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Relativistic Similarity Parameter
In relativistic laser-plasma physics the relativistic similarity parameter ''S'' is a dimensionless parameter defined as : S=\frac, where is the electron plasma density, is the critical plasma density and is the normalized vector potential. Here is the electron mass, is the electron charge, is the speed of light and is the laser frequency. Note that CGS units were used above. The concept of similarity and the similarity parameter were first introduced in plasma physics by Sergey Gordienko. It allows distinguishing between relativistically overdense and underdense plasmas . The similarity parameter is connected to basic symmetry properties of the collisionless Vlasov equation and is thus the relativistic plasma analog of the Reynolds number in fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless Parameter
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Rest Mass
The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of about or about Terminology The term "rest mass" is sometimes used because in special relativity the mass of an object can be said to increase in a frame of reference that is moving relative to that object (or if the object is moving in a given frame of reference). Most practical measurements are carried out on moving electrons. If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass. Such correction becomes substantial for electrons accelerated by voltages of over . For example, the relativistic expression for the total energy, ''E'', of an electron moving at speed v is :E = \gamma m_\text c^2 , where the Lorentz factor is \gamma = 1/\sqrt . In this expression ''m''e is the "re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vlasov Equation
The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction, e.g. 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 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 collisions is formally not applicable to Coulomb interaction due to the divergence of the kinetic terms. # Theory of pair collisions cannot explain experim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relativistic Plasma
Relativistic plasmas in physics are plasmas for which relativistic corrections to a particle's mass and velocity are important. Such corrections typically become important when a significant number of electrons reach speeds greater than 0.86 c (Lorentz factor \gamma=2). Such plasmas may be created either by heating a gas to very high temperatures or by the impact of a high-energy particle beam. A relativistic plasma with a thermal distribution function has temperatures greater than around 260 keV, or 3.0 GK (5.5 billion degrees Fahrenheit), where approximately 10% of the electrons have \gamma > 2. Since these temperatures are so high, most relativistic plasmas are small and brief, and are often the result of a relativistic beam impacting some target. (More mundanely, "relativistic plasma" might denote a normal, cold plasma moving at a significant fraction of the speed of light relative to the observer.) Relativistic plasmas may result when two particle beams collide at speed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a ''macroscopic'' viewpoint rather than from ''microscopic''. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Waist
In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or TEM00) transverse Gaussian mode describes the intended output of most (but not all) lasers, as such a beam can be focused into the most concentrated spot. When such a beam is refocused by a lens, the transverse ''phase'' dependence is altered; this results in a ''different'' Gaussian beam. The electric and magnetic field amplitude profiles along any such circular Gaussian beam (for a given wavelength and polarization) are determined by a single parameter: the so-called waist . At any position relative to the waist (focus) along a beam having a specified , the field amplitudes and phases are thereby determinedSvelto, pp. 153–5. as detailed below. The equations below assume a beam with a circular cross-section at all val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
