Nonlinear saturation of a beta-induced Alfvén eigenmode, driven by slowing down energetic particles via transit resonance, is investigated by the nonlinear hybrid magnetohyrodynamic gyrokinetic code. Saturation is characterized by frequency chirping and symmetry breaking between co- and counter-passing particles, which can be understood as the evidence of resonance detuning. The scaling of the ...

We study the coherent dynamics of excitations on vibrating chains. By applying an external field and matching the field strength with the oscillation frequency of the chain it is possible to obtain an (average) transport of an initial Gaussian wave packet. We distinguish between a uniform oscillation of all nodes of the chain and the chain being in its lowest eigenmode. Both cases can lead to d...

Eigenmode solutions are very important in stability analysis of dynamical systems. The set of eigenvalues of a non-self-adjoint differential operator originated from the linearization of some Cauchy problem is investigated. It is shown that the eigenvalues are purely imaginary, and that they are related to the eigenvalues of Heun’s differential equation. These two results are used to derive the...

In a closed volume of molten sodium an intense single-vortex-like helical flow has been produced by an outside powered propeller. At a flow rate of 0.67 m(3)/s a slowly growing magnetic field eigenmode was detected. For a slightly lower flow, additional measurements showed a slow decay of this mode. The measured results correspond satisfactorily with numerical predictions for the growth rates a...

In this paper, a high-precision eigenmode-computation analysis of arbitrary azimuthal mode numbers in periodic disc-loaded structure based on variational method will be discussed. It allows for rounding the edge of a disk hole without any approximation in shape treatment and calculates the modes exactly synchronous to the beam. It converges much faster than the mesh-based computer code. Good ag...

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schrödinger operators with a sufficien...

The non-normality of Wilson-type lattice Dirac operators has important consequences — the application of the usual concepts from the textbook (hermitian) quantum mechanics should be reconsidered. This includes an appropriate definition of observables and the refinement of computational tools. We show that the truncated singular value expansion is the optimal approximation to the inverse operato...

We analyze the output of a degenerate optical parametric amplifier using a different approach to understanding and characterizing multimode squeezed light. This approach is based on the concept of eigenmodes of the squeezing and predicts the mode structure of the local oscillator that should be used in order to measure the smallest quadrature noise. Although the importance of mode matching is w...

Eigenmode analysis is one of the most promising methods of analyzing large data sets in ongoing and near-future galaxy surveys. In such analyses, a fast evaluation of the correlation matrix in arbitrary cosmological models is crucial. The observational effects, including peculiar velocity distortions in redshift space, light-cone effects, selection effects, and effects of the complex shape of t...

We demonstrate that anisotropy of Fresnel diffraction in a birefringent medium can be quantitatively characterized by planar tensor. Eigenvectors the tensor correspond to directions minimum and maximum beam divergence. Zero eigenvalues exist for fast eigenmode near optic axis biaxial crystals autocollimated propagation. Applications are demonstrated analysis noncritical phase matching acousto-o...