In order to understand the various appearances of geodesic acoustic modes ͑GAM͒ in experiments, the following specific problems are theoretically addressed: ͑1͒ The asymmetry of the potential field of GAMs, which is enhanced by the coupling with ion acoustic modes. It may affect GAMs in plasmas with electron temperatures higher than those of the ions. ͑2͒ The possible existence of GAMs in the lower frequency range: This is discussed in connection with the uniqueness of the kinetic response of the plasma to an external field associated with the geodesic curvature of the magnetic lines of force. ͑3͒ The extension of the theory to cover both tokamaks and helical systems: Differences between the helical-type and the tokamak-type GAMs are discussed in terms of their differences in connection length. In a device of mixed helicity, helical natured GAMs are predicted to appear depending on the intensity of the corresponding geodesic curvature and electron temperature.

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In this study, a numerical simulation of nonlinear sound wave propagation in the time domain is performed by the constrained interpolation profile (CIP) method. The CIP method is one kind of method of characteristics, and is a high-accuracy scheme in which numerical dispersion errors are hardly caused because not only the acoustic field values on the grid point but also their spatial derivatives are used in the scheme. Two CIP formulations are made for one-dimensional nonlinear sound wave propagation: one is the standard formulation in which the nonlinear equation is divided into the advection term and the nonadvection one corresponding to the nonlinear term, and the other is the formulation based on the dependence of local sound speed on particle velocity. In the latter method, the nonlinear term is included in the local sound speed of the advection term, which can be directly solved by the CIP method. The CIP conservative semi-lagrangian of the fourth-order (CIP-CSL4) scheme, which is a higher-order accuracy version of the CIP method, is also formulated. Some numerical demonstrations are performed for one-dimensional nonlinear sound propagation in air. The numerical results are compared with the analytical results. It is confirmed that the present formulation based on the dependence of local sound speed on particle velocity is more suitable for the simulation of nonlinear sound wave propagation.

Development of accurate schemes is a technical issue related to calculation of electromagnetic fields. This study uses constrained interpolation profile (CIP) method to analyze electromagnetic fields created by line current. This is a novel method proposed by Yabe. Comparison of results obtained using finite difference time domain (FDTD) analysis and CIP analysis indicates that CIP analysis provides higher accuracy using identical discretization. In addition, given the same level of accuracy, CIP analysis requires less memory and less calculation time.Index Terms-Constrained interpolation profile (CIP) method, electromagnetic field analysis, finite-difference time-domain (FDTD) method, line current, method of characteristics.

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