Arbitrary Electric Field Research Articles

Nonlinear nonviscous hydrodynamical models for charge transport in the framework of extended thermodynamic methods

This paper develops a procedure, based on methods of extended thermodynamics, to design nonlinear hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. Models obtained in this way allow the study of the motion of electric charges in the presence of arbitrary external electric fields and may be useful when one wishes to study phenomena in a neighborhood of a stationary nonequilibrium process: indeed, the drift velocity of the charge gas with respect to the crystal lattice is not regarded as a small parameter.

Fluid dynamics of a sphere in an arbitrary electric field

The method of symbolic operator representation (SOR), which was introduced by Rayleigh [The Theory of Sound, vol. II, 2nd edn., Dover, New York] and applied to colloidal particles by Brenner [Chem. Eng. Sci. 19 (1964) 519], Brenner and Haber [Chem. Eng. Commun. 27 (1984) 283] and Haber and Brenner [Chem. Eng. Commun. 27 (1984) 296], is used to derive an exact solution for the velocity and electric fields of a particle in an infinite medium. The solution is obtained as an infinite series of pertinent vector functions. The first two terms of the solution are identical to a known expression, which was derived by an expansion method. Furthermore, an example is given to demonstrate the usefulness of the method of SOR in solving complex problems of particulate flows.

Operator representation of the wave function for a charged particle in an external field and its applications

A consistent derivation of the operator form for the solution of the wave equation for a charged particle in an arbitrary external electromagnetic field is presented. The expressions obtained can be used for solving any problems in quantum electrodynamics in external fields in the framework of the semiclassical operator method. The peculiarities of the application of this method are demonstrated for the small-angle elastic scattering of a high-energy photon in an arbitrary localized electric field. The problem is solved for the first time without presuming the central symmetry of the external field potential.

Interband transitions of superlattices in arbitrary time-dependent electric fields: an analytical approach of closed-form solutions in the real space

Within a two-band tight-binding model driven by arbitrary time-dependent electric fields, we investigate the interband transitions and obtain closed-form solutions in the real space, from which we show that there are two essentially opposite evolution behaviors of the system: interband resonances and miniband localization. We also find that in weak interband coupling, as expected, the perturbative solutions are in good agreement with the exact numerical calculations.

Ideal Space Focusing in a Time-of-Flight Mass Spectrometer: An Optimization Using an Analytical Approach

An exact, analytical solution for an electric field in a nonlinear acceleration region of an ion source for the cases of linear and reflectron time-of-flight (TOF) mass spectrometers has been found to achieve universal temporal focusing of ions having an initial space distribution. The general solutions are valid for an arbitrary electric field distribution in the drift region (from the ion source to an ion detector) of a linear TOF mass spectrometer, and in the upstream (from the ion source to the reflectron) and downstream (from the reflectron to an ion detector) regions of a reflectron TOF instrument. This may include, for example, electrostatic lenses commonly used after an ion source for angular focusing of ions onto the detector to increase the instrument sensitivity and additional acceleration of ions before their detection. Using analytical expressions obtained for an arbitrary case, convenient working formulae are derived for the widely used single- and dual-stage ion extraction schemes in the cases of linear and reflectron TOF mass spectrometers. The formulae are used in optimizing the TOF mass spectrometer design by decreasing the curvature of the nonlinear acceleration potential in the ion source. The relationship has been shown between the conditions for an ideal space focusing using an optimized curved extraction field and a finite-order space-focusing using a linear extraction field in an ion source. The results obtained are especially useful for designing miniature TOF mass spectrometers or instruments with large volume ion sources.

An empirical ferroelectric capacitor model utilizing a dual curve-fit technique

Empirical modeling of the polarization-electric field (P-E) relationship of ferroelectric capacitors subjected to the application of arbitrary electric fields is investigated. Experimental data generated by other researchers has shown that ferroelectric switched charge remains approximately constant when the capacitor is subjected to electric fields which alternate between two fixed values. The current model is based on a dual curve-fit approach to achieve the desired response. The model predicts both saturated- and minor-loop hysteresis when compared to experimental data.

Augmented Fokker–Planck equation for electron transport in arbitrary electric fields

Electron transport in a solid subjected to an arbitrary electric field is analyzed in the energy-position manifold instead of phase space. In the absence of deeply inelastic electron-lattice scattering, the spectral carrier density satisfies a differential equation of the Fokker–Planck type. Subsumption of deeply inelastic events results in an integrodifferential equation which agrees exactly with Monte Carlo simulations in the limit of a vanishing drift-to-instantaneous velocity ratio. Reasonable agreement is found for ratios as high as 0.4, enabling the augmented Fokker–Planck equation to tackle a number of transport issues at a much lower cost than Monte Carlo simulations.

