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Bernstein–Greene–Kruskal Modes
Bernstein–Greene–Kruskal modes (a.k.a. BGK modes) are nonlinear electrostatic waves that propagate in an unmagnetized, collisionless plasma. They are nonlinear solutions to the Vlasov–Poisson equation in plasma physics, and are named after physicists Ira B. Bernstein, John M. Greene, and Martin D. Kruskal, who solved and published the exact solution for the one-dimensional case in 1957. BGK modes have been studied extensively in numerical simulations for two- and three-dimensional cases, and are believed to be produced by the two-stream instability. They have been observed as electron phase space holes (electrostatic solitary structures) and double layers in space plasmas, as well as in scattering experiments in the laboratory. Small-amplitude limit: Van Kampen modes ? It is generally claimed that in the linear limit BGK modes (e.g. in the small amplitude approximation) reduce to what is known as Van Kampen modes, named after Nico van Kampen who derived the solution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bhatnagar–Gross–Krook Operator
The Bhatnagar–Gross–Krook operator (abbreviated BGK operator) term refers to a collision operator used in the Boltzmann equation and in the lattice Boltzmann method, a computational fluid dynamics technique. It is given by the following formula: :\Omega_i=-\tau^(n_i-n_i^) where n_i^ is a local equilibrium value for the population of particles in the direction of link \mathbf_i The term \tau is a relaxation time, and related to the viscosity. The operator is named after Prabhu L. Bhatnagar, Eugene P. Gross, and Max Krook, the three scientists who introduced it in a paper in ''Physical Review ''Physical Review'' is a peer-reviewed scientific journal established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical ...'' in 1954. References * Statistical mechanics Computational fluid dynamics {{compu-physics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrostatic Wave
In plasma physics, waves in plasmas are an interconnected set of particles and fields which propagate in a periodically repeating fashion. A plasma is a quasineutral, electrically conductive fluid. In the simplest case, it is composed of electrons and a single species of positive ions, but it may also contain multiple ion species including negative ions as well as neutral particles. Due to its electrical conductivity, a plasma couples to electric and magnetic fields. This complex of particles and fields supports a wide variety of wave phenomena. The electromagnetic fields in a plasma are assumed to have two parts, one static/equilibrium part and one oscillating/perturbation part. Waves in plasmas can be classified as electromagnetic or electrostatic according to whether or not there is an oscillating magnetic field. Applying Faraday's law of induction to plane waves, we find \mathbf\times\tilde=\omega\tilde, implying that an electrostatic wave must be purely longitudinal. An el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma (physics)
Plasma () 1, where \nu_ is the electron gyrofrequency and \nu_ is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are ''anisotropic'', meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the plasma high conductivity, the electric field associated with a plasma moving with velocity \mathbf in the magnetic field \mathbf is given by the usual Lorentz force, Lorentz formula \mathbf = -\mathbf\times\mathbf, and is not affected by Debye shielding. Mathematical descriptions To completely describe the state of a plasma, all of the particle locations and velocities that describe the electromagnetic field in the plasma region would need to be written down. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vlasov Equation
The Vlasov equation is a differential equation describing time evolution of the Distribution function (physics), distribution function of plasma (physics), plasma consisting of charged particles with long-range interaction, e.g. Coulomb's law, Coulomb. The equation was first suggested for description of plasma by Anatoly Vlasov in 1938 and later discussed by him in detail in a monograph. Difficulties of the standard kinetic approach First, Vlasov argues that the standard kinetic theory of gases, kinetic approach based on the Boltzmann equation has difficulties when applied to a description of the plasma with long-range Coulomb's law, Coulomb interaction. He mentions the following problems arising when applying the kinetic theory based on pair collisions to plasma dynamics: # Theory of pair collisions disagrees with the discovery by John Strutt, 3rd Baron Rayleigh, Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma. # Theory of pair collisions is formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma Physics
Plasma ()πλάσμα , Henry George Liddell, Robert Scott, ''A Greek English Lexicon'', on Perseus is one of the . It contains a significant portion of charged particles – s and/or s. The presence of these charged particles is what primarily sets plasma apart from the other fundamental states of matter. It is the most abundant form of |
