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 the, difficulties of, difficulties, standard, kinetic and/or approach:
“So far as my experience goes, travelers generally exaggerate the difficulties of the way. Like most evil, the difficulty is imaginary; for what’s the hurry?”
—Henry David Thoreau (1817–1862)
“Only a great actor finds the difficulties of the actor’s art infinite.”
—Ellen Terry (1847–1928)
“It appeared that he had once represented his tribe at Augusta, and also once at Washington, where he had met some Western chiefs. He had been consulted at Augusta, and gave advice, which he said was followed, respecting the eastern boundary of Maine, as determined by highlands and streams, at the time of the difficulties on that side. He was employed with the surveyors on the line. Also he called on Daniel Webster in Boston, at the time of his Bunker Hill oration.”
—Henry David Thoreau (1817–1862)
“Where shall we look for standard English but to the words of a standard man?”
—Henry David Thoreau (1817–1862)
“The poem has a social effect of some kind whether or not the poet wills it to have. It has kinetic force, it sets in motion ... [ellipsis in source] elements in the reader that would otherwise be stagnant.”
—Denise Levertov (b. 1923)
“A lady with whom I was riding in the forest said to me that the woods always seemed to her to wait, as if the genii who inhabit them suspend their deeds until the wayfarer had passed onward; a thought which poetry has celebrated in the dance of the fairies, which breaks off on the approach of human feet.”
—Ralph Waldo Emerson (1803–1882)