Showing papers on "Scalar potential published in 1997"
Book•
17 Dec 1997
TL;DR: In this article, the Scalar Magnetic Potential (SGP) approach is used to solve the problem of approximating the SGP with respect to the Wasserstein equation. But this approach is not suitable for all applications.
Abstract: Maxwell Equations: Overview. Magnetostatics: "Scalar Potential" Approach. Solving for the Scalar Magnetic Potential. The Approximate Magnetic Potential: Properties and Shortcomings. New Tools: Whitney Elements, Symmetry. Complementary in Magnetostatistics. Magnetostatistics in Infinite Domains. Eddy-Current Problems. Mathematical Background. Appendices. Subject Index.
408 citations
TL;DR: In this paper, the authors discuss the potential of CBR anisotropy or polarization and of direct detection by the laser-interferometers to test the key prediction of inflation, which is to extend our understanding of the Universe to as early as 10 −32 sec and open a window on physics at energies of order 10 15 GeV.
Abstract: Introduction Inflation addresses most of the fundamental problems in cosmology – the origin of the flatness, large-scale smoothness, and small density inhomogeneities needed to seed all the structure seen in the Universe today. If correct, it would extend our understanding of the Universe to as early as 10 −32 sec and open a window on physics at energies of order 10 15 GeV. However, at the moment there is little evidence to confirm or to contradict inflation and no standard model of inflation. The key to testing inflation is to focus on its three basic predictions [1]: spatially flat Universe (total energy density equal to the critical energy density); almost scaleinvariant spectrum of gaussian density perturbations [2]; and almost scale-invariant spectrum of stochastic gravitational waves [3]. The first two predictions have important implications: the existence of nonbaryonic dark matter, as big-bang nucleosynthesis precludes baryons from contribution more than about 10% of the critical density [4], and the cold dark matter scenario for structure formation, based upon the idea that the nonbaryonic dark matter is slowly moving elementary particles left over from the earliest moments [5,6]. A host of cosmological observations are now beginning to sharply test the first two predictions [6]. Gravity waves are a telling test and probe of inflation: They provide a consistency check (see below); they are essential to learning about the scalar potential that drives inflation [7]; and they are a compelling signature of inflation – both a flat Universe and scale-invariant density perturbations were advocated before inflation. Detecting inflation-produced gravity waves presents a great experimental challenge [8]. In this Letter we discuss the potential of CBR anisotropy or polarization and of direct detection by the laser-interferometers to test this key prediction of inflation. Quantum Fluctuations The (Fourier) spectra of metric fluctuations excited during inflation are characterized by power laws in wavenumber k, k n for density perturbations (scalar metric fluctuations) and k nT −3 for gravity waves (tensor metric fluctuations). Scale invariance for density perturbations (n = 1) corresponds to fluctuations in the Newtonian potential that are independent of wavenumber; scale invariance for gravity waves (nT = 0) corresponds to dimensionless horizon-crossing strain amplitudes that are independent of wavenumber. The power-law indices are related to the scalar field potential, V (�), that drives inflation: n − 1 = − m 2
175 citations
TL;DR: In this paper, it was shown that a classical scalar potential with V″ V ∼ 1 can be sufficiently flattened by quantum corrections to give rise to slow roll inflation, which is the simplest way to generate an inflationary potential without fine-tuning.
125 citations
Journal Article•
TL;DR: These vector fields are shown to be connected with both an intrinsic phase characterization and a scalar potential, which allows for the generalization of the original reassignment process to a differential version based on a dynamical evolution of time-frequency particles.
Abstract: A geometrical description is given for reassignment vector fields of spectrograms. These vector fields are shown to be connected with both an intrinsic phase characterization and a scalar potential. This allows for the generalization of the original reassignment process to a differential version based on a dynamical evolution of time-frequency particles.
87 citations
TL;DR: The effects of human body model resolution on computed electric fields induced by 60 Hz uniform magnetic fields are investigated using a recently-developed scalar potential finite difference code for low-frequency electromagnetic computations in two anatomically realistic human body models.
