Oscillations of charged particles in an external magnetic field about steady motion

We develop a Hamiltonian formalism that can be used to study the particle dynamics near stable equilibria. The construction of an original canonical transformation allowed us to prove the conservation of the linear momentum P₃, which permitted the expansion of the Hamiltonian about a fixed point. The definition of the rotational variable h whose Poisson algebra properties played the essential role in the diagonalization of the quadratic Hamiltonian yielding two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable near a fixed point that come to light Heisenberg's and Harmonic Oscillator equations of motion of the particles, leading thus the association of the fixed point trajectories with arbitrary trajectories in its immediate neighborhood. The present formalism succeeded to treat the problem of free-electron laser dynamics and may be applied to similar cases. Received 20 October 2001     

Self-consistent calculation of electrostatic force for two kinds of mesoscopic surface structures

The scanning electrostatic force microscopy (SEFM) can acquire information of surface structures in a non-contact way. We calculate the electrostatic force between the charged tip and polarized surface structure in SEFM in the framework of self-consistent integral equation formalism (SCIEF), incorporating the image method to treat the electrostatic coupling of substrate and tip. We consider two kinds of surface structures, one is the topographic structure on the surface, the other is the dielectric structure embedded in the substrate. The force pattern of the topographic structure shows a protrusion around the surface structure. However, the force pattern displays a hollow around an embedded structure with a dielectric constant less than that of substrate medium. For an embedded structure with a larger dielectric constant, the force pattern exhibits a protrusion, and the force signal is much weaker than that of the topographic structure. Therefore, it is expected that one may identify these surface structures from the pure electrostatic force information in SEFM. The force signal of the densely arranged dielectric pads is simply the superposition of force signal of each pad individually, the interference effect of electric field is not remarkable. Received: 26 March 1998 / Accepted: 9 June 1998     

Can Superconducting Cosmic Strings Piercing Seed Black Holes Generate Supermassive Black Holes in the Early Universe?

The discovery of a large number of supermassive black holes (SMBH) at redshifts , when the Universe was only 900 million years old, raises the question of how such massive compact objects could form in a cosmologically short time interval. Each of the standard scenarios proposed, involving rapid accretion of seed black holes or black hole mergers, faces severe theoretical difficulties in explaining the short‐time formation of supermassive objects. In this work we propose an alternative scenario for the formation of SMBH in the early Universe, in which energy transfer from superconducting cosmic strings piercing small seed black holes is the main physical process leading to rapid mass increase. As a toy model, the accretion rate of a seed black hole pierced by two antipodal strings carrying constant current is considered. Using an effective action approach, which phenomenologically incorporates a large class of superconducting string models, we estimate the minimum current required to form SMBH with masses of order by . This corresponds to the mass of the central black hole powering the quasar ULAS J112001.48+064124.3 and is taken as a test case scenario for early‐epoch SMBH formation. For GUT scale strings, the required fractional increase in the string energy density, due to the presence of the current, is of order 10⁻⁷, so that their existence remains consistent with current observational bounds on the string tension. In addition, we consider an “exotic” scenario, in which an SMBH is generated when a small seed black hole is pierced by a higher‐dimensional string, predicted by string theory. We find that both topological defect strings and fundamental strings are able to carry currents large enough to generate early‐epoch SMBH via our proposed mechanism.     

Enhancement of the guide field during the current sheet formation in the three-dimensional magnetic configuration with an X line

Results are presented from studies of the formation of current sheets during exciting a current aligned with the X line of the 3D magnetic configuration, in the CS-3D device. Enhancement of the guide field (parallel to the X line) was directly observed for the first time, on the basis of magnetic measurements. After the current sheet formation, the guide field inside the sheet exceeds its initial value, as well as the field outside. It is convincingly demonstrated that an enhancement of the guide field is due to its transportation by plasma flows on the early stage of the sheet formation. The in-plane plasma currents, which produce the excess guide field, are comparable to the total current along the X line that initiates the sheet itself.     

