Complete Dispersion Relation Research Articles

Wavelet-based spatial and temporal multiscaling: Bridging the atomistic and continuum space and time scales

A wavelet-based multiscale methodology is presented that naturally addresses time scaling in addition to spatial scaling. The method combines recently developed atomistic-continuum models and wavelet analysis. An atomistic one-dimensional harmonic crystal is coupled to a one-dimensional continuum. The methodology is illustrated through analysis of the dispersion relation, which is highly dispersive at small spatial scales and, as usual, nondispersive at large (continuum) scales. It is feasible to obtain the complete dispersion relation through the combination of the atomistic and the continuum analyses. Wavelet analysis in this work is not only used for bridging the atomistic and continuum scales but also for efficiently extracting the dispersion relation from the solution of wave propagation problems.

A mixed magnetohydrodynamic‐kinetic theory of low‐frequency waves and instabilities in homogeneous, gyrotropic plasmas

We study low‐frequency waves and instabilities in homogeneous, collisionless plasmas whose thermal pressure is gyrotropic, i.e., characterized by two distinct components, P⊥ and P∥, perpendicular and parallel, respectively, to the magnetic field. In order to obtain the complete dispersion relation of low‐frequency waves, we need equations of state for P⊥ and P∥. After showing that these equations differ from the widely used double‐adiabatic, or CGL, magnetohydrodynamic (MHD) equations, we derive their correct expressions by resorting to the Vlasov equation. We thus obtain a dispersion relation, which is no longer strictly MHD: in addition to the three standard (fast, slow, and Alfvén) modes from double‐adiabatic MHD theory, our dispersion relation also contains the mirror mode from kinetic theory. We examine the physical characteristics and stability properties of each of these four modes and provide numerical solutions for their frequency and growth/decay rate, both for simple proton–electron plasmas and for multispecies plasmas.

On the nature of solutions produced by finite difference schemes in time domain

This paper is a review discussing properties of field solutions produced by various finite difference schemes in the time domain. Considered algorithms include standard FDTD as well as its modifications based on different sets of electromagnetic equations and/or different discretization in space. By developing their complete dispersion relations, conclusions are drawn regarding divergence, curl, and energy conserva tion by each of the emulated eigenmodes separately. This is in extension to previous works which were concerned with the total solution, and permits to formulate conditions for restricting the total solutions to physical uncoupled solenoidal and potential modes. Original classification of spurious modes for the time domain finite difference modelling is also proposed. It is shown that spurious compensating modes can propagate over the mesh in the case of penalty schemes with p≠0, and that spurious degenerate modes at high- and low-frequencies appear in the case of condensed node discretization. Copyright © 1999 John Wiley & Sons, Ltd.

On the nature of solutions produced by finite difference schemes in time domain

This paper is a review discussing properties of field solutions produced by various finite difference schemes in the time domain. Considered algorithms include standard FDTD as well as its modifications based on different sets of electromagnetic equations and/or different discretization in space. By developing their complete dispersion relations, conclusions are drawn regarding divergence, curl, and energy conserva tion by each of the emulated eigenmodes separately. This is in extension to previous works which were concerned with the total solution, and permits to formulate conditions for restricting the total solutions to physical uncoupled solenoidal and potential modes. Original classification of spurious modes for the time domain finite difference modelling is also proposed. It is shown that spurious compensating modes can propagate over the mesh in the case of penalty schemes with p≠0, and that spurious degenerate modes at high- and low-frequencies appear in the case of condensed node discretization. Copyright © 1999 John Wiley & Sons, Ltd.

Two-chain spin ladder with frustrating second-neighbor interactions

The Heisenberg model on a 2-chain spin-1/2 ladder with frustrating second neighbor interactions is studied by using series expansions about the Ising and dimer limits, numerical diagonalization, and by Abelian bosonization analysis. The phase diagram is determined, and pair correlations and the complete dispersion relations for the triplet spin-wave excitations are also computed.

