by Higgsy » Wed Dec 30, 2020 6:53 pm
paladin17 wrote: ↑Tue Dec 29, 2020 11:36 am
Let's make some estimates.
Based on
this we may assume that the charge of the Sun due to ambipolar diffusion is some tens of coulombs. Therefore, if we suppose that there is a spherical double layer with this charge and of the thickness d, we get V = kQd/R^2, where k is the constant (1/4*Pi etc.), V is the total voltage between the two layers, and R is the distance of the layer from the Sun's center (roughly equal to the radius of the Sun itself) - we also assume d << R, obviously.
Therefore, V/d = kQ/R^2, which gives us the field of only about 10^(-6) V/m in the double layer. I have no problems believing such a field may exist, though whether it would be enough to produce the runaway electron population is pretty doubtful. I'd have to find the exact expression of the needed ratio. It is also possible that in case of the field being confined to a thin DL the solar charge would need to be bigger than the estimate given in the cited paper, which would make the field stronger.
I also have no trouble believing that a field of that magnitude might exist, but it's too low by four orders of magnitude to reach the Dreicer field in the corona (which I make ~15mV/m assuming n=10^16 m^-3, T=2 x 10^6K, and lnΛ=10).
I want to think about differential diffusion of the two electron populations across the transition zone which have a different temperature by a factor of 10^3 at least (assuming plasma is collisional on both sides, the ion and electron temperatures are in equilibrium (doubtful?) and yadda, yadda), which would set up a double layer with a potential drop of some 10s of volts (see
here and
here), φ = kT/2e, say ~86V based on assumptions above. If the DL thickness is less than about 5km the field will exceed the Dreicer limit. 100 x Debye lengths in the corona is about 0.1m so there is a lot of scope for a field much higher than the Dreicer limit in the corona, even with this back of a postage stamp estimate.
The problem is the location of this double layer as the DL potential goes with temperature while the Dreicer field goes with the inverse of temperature and goes with number density, so if we locate the DL in the transition zone, it becomes much more difficult to explain suprathermal electrons by a DL. It works better if we take the coronal electron temperature to be higher than the ion temperature.
[quote=paladin17 post_id=4095 time=1609241762 user_id=29470]
Let's make some estimates.
Based on [url=https://www.aanda.org/articles/aa/full/2001/24/aah2649/aah2649.html]this[/url] we may assume that the charge of the Sun due to ambipolar diffusion is some tens of coulombs. Therefore, if we suppose that there is a spherical double layer with this charge and of the thickness d, we get V = kQd/R^2, where k is the constant (1/4*Pi etc.), V is the total voltage between the two layers, and R is the distance of the layer from the Sun's center (roughly equal to the radius of the Sun itself) - we also assume d << R, obviously.
Therefore, V/d = kQ/R^2, which gives us the field of only about 10^(-6) V/m in the double layer. I have no problems believing such a field may exist, though whether it would be enough to produce the runaway electron population is pretty doubtful. I'd have to find the exact expression of the needed ratio. It is also possible that in case of the field being confined to a thin DL the solar charge would need to be bigger than the estimate given in the cited paper, which would make the field stronger.
[/quote]
I also have no trouble believing that a field of that magnitude might exist, but it's too low by four orders of magnitude to reach the Dreicer field in the corona (which I make ~15mV/m assuming n=10^16 m^-3, T=2 x 10^6K, and lnΛ=10).
I want to think about differential diffusion of the two electron populations across the transition zone which have a different temperature by a factor of 10^3 at least (assuming plasma is collisional on both sides, the ion and electron temperatures are in equilibrium (doubtful?) and yadda, yadda), which would set up a double layer with a potential drop of some 10s of volts (see [url=http://articles.adsabs.harvard.edu//full/1978Ap%26SS..55...59B/0000067.000.html]here[/url] and [url=https://aip.scitation.org/doi/abs/10.1063/1.865390]here[/url]), φ = kT/2e, say ~86V based on assumptions above. If the DL thickness is less than about 5km the field will exceed the Dreicer limit. 100 x Debye lengths in the corona is about 0.1m so there is a lot of scope for a field much higher than the Dreicer limit in the corona, even with this back of a postage stamp estimate.
The problem is the location of this double layer as the DL potential goes with temperature while the Dreicer field goes with the inverse of temperature and goes with number density, so if we locate the DL in the transition zone, it becomes much more difficult to explain suprathermal electrons by a DL. It works better if we take the coronal electron temperature to be higher than the ion temperature.