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:
“Only a great actor finds the difficulties of the actor’s art infinite.”
—Ellen Terry (1847–1928)
“All human beings hang by a thread, an abyss may open under their feet at any moment, and yet they have to go and invent all sorts of difficulties for themselves and spoil their lives.”
—Ivan Sergeevich Turgenev (1818–1883)
“This unlettered man’s speaking and writing are standard English. Some words and phrases deemed vulgarisms and Americanisms before, he has made standard American; such as “It will pay.” It suggests that the one great rule of composition—and if I were a professor of rhetoric I should insist on this—is, to speak the truth. This first, this second, this third; pebbles in your mouth or not. This demands earnestness and manhood chiefly.”
—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)
“... the ordinary is simply the universal observed from the surface, that the direct approach to reality is not without, but within. Touch life anywhere ... and you will touch universality wherever you touch the earth.”
—Ellen Glasgow (1873–1945)