Abstract: The effects of human body model resolution on computed electric fields induced by 60 Hz uniform magnetic fields are investigated. A recently-developed scalar potential finite difference code for low-frequency electromagnetic computations is used to model induction in two anatomically realistic human body models. The first model consists of 204 290 cubic voxels with 7.2-mm edges, while the second comprises 1 639 146 cubic voxels with 3.6-mm edges. Calculations on the lower-resolution model using, for example, the finite difference time domain or impedance methods, push the capabilities of workstations. The scalar method, in contrast, can handle the higher-resolution model using comparable resources. The results are given in terms of average and maximum electric field intensities and current density magnitudes in selected tissues and organs. Although the lower-resolution model provides generally acceptable results, there are important differences that make the added computational burden of the higher-resolution calculations worthwhile. In particular, the higher-resolution modelling generally predicts peak electric fields intensities and current density magnitudes that are slightly higher than those computed using the lower-resolution modelling. The differences can be quite large for small organs such as glands. Bioelectromagnetics 18:478–490, 1997. © 1997 Wiley-Liss, Inc.
86 citations
TL;DR: In this article, a robust and effective method is presented to solve Laplace's equation in general azimuthally symmetric geometry for the magnetic scalar potential in the region surrounding a plasma discharge which may or may not contain external conductors.
Abstract: A robustly accurate and effective method is presented to solve Laplace’s equation in general azimuthally symmetric geometry for the magnetic scalar potential in the region surrounding a plasma discharge which may or may not contain external conductors. These conductors can be topologically toroidal or spherical, and may have toroidal gaps in them. The solution is incorporated into the various magnetohydrodynamic stability codes either through the volume integrated perturbed magnetic energy in the vacuum region or through the continuity requirements for the normal component of the perturbed magnetic field and the total perturbed pressure across the unperturbed plasma–vacuum boundary. The method is based upon using Green’s second identity and the method of collocation. As useful by-products, the eddy currents and the simulation of Mirnov loop measurements are calculated.
81 citations
DOI•
01 Jan 1997
TL;DR: In this article, the authors describe the magnetic field in the aperture of an accelerator magnet in terms of the vector and complex potentials, and the relationship between a given current distribution and the resulting field harmonics is explored.
Abstract: The description of two dimensional magnetic fields of magnets used in accelerators is discussed in terms of a harmonic expansion. The expansion is derived for cylindrical components and extended to Cartesian components. The Cartesian components are also described in terms of a complex field. The rules for transformation of the expansion coefficients under various types of coordinate transformation are given. The relationship between a given current distribution and the resulting field harmonics is explored in terms of the vector and complex potentials. Explicit results are presented for some simple geometries. Finally, the harmonics allowed under various symmetries in the magnet current are discussed. 1. MULTIPOLE EXPANSION OF A TWO-DIMENSIONAL FIELD For most practical purposes related to magnetic measurements in an accelerator magnet, one is interested in the magnetic field in the aperture of the magnet, which is in vacuum and carries no current. Also, most accelerator magnets tend to be long compared to their aperture. Thus, a two dimensional description is valid for most of the magnet, except at the ends. We shall at first confine ourselves to a description of a purely two dimensional field in a current free region. The relationship between the field and the currents will be treated later in Sec. 5 and onwards. In free space, with no true currents, the curl of the magnetic field, H, is zero. Also, the magnetic induction, B, is given by μ0H, where μ0 = 4π ×10 -7 Henry/m is the permeability of free space. Consequently, the magnetic induction, B, can be expressed as the gradient of a magnetic scalar potential, Φm:
53 citations
TL;DR: In this paper, a propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in Riemann-Cartan spacetimes.
Abstract: A propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in Riemann-Cartan spacetimes. In the proposed model, the trace of the torsion tensor is derived from a scalar potential that determines the volume element of the spacetime. The equations of the model are written down for the vacuum and for various types of matter fields. Some of their properties are discussed. In particular, we show that gauge fields can interact minimally with the torsion without the breaking of gauge symmetry.
35 citations
01 Mar 1997
TL;DR: In this paper, a finite element formulation for ferromagnetic thin sheets carrying time-harmonic eddy currents is presented, where the static field outside the sheets is described by a magnetic scalar potential on one side of the sheet and by magnetic vector potential on the other side.
Abstract: A finite element formulation for ferromagnetic thin sheets carrying time-harmonic eddy currents is presented. The static field outside the sheets is described by a magnetic scalar potential on one side of the sheet and by a magnetic vector potential on the other side. Special interface conditions resulting in a symmetric finite element system matrix are developed to take account of the sheet. A simple example is presented to demonstrate the efficiency of the method.
