Cyclotron Frequency Ωc Research Articles

Extremely low frequency ion cyclotron resonances on the surface boundaries of coherent water domains

Pure Water under standard pressure, temperature and dilute solution conditions contain coherent Preparata-Del Giudice domains approximately a tenth of a micron in size. Ions of charge q = Z e can be confined to the surface boundaries of coherent water domains. Solving for the motion of ionic charges confined to surfaces in a uniform magnetic field B = curlA it is shown that there exist resonances scaled by the ionic cyclotron frequency ωc = (qB/Mc). The surface classical ionic motions described by the vector potential lagrangian L = (M/2)vμVμ + (q/c)vμAμ are integrable for a spherically symmetric surface. The resulting extremely low frequency (ELF) resonant modes are only weakly damped by fluid viscosity due to the small length scales of the confining surface and these modes are of importance in biophysical processes.

Terahertz optical properties of surface magnetoplasmons in both prism–semiconductor–metal and prism–metal–semiconductor coupled systems

In this work, we have theoretically investigated the terahertz non-reciprocal properties of surface magnetoplasmons (SMPs) in two structures, which are prism–semiconductor–metal and prism–metal–semiconductor coupled systems, respectively. The properties of non-reciprocal SMPs can be modulated by external magnetic fields, and there exists an excitation frequency band above the plasma frequency ωp of the semiconductor. For prism–semiconductor–metal coupled systems, when the electron cyclotron frequency ωc>0 (which is proportional to the magnetic field), the excitation frequency of the SMPs is located in the range of θ<0; and the excitation frequency may increase and the corresponding optimal thickness for exciting SMPs decreases with increasing of the magnetic field. For the prism–metal–semiconductor coupled systems, when ωc>0, the excitation of the electromagnetic coupling between the metal and semiconductor is in the region of θ>0, and the corresponding property of such coupling is explored by changing the magnetic field. We believe that these properties of SMPs in the proposed structures could be promising in the application of photonic devices.

Characteristics of Surface Plasmon Polaritons in Magnetized Plasma Film Walled by Two Graphene Layers

The theoretical analysis of surface plasmon polaritons in magnetized plasma film walled by two graphene layers is presented in this manuscript. The conductivity of graphene is calculated from the Kubo's formula. By tailoring the graphene conductivity, the propagation of Surface Plasmon Polariton wave can be controlled. Under the certain boundary conditions Maxwell's Equations in differential form are used to solve the problem. For using these wave guides we also investigate factor of confinement and comparatively length of shorter propagation for parallel plate waveguide. The effects of chemical potential (μ), plasma frequency (ωp), cyclotron frequency (ωc), relaxation time (τ), and number of layers of graphene (N) on the dispersion curve are investigated. The present work may have potential applications in nano-waveguide designing and plasma optics technology in the gigahertz frequency range.

Electron cyclotron waves in plasma in magnetosphere of a planet having perpendicular AC electric field

In a series of papers, scientists have discussed about electron cyclotron waves in plasma having AC electric field perpendicular to ambient magnetic field. In some investigations, scientists have claimed to consider relativistic plasma. We have reinvestigated the work and found that their claim of relativistic treatment of plasma is not valid. We have further found that the dispersion relation used by them is erroneous and therefore their results are not reliable. Using, individually, two distribution functions: (i) bi-Maxwellian distribution function, and (ii) Lorentzian (kappa) distribution function, for propagation of waves parallel to magnetic field, for both distribution functions, we have found that for known value of electron cyclotron frequency ωc, the real oscillation frequency ωr depends on temperature anisotropy only. We have also found that the growth rate γ increases continuously with the increase of wavevector k. These results are very different from earlier investigations. We have also found that the study of oblique propagation, carried out in a number of investigations, is not correct.

Electron cyclotron waves in plasma in magnetosphere of a planet having perpendicular DC electric field

Scientists have always been interested in the study of electron cyclotron waves in plasma in magnetosphere of a planet. Series of papers are published where AC electric field is taken perpendicular to magnetic field in the magnetosphere. Some scientists have claimed to consider DC electric field, but they are found not to have any electric field. We have discussed propagation of electron cyclotron waves when constant electric field is perpendicular to magnetic field in megnetosphere of a planet. Using bi-Maxwellian distribution function, we have found that for the known value of electron cyclotron frequency ωc, the real oscillation frequency ωr depends only on the temperature anisotropy. We have also found that the growth rate γ increases continuously with the increase of the wavevector k. It is interesting to note that the dispersion relation used in series of papers is erroneous, and it has been taken as universal relation.