Signal-to-noise ratio enhancement based on wavelet filtering in ultrasonic testing

In ultrasonic non-destructive testing of materials with a coarse-grained structure the scattering from the grains causes backscattering noise, which masks flaw echoes in the measured signal. Several filtering methods have been proposed for improving the signal-to-noise ratio. In this paper we present a comparative study of methods based on the wavelet transform. Experiments with stationary, discrete and wavelet packet de-noising are evaluated by means of signal-to-noise ratio enhancement. Measured and simulated ultrasonic signals are used to verify the proposed de-noising methods. For comparison, we use signal-to-noise ratio enhancement related to fault echo amplitudes and filtering efficiency specific for ultrasonic signals. The best results in our setup were achieved with the wavelet packet de-noising method.     

Generalised Chern–Simons actions for 3d gravity and κ-Poincaré symmetry

We consider Chern–Simons theories for the Poincaré, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern–Simons formulation of 3d gravity. We determine conditions under which κ-Poincaré symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern–Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that κ-Poincaré symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern–Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of κ-de Sitter symmetry, and carry out the first steps in that construction.     

Dual equilibrium in a finite aspect ratio tokamak

A new approach to high pressure magnetically-confined plasmas is necessary to design efficient fusion devices. This Letter presents a new sort of equilibrium combining two solutions of the Grad-Shafranov equation, which describes the magnetohydrodynamic equilibrium in toroidal geometry. The outer equilibrium is paramagnetic and confines the inner equilibrium, whose strong diamagnetism permits to balance large pressure gradients. The existence of both equilibria in the same volume yields a dual equilibrium structure. This combination improves free-boundary mode stability.     

Dixon's extended bodies and impulsive gravitational waves

The “reaction” of an extended body to the passage of an exact plane gravitational wave is discussed following Dixon's model. The analysis performed shows several general features, e.g. even if initially absent, the body acquires a spin induced by the quadrupole structure, the center of mass moves from its initial position, as well as certain “spin-flip” or “spin-glitch” effects which are being observed.     

Storm-Time Strong Field-Aligned Ion Upflow in Region of the SED Plume

We report the observations from the GPS TEC and DMSP F-13 satellites showing that very strong upward field-aligned （FA） ion velocity and flux in the outer region of the storm-enhanced density （SED） occurred in the event of the geomagnetic storm on 29-31 May 2003. By a method of coordinate transformation, upward FA ion velocities in excess of 25Orals are obtained from the observations of the DMSP F-13 satellite. Further, an FA ion flux is estimated to be about 4.5 x 1013 ions/m2 s in the dusk sector. The estimated FA ion velocity and flux provide a powerful direct proof to support the scenario that there is a strong coupling of particles between the ionosphere and plasmasphere in the region of the SED plume. In the process, FA ion flux transports from the ionosphere to the plasmasphere in the region of the SED plume. Therefore, the plume of SED in the ionosphere provides an important source to the enhanced density of O^＋ in the storm-time plasmasphere.     

Complex Lorentz rotations on vectors⊕pseudovectors

We study the complex structure of the space of vectors and pseudovectors Λ≡ ≡ Λ₁ ⊕ Λ₃ arising from the properties of the Hodge duality in 4-dimensional spacetimes. This structure appears naturally in the framework of its real Clifford geometric algebraCl _1,3 orCl _3,1, in which the Hodge duality is the simple multiplication by the volume unit ∈. Interpreting the linear combination of a scalar and a pseudoscalar α+β∈ as a complex number (Λ₀ ⊕ Λ₄ ⋍ ℂ), the odd subspace Λ_ ∈Cl is a left/right complex linear space, previously studied by Sobczyk. From the real metric definingCl, Λ_ inherits a natural complex bilinear normN(a). Corresponding to this norm there is the group of complex Lorentz rotations Spin_1,3 (ℂ), for which we find a formulation using exclusively the real algebraCl. We discuss its behaviour in some examples and find expressions for different decompositions into real and selfdual, real and anti-selfdual, and real and pure imaginary angle rotations. We finally apply our results to the implementation of the rotations corresponding to Euclidean and null signatures inside the real Lorentzian Clifford algebraCl.