ion temperature is the important metric because it is ions that do the fusion, not electrons. The sun has immense gravity and mass that produce very high pressures which permit fusion at 'low' temperatures. Maintaining high plasma pressure is difficult on Earth, so higher temperatures are used. Temperature is fairly well understood as simply the average kinetic energy of the particles of whatever you're measuring. For more nuance, start here: https://en.wikipedia.org/wiki/Temperature#Theoretical_foundation https://en.wikipedia.org/wiki/Temperature#Theoretical_founda...
contact_fusion 8y ago
Other replies have explained that the ions and electrons can be at different temperatures, and that is of course true. I can offer some more explanation why. While you have linked temperature to some average kinetic energy, this is not a strictly accurate notion of temperature. Temperature only means something in the context of thermodynamic equilibrium; for any system out of equilibrium, often a temperature cannot be defined, even as an average kinetic energy. The two concepts are linked to each other, in the sense that an average kinetic energy at the particle scale is a significant (and sometimes only, but not always) component of the internal energy of the system. But temperature is first and foremost an equilibrium concept. A plasma is composed of both ions (partially ionized atoms, or if they are fully ionized, bare nuclei) and electrons. Together, they constitute two co-located but separate fluids, whose motions may be distinct; indeed, because electrons are so much lighter than ions, they respond to forces much more readily. In equilibrium, a single fluid must have sufficiently rapid interactions so that the particle distributions are driven to a Maxwellian. In that case, for a single fluid, a temperature is well defined. In the case of a two-fluid system, self-interactions (such as interactions between ions and themselves, and electrons and themselves) may be sufficient to establish two separate equilibria corresponding to each fluid; hence, the electron vs. ion temperature. Only in the case that ion-electron interactions are sufficiently rapid would those equilibria be driven together to a single-temperature fluid, in which case, Te = Ti. This picture becomes rapidly more complicated at very high temperature (usually, around 0.1 keV or about a million K), at which point the photons being exchanged by hot charged particles become dynamically important, and a third temperature, the radiation temperature, may emerge. At this point, the plasma must be described using three temperatures - if, and only if, you are in a situation lucky enough for equilibrium to manifest. (Fortunately, equilibrium is not usually that hard to access.) In many cases, such as when the system undergoes a strong shock, the system may be driven very far from equilibrium, but only temporarily. In others, some underlying energetic process may continuously drive the system away from equilibrium, resulting in a metastable state; this is the case in stellar atmospheres, in which NLTE (non-local thermodynamic equilibrium) processes matter a great deal. Usually, physicists resort to kinetic theory to try to understand such situations.
- saganus 8y ago
  Awesome explanation! Thanks a lot. It's amazing how something seemingly simple as "temperature" can be so counter-intuitive.

Certhas 8y ago

In a plasma electrons and ions can have very different temperatures: "[...] the ion temperature may be very different from (usually lower than) the electron temperature" https://en.wikipedia.org/wiki/Plasma_(physics)#Temperature https://en.wikipedia.org/wiki/Plasma_(physics)#Temperature