The electron density of semiconductors with charged dislocations placed in external fields

Variations in the electron density due to variations in the capture cross section and the thermal ionization upon application of an external electric field and a quantizing magnetic field are considered. Analytical expressions for the electron density in arbitrary electric and quantizing magnetic fields and also in crossed electric and quantizing magnetic fields are obtained. It is assumed that the electrons relax in energy as a result of interacting with acoustic phonons. Calculations for a quantizing magnetic field in the ultraquantum limit are presented.

Ideal velocity focusing in a reflectron time-of-flight mass spectrometer

A single-stage ion mirror in a time-of-flight (TOF) mass spectrometer (MS) can perform first order velocity focusing of ions initially located at a start focal plane while second order velocity focusing can be achieved using a double-stage reflectron. The situation is quite different when an ion source extraction field is taken into account. In this case which is common in any practical matrix-assisted laser desorption/ionization (MALDI) TOF-MS a single-stage reflectron, for example, cannot perform velocity focusing at all. In this paper an exact, analytic solution for an electric field inside a one-dimensional reflectron has been found to achieve universal temporal focusing of ions having an initial velocity distribution. The general solution is valid for arbitrary electric field distributions in the upstream (from the ion source to the reflectron) and downstream (from the reflectron to an ion detector) regions and in a decelerating part of the reflectron of a reflectron TOF mass spectrometer. The results obtained are especially useful for designing MALDI reflectron TOF mass spectrometers in which the initial velocity distribution of MALDI ions is the major limiting factor for achieving high mass resolution. Using analytical expressions obtained for an arbitrary case, convenient working formulas are derived for the case of a reflectron TOF-MS with a dual-stage extraction ion source. The special case of a MALDI reflectron TOF-MS with an ion source having a low acceleration voltage (or large extraction region) is considered. The formulas derived correct the effect of the acceleration regions in a MALDI ion source and after the reflectron before detecting ions.

Universal properties in the free energy of the asymmetricN-state vertex model

Electric-field-dependent free energy of the exactly solvable asymmetric N-state vertex model (i.e. in an arbitrary vertical and an arbitrary horizontal electric field v and h) in the low-temperature antiferroelectric phase is obtained in the form of the expansion in terms of small but nonzero polarization p. Exact mapping onto a microscopic surface model (solid-on-solid (SOS) model) is employed to study the vicinal-surface free energy below the roughening temperature TR which determines the equilibrium crystal shape (ECS) near the facet edge of a crystal. The obtained expansion of the free energy is of the well-established Gruber-Mullins-Pokrovsky-Talapov (GMPT) type: f(p,h) = f(0,h) + a(h)p + b(h)p3 + O(p4). It is found that the coefficients a(h) and b(h) are identical with those of the asymmetric six-vertex model. Based on this expansion, in cooperation with the Andreev construction of the ECS, universal properties are verified along the whole facet contour. First, directly from the GMPT-type expansion, the critical exponents governing the rounding of the crystal facet are obtained; the exponent is (3/2) in all direction except the tangential one in which case it is 3. Second, the universal relation between a(h) and b(h) is verified, leading to the universal Gaussian curvature jump at the facet edge and a universal relation between the critical amplitudes of the ECS profiles of the vicinal surface.

The ray-tracing code Zgoubi

Abstract The ray-tracing code Zgoubi computes particle trajectories in arbitrary magnetic and/or electric field maps or analytical models. The code is a genuine compendium of numerical recipes for simulation of most types of optical elements encountered in beam optics. It contains a built-in fit procedure, synchrotron radiation calculation, spin tracking, many Monte Carlo processes, etc. The high accuracy of the integration method allows efficient multiturn tracking in periodic machines.

Study ofthe single-band Bloch oscillation effect with the pseudo-spectralmethod

Using the pseudo-spectral method for wave-packet evolution, we formulate and implement a new theoretical approach for studying the Bloch oscillation effect in a general number of dimensions. For this purpose, a novel recursive formula is obtained in the representation of Wannier functions for the infinitesimal time evolution of an electronic wave packet within the single-band approximation. This formula is valid for general position-dependent applied electric fields and arbitrary initial wave-packet shapes and crystal structures, and can also be generalized for time-dependent fields. For a tight-binding simple `cubium' band, the infinitesimal time evolution can always be expressed in terms of Bessel functions of integer order; and for the `empty-lattice model' band it can be expressed in terms of Fresnel functions for arbitrary electric fields also. As a further analytical application of our formalism, we derive an exact (finite-time) wave-packet evolution for the homogeneous and static electric field in the simple `cubium' band. For this case, an estimate of the numerical error of the pseudo-spectral method is obtained for the mean position of the wave packet. As an illustrative example of the numerical implementation of our theoretical formalism, we present a simple one-dimensional numerical simulation for a Gaussian wave packet moving in a parabolic potential well. Finally, a general proof of the unitarity of the predicted time evolution is also presented, and different properties of our formalism pointed out.

