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:
“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)
“I often think that all the difficulties we encounter only give us the more strength if we keep hold of our work, and we must not now give up while in the prime of life. It is best to keep trying, and by and by the opportunity will come. If we have given up, then we shall not be ready for it when it does come.”
—Ellen Henrietta Swallow Richards (1842–1911)
“Gentlemen, those confederate flags and our national standard are what has made this union great. In what other country could a man who fought against you be permitted to serve as judge over you, be permitted to run for reelection and bespeak your suffrage on Tuesday next at the poles.”
—Laurence Stallings (1894–1968)
“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)
“Do not approach with anything even resembling assurance a restaurant that moves.”
—Fran Lebowitz (b. 1950)