What models are there for light in a plasma and in a lightning at thunder?
Maxwell's equations is not so easy to invoke in continuum mechanics.
Dear Lena,
I can answer the second part of your question.
The emission of light from thunderstorms was first investigated by Wilson in 1920s who associated the entire process with the runaway electrons accelerated in the strong electric field. The history of his research work with thunderstorms is outlined in the paper
http://onlinelibrary.wiley.com/doi/10.1029/2009JA014581/full
The modern explanation of the runaway breakdown mechanism is discussed at
http://www.phy.olemiss.edu/~jgladden/phys510/spring06/Gurevich.pdf
The problem of light emission from the thunderstorm is still an area of the active research.
Better understanding of thunderclouds and the global electric circuit of the atmosphere is one of the important elements of the future atmospheric models. I agree with your opinion that the application of the Maxwell equations in this case is not easy.
Kind regards,
Janusz
Dear Lena,
I can answer the second part of your question.
The emission of light from thunderstorms was first investigated by Wilson in 1920s who associated the entire process with the runaway electrons accelerated in the strong electric field. The history of his research work with thunderstorms is outlined in the paper
http://onlinelibrary.wiley.com/doi/10.1029/2009JA014581/full
The modern explanation of the runaway breakdown mechanism is discussed at
http://www.phy.olemiss.edu/~jgladden/phys510/spring06/Gurevich.pdf
The problem of light emission from the thunderstorm is still an area of the active research.
Better understanding of thunderclouds and the global electric circuit of the atmosphere is one of the important elements of the future atmospheric models. I agree with your opinion that the application of the Maxwell equations in this case is not easy.
Kind regards,
Janusz
There is a good model for light in plasma. See for example https://ocw.mit.edu/courses/nuclear-engineering/22-611j-introduction-to-plasma-physics-i-fall-2003/lecture-notes/chap5.pdf
Many thanks.
Mr White, It concerned interaction with dispersion, various ways(?)
Janusz. That said Cosmic rays, to be governing at thunder.
From a previous reference you gave, I found other applications where invoked in continuum mechanics. Freund, with entropic forces, beam optics and elastic fluid(not whirls, but the energy could have been due to rotation, also but the viscous coefficients in Navier-Stokes are for lin displacements) ,
that I quoted in a recent report relating to gait,
and one general about scalar measures for frequencies(in a usual continuum without whirls) and how they scale with size.c x
About thunder. It looks like cracking in anisotropic materials, at first, and then sometimes bifurcates into many, but it do not extend space permanently. Time scale for electron diffusion afterwards, is also measurable, and the speed in the rays, they say is 1/3 of c.
I was once very knowledgable about charge separation in cloud - at least the mechanisms that had been proposed and the data. Seems like we are still far from understanding that part of the process of generating lightning.
Continuum mechanics is of dubious value for breakdown problems. Inhomogeneities and fluctuations seem to dominate. An external factor like cosmic rays, as was mentioned seems promising.
It is assumed continuous, maybe valid for heaviside solution also.
There is a derivation giving breakdown or singularities for electromagnetism in elasticity, but I am not entirely familiar with the notation. I can attach.
Elasticity has wave solutions, longitudinal wave and torsional waves. In (D42), or all the equations in Appendix D, they show correspondence. The wave number is related to displacement, in a way. I think it could be done different ways, but this is conceptually interesting(!!??). It is more direct and without assuming an explicit solution to the waves in elasticity, and identify with that.
But I did not read all, and it may be the same thing, but I think not.
My general comment: The electromagnetic wave show discrete on matter, and such constraints are easily put, and gives solutions to nonlinear equations too.
Thank you for the article. I now see what you are talking about somewhat. Not sure how this lets me know about breakdown and catastrophic behavior. Nonlinear behavior out of QM is alway a bit of computational freewheeling. I mean that, while people get nonlinear effects from QM, since it is a totally linear theory, the computational approximations to get there are more of a matter of familiarly accepted practice than a clear consequence of the equation.
The "breakdown" in the article looks like breakdown of F-L theory not breakdown of a material under electrical strain. Also such theories are about condensed matter not gases or suspensions.
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