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)
“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)
“Any honest examination of the national life proves how far we are from the standard of human freedom with which we began. The recovery of this standard demands of everyone who loves this country a hard look at himself, for the greatest achievments must begin somewhere, and they always begin with the person. If we are not capable of this examination, we may yet become one of the most distinguished and monumental failures in the history of nations.”
—James Baldwin (1924–1987)
“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 modern world needs people with a complex identity who are intellectually autonomous and prepared to cope with uncertainty; who are able to tolerate ambiguity and not be driven by fear into a rigid, single-solution approach to problems, who are rational, foresightful and who look for facts; who can draw inferences and can control their behavior in the light of foreseen consequences, who are altruistic and enjoy doing for others, and who understand social forces and trends.”
—Robert Havighurst (20th century)