New degeneracies and modification of Landau levels in the presence of a parallel linear electric field

We consider a three-dimensional system where an electron moves under a constant magnetic field (in the z-direction) and a linear electric field parallel to the magnetic field above the z = 0 plane and anti-parallel below the plane. The linear electric field leads to harmonic oscillations along the z-direction. There are therefore two frequencies characterizing the system: the usual cyclotron frequency ωc corresponding to motion along the x-y plane and associated with Landau levels and a second frequency ωz for motion along the z-direction. Most importantly, when the ratio W = ωc/ωz is a rational number, the degeneracy of the energy levels does not remain always constant as the energy increases. At some energies, the degeneracy jumps i.e. it increases. In particular, when the two frequencies are equal, the degeneracy increases with each energy level. This is in stark contrast to the usual Landau levels where the degeneracy is independent of the energy. We derive compact analytical formulas for the degeneracy. We also obtain an analytical formula for the energy levels and plot them as a function of W. The increase in degeneracy can readily be seen in the plot at points where lines intersect. For concreteness, we consider the electric field produced by a uniformly charged ring. Besides a linear electric field in the z direction the ring produces an extra electric field in the xy plane which we treat via perturbation theory. The Landau degeneracy is now lifted and replaced by tightly spaced levels that come in ‘bands’. The plot of the energy levels shows that there is still a degeneracy where the bands intersect.

Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

In this work, we study the (2+1)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Bohm-Coulomb system. To solve our system, we apply the left-handed and right-handed projection operators in the Dirac oscillator to obtain a biconfluent Heun equation. Next, we explicitly determine the energy spectrum for the bound states of the system and their exact dependence on the cyclotron frequency ωc and on the parameters Z and ΦAB that characterize the Aharonov-Bohm-Coulomb system. As a result, we observe that by adjusting the frequency of the Dirac oscillator to resonate with the cyclotron half-frequency the energy spectrum reduces to the rest energy of the particle. Also, we determine the exact eigenfunctions, angular frequencies, and energy levels of the Dirac oscillator for the ground state (n=1) and the first excited state (n=2). In this case, the energy levels do not depend on the homogeneous magnetic field, and the angular frequencies are real and positive quantities, increase quadratically with the energy and linearly with ωc.

Effects of hydrogen-like impurity and electromagnetic field on quantum transition of an electron in a Gaussian potential with QD thickness

Considering Hydrogen-like impurity and the thickness effect, the eigenvalues and eigenfunctions of the electronic ground and first exited states in a quantum dot (QD) are derived by using the Lee-Low-Pins-Pekar variational method with the harmonic and Gaussian potentials as the transverse and longitudinal confinement potentials, respectively. A two-level system is constructed on the basis of those two states, and the electronic quantum transition affected by an electromagnetic field is discussed in terms of the two-level system theory. The results indicate the Gaussian potential reflects the real confinement potential more accurately than the parabolic one; the influence of the thickness of the QD on the electronic transition probability is interesting and significant, and cannot be ignored; the electronic transition probability Γ is influenced significantly by some physical quantities, such as the strength of the electron-phonon coupling α, the electric-field strength F, the magnetic-field cyclotron frequency ωc, the barrier height V0 and confinement range L of the asymmetric Gaussian potential, suggesting the transport and optical properties of the QD can be manipulated further though those physical quantities.

Bound magnetopolaron in delta GaAs quantum dot under Rashba effect

This paper presents the influence of Rashba effect on bound magnetopolaron in delta quantum dot. The unitary transformation method and the variational method of Pekar type have been used to derive the ground and first excited state energy. Due to Rashba effect, the ground and first excited states each split into two energies (spin up and down). Results show that the split up(down) energy of ground and first excited states are increasing (decreasing) function of wave vector; the spin splitting of the ground and first excited states are decreasing function of the delta parameter and the increasing function of Rashba parameter. It has also be seen that the splitting of energies levels occur around the value q=0. The density of probability has its minimum value at the center of the dot while it is maximal at the boundary of the dot. The decoherence has been studied through the Shannon entropy and the results show increase of entropy with time, delta parameter K, and cyclotron frequency ωc. It also suggests a way to encrypt information and to control decoherence.