26 citations
Posted Content•
TL;DR: Scalar fields have had a long and controversial life in gravity theories, having progressed through many deaths and resurrections as mentioned in this paper, and the first scientific gravity theory, Newton's, was that of a scalar potential field, so it was natural for Einstein and others to consider the possibility of incorporating gravity into special relativity as scalar theory.
Abstract: Scalar fields have had a long and controversial life in gravity theories, having progressed through many deaths and resurrections. The first scientific gravity theory, Newton's, was that of a scalar potential field, so it was natural for Einstein and others to consider the possibility of incorporating gravity into special relativity as a scalar theory. This effort, though fruitless in its original intent, nevertheless was useful in leading the way to Einstein's general relativity, a purely two-tensor field theory. However, a universally coupled scalar field again appeared, both in the context of Dirac's large number hypothesis and in five dimensional unified field theories as studied by Fierz, Jordan, and others. While later experimentation seems to indicate that if such a scalar exists its influence on solar system size interactions is negligible, other reincarnations have been proposed under the guise of dilatons in string theory and inflatons in cosmology. This paper presents a brief overview of this history.
18 citations
TL;DR: In this paper, the Dirac equation for a particle subject to a Coulomb potential, a 1/r scalar potential, and the potential of a magnetic monopole is solved by separation of variables using the spin-weighted spherical harmonics and the bound states are obtained.
Abstract: The Dirac equation for a particle subject to a Coulomb potential, a 1/r scalar potential, and the potential of a magnetic monopole is solved by separation of variables using the spin-weighted spherical harmonics and the bound states are obtained. It is shown that the separation constants are the eigenvalues of the z-component and the square of the total angular momentum, which includes that of the electromagnetic field and the spin of the particle. We find that, under certain conditions, there exist solutions where the spin is in the outward or inward radial direction.
TL;DR: In this paper, two ways of secondary field quantities and force calculation are discussed and compared and compared for the magnetostatic case both approaches, scalar potential and vector potential method can be applied.
Abstract: Two ways of secondary field quantities and force calculation are discussed and compared. For the magnetostatic case both approaches, scalar potential and vector potential method can be applied. The scalar potential formulation have proved to be very effective and finally the normal component of the magnetic flux density can be computed. If the vector potential method is used, it is necessary to determine the tangential component of the magnetic field strength as the secondary field value. The paper describes the method of the calculation of 3D static fields using finite difference solutions. For calculation of forces the Maxwell stress is used.
TL;DR: In the simplified version of the scalar potential model, the quantity minimized is instead the variance of the mean-square tangential component of the B field over the source surface as discussed by the authors.
Abstract: . The source-surface method offers an alternative to full MHD simulation of the heliosphere. It entails specification of a surface from which the solar wind flows normally outward along straight lines. Compatibility with MHD results requires this (source) surface to be non-spherical in general and prolate (aligned with the solar dipole axis) in prototypical axisymmetric cases. Mid-latitude features on the source surface thus map to significantly lower latitudes in the heliosphere. The model is usually implemented by deriving the B field (in the region surrounded by the source surface) from a scalar potential formally expanded in spherical harmonics, with coefficients chosen so as to minimize the mean-square tangential component of B over this surface. In the simplified (scalar) version the quantity minimized is instead the variance of the scalar potential over the source surface. The scalar formulation greatly reduces the time required to compute required matrix elements, while imposing essentially the same physical boundary condition as the vector formulation (viz., that the coronal magnetic field be, as nearly as possible, normal to the source surface for continuity with the heliosphere). The source surface proposed for actual application is a surface of constant F ≡ r - k B , where r is the heliocentric distance and B is the scalar magnitude of the B field produced by currents inside the Sun. Comparison with MHD simulations suggests that k ≈ 1.4 is a good choice for the adjustable exponent. This value has been shown to map the neutral line on the source surface during Carrington Rotation 1869 (May–June 1993) to a range of latitudes that would have just grazed the position of Ulysses during that month in which sector structure disappeared from Ulysses' magnetometer observations.
TL;DR: In this article, the authors discuss the implications of the inflaton induced scalar masses, of the supersymmetry breaking effects generated during the preheating stage as well as of the thermal corrections to the scalar potential which appear after reheating.
TL;DR: In this article, a vector plus scalar potential model was proposed for the charmonium system with a Salpeter model and general eigenvalue equations and expressions for decay observables in an onium system for such a potential both in the Feynman and Coulomb gauges.
