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Electrostatic Ion Cyclotron Wave
In plasma physics, an electrostatic ion cyclotron wave is a longitudinal oscillation of the ions (and electrons) in a magnetized plasma, propagating nearly (but not exactly) perpendicular to the magnetic field. The angle (in radians) between the direction of propagation and the direction perpendicular to the magnetic field must be greater than about the square root of the mass ratio, :\sqrt, in order that the electrons can move along the field lines from crest to trough to satisfy the Boltzmann relation. The dispersion relation is :\omega^2=\Omega_c^2+k^2v_s^2, where Ωc is the ion cyclotron frequency and ''v''s is the ion sound speed. This relation is the result of restoring forces due to the Lorentz force (see Upper hybrid oscillation for more details), the electrostatic force (the ''T''e term in ''v''s), and the ion pressure (the ''T''i term in ''v''s). See also * Waves in plasmas * Ion acoustic wave * Upper hybrid oscillation In plasma physics, an upper hybrid oscill ... [...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 |
Cyclotron Frequency
Cyclotron resonance describes the interaction of external forces with charged particles experiencing a magnetic field, thus already moving on a circular path. It is named after the cyclotron, a cyclic particle accelerator that utilizes an oscillating electric field tuned to this resonance to add kinetic energy to charged particles. Cyclotron resonance frequency The cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicular to the direction of a uniform magnetic field ''B'' (constant magnitude and direction). Since that motion is always circular,Physics by M. Alonso & E. Finn, Addison Wesley 1996. the cyclotron frequency is given by equality of centripetal force and magnetic Lorentz force :\frac = qBv with the particle mass ''m'', its charge ''q'', velocity ''v'', and the circular path radius ''r'', also called gyroradius. The angular speed of the rotation is then: :\omega = \frac = \frac. Giving the rotational frequency (being the cyclotron ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ion Acoustic Wave
In plasma physics, an ion acoustic wave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acoustic waves traveling in neutral gas. However, because the waves propagate through positively charged ions, ion acoustic waves can interact with their electromagnetic fields, as well as simple collisions. In plasmas, ion acoustic waves are frequently referred to as acoustic waves or even just sound waves. They commonly govern the evolution of mass density, for instance due to pressure gradients, on time scales longer than the frequency corresponding to the relevant length scale. Ion acoustic waves can occur in an unmagnetized plasma or in a magnetized plasma parallel to the magnetic field. For a single ion species plasma and in the long wavelength limit, the waves are dispersionless (\omega=v_sk) with a speed given by (see derivation below) :v_s = \sqrt where k_\text is the Boltzmann constant, M is the mass of the ion, Z is its charge, T_e is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waves In Plasmas
In plasma physics, waves in plasmas are an interconnected set of particles and fields which propagate in a periodically repeating fashion. A Plasma (physics), plasma is a Plasma (physics)#Plasma_potential, quasineutral, electrical conductivity, 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 field, 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\ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrostatic Force
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called ''electrostatic force'' or Coulomb force. Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb, hence the name. Coulomb's law was essential to the development of the theory of electromagnetism, maybe even its starting point, as it made it possible to discuss the quantity of electric charge in a meaningful way. The law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. Coulomb studied the repulsive force between bodies having electrical charges of the same sign: Coulomb also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper Hybrid Oscillation
In plasma physics, an upper hybrid oscillation is a mode of oscillation of a magnetized plasma. It consists of a longitudinal motion of the electrons perpendicular to the magnetic field with the dispersion relation : \omega^2 = \omega_^2 + \omega_^2 + 3 k^2 v_^2 , where (in cgs units) :\omega_ = (4\pi n_ee^2/m_e)^ is the electron plasma frequency, and :\omega_ = eB/ is the electron cyclotron frequency. This oscillation is closely related to the plasma oscillation found in unmagnetized plasmas or parallel to the magnetic field, where the ωpe term arises from the electrostatic Coulomb restoring force and the 3''k''²''v''e,th² term arises from the restoring force of electron pressure. In the upper hybrid oscillation there is an additional restoring force due to the Lorentz force. Consider a plane wave where all perturbed quantities vary as