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Lundquist Number
In plasma physics, the Lundquist number (denoted by S) is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the timescale of resistive diffusion. It is a special case of the magnetic Reynolds number when the Alfvén velocity is the typical velocity scale of the system, and is given by :S = \frac , where L is the typical length scale of the system, \eta is the magnetic diffusivity and v_A is the Alfvén velocity of the plasma. High Lundquist numbers indicate highly conducting plasmas, while low Lundquist numbers indicate more resistive plasmas. Laboratory plasma experiments typically have Lundquist numbers between 10^2-10^8, while in astrophysical situations the Lundquist number can be greater than 10^. Considerations of Lundquist number are especially important in magnetic reconnection. See also * Magnetic Prandtl number * Péclet number In continuum mechanics, the Péclet number (, after Jean Claude Eugène Péclet) is a class of dimensi ... [...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 |
Dimensionless
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 d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfvén Wave
In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of plasma wave in which ions oscillate in response to a restoring force provided by an effective tension on the magnetic field lines. Definition An Alfvén wave is a low-frequency (compared to the ion gyrofrequency) travelling oscillation of the ions and magnetic field in a plasma. The ion mass density provides the inertia and the magnetic field line tension provides the restoring force. Alfvén waves propagate in the direction of the magnetic field, and the motion of the ions and the perturbation of the magnetic field are transverse to the direction of propagation. However, Alfvén waves existing at oblique incidences will smoothly change into magnetosonic waves when the propagation is perpendicular to the magnetic field. Alfvén waves are dispersionless. Alfvén velocity The low-frequency relative permittivity \varepsilon of a magnetized plasma is given by : \varepsilon = 1 + \frac where is the ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Diffusion
Magnetic diffusion refers to the motion of magnetic fields, typically in the presence of a conducting solid or fluid such as a plasma. The motion of magnetic fields is described by the magnetic diffusion equation and is due primarily to induction and diffusion of magnetic fields through the material. The magnetic diffusion equation is a partial differential equation commonly used in physics. Understanding the phenomenon is essential to magnetohydrodynamics and has important consequences in astrophysics, geophysics, and electrical engineering. Equation The magnetic diffusion equation is \frac = \nabla \times \left vec \times \vec\right+ \frac\nabla^2 \vec where \mu_0 is the permeability of free space and \sigma is the electrical conductivity of the material, which is assumed to be constant. \vec denotes the (non-relativistic) velocity of the plasma. The first term on the right hand side accounts for effects from induction of the plasma, while the second accounts for diffusio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Reynolds Number
In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the magnetic analogue of the Reynolds number in fluid mechanics and is typically defined by: : \mathrm_\mathrm = \frac ~~ \sim \frac where * U is a typical velocity scale of the flow, * L is a typical length scale of the flow, * \eta is the magnetic diffusivity. The mechanism by which the motion of a conducting fluid generates a magnetic field is the subject of dynamo theory. When the magnetic Reynolds number is very large, however, diffusion and the dynamo are less of a concern, and in this case focus instead often rests on the influence of the magnetic field on the flow. Derivation In the theory of magnetohydrodynamics, the magnetic Reynolds number can be derived from the induction equation: : \frac = \nabla \times (\mathbf \times \mathb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Diffusivity
The magnetic diffusivity is a parameter in plasma physics which appears in the magnetic Reynolds number. It has SI units of m²/s and is defined as:W. Baumjohann and R. A. Treumann, ''Basic Space Plasma Physics'', Imperial College Press, 1997. :\eta = \frac, while in Gaussian units it can be defined as :\eta = \frac. In the above, \mu_0 is the permeability of free space, c is the speed of light, and \sigma_0 is the electrical conductivity of the material in question. In case of a plasma, this is the conductivity due to Coulomb or neutral collisions: \sigma_0=\frac, where * n_e is the electron density. * e is the electron charge. * m_e is the electron mass. * \nu_c is the collision frequency. See also * Electrical resistivity and conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Reconnection
Magnetic reconnection is a physical process occurring in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection occurs on timescales intermediate between slow resistive diffusion of the magnetic field and fast Alfvénic timescales. The concept of magnetic reconnection was first introduced in 1950 in the PhD thesis of James Dungey to explain the coupling of mass, energy and momentum from the solar wind into Earth's magnetosphere and was published for the first time on the open literature in his seminal paper in 1961. Fundamental principles Magnetic reconnection is a breakdown of "ideal-magnetohydrodynamics" and so of "Alfvén's theorem" (also called the "frozen-in flux theorem") which applies to large-scale regions of a highly-conducting magnetoplasma, for which the Magnetic Reynolds Number is very large: this makes the convective term in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Prandtl Number
The Magnetic Prandtl number (Prm) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. It is defined as: :\mathrm_\mathrm = \frac = \frac = \frac where: * Rem is the magnetic Reynolds number * Re is the Reynolds number * ''ν'' is the momentum diffusivity (kinematic viscosity) * ''η'' is the magnetic diffusivity At the base of the Sun's convection zone A convection zone, convective zone or convective region of a star is a layer which is unstable due to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiatio ... the Magnetic Prandtl number is approximately 10−2, and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10−5. See also * Prandtl number References {{NonDimFluMech Dimensionless numbers of fluid mechanics Fluid dynamics Magnetohydr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Péclet Number
In continuum mechanics, the Péclet number (, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is defined to be the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. In the context of species or mass transfer, the Péclet number is the product of the Reynolds number and the Schmidt number (). In the context of the thermal fluids, the thermal Péclet number is equivalent to the product of the Reynolds number and the Prandtl number (). The Péclet number is defined as: : \mathrm = \dfrac For mass transfer, it is defined as: :\mathrm_L = \frac = \mathrm_L \, \mathrm Such ratio can also be re-written in terms of times, as a ratio between the characteristic temporal intervals of the system: :\mathrm_L = \frac = \frac = \frac For \mathrm \gg 1 the diffusion happens in a much longer time compared to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stuart Number
The Stuart number (N), also known as magnetic interaction parameter, is a dimensionless number of fluids, i.e. gases or liquids. It is defined as the ratio of electromagnetic to inertial forces, which gives an estimate of the relative importance of a magnetic field on a flow. The Stuart number is relevant for flows of conducting fluids, e.g. in fusion reactors, steel casters or plasmas. Definition : \mathrm = \frac = \frac * ''B'' – magnetic field * ''Lc'' – characteristic length * ''σ'' – electric conductivity * ''U'' – characteristic velocity scale * ''ρ'' – density * Ha – Hartmann number * Re – 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 domi ... References Further reading * R. Moreau: ''Magnetohydrodynamics'' (= ''Fluid Mechanics and i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