TL;DR: In this article, a scalar/vector (S/V) potential formulation was proposed for computing accurate solutions of Maxwell's equations in the presence of perfect electrical conductors with sharp corners and highly curved surfaces.
Abstract: A method is presented for computing accurate solutions of Maxwell's equations in the presence of perfect electrical conductors (PECs) with sharp corners and highly curved surfaces using conventional nodal finite elements and a scalar/vector (S/V) potential formulation. This technique approximates the PEC with an impedance boundary condition (IBC) where the impedance is small. Critically, it couples both potentials through this boundary condition, rather than setting the scalar potential to zero. This permits cancellation of the tangential components of the vector potential, resulting in an accurate normal electric field. The cause for the inaccuracies that nodal methods experience In the presence of sharp PEC corners or highly curved PEC surfaces is elucidated. It is then shown how the inclusion of the scalar potential cures these deficiencies permitting accurate solutions. Spectral analysis of the resulting finite element matrices are shown validating the boundary conditions used. Examples are presented comparing a benchmark solution, conventional PEC and IBC boundary conditions, and the new S/V potential IBC on a PEC wedge and PEC ellipse. In both cases the new S/V IBC produces superior results.
TL;DR: In this paper, the authors proposed a novel scheme of drawing the electric lines of force based on the electric displacement using the scalar potential and illustrates the distribution of electric field of the capacitor with a long distance as an example.
Abstract: The electric lines of force are trajectories comprising the tangents of the lines of forces that act on the electric charge in the electric field. In the complicated system of the multi-dielectric and multi-conductor media, the lines of force are not necessarily continuous on the interface of the dielectric media. In the engineering application, the visualization of the electric fields is quite essential. It has been strongly believed that the electric lines of force can relatively easily be plotted using numerical analysis. However it is practically difficult to draw the electric lines of force proportional to the intensity of electric field using a scalar potential with the 2-D finite element method. The paper proposes the novel scheme of drawing the electric lines of force based on the electric displacement using the scalar potential and illustrates the distribution of electric field of the capacitor with a long distance as an example.
Posted Content•
TL;DR: In this article, a new approach to the inclusion of the chemical potential in a relativistic bosonic field theory is presented, which is mathematically more rigorous since it excludes the presence of the multiplicative anomaly.
Abstract: There are two possible methods for the inclusion of the chemical potential in a relativistic bosonic field theory. The most popular method has recently been criticised by some authors, so much so as to require a re-analysis of the entire problem. I here present a new approach to the inclusion of the chemical potential that uses the second method and zeta-function regularisation techniques. I first apply it to the non-interacting field, obtaining an expression for the effective potential which is formally coincident with the well-known one from the first method. My approach, however, seems here mathematically more rigorous since it excludes the presence of the multiplicative anomaly. I then obtain a new expression for the one loop effective potential for the interacting field. This is regularised, presents less cryptic excitation energies, shows Goldstone excitations, and in the non-interacting limit gives the expected expression. The high-temperature expansion is calculated easily and with clarity, and confirms the results of the first method for the critical temperature.
01 Jan 1997
TL;DR: The scalar potential of theories with broken supersymmetry can have a number of local minima characterized by different gauge groups as discussed by the authors, in particular those that result from the vacuum stability with respect to quantum tunneling.
Abstract: The scalar potential of theories with broken supersymmetry can have a number of local minima characterized by different gauge groups. Symmetry properties of the physical vacuum constrain the parameters of the MSSM. We discuss these constraints, in particular those that result from the vacuum stability with respect to quantum tunneling.
TL;DR: In this article, a finite-volume Maxwell solver in cartesian coordinates was developed as a part of a 3-D transient MHD code MAPS, which is capable of solving a broad class of magnetoquasistatic electromagnetic problems with moving conductors.
Abstract: A finite-volume Maxwell solver in cartesian coordinates was developed as a part of a 3-D transient MHD code MAPS. The code is capable of solving a broad class of magnetoquasistatic electromagnetic problems with moving conductors. A Coulomb gauge is easily implemented by imposing a numerical constraint on boundaries of the computational domain. To simulate problems with moving conductors, a new boundary condition for electric scalar potential on the current source surface is used. The presence of the electric scalar potential in the formulation ensures current conservation in the MAPS solution. The results of MAP3 benchmarking against 3-D finite-element code MEGA are presented.