Ira B
Ira or IRA may refer to: *Ira (name), a Hebrew, Sanskrit, Russian or Finnish language personal name * Ira (surname), a rare Estonian and some other language family name *Iran, UNDP code IRA Law *Indian Reorganization Act of 1934, US, on status of Native Americans *Individual retirement account, in the US, giving tax benefits *Inflation Reduction Act of 2022, a US budget reconciliation bill *Internal Revenue Allotment, a local share of Philippines government revenue Music *Ira (Polish band), a Polish heavy metal band *Ira!, a Brazilian rock band * I.R.A. (band), a Colombian punk band *One part of an Andean wind instrument, the siku Organizations * Indian Reunification Association * Indian Rationalist Association * Indian Rights Association, US, for Native Americans * Initiative for the Resurgence of the Abolitionist Movement (IRA), a Mauritania anti-slavery group * Insurance Regulatory Authority (Kenya), the authority charged with regulation and supervision of Kenya's insurance i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John M
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin David Kruskal
Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His most celebrated contribution was in the theory of solitons. He was a student at the University of Chicago and at New York University, where he completed his Ph.D. under Richard Courant in 1952. He spent much of his career at Princeton University, as a research scientist at the Plasma Physics Laboratory starting in 1951, and then as a professor of astronomy (1961), founder and chair of the Program in Applied and Computational Mathematics (1968), and professor of mathematics (1979). He retired from Princeton University in 1989 and joined the mathematics department of Rutgers University, holding the David Hilbert Chair of Mathematics. Apart from serious mathematical work, Kruskal was k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-stream Instability
The two-stream instability is a very common instability in plasma physics. It can be induced by an energetic particle stream injected in a plasma, or setting a current along the plasma so different species (ions and electrons) can have different drift velocities. The energy from the particles can lead to plasma wave excitation. Two-stream instability can arise from the case of two cold beams, in which no particles are resonant with the wave, or from two hot beams, in which there exist particles from one or both beams which are resonant with the wave. Two-stream instability is known in various limiting cases as beam-plasma instability, beam instability, or bump-on-tail instability. Dispersion relation in cold-beam limit Consider a cold, uniform, and unmagnetized plasma, where ions are stationary and the electrons have velocity v_0, that is, the reference frame is moving with the ion stream. Let the electrostatic waves be of the form: \mathbf_1 = \xi_1 \exp (kx - \omega t)\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Layer (plasma Physics)
A double layer is a structure in a plasma consisting of two parallel layers of opposite electrical charge. The sheets of charge, which are not necessarily planar, produce localised excursions of electric potential, resulting in a relatively strong electric field between the layers and weaker but more extensive compensating fields outside, which restore the global potential. Ions and electrons within the double layer are accelerated, decelerated, or deflected by the electric field, depending on their direction of motion. Double layers can be created in discharge tubes, where sustained energy is provided within the layer for electron acceleration by an external power source. Double layers are claimed to have been observed in the aurora and are invoked in astrophysical applications. Similarly, a double layer in the auroral region requires some external driver to produce electron acceleration. Electrostatic double layers are especially common in current-carrying plasmas, and are ver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nico Van Kampen
Nicolaas 'Nico' Godfried van Kampen (June 22, 1921 – October 6, 2013) was a Dutch theoretical physicist, who worked mainly on statistical mechanics and non-equilibrium thermodynamics. Van Kampen was born in Leiden, and was a nephew of Frits Zernike. He studied physics at Leiden University, where in 1952 under the direction of Hendrik Anthony Kramers he earned his PhD with thesis ''Contributions to the quantum theory of light scattering''. He showed in his thesis how to deal with singularities in quantum mechanical scattering processes, an important step in the development of renormalization, according to Kramers. Van Kampen made fundamental contributions to non-equilibrium processes (in particular on the master equation) and in many-body theory (especially in plasma physics). His work on non-equilibrium processes began in 1953 in the research group of Sybren Ruurds de Groot (the successor to Kramers) in Leiden. In 1955 Van Kampen joined the Institute of Theoretical Physics at Utr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
