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Vlasov Equation
In plasma physics, the Vlasov equation is a differential equation describing time evolution of the distribution function of collisionless plasma consisting of charged particles with long-range interaction, such as the Coulomb interaction. The equation was first suggested for the description of plasma by Anatoly Vlasov in 1938 and later discussed by him in detail in a monograph. The Vlasov equation, combined with Landau kinetic equation describe collisional plasma. 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 disagrees with the discovery by Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma. # Theory of pair collisi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma (physics)
Plasma () is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including the Sun), but also dominating the rarefied intracluster medium and Outer space#Intergalactic space, intergalactic medium. Plasma can be artificially generated, for example, by heating a neutral gas or subjecting it to a strong electromagnetic field. The presence of charged particles makes plasma electrically conductive, with the dynamics of individual particles and macroscopic plasma motion governed by collective electromagnetic fields and very sensitive to externally applied fields. The response of plasma to electromagnetic fields is used in many modern devices and technologies, such as plasma display, plasma televisions or plasma etching. Depending on temperature and density, a certain number of neutral particles may also be present, in wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae for solutions of partial differential equations. There is correspondingly a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity and stability. Among the many open questions are the existence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau Damping
In physics, Landau damping, named after its discoverer,Landau, L. "On the vibration of the electronic plasma". ''JETP'' 16 (1946), 574. English translation in ''J. Phys. (USSR)'' 10 (1946), 25. Reproduced in Collected papers of L.D. Landau, edited and with an introduction by D. ter Haar, Pergamon Press, 1965, pp. 445–460; and in Men of Physics: L.D. Landau, Vol. 2, Pergamon Press, D. ter Haar, ed. (1965). Soviet Union, Soviet physicist Lev Landau, Lev Davidovich Landau (1908–68), is the effect of Damping ratio, damping (exponential decay, exponential decrease as a function of time) of plasma oscillation, longitudinal space charge waves in Plasma (physics), plasma or a similar environment.Chen, Francis F. ''Introduction to Plasma Physics and Controlled Fusion''. Second Ed., 1984 Plenum Press, New York. This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space. It was later argued by Donald Lynden-Bell that a similar phenomeno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permittivity
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor. In the simplest case, the electric displacement field resulting from an applied electric field E is \mathbf = \varepsilon\ \mathbf ~. More generally, the permittivity is a thermodynamic State function, function of state. It can depend on the Dispersion (optics), frequency, Nonlinear optics, magnitude, and Anisotropy, direction of the applied field. The International System of Units, SI unit for permittivity is farad per meter (F/m). The permittivity is often represented by the relative permittivity which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Charge
Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and unlike charges attract each other. An object with no net charge is referred to as neutral particle, electrically neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum mechanics, quantum effects. In an isolated system, the total charge stays the same - the amount of positive charge minus the amount of negative charge does not change over time. Electric charge is carried by subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the atomic nucleus, nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Potential
Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physics), work needed to move a test charge from a reference point to a specific point in a static electric field. The test charge used is small enough that disturbance to the field is unnoticeable, and its motion across the field is supposed to proceed with negligible acceleration, so as to avoid the test charge acquiring kinetic energy or producing radiation. By definition, the electric potential at the reference point is zero units. Typically, the reference point is Earth (electricity), earth or a point at infinity, although any point can be used. In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar (physics), scalar quantity denoted by or occasi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Field
An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) describes their capacity to exert attractive or repulsive forces on another charged object. Charged particles exert attractive forces on each other when the sign of their charges are opposite, one being positive while the other is negative, and repel each other when the signs of the charges are the same. Because these forces are exerted mutually, two charges must be present for the forces to take place. These forces are described by Coulomb's law, which says that the greater the magnitude of the charges, the greater the force, and the greater the distance between them, the weaker the force. Informally, the greater the charge of an object, the stronger its electric field. Similarly, an electric field is stronger nearer charged objects and weaker f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson's Equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson who published it in 1823. Statement of the equation Poisson's equation is \Delta\varphi = f, where \Delta is the Laplace operator, and f and \varphi are real or complex-valued functions on a manifold. Usually, f is given, and \varphi is sought. When the manifold is Euclidean space, the Laplace operator is often denoted as , and so Poisson's equation is frequently written as \nabla^2 \varphi = f. In three-dimensional Cartesian coordinates, it takes the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of second. The speed of light is invariant (physics), the same for all observers, no matter their relative velocity. It is the upper limit for the speed at which Information#Physics_and_determinacy, information, matter, or energy can travel through Space#Relativity, space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. Much starlight viewed on Earth is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When Data communication, comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Charge
The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . In SI units, the coulomb is defined such that the value of the elementary charge is exactly or 160.2176634 zeptocoulombs (zC). Since the 2019 revision of the SI, the seven SI base units are defined in terms of seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from blackb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Position (vector)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point ''P'' in space. Its length represents the distance in relation to an arbitrary reference origin ''O'', and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from ''O'' to ''P''. In other words, it is the displacement or translation that maps the origin to ''P'': :\mathbf=\overrightarrow. The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus. Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.Keller, F. J., Gettys, W. E. et al. (1993), p. 28–29. Relative position The relative position of a point ''Q'' with respect to point ''P'' is the Euclidean vector res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up quark, up and down quark, down quarks. Electrons are extremely lightweight particles that orbit the positively charged atomic nucleus, nucleus of atoms. Their negative charge is balanced by the positive charge of protons in the nucleus, giving atoms their overall electric charge#Charge neutrality, neutral charge. Ordinary matter is composed of atoms, each consisting of a positively charged nucleus surrounded by a number of orbiting electrons equal to the number of protons. The configuration and energy levels of these orbiting electrons determine the chemical properties of an atom. Electrons are bound to the nucleus to different degrees. The outermost or valence electron, valence electrons are the least tightly bound and are responsible for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