saganus 8y ago
Oh, that's interesting. From that Wikipedia article: "For this reason, the ion temperature may be very different from (usually lower than) the electron temperature." So if the ion temperature of the plasma in the Wendelstein 7-X is about 40 million degrees...the electron temperature could be even higher? What does it even mean to have a temperature of 40 million degrees? AFAIU, the Sun has temperatures much lower than that. That's utterly mind blowing...
- wolf550e 8y ago
  The core of the sun is 15 million Kelvin [1]. The surface temperature of the sun is approximately 5,778 K (5,505 °C, 9,941 °F) [2]. I can guess what the insane pressure means ("estimated at 265 billion bar (3.84 trillion psi or 26.5 petapascals (PPa))"), but I don't know what millions Kelvin means. It should be kinetic energy. So maybe it means the ions vibrate very fast? 1 - https://en.wikipedia.org/wiki/Solar_core https://en.wikipedia.org/wiki/Solar_core 2 - https://en.wikipedia.org/wiki/Sun#Sunlight https://en.wikipedia.org/wiki/Sun#Sunlight
  - wolfram74 8y ago
    if it were a solid, vibration would be a reasonable guess, but unbound particles, the primary form of kinetic energy is basic translational movement, like a baseball's got most of it's kinetic energy in moving from the mound to the batter and a bit of it in how it's spinning.
    - sounds 8y ago
      Keep in mind the mean free path of translational movement, even at those very high pressures, is quite large relative to the size of a proton (even more so an electron).
  - contact_fusion 8y ago
    High energy density systems are quite hard to develop an intuition for. While average kinetic energy is one way to think about temperature, think about it instead in terms of the Maxwellian particle distribution [1]. In this sense, the Maxwellian is a parameter of this distribution, and as it increases, the location of the distribution changes. A high temperature corresponds to, in this hypothetical system, more particles with higher velocities in the system. (This technically only applies to certain systems in which the assumptions hold. For example, in systems in which other degrees of freedom matter, such as vibration/rotation of molecules, the interpretation is harder. At high temperatures, these degrees of freedom are destroyed, though others, like ionization, can matter significantly.) Of course, these systems are highly collisional, in the sense that each particle will probably go only a short distance before Coulomb scattering off another particle. So the particles are not really vibrating; the energy is in translational motion, but in the mean, there is no real directionality to it, so the particles won't typically stream out of the plasma. This can be readily understood in the context of achieving controlled fusion. Nuclei are positively charged, and therefore exert forces that tend to repel them away from other nuclei. The nuclear scale, at which nuclear reactions must occur, is very small, and the 1/r* Coulomb potential is quite large at those distances. As a result, it is to be expected that an individual fusion reaction should only occur when the kinetic energy of an incoming nucleus is sufficiently strong to overcome the Coulomb barrier. (Practically, quantum mechanics effectively reduces the barrier through tunneling, but nevertheless it is quite high.) As a result, you need a sufficiently large number of nuclei with high speed to have an appreciable fusion rate, i.e. your temperature must be high enough. (Hence, "thermonuclear" fusion.) This has to be contrasted with your confinement quality, in the sense that you have to keep your fuel at that temperature and at a sufficient density (so that your collision rate is high enough) long enough for fusion burn to consume an appreciable fraction of your fuel. In context, the temperature seems a simpler quantity to discuss rather than the pressure. It is easier to conceive of this pressure as a momentum flux, and in stars, gravitational confinement demands that the plasma pressure balance the crushing momentum flux of the weight of the star. Such static pressures are simply outside of our ability to intuit, and result in quite counterintuitive properties of matter. [1] https://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution https://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution *edit: inverse square is the force, the potential goes as 1/r... update for clarity.

Obi_Juan_Kenobi 8y ago

Ion temperature is the important metric because it is ions that do the fusion, not electrons. The sun has immense gravity and mass that produce very high pressures which permit fusion at 'low' temperatures. Maintaining high plasma pressure is difficult on Earth, so higher temperatures are used. Temperature is fairly well understood as simply the average kinetic energy of the particles of whatever you're measuring. For more nuance, start here: https://en.wikipedia.org/wiki/Temperature#Theoretical_foundation https://en.wikipedia.org/wiki/Temperature#Theoretical_founda...

contact_fusion 8y ago

Other replies have explained that the ions and electrons can be at different temperatures, and that is of course true. I can offer some more explanation why. While you have linked temperature to some average kinetic energy, this is not a strictly accurate notion of temperature. Temperature only means something in the context of thermodynamic equilibrium; for any system out of equilibrium, often a temperature cannot be defined, even as an average kinetic energy. The two concepts are linked to each other, in the sense that an average kinetic energy at the particle scale is a significant (and sometimes only, but not always) component of the internal energy of the system. But temperature is first and foremost an equilibrium concept. A plasma is composed of both ions (partially ionized atoms, or if they are fully ionized, bare nuclei) and electrons. Together, they constitute two co-located but separate fluids, whose motions may be distinct; indeed, because electrons are so much lighter than ions, they respond to forces much more readily. In equilibrium, a single fluid must have sufficiently rapid interactions so that the particle distributions are driven to a Maxwellian. In that case, for a single fluid, a temperature is well defined. In the case of a two-fluid system, self-interactions (such as interactions between ions and themselves, and electrons and themselves) may be sufficient to establish two separate equilibria corresponding to each fluid; hence, the electron vs. ion temperature. Only in the case that ion-electron interactions are sufficiently rapid would those equilibria be driven together to a single-temperature fluid, in which case, Te = Ti. This picture becomes rapidly more complicated at very high temperature (usually, around 0.1 keV or about a million K), at which point the photons being exchanged by hot charged particles become dynamically important, and a third temperature, the radiation temperature, may emerge. At this point, the plasma must be described using three temperatures - if, and only if, you are in a situation lucky enough for equilibrium to manifest. (Fortunately, equilibrium is not usually that hard to access.) In many cases, such as when the system undergoes a strong shock, the system may be driven very far from equilibrium, but only temporarily. In others, some underlying energetic process may continuously drive the system away from equilibrium, resulting in a metastable state; this is the case in stellar atmospheres, in which NLTE (non-local thermodynamic equilibrium) processes matter a great deal. Usually, physicists resort to kinetic theory to try to understand such situations.

saganus 8y ago
Awesome explanation! Thanks a lot. It's amazing how something seemingly simple as "temperature" can be so counter-intuitive.