Difficulties of The Standard Kinetic Approach
First, Vlasov argues that the standard kinetic approach based on the Boltzmann equation has difficulties when applied to a description of the plasma with long-range Coulomb interaction. He mentions the following problems arising when applying the kinetic theory based on pair collisions to plasma dynamics:
- Theory of pair collisions disagree with the discovery by Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma.
- Theory of pair collisions formally not applicable to Coulomb interaction due to the divergence of the kinetic terms.
- Theory of pair collisions cannot explain experiments by Harrison Merrill and Harold Webb on anomalous electron scattering in gaseous plasma.
Vlasov suggests that these difficulties originate from the long-range character of Coulomb interaction. He starts with the collisionless Boltzmann equation (sometimes anachronistically called the Vlasov equation in this context),
and adapted it to the case of a plasma, leading to the systems of equations shown below.
Read more about this topic: Vlasov Equation
Famous quotes containing the words difficulties of, difficulties, standard, kinetic and/or approach:
“If the underdog were always right, one might quite easily try to defend him. The trouble is that very often he is but obscurely right, sometimes only partially right, and often quite wrong; but perhaps he is never so altogether wrong and pig-headed and utterly reprehensible as he is represented to be by those who add the possession of prejudices to the other almost insuperable difficulties of understanding him.”
—Jane Addams (1860–1935)
“The intellectual life may be kept clean and healthful, if man will live the life of nature, and not import into his mind difficulties which are none of his.”
—Ralph Waldo Emerson (1803–1882)
“A dwarf who brings a standard along with him to measure his own size—take my word, is a dwarf in more articles than one.”
—Laurence Sterne (1713–1768)
“All my stories are webs of style and none seems at first blush to contain much kinetic matter.... For me “style” is matter.”
—Vladimir Nabokov (1899–1977)
“A novel which survives, which withstands and outlives time, does do something more than merely survive. It does not stand still. It accumulates round itself the understanding of all these persons who bring to it something of their own. It acquires associations, it becomes a form of experience in itself, so that two people who meet can often make friends, find an approach to each other, because of this one great common experience they have had ...”
—Elizabeth Bowen (1899–1973)