exp(''i''(''kx''-ω''t'')). If the displacement in the direction of propagation is δx, then :''v''x = -''i''ωδ :''f''y = ''n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an electric field and a magnetic field experiences a force of \mathbf = q\,\mathbf + q\,\mathbf \times \mathbf (in SI unitsIn SI units, is measured in teslas (symbol: T). In Gaussian-cgs units, is measured in gauss (symbol: G). See e.g. )The -field is measured in amperes per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. ). It says that the electromagnetic force on a charge is a combination of a force in the direction of the electric field proportional to the magnitude of the field and the quantity of charge, and a force at right angles to the magnetic field and the velocity of the charge, proportional to the magnitude of the field, the charge, and the velocity. Variations on this basic formula describe the magnetic force on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ion Acoustic Wave
In plasma physics, an ion acoustic wave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acoustic waves traveling in neutral gas. However, because the waves propagate through positively charged ions, ion acoustic waves can interact with their electromagnetic fields, as well as simple collisions. In plasmas, ion acoustic waves are frequently referred to as acoustic waves or even just sound waves. They commonly govern the evolution of mass density, for instance due to pressure gradients, on time scales longer than the frequency corresponding to the relevant length scale. Ion acoustic waves can occur in an unmagnetized plasma or in a magnetized plasma parallel to the magnetic field. For a single ion species plasma and in the long wavelength limit, the waves are dispersionless (\omega=v_sk) with a speed given by (see derivation below) :v_s = \sqrt where k_\text is the Boltzmann constant, M is the mass of the ion, Z is its charge, T_e is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McGraw-Hill
McGraw Hill is an American educational publishing company and one of the "big three" educational publishers that publishes educational content, software, and services for pre-K through postgraduate education. The company also publishes reference and trade publications for the medical, business, and engineering professions. McGraw Hill operates in 28 countries, has about 4,000 employees globally, and offers products and services to about 140 countries in about 60 languages. Formerly a division of The McGraw Hill Companies (later renamed McGraw Hill Financial, now S&P Global), McGraw Hill Education was divested and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash. McGraw Hill was sold in 2021 to Platinum Equity for $4.5 billion. Corporate History McGraw Hill was founded in 1888 when James H. McGraw, co-founder of the company, purchased the ''American Journal of Railway Appliances''. He continued to add further publications, eventually establishing The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longitudinal Wave
Longitudinal waves are waves in which the vibration of the medium is parallel ("along") to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called ''compressional'' or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. Real-world examples include sound waves (vibrations in pressure, a particle of displacement, and particle velocity propagated in an elastic medium) and seismic P-waves (created by earthquakes and explosions). The other main type of wave is the transverse wave, in which the displacements of the medium are at right angles to the direction of propagation. Transverse waves, for instance, describe ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dispersion Relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the phase velocity and group velocity of waves in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency dependence of wave propagation and attenuation. Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media. In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Relation
In a plasma, the Boltzmann relation describes the number density of an isothermal charged particle fluid when the thermal and the electrostatic forces acting on the fluid have reached equilibrium. In many situations, the electron density of a plasma is assumed to behave according to the Boltzmann relation, due to their small mass and high mobility. Equation If the local electrostatic potentials at two nearby locations are ''φ''1 and ''φ''2, the Boltzmann relation for the electrons takes the form: :n_\text (\phi_2) = n_\text(\phi_1) e^ where ''n''e is the electron number density, ''T''e is the temperature of the plasma, and ''k''B is the Boltzmann constant. Derivation A simple derivation of the Boltzmann relation for the electrons can be obtained using the momentum fluid equation of the two-fluid model of plasma physics in absence of a magnetic field. When the electrons reach dynamic equilibrium, the inertial and the collisional terms of the momentum equations are zero, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