TL;DR: In this article, a scaling limit of Hamiltonians was proposed to describe interactions of N-nonrelativistic charged particles in a scalar potential and a quantized radiation field in the Coulomb gauge with the dipole approximation.
Abstract: This paper presents a scaling limit of Hamiltonians which describe interactions of N-nonrelativistic charged particles in a scalar potential and a quantized radiation field in the Coulomb gauge with the dipole approximation. The scaling limit defines effective potentials. In one-nonrelativistic particle case, the effective potentials have been known to be Gaussian transformations of the scalar potential [J. Math. Phys.34 (1993) 4478–4518]. However it is shown that the effective potentials in the case of N-nonrelativistic particles are not necessary to be Gaussian transformations of the scalar potential.
TL;DR: In this paper, an alternative finite element T-H/sub j/-/spl psi/ formulation using cutting surfaces is proposed, where a cutting surface describing the given net current in the conductor is introduced in the nonconducting multi-connected region in order to allow a discontinuity of the scalar potential.
Abstract: Since the traditional formulation in terms of a current vector potential T and a magnetic scalar potential /spl psi/ enforces zero net current in conductors, they cannot be used to solve current driven eddy current problems. For this reason, an alternative using T-T/sub 0/-/spl psi/ formulation where T/sub 0/ described an arbitrary current distribution with the given net current in conductors has been proposed some years ago. An alternative finite element T-H/sub j/-/spl phi/ formulation using cutting surfaces is proposed. A cutting surface describing the given net current in the conductor is introduced in the nonconducting multi-connected region in order to allow a discontinuity of the scalar potential. This method also avoids cancellation errors in permeable regions and ensures a good numerical stability of the finite element scheme. The present method is validated with a 3-D current driven eddy current problem. Results are compared to T-T/sub 0/-/spl psi/ formulation computation.
21 May 1997
TL;DR: In this article, the electric field experienced by a long conductor at the Earth's surface extending from point a to point b can be represented by a voltage source V/sub ab/=/spl int/sub a//sub a/sup b/E.dl where, because of the vector potential part of electric field integration has to be done along the path of the conductor, it is shown that these parts can be uniquely identified with a distribution of charge and a changing magnetic field.
Abstract: Electric fields can be resolved into scalar potential and vector potential terms that are respectively irrotational and solenoidal: E=-/spl nabla//spl phi/-/spl part/A/sup s///spl part/t. It is shown that these parts can be uniquely identified with different sources: a distribution of charge and a changing magnetic field. Examining induction in a uniform and non-uniform earth shows that the geoelectric field affecting long conductors is principally due to an induced electric field associated with magnetic field changes. Potential gradients are a secondary effect that results from charge accumulation at conductivity boundaries. The electric field experienced by a long conductor at the Earth's surface extending from point a to point b can be represented by a voltage source V/sub ab/=/spl int//sub a//sup b/E.dl where, because of the vector potential part of the electric field integration has to be done along the path of the conductor.
TL;DR: In this article, the authors compared finite element formulations for modeling eddy current problems with jumps in conductivity and found that the nodal A scheme produced misleading results at low frequencies whilst the edge A and edge A schemes are acceptable.
Abstract: This paper compares finite element formulations for modelling eddy current problems with jumps in conductivity. We study schemes which represent the eddy current regions using nodal or edge based magnetic vector potentials. The use of an additional electric scalar potential, V, in the eddy current regions is discussed. The nodal A scheme is shown to produce misleading results at low frequencies whilst the AV and edge A schemes are acceptable.
TL;DR: The spatial power spectrum of the scalar potential of the main geomagnetic field shows a power-law behaviour at the core-mantle boundary (CMB) and an almost uniform distribution of the corresponding phases as mentioned in this paper.
Abstract: —The spatial power spectrum of the scalar potential (V) of the main geomagnetic field shows a power-law behaviour at the core-mantle boundary (CMB) and an almost uniform distribution of the corresponding phases. This is strong evidence for a fractal topography of V having a non-integer dimension of 2.2 (with an uncertainty of ± 0.1) which is, indeed, found from an analysis of the power spectra of 32 spherical harmonic models of V spanning the interval 1647 to 1990.
TL;DR: In this paper, the authors derived the wave equation of the magnetic vector potential both in the classical Lorentz gauge and in the Coulomb gauge, and analyzed the current-density fields in the environment of a dipole antenna in the nonstationary case.
