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Centrifugal Mechanism Of Acceleration
Centrifugal acceleration of astroparticles to relativistic energies might take place in rotating astrophysical objects (see also Fermi acceleration). It is strongly believed that active galactic nuclei and pulsars have rotating magnetospheres, therefore, they potentially can drive charged particles to high and ultra-high energies. It is a proposed explanation for ultra-high-energy cosmic rays (UHECRs) and extreme-energy cosmic rays (EECRs) exceeding the Greisen–Zatsepin–Kuzmin limit. Acceleration to high energies It is well known that the magnetospheres of AGNs and pulsars are characterized by strong magnetic fields that force charged particles to follow the field lines. If the magnetic field is rotating (which is the case for such astrophysical objects), the particles will inevitably undergo centrifugal acceleration. The pioneering work by Machabeli & Rogava was a thought experiment in which a bead moves inside a straight rotating pipe. Dynamics of the particle were analyz ...
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Astroparticle
Cosmic rays or astroparticles are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own galaxy, and from distant galaxies. Upon impact with Earth's atmosphere, cosmic rays produce showers of secondary particles, some of which reach the surface, although the bulk are deflected off into space by the magnetosphere or the heliosphere. Cosmic rays were discovered by Victor Hess in 1912 in balloon experiments, for which he was awarded the 1936 Nobel Prize in Physics. Direct measurement of cosmic rays, especially at lower energies, has been possible since the launch of the first satellites in the late 1950s. Particle detectors similar to those used in nuclear and high-energy physics are used on satellites and space probes for research into cosmic rays. Data from the Fermi Space Telescope (2013) have been in ...
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Poloidal
The terms toroidal and poloidal refer to directions relative to a torus of reference. They describe a three-dimensional coordinate system in which the poloidal direction follows a small circular ring around the surface, while the toroidal direction follows a large circular ring around the torus, encircling the central void. The earliest use of these terms cited by the Oxford English Dictionary is by Walter M. Elsasser (1946) in the context of the generation of the Earth's magnetic field by currents in the core, with "toroidal" being parallel to lines of constant latitude and "poloidal" being in the direction of the magnetic field (i.e. towards the poles). The OED also records the later usage of these terms in the context of toroidally confined plasmas, as encountered in magnetic confinement fusion. In the plasma context, the toroidal direction is the long way around the torus, the corresponding coordinate being denoted by in the slab approximation or or in magnetic coordinat ...
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Zakharov System
In mathematics, the Zakharov system is a system of non-linear partial differential equations, introduced by Vladimir Zakharov in 1972 to describe the propagation of Langmuir waves in an ionized plasma. The system consists of a complex field ''u'' and a real field ''n'' satisfying the equations :\begin i \partial_t^ u + \nabla^2 u &= un\\ \Box n &= -\nabla^2 (, u, ^2_)\end where \Box is the d'Alembert operator. See also * Resonant interaction In nonlinear systems a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave vectors and the dispersion equation are met. ...; the Zakharov equation describes non-linear resonant interactions. References * Zakharov, V. E. (1968). ''Stability of periodic waves of finite amplitude on the surface of a deep fluid.'' Journal of Applied Mechanics and Technical Physics, 9(2), 190-194. *. Partial differential equations W ...
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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 ...
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Crab Nebula
The Crab Nebula (catalogue designations M1, NGC 1952, Taurus A) is a supernova remnant and pulsar wind nebula in the constellation of Taurus (constellation), Taurus. The common name comes from a drawing that somewhat resembled a crab with arms produced by William Parsons, 3rd Earl of Rosse, in 1842 or 1843 using a telescope. The nebula was discovered by English astronomer John Bevis in 1731. It corresponds with SN 1054, a bright supernova observed in 1054 C.E. by Native American, Japanese, and Arabic stargazers; this supernova was also recorded by Chinese astronomy, Chinese astronomers as a Guest star (astronomy), guest star. The nebula was the first astronomical object identified that corresponds with a historically-observed supernova explosion. At an apparent magnitude of 8.4, comparable to that of Titan (moon), Saturn's moon Titan, it is not visible to the naked eye but can be made out using binoculars under favourable conditions. The nebula lies in the Perseus Arm of the ...
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Plasma Oscillation
Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency depends only weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the '' plasmon''. Langmuir waves were discovered by American physicists Irving Langmuir and Lewi Tonks in the 1920s. They are parallel in form to Jeans instability waves, which are caused by gravitational instabilities in a static medium. Mechanism Consider an electrically neutral plasma in equilibrium, consisting of a gas of positively charged ions and negatively charged electrons. If one displaces by a tiny amount an electron or a group of electrons with respect to the ions, the Coulomb force pulls the electrons back, acting as a ...