A novel numerical synthetic technique for determination of the TMon dispersion relation in a coaxial corrugated cylindrical waveguide

A novel, highly accurate numerical synthetic technique for determining the complete dispersive characteristics of electromagnetic modes in a spatially periodic structure is presented. The numerical method based on the coupling of the finite difference method in time domain with the discrete fourier transform is applied to calculate the eigenfrequencies and eigenfield distribution of a resonant cavity which is an appropriately shorted periodic slow wave circuit of N periods at both ends. The analytical synthetic technique, which is based on the intrinsic characteristic of spatially periodic structure, is used to derive the complete dispersion relation using the numerically measured resonances. The method was successfully applied for the case of TMon modes in a coaxial corrugated waveguide and is applicable to slow wave structures of arbitrary geometry.

Quantum spin ladders atT=0 and at high temperatures studied by series expansions

We have carried out extensive series studies, at T=0 and at high temperatures, of two-chain and three-chain spin-half ladder systems with antiferromagnetic intrachain and both antiferromagnetic and ferromagnetic interchain couplings. Our results confirm the existence of a gap in the two-chain Heisenberg ladders for all nonzero values of the interchain couplings. Complete dispersion relations for the spin-wave excitations are computed. For three-chain systems, our results are consistent with a gapless spectrum. We also calculate the uniform magnetic susceptibility and specific heat as a function of temperature. We find that as T\ensuremath{\rightarrow}0, for the two-chain system the uniform susceptibility goes rapidly to zero, whereas for the three-chain system it approaches a finite value. These results are compared in detail with previous studies of finite systems. \textcopyright{} 1996 The American Physical Society.

Field analysis of a tape helix with embedded bio-media for microwave hyperthermia.

A general field theory has been developed for the EM wave propagation on a tape helix with embedded bone, muscle, fat and skin co-axial biological layers in a multilayered dielectric environment. The electric and magnetic fields in every biological/dielectric layer is formulated in terms of complex modified Bessel functions and complex exponentials, i.e. in terms of complex radial and axial propagation constants for the azimuthally symmetric and higher order spatial harmonics. A complete dispersion relation is derived by substituting the field expressions into as many boundary conditions as there are unknown constants. The dispersion relation is numerically solved for the complex axial propagation constant and hence for the phase velocity and depth of penetration for n = 0 and 1 modes propagating along three dielectric loaded tape helices of different dimensions at several spot frequencies within the range of 300 MHz to 3.00 GHz. The results for variations in normalized phase velocity and depth of penetration with frequency for these modes separately and for the combined mode are presented. The patterns of specific absorption rate (SAR) across the cross-section of the dielectric loaded helices are also computed and presented. The variations with frequency, and cross-sectional dimension of the helix of the normalized phase velocity, axial depth and SAR across the cross-section of each of the helices are discussed for the modes considered. The theoretical results for the propagation constant obtained by using a tape helix model for the azimuthally symmetric mode propagating along a wire helix loaded with a phantom muscle sample of known dielectric constant are compared with experimental results and with those obtained theoretically employing a sheath helix model at 2.45 and 2.55 GHz. The use of a helix for human limb hyperthermia is also discussed.

Parallel electric field-induced instability in the magnetospheric ion-electron plasma

A complete dispersion relation for a whistler mode wave propagation in an anisotropic warm ion-electron magnetoplasma in the presence of parallel electric field using the dispersion relation for a circularly polarized wave has been derived. The dispersion relation includes the effect of anisotropy for the ion and electron velocity distribution functions. The growth rate of electron-ion cyclotron waves for different plasma parameters observed atL = 6.6REhas been computed and the results have been discussed in detail in the light of the observed features of VLF emissions and whistlers. The role of the combination of ion-cyclotron and whistler mode electromagnetic wave propagation along the magnetic field in an anisotropic Maxwellian weakly-ionized magnetoplasma has been studied.