Abstract: Electric and magnetic fields of wave problems are, usually, calculated from derivatives of the scalar potential, /spl phi/, and the vector potential, H=1//spl mu/ curl A and E=-grad/spl phi/-(/spl part/A)/(/spl part/t). The potentials /spl phi/ and A are obtained as solutions of wave equations in the so-called Lorentz gauge. However, in this gauge, the familiar semantics of the potentials /spl phi/ and A have significantly changed. This is particularly true for A, which, usually, manifests itself as a rotational field, and which is now augmented by an irrotational field A/sub irr/. This irrotational field component can be clearly explained if the magnetic vector potential wave equation is derived in the Coulomb gauge. Simultaneously, this derivation leads to a better understanding of the fields in the environment of a dipole antenna. We derive the wave equation of the magnetic vector potential both in the classical Lorentz gauge and in the Coulomb gauge. Subsequently, this will allow us to clearly point out the differences between the Coulomb gauge and the Lorentz gauge. In between both derivations, we elaborate the current-density fields in the environment of a dipole antenna in the non-stationary case.
30 Oct 1997
TL;DR: In this paper, a quasi-static FDTD formulation was used to compute induced electric fields and currents in a realistic human model with a high resolution for exposures to 60 Hz electric and magnetic fields.
Abstract: The objective of the research presented was to reliably compute induced electric fields and currents in a realistic human model with a high resolution for exposures to 60 Hz electric and magnetic fields. All computations were for an anatomically-derived human full-body model discretized into a set of 3.6 mm cubes. For electric field induction a hybrid method was used. In this method a new quasi-static FDTD formulation was used to compute the fields with the lower resolution of 7.2 mm. The electric field at the body surface was then used to compute the surface charge density. The charge densities from the FDTD were interpolated onto a 3.6 mm grid and used as the source of the body interior potentials and electric fields in the scalar potential finite difference method (SPFD). For magnetic induction the SPFD method was used with the magnetic vector potential as the source. Organ average, organ maximum and spatial maps of the induced electric and current density fields were obtained. These dosimetric data for 30 different organs and tissues can be analyzed from various perspectives.
TL;DR: The introduction of vector potential theory simplifies the computation of spontaneous potential (SP) and brings about the innovation of concept.
Abstract: Just as scalar potential theory can be applied to magnetostatic field, where vector potential theory is the dominating theory, so may vector potential theory be used in steady current field computations, dominated by scalar potential theory. The introduction of vector potential theory simplifies the computation of spontaneous potential (SP) and brings about the innovation of concept. Finite element method is applied to the computation based upon both vector potential theory and scalar potential theory. Their results agree very well with each other. SP correction charts computed on vector potential agree with existing ones.
TL;DR: In this paper, the authors used a particular reduced scalar potential technique enabling 3D eddy currents modeling in cases where the currents are developed in well defined paths (such as shading rings, cages etc.).
Abstract: The paper uses a particular reduced scalar potential technique enabling 3D eddy currents modelling in cases where the currents are developed in well defined paths (such as shading rings, cages etc.). This method involves a scalar potential in the whole solution domain and a single component vector quantity in the conducting parts. Experimental verification is performed by comparing computed and measured forces, developed in a contactor consisting of an E-shape electromagnet with shading rings.
07 May 1997
TL;DR: Experiments on a set of CT images show that this novel direction-based interpolation approach with discrete orthogonal polynomial decomposition not only preserves the shape structure efficiently even for the objects with complicated structures but also has a low time complexity.
Abstract: In this paper, a novel direction-based interpolation approach with discrete orthogonal polynomial decomposition is introduced. A 2D digital image is usually regarded as a sampling of an underlying 2D continuous function, which is called an image field. When the image field is considered as a scalar potential field, the interpolation problem is converted to that if the values at some points in a potential field are given, how to estimate the value of any point more accurately. Both the edges of the image and the content of the objects are well preserved if the image is interpolated along the equipotential lines instead of the coordinate axes. In this study, the equipotential direction at each pixel in the interpolated plane is calculated from the partial derivatives of the discrete orthogonal polynomial decomposition of the original image. For each point, the equipotential line through it is searched in a step-by-step way, guided by the equipotential directions. The value of a point is interpolated linearly from the values of points with known values along the equipotential line. Refinement scheme is applied to interpolate the images to the desired scale. Experiments on a set of CT images show that this method not only preserves the shape structure efficiently even for the objects with complicated structures but also has a low time complexity.