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Klein–Nishina Formula
In particle physics, the Klein–Nishina formula gives the differential cross section (i.e. the "likelihood" and angular distribution) of photons scattered from a single free electron, calculated in the lowest order of quantum electrodynamics. It was first derived in 1928 by Oskar Klein and Yoshio Nishina, constituting one of the first successful applications of the Dirac equation. The formula describes both the Thomson scattering of low energy photons (e.g. visible light) and the Compton scattering of high energy photons (e.g. x-rays and gamma-rays), showing that the total cross section and expected deflection angle decrease with increasing photon energy. In quantum field theory it is known as Klein–Nishina–Tamm formula, adding the name of Igor Tamm who derived the formula from field quantization. Formula For an incident unpolarized photon of energy E_\gamma, the differential cross section is: : \frac = \frac r_e^2 \left(\frac\right)^ \left frac + \frac - \sin ...
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Compton Scattering
Compton scattering (or the Compton effect) is the quantum theory of high frequency photons scattering following an interaction with a charged particle, usually an electron. Specifically, when the photon hits electrons, it releases loosely bound electrons from the outer valence shells of atoms or molecules. The effect was discovered in 1923 by Arthur Holly Compton while researching the scattering of X-rays by light elements, and earned him the Nobel Prize in Physics in 1927. The Compton effect significantly deviated from dominating classical theories, using both special relativity and quantum mechanics to explain the interaction between high frequency photons and charged particles. Photons can interact with matter at the atomic level (e.g. photoelectric effect and Rayleigh scattering), at the nucleus, or with just an electron. Pair production and the Compton effect occur at the level of the electron. When a high frequency photon scatters due to an interaction with a charged part ...
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Lorentz Factor
The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentz ether theory, Lorentzian electrodynamics – named after the Netherlands, Dutch physicist Hendrik Lorentz. It is generally denoted (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as (Greek uppercase-gamma) rather than . Definition The Lorentz factor is defined as \gamma = \frac = \frac = \frac , where: * is the relative velocity between inertial reference frames, * is the speed of light in vacuum, * is the ratio of to , * is coordinate time, * is the proper time for an observer (measuring time intervals in ...
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Fermi Acceleration
Fermi acceleration, sometimes referred to as ''diffusive shock acceleration'' (a subclass of Fermi accelerationOn the Origin of the Cosmic Radiation, E. Fermi, Physical Review 75, pp. 1169-1174, 1949), is the acceleration that charged particles undergo when being repeatedly reflected, usually by a magnetic mirror (see also Centrifugal mechanism of acceleration). It receives its name from physicist Enrico Fermi who first proposed the mechanism. This is thought to be the primary mechanism by which particles gain non-thermal energies in astrophysical shock waves. It plays a very important role in many astrophysical models, mainly of shocks including solar flares and supernova remnant A supernova remnant (SNR) is the structure resulting from the explosion of a star in a supernova. The supernova remnant is bounded by an expanding shock wave, and consists of ejected material expanding from the explosion, and the interstellar mat ...s. There are two types of Fermi acceleration: first ...
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Thought Experiment
A thought experiment is an imaginary scenario that is meant to elucidate or test an argument or theory. It is often an experiment that would be hard, impossible, or unethical to actually perform. It can also be an abstract hypothetical that is meant to test our intuitions about morality or other fundamental philosophical questions. History The ancient Greek , "was the most ancient pattern of mathematical proof", and existed before Euclidean geometry, Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought experiment. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the equivalent German term . Ørsted was also the first to use the equivalent term in 1820. By 1883, Ernst Mach used in a different sense, to denote exclusively the conduct of a experiment that would be subsequently performed as a by his students. Physical and mental experimentation could then be contrasted: Mach asked hi ...
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Centrifugal Force
Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axis of rotation of the frame. The magnitude of the centrifugal force ''F'' on an object of mass ''m'' at the perpendicular distance ''ρ'' from the axis of a rotating frame of reference with angular velocity is F = m\omega^2 \rho. This fictitious force is often applied to rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits and banked curves, when they are analyzed in a non–inertial reference frame such as a rotating coordinate system. The term has sometimes also been used for the '' reactive centrifugal force'', a real frame-independent Newtonian force that exists as a reaction to a centripetal force in some scenarios. History F ...
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