Thermoelectric phenomena in layered conductors near the Lifshitz electron topological transition

This is a theoretical study of the response of an electron system to nonuniform heating of layered conductors with a quasi-two dimensional charge carrier energy spectrum near the Lifshitz electron topological transition when external interactions with the conductor, such as pressure, cause a change in the connectivity of the Fermi surface. With a variety of dispersion relations for the conduction electrons as examples, it is shown that there is a great variety of electronic topological transitions in layered conductors, which are accompanied by unusual magnetic field dependences of the kinetic coefficients. The migration of conduction electrons over different cavities (sheets) of the Fermi surface owing to magnetic breakdown is analyzed for close proximity of individual cavities of the Fermi surface. The dependence of the thermoelectric coefficients on the magnitude and orientation of strong magnetic fields B, such that the cyclotron frequency ωc is much higher than the collision frequency 1/τ of the conduction electrons, is calculated. An experimental study of these effects yields important information on the energy spectrum of the charge carriers.

Magnetic-breakdown oscillations of the thermoelectric field in layered conductors

The response of an electron system to nonuniform heating of layered conductors with an arbitrary quasi-two-dimensional electron energy spectrum in a strong magnetic field B is investigated theoretically in the case when cyclotron frequency ωc is much higher than the frequency 1/τ of collisions between charge carriers. In the case of a multisheet Fermi surface (FS), we calculate the dependence of the thermoelectric coefficients on the magnitude and orientation of the magnetic field in the vicinity of the Lifshitz topological transition when the FS connectivity changes under the action of an external force (e.g., pressure) on the conductor. Upon a decrease in the spacing between individual pockets (sheets) of the FS, conduction electrons can tunnel as a result of the magnetic breakdown from one FS sheet to another; their motion over magneticbreakdown trajectories becomes complicated and entangled. The thermoelectric field exhibits a peculiar dependence on the magnetic field: for a noticeable deviation of vector B from the normal through angle ϑ to the layers, the thermoelectric field oscillates as a function of tanϑ. The period of these oscillations contains important information on the distance between individual FS sheets and their corrugation.

Hot plasma dielectric response to radio-frequency fields in inhomogeneous magnetic field

Hot plasma dielectric response models, which are now used in most linear full wave codes, are formulated in Fourier space assuming that particle's Larmor radius is much smaller than the scale of spatial nonuniformity of magnetic field. Such approximation assumes that the spatial scale of plasma dielectric response to the RF field is limited to a few Larmor radii, which is accurate for a limited range of wave frequencies ω. The scale of plasma dielectric response along the magnetic field line could be comparable to the scale of the magnetic field nonuniformity when ω is close to the particle's cyclotron frequency ωc or when ω is much smaller than ωc, which requires the use of a more accurate model. In the present approach, the hot plasma dielectric response is formulated in configuration space without limiting approximations by numerically calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in nonuniform magnetic field. Results of the conductivity kernel calculation in hot collisionless plasma are presented for 1-D mirror and 2-D tokamak magnetic field configurations for ω∼ωc. Self-consistent simulation of RF fields using the calculated conductivity kernel of 1-D mirror magnetic field is made. A new parallel full wave RF code, based on the presented approach of accurate self-consistent modeling of plasma dielectric response in configuration space, is under development.

Galvanomagnetic phenomena in organic conductors under topological phase transition

The magnetoresistance of layered organic conductors with a multisheet Fermi surface (FS) is studied theoretically under conditions of the Lifshitz topological transition, where the FS topology may change in response to external effects acting on the conductor, such as pressure or doping with impurity atoms. Using as an example the Fermi surface consisting of a cylinder and two planes, which are slightly corrugated along the projection of the momentum pz=pn along the normal to the layers n, we analyze the magnetic-field dependence of the resistance and the Hall field in a strong external magnetic field H, where the cyclotron frequency ωc of the conduction electrons is much higher than their collision frequency 1/τ. In the immediate vicinity of the topological transition, where the distance between the different sheets of the FS becomes small, an electron can move from one sheet of the FS to another with the probability w due to the magnetic breakdown. In this case, a quadratic increase of the electric resistance across the layers with magnetic field, which occurs in the absence of the magnetic breakdown, is replaced by a linear dependence on H for w≥γ=1/ωcτ, and then reaches saturation for (1−w)≤γ. The Hall field depends substantially on the probability of a magnetic breakdown, but in the case of ωcτ≫1, its asymptote is independent of τ for all values of w. At w = 1, the quasi-planar sheets of the Fermi surface touch the corrugated cylinders, and under further perturbation acting on the conductor, there occurs a break of a flat sheet along the line of contact. As a result, separate sections of the flat FS sheet together with the cut halves of the corrugated cylinder form a new corrugated cylinder with the sign of charge carriers reversed. This is not the only scenario of the Lifshitz topological transition. Studies of the Hall effect will allow us to obtain further important information on the nature of changes in the topological structure of the electron energy spectrum under the phase transition.

