CC: Yes. What I’m wondering is how we conclude that this is E.D. I think that it is, but I’m not sure that what I’m thinking is what others are thinking. First, I’m questioning how we determine the temperature. Am I right in thinking that this is entirely based on degree of ionization, where we expect hotter plasma to be more highly ionized? If so, we should consider that there is another factor that can cause ionization: electric fields. So the conclusion that these are iron lines at 1 MK might not be correct. In fact, I’m wondering if ALL of the temperatures might be incorrect, as none of them take electric fields into account. So the temps might be far lower, and this might be evidence of electric fields. What do you guys think?
MM: You’re on to something as it relates to the temperature of the WHOLE corona and the WHOLE chromosphere. They don’t have to reach the same temperatures as the current carrying loops. Thompson scattering happens in plasma. While the loops are the actual light source, that light will in fact be scattered and absorbed by surrounding plasma. The loops themselves however are HOT HOT HOT IMO. They are like ordinary electrical discharges in the Earths atmosphere in terms of the way they heat plasma.
CharlesChandler wrote:I think that something is wrong with the way we're estimating temperatures. Electric arcs can certainly get hot, as there is no theoretical limit to the temperature that can be generated by electron streams. But there are very definitely practical limits.
Most of what I know comes from the study of lightning here on Earth, so I'll begin there. Air is an insulator, so voltages can build up without there being a discharge. But above 3 MV/m (at STP), we see dielectric breakdown, and an arc discharge begins. The loss of the insulating capacity of the air is a consequence of heat that was generated by the flow of an electric current below the threshold for lightning (in glow or dark discharge mode). The current heats the air, which causes it to expand. The less dense air has less electrical resistance. This allows the current to flow more easily. More current means more ohmic heating, which causes the air to expand even more, which further reduces the resistance, which enables even more current. The next thing that happens is an arc discharge.
The temperature within the discharge channel is relatively consistent, the main body of which is about 2500 K (though there are much higher temps caused by other processes that we can neglect for our purposes). This is also roughly the average sustained temperature of EDM. The reason for the consistency of the temperature is that it is self-limiting. Once the discharge gets going, the more current that flows, the more heat is generated. But the heat causes the plasma to expand, which reduces its resistance. With less resistance, there is less ohmic heating. So excess temps simply create a wider discharge channel, with the same current density per unit of sectional area.
CharlesChandler wrote:The thing that actually determines the average sustained temperature within the discharge channel is the surrounding atmospheric pressure. The degree to which the ambient pressure resists the expansion of the discharge channel determines the amount of ohmic heating inside the channel. If the ambient pressure is less, the discharge channel expands more easily. In a higher-pressure atmosphere, the discharge channel cannot expand as much, and with higher-density plasma inside the channel, there is more ohmic heating. So the atmospheric pressure determines the temperature of an arc discharge.
Since these are physical laws that should apply everywhere in the Universe, we can then wonder what this means for our study of arc discharges in the Sun. At the top of the photosphere, the density of the plasma drops below that of the Earth's atmosphere at STP. In the extremely thin chromosphere and corona, the density is way, way below the Earth's atmosphere.
This means that arc discharges should be way cooler than 2500 K. We might see instantaneous surges in temperature, as the discharge begins, and the ohmic heating shoots up faster than the plasma can expand. But the average sustained temps should stabilize based on ambient pressure.
This is interesting because in the corona, we're measuring temps in excess of 1 MK, when it shouldn't have the density for discharges above 1 K. This has led some people to conclude that those aren't arc discharges, and they went looking for something else, such as "magnetic reconnection" that somehow generates unbelievable temperatures in some sort of poorly-understood process.
Actually, they ARE arc discharges, but the way we measure temperature needs a second look. In fact, we haven't sent thermometers in there to get the measurements. So how do we conclude that the corona is running at 1 MK?
This we do on the basis of the degree of ionization. Hotter plasma atoms, bouncing around faster, can hold onto fewer electrons. Then we get distinctive photons when electrons pass by, depending on the available electron shells. (The relationship of temperature to ionization is so direct that temperatures are sometimes reported in electron-volts, where each eV = 11,605 K.)Yet temperature isn't the only thing that can cause ionization. Electric fields can also do this. Hence the degree of ionization is only a direct index of temperature if there is no electric field. If there is an electric field, you have to take that into account as well, and nobody is doing that. So when Alfven tells us that there is 1.6 GV of potential, and when we see photons indicating 100 eV of ionization, we shouldn't conclude that the temps are in the 1 MK range. Rather, we should conclude that the electric field has ionized the plasma, and the electric current is actually flowing through relatively cool plasma. This means that the coronal heating problem isn't actually a problem at all -- it was just poorly interpreted data. If we take the electric field between the Sun and the heliosphere into account, everything makes more sense.
Michael said: FYI, Lloyd, while I missed the online meeting last night, I did add some considerable content to the discussion which you're welcome to add here if you like.
CC: As concerns the difference between typical negative glows and typical anode tufts, I’m thinking that if we take the stringy plasma in a negative glow, and subject it to an enormous gravitational and electric force, such that it clings tightly to the negative electrode, we’ll get the kind of “tufting” that would be somewhat more typical at the anode.
MM: I think you will also need to consider the effects of plasma separation on plasma layer emissions.
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