Errata: 2D Saddle Potential Schröinger Green's Function in the Presence of an Arbitrary Time-Dependent Electric Field

Errata: 2D Saddle Potential Schröinger Green's Function in the Presence of an Arbitrary Time-Dependent Electric Field

The Influence of Periodic Doping on the Nonequilibrium Phase Transitions in Lateral Superlattice

The current in a lateral superlattice in arbitrary (but nonquantizing) electric field is calculated. It is shown that the sample being open-circuited in transverse (with respect to current) direction the second-order nonequilibrium phase transition consisting in the spontaneous appearance of a trans verse electric field is possible. Periodical δ-doping of such superlattices makes also possible first-order phase transitions. The character of phase transitions depends on the ratio of conductivities of two autonomous groups of carriers (in the conductivity band and in the additional one stipulated by the periodical δ-doping).

Current-voltage characteristic of asymmetric superlattice

The kinetic equation for electrons of an asymmetric superlattice under conditions when the asymmetry appears in the processes of intra-miniband electron scattering is solved. The current-voltage characteristic for arbitrary non-quantizing electric fields is calculated. The existence of an even (with respect to field) component of current-voltage characteristic stipulates the appearance of constant current (or constant electromotive force) in the sample placed in a microwave radiation field.

2D Saddle Potential Schrödinger Green's Function in the Presence of an Arbitrary Time-Dependent Electric Field

We derive the retarded nonrelativistic Green's function for a Schrödinger electron confined to a plane and subject to a parabolic saddle potential and an electric field having arbitrary time dependence and orientation on the plane. This derivation is carried out using Heisenberg equations of motion for position and momentum operators, following an earlier analysis of Schwinger, to obtain the retarded Green's function in closed form, as an explicit function of position and time variables.

Exact Solutions for the Collisional Plasma Problem

By means of the Lie group approach the symmetry of Vlasov-Fokker Planck equation (VFPE) with an arbitrary electric field of space and time are found. Mathematical forms are obtained for the electric field permit symmetry. Maxwell's equations are then used to constrain the solution further. Finally, we obtain a complete classification of all possible nontrivial similarity solutions of the VFPE plus Maxwell equations.

Cooling and heating of a quantum oscillator

The temporal evolution of a quantum oscillator under the action of an arbitrary electric field is considered bearing in mind the comparative role of absorption and induced radiation processes. An exact solution for the wave function is found for dipole and quandrupole (parametric) excitations

Particle transport in the magnetosphere: A new diffusion model

Previous transport models of the plasmasphere, ring current and radiation belts have considered either diffusive or convective transport, but not both. Since the ∇B drift speed is proportional to energy, analyses of particles with E > 100 keV have generally used only ∇B drift and diffusive transport. Conversely, particles of E < 30 keV have been treated with only E × B drift and convective transport. The ring current, which lies between these two regimes, cannot be described by either mechanism alone, so that these standard models, though widely used and otherwise applicable, fail in detail to describe the trapped ion population as observed with modern instrumentation. We develop a formalism that can describe both diffusive and convective transport in a completely general way, including UT, LT, radial, and pitch angle dependence, with arbitrary magnetic and electric field models. The formalism is general enough to rederive the electric or magnetic diffusion coefficients for trapped particles without the simplifying assumption of axial symmetry or a vanishing convection electric field, thus improving on the standard coefficients derived nearly 30 years ago. More importantly, we include the previously neglected diffusion term due to a localized, non‐global perturbation of the fields, and show that under some circumstances this term may dominate over the resonant diffusion caused by global perturbations.

The electrostatic problem for the SAW interdigital transducers in an external electric field. II. Periodic structures

For pt.I see ibid., vol.43, no.6, pp.1150-9 (1996). An exact solution of the electrostatic problem for calculating the surface charge and electric field distributions in an arbitrary periodic interdigital transducer (IDT) is given using the results of our companion paper. An arbitrary external electric field may be specified along the electrode structure with the unit cell containing one electrode, or several electrodes, of different widths. The potentials of the electrodes that may be specified are also arbitrary. It is shown that in the case without an external field, the solution includes all the known results as special cases. The case of shorted electrodes in the external electric field is investigated in detail. The surface charge and electric field distributions are calculated for a spatially harmonic external field with an arbitrary wavenumber. The results of the calculations are represented graphically for various ratios between the period of the electrode structure and the wavelength of the external field for the case of a unit cell containing one or two electrodes of different widths.