Influence of Szigeti effective charge on coherent Raman scattering of laser radiation in magnetized direct gap semiconductors

By considering the hydrodynamic model of semiconductor-plasmas, an analytical investigation is performed to study the influence of Szigeti effective charge (qs) on coherent Raman scattering (CRS) of laser radiation in a transversely magnetized direct gap semiconductor arising from electron density perturbations and molecular vibrations of the medium both produced at the transverse optical phonon frequency. Assuming that the origin of CRS lies in the third-order susceptibility of the medium, an expression is obtained for Raman gain coefficient (gR). Numerical estimates are made for a representative n-type InSb crystal duly shined by pulsed 10.6 μm CO 2 laser. The threshold field (E0 th ) for inciting CRS is identified. The dependence of gR on pump field strength E0, externally applied magnetic field (in terms of electron cyclotron frequency ωc) and doping concentration (in terms of plasma frequency ωp) is reported for both cases viz., qs = 0 and qs ≠ 0. In absence of qs, the results are found to be well in agreement with available literature.

Properties of the internal excited state of the strong-coupling magneto-bipolaron in a parabolic quantum dot

The properties of the internal excited state of the strong coupling magneto-bipolarons in a parabolic quantum dot are studied by using the variational method of Pekar type based on the Lee-Low-Pines’ unitary transformation. With the influences of the electronic spin and the external magnetic field taken into consideration, the change law of ground state energy E0, the average number of phonon N0, the first excited state energy E1 and the average number of phonon N1 of the magneto-bipolarons with the confinement strength ω0, the dielectric constant ratio η, the electron-phonon coupling α, and the cyclotron frequency ωc are derived in two-dimensional quantum dot. Numerical results indicate that the ground state energy E0 and the first excited state energy E1 consist of four parts: the single-article energy Ee of two electrons, the Coulomb interaction energy EC between two electrons, the interaction energy Es between the electronic spin and the external magnetic field, and the interaction energy Ee-ph of the electron with the longitudinalo optical phonons. The energy E1 of the first excited state splits into two lines, i.e., E1(1+1) and E1(1-1) due to the interaction between the “orbital” motion of the single-particle and the magnetic field, and each level of the ground-state energy and the first excited state energies set produces three “fine structures” due to the interaction between the electronic spin and the magnetic field. N0 and N1 increase with ω0, α and ωc increasing; Ee-ph is always less than zero, and absolute value |Ee-ph| increases with ω0, α and ωc increasing. The electron-phonon interaction has an important influence on the formation of bound state of the magneto-bipolaron; but the confinement potential and coulomb repulsive energy between electrons are unfavorable for the formation of magneto-bipolaron in the bound state.

Modulational Amplification of the Polaron Mode in a Magnetized Semiconductor

The present paper is concerned with the analytical study of the modulational amplification of the polaron mode in a magnetized semiconductor. Using the hydrodynamical approach and coupled mode theory we developed analytical expressions for the necessary threshold pump field, third-order susceptibility, and growth rate. Numerical estimations are made for n-InSb crystal at 77 K, irradiated with a 10.6 μm CO2 laser. In a limited range of the parameters (external electric field E0, carrier concentration n0, and cyclotron frequency ωc) a stable behavior of the growth rate and threshold for amplification of the polaron mode are observed. Beyond a certain range of parameters we obtain anomalous behaviour. Heavily doped medium is found to require a lower threshold field. An appropriate magnitude of the transverse magnetic field effectively enhances the growth rate (≈ 10^10 m^(-1)). Hence, the presence of an external magnetic field is favourable for the onset of modulational amplification of the polaron mode in the heavily doped regime.