Experimental investigation of minority ion concentration in a weakly ionized hydrogen plasma

H3+ and H2+ ion minority concentrations in a weakly ionized hydrogen plasma are determined through the comparison between the measured wavelength of the neutralized in Bernstein waves and the theoretical one, given by the solution of the complete electrostatic dispersion relation. A simple model based on the resolution of fluid balance equations permits one to explain the presence of a high percentage of H3+ ( approximately=30%).

A novel highly accurate synthetic technique for determination of the dispersive characteristics in periodic slow wave circuits

A highly accurate (0.1-0.5%) synthetic technique for determining the complete dispersive characteristics of electromagnetic modes in a spatially periodic structure is presented. It was successfully applied for the cases of the fundamental (TM/sub 0(1)/) as well as higher-order (TM/sub 0(2)/, TM/sub 0(3)/) passband modes in a corrugated waveguide. This structure is commonly used in relativistic backward wave oscillators, traveling wave tubes, extended interaction oscillators, and a variety of multiwave Cerenkov generators. An appropriately shorted periodic structure resonates at specific frequencies. To measure these frequencies accurately and unambiguously, the authors used unique antenna radiators to excite pure modes in the circuit under test. An analytical technique for deriving the complete dispersion relation using the experimentally measured resonances is presented. This technique, which is based on the intrinsic characteristics of spatially periodic structures, is applicable to slow wave structures of arbitrary geometry. >

Cubic dispersion relation for a relativistic backward-wave oscillator

The cubic approximation to the dispersion relation for a relativistic backward-wave oscillator is obtained, and the utility and limits of the approximation are presented. The approximation is obtained by Taylor series expansion of the wave admittance in the dispersion relation for the transverse-magnetic and free-streaming modes of a relativistic, thin, hollow, cylindrical electron beam moving along the axis of a disc-loaded waveguide in a strong axial magnetic field. The resulting cubic dispersion relation yields instability growth rates and frequencies which fall off beyond their maximum more sharply with increasing wavenumber than for the complete dispersion relation. The approximation is found to be quite good near the operating points of contemporary high-power relativistic backward-wave oscillators, namely, for relatively long wavelength and small ratio of Budker's parameter to the relativistic gamma factor of the beam.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The surface spin wave dispersion relation in thin ferromagnetic films

The dynamic susceptibility of a ferromagnetic thin film and the surface spin waves are investigated within the framework of the one-band Hubbard model. Calculations are performed with properly taking into account both the thin film geometry and a change of the one-electron HF potential near the surface. The one-electron states are calculated self-consistently. The nondamped surface spin waves with energies lower than the energies of spin wave modes of bulk character are numerically obtained. The complete dispersion relation for the surface modes is found and profoundly discussed.

Direct generation of the auroral kilometric radiation by the maser synchrotron instability: An analytical approach

It has recently been shown that radio emission from the Earth, the so-called auroral kilometric radiation, is emitted inside cold plasma depleted regions. These observations have motivated a new interest in direct generation processes. Since it allows the generation of an X mode just above the cutoff frequency of this mode (in agreement with observations) the maser synchrotron instability is a promising candidate. A detailed analytical approach to the understanding of this instability is proposed. The complete dispersion relation is derived in a situation where the cold plasma density is small (εc=ω2pe/ω2c≪1). The physical significance of this instability is discussed; in particular, the difference between the maser synchrotron instability and the classical Weibel instability is stressed. Depending upon the ratio between ‘‘cold’’ and energetic electron components, two regimes, the ‘‘kinetic’’ and the monoenergetic ‘‘ring-like’’ distribution, are considered and the results are compared with the numerical solution of the dispersion relation. Finally the saturation process of this instability is discussed in a homogeneous infinite medium; it is shown that trapping effects can insure an efficient saturation of the maser synchrotron instability.