Obliquely propagating waves in the magnetized strongly coupled one-component plasma

The quasi-localized charge approximation is used to calculate the wave spectrum of the magnetized three-dimensional strongly coupled one-component plasma at arbitrary angles θ between the wave vector and the magnetic field axis. Three frequency branches are identified whose interplay is strongly determined by β=ωc/ωp, the ratio of the cyclotron frequency ωc, and the plasma frequency ωp. The frequency dispersion relations for the three principal modes along the magnetic field cross in the case β&amp;lt;1, which strongly affects the transition from parallel to perpendicular wave propagation. For β&amp;gt;1, the frequencies of the different branches are well separated, and the long-wavelength dispersion in the intermediate and upper branch changes sign as θ is varied from 0 to π/2. In addition to the frequencies, we also investigate the waves' polarization properties.

Study of second harmonic generation by high power laser beam in magneto plasma

This paper examines the problem of nonlinear generation of second harmonic of a high power laser pulse propagating in magnetized plasma. The propagation of strong laser beam is proposed in the direction perpendicular to a relatively weak static magnetic field. The laser pulse is taken to be linearly polarized, with the orientation of its electric field that corresponds to an ordinary electromagnetic wave. Besides the standard ponderomotive nonlinearity, the appropriate wave equation also contains the nonlinearity that arises from the relativistic electron jitter velocities. During its propagation, the laser beam gets filamented on account of relativistic and pondermotive nonlinearities present in the plasma. The generated plasma wave gets coupled into the filamentary structures of the pump beam. Due to the expected presence of the beam filamentation, the work has been carried out by considering modified paraxial approximation (i.e., beyond the standard paraxial approximation of a very broad beam). It is found that the power of the plasma wave is significantly affected by the magnetic field strength in the presence of both relativistic and pondermotive nonlinearities. It is investigated that the second harmonic generation is also considerably modified by altering the strength of magnetic field. To see the effect of static magnetic field on the harmonic generation, a key parameter, i.e., the ratio of the cyclotron frequency ωc=eB0/mc over the laser frequency ω0 has been used, where c is the velocity of light, m and e are the mass and charge of the electron and B0 is the externally applied magnetic field.

Relativistic and ponderomotive self-focusing of a laser pulse in magnetized plasma

AbstractThe self-focusing of an intense right circularly polarized Gaussian laser pulse in magnetized plasma is studied. The ions are taken to be immobile and relativistic mass effect is incorporated in both the plasma frequency (ωp) and the electron cyclotron frequency (ωc) while determining the ponderomotive force on electrons. The ponderomotive force causes electron expulsion when the effective electron cyclotron frequency is below twice the laser frequency. The nonlinear plasma dielectric function due to ponderomotive and relativistic effects is derived, which is then employed in beam-width parameter equation to study the self-focusing of the laser beam. From this, we estimate the importance of relativistic self-focusing in comparison with ponderomotive self-focusing at moderate laser intensities. The beam width parameter decreases with magnetic field indicating better self-focusing. When the laser intensity is very high, the relativistic gamma factor can be modeled as ${\rm \gamma} = 0.8\left({{{{\rm \omega} _c } / {\rm \omega} }} \right)+ \sqrt {1 + a_0^2 }$γ=0.8(ωc/ω)+1+a02 where ω and a0 are the laser frequency and the normalized laser field strength, respectively. The cyclotron effects on the self-focusing of laser pulse are reduced at high field strengths.

Investigation of the diocotron instability of an infinitely wide sheet electron beam by using the macroscopic cold-fluid model theory

This paper investigates the diocotron instability of an infinitely wide relativistic sheet electron beam in conducting walls propagating through a uniform magnetic field by using the macroscopic cold-fluid model theory. Assuming low-frequency perturbations with long axial wavelengths, the eigenvalue equation and the dispersion relation are acquired for a sheet electron beam with sharp boundary profile and uniform density. The results presented in this paper has developed the use of the macroscopic cold-fluid model theory by extending the parameter of the electron cyclotron frequency ωc to a wider usage range, which is restricted to be much larger than the plasma frequency ωp in the previous research work. Theoretical analyses and numerical calculations indicate that the transport of the sheet electron beam will be completely stabilized by augmenting the normalized beam thickness to a conductor gap larger than a threshold λb, which is greatly dependent on the parameter ωc/ωp. The larger ωc/ωp is, the smaller λb will be needed. Moreover, the system parameters, including the wave number kx of the perturbations and the relativistic mass factor γb, will also influence the growth rate of diocotron instability obviously.