Electromagnetic-Wave Propagation in a Conducting Waveguide Loaded with a Tape Helix

Dispersion properties of the electromagnetic (EM) waves, propagating through a tape helix located inside a waveguide, are investigated. A complete dispersion relation for the eigenfrequency omega and the axial wavenumber kappa is obtained, including influence of the outer conducting wall on the EM-wave propagation. It is shown that the fimiting case where the outer conducting wall is very close to the helix, the helix mode is nearly a straight line in the (omega, kappa) parameter space, and is independent of the width of the helix tape. Moreover, contrary to the conventional helix theory, the outer conducting wall completely eliminates the forbidden regions in the (omega, kappa) parameter space.

The lattice vibrations of CeD 2.12

The complete phonon dispersion relation including both optic and acoustic modes has been measured along the major symmetry axes of a single crystal of CeD 2.12 at 295 K by coherent neutron scattering. The results show the inadequacy of simple models previously used for the analysis of neutron incoherent scattering studies of rare earth dihydrides. The interstitial mode of vibration due to the excess deuterium (above CeD 2 in octahedral sites has also been observed.

Low-frequency instabilities of a warm plasma in a magnetic field: Part 1. Instabilities driven by field-aligned currents

The marginal stability of a plasma carrying current along the static magnetic field with isotropic Maxwellian ions and isotropic Maxwellian electrons drifting relative to the ions is investigated. The complete electromagnetic dispersion relation is studied using numerical techniques; the electron sums are restricted to three terms which limits the analysis to frequencies much less than the electron gyro-frequency, but includes frequencies somewhat above the ion gyro-frequency. A ‘kink-like’ instability and an instability of the Alfvén mode are found to have the lowest threshold drift velocities in most cases. In fact the threshold drift for the kink-like instability can be significantly less than the ion thermal speed. Electrostatic and electromagnetic ion-cyclotron instabilities are also found as well as the electro-static ion-acoustic instability. No instability of the fast magnetosonic mode was found. The stability analysis provides only threshold drift velocities and gives no information about growth rates.

Excitation of generalized Bernstein mode by interaction of two extraordinary electromagnetic waves

The excitation of a generalized Bernstein mode is studied by coupling two electromagnetic extraordinary modes, the frequencies of which are much higher than that of the plasma. The complete dispersion relation is used to describe the Bernstein mode propagation. In order to simplify the problem only the case of three co-linear waves is studied. Relativistic effects are not considered and it is assumed that the plasma is collisionless with a Maxwellian velocity distribution.

New, almost electrostatic, temperature anisotropy instability

A new, purely growing instability has been found for a bi-Maxwellian plasma in a uniform magnetic field. Instability exists for β;11 = 4βnkT11/B2 &gt; O.591 when Tboxhu;= 0, and ions are neglected. The growth rate is near the electron gyro frequency (or v/c the plasma frequency), and the polarization is almost electrostatic for almost perpendicular propagation. The instability is obtainable only from the complete dispersion relation.

Lattice Dynamics of Gold

The complete phonon dispersion relations for gold in the high-symmetry directions have been measured at room temperature by the coherent inelastic scattering of neutrons. It is found that the forces in gold are not homologous with the other noble metals, the frequencies of gold lying appreciably higher than those scaled from copper and silver. An analysis of the data in terms of different force-constant models reveals that a general tensor force is required for the first-neighbor interaction, whereas for neighbors beyond the first either general tensor or axially symmetric forces give an excellent fit to the data. The axially symmetric model alone does not adequately describe the data even when forces extending to ninth-nearest neighbors are included in the fit. In addition, simple screened-pseudopoential models were fit to the data and these results also indicate the need for the first-neighbor interaction to be general. Frequency distribution functions and related thermodynamic quantities were calculated from the various force-constant models. The Debye temperature ${\ensuremath{\Theta}}_{C}$ versus temperature curves obtained show an anomaly at low temperatures consistent with the ${\ensuremath{\Theta}}_{C}(T)$ obtained from specific-heat measurements. The relation between this anomaly and the character of the dispersion curves is given.