Parametric excitation of high-frequency surface waves in a plasma-metal waveguide structure

The problem concerning the excitation of high-frequency surface waves (SW) propagating across an external magnetic field at a plasma-metal interface is considered. A homogeneous electric pump field is applied in the direction transverse with respect to the plasma-metal interface. Two high-frequency SW from different frequency ranges of existence and propagating in different directions are shown to be excited in this pump field. The instability threshold pump-field values and increments are obtained for different parameters of the considered waveguide structure. The results associated with saturation of the nonlinear instability due to self-interaction effects of the excited SW are given as well. The results are appropriate for both gaseous and semiconductor plasmas.

The dynamic stability of degenerate systems under parametric excitation

The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Parametric excitation of Rb-87 atoms in a quadrupole-Ioffe-configuration trap

We have experimentally studied the parametric excitation of Rb-87 atoms in a quadrupole-Ioffe-configuration trap. The temperature of an atomic cloud and number of trapped atoms versus time and modulation frequency of the parametric excitation field have been measured. We also noticed that the contribution of atomic collisions to the energy distributions can not be ignored in the case of weak excitation, which results in a lower temperature of the atomic cloud than by Gehm [Phys. Rev. A 58, 3914 (1998)] predicted.

Anomalous helicon wave absorption and parametric excitation of electrostatic fluctuations in a helicon-produced plasma

The nonlinear nature of the rf absorption in a helicon-produced plasma was recently evidenced by the observation that the helicon wave damping as well as the level of short-scale electrostatic fluctuations excited in the helicon plasma increases with rf power. Correlation methods using electrostatic probes as well as microwave back-scattering at the upper-hybrid resonance allow identifying the fluctuations as ion-sound and Trivelpiece– Gould waves satisfying the frequency and wavenumber matching conditions for the parametric decay instability of the helicon pump wave. Furthermore, the growth rates and thresholds deduced from their temporal growth are in good agreement with theoretical predictions for the parametric decay instability that takes into account realistic damping rates for the decay waves as well as a non-vanishing parallel wavenumber of the helicon pump. The close relationship between the rf absorption and the excitation of the fluctuations was investigated in more detail by performing time- and space-resolved measurements of the helicon wave field and the electrostatic fluctuations.

Higher order parametric excitation modes for spaceborne quadrupole mass spectrometers

This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupolemass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for both improved commercial applications and spaceflight instruments. Auxiliary excitation at frequencies near twice that of the fundamental quadrupole RF frequency provides the advantages of previously studied parametric excitation techniques, but with the added benefit of increased sensed excitation amplitude dynamic range and the ability to operate voltage scan lines through the center of upper stability islands. Using a field programmable gate array, the amplitudes and frequencies of all QMS signals are digitally generated and managed, providing a robust and stable voltage control system. These techniques are experimentally verified through an interface with a commercial Pfeiffer QMG422 quadrupole rod system. When operating through the center of a stability island formed from higher order auxiliary excitation, approximately 50% and 400% improvements in 1% mass resolution and peak stability were measured, respectively, when compared with traditional QMS operation. Although tested with a circular rod system, the presented techniques have the potential to improve the performance of both circular and hyperbolic rod geometry QMS sensors.

The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors

Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.

A rational fraction polynomials model to study vertical dynamic wheel-rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel-rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel-rail contact passing over a welding defect at different speeds.

蒙特卡罗模拟四极阱中原子的参变激发

在中性原子的磁囚禁实验中,磁阱线圈的电流噪声会激发磁阱中的原子运动,势必对原子团的温度和寿命产生不可忽视的影响。对于非简谐阱,这种激发具有能量选择特性,它又取决于电流噪声的频谱分布。选择了实验中常用的四极阱为研究对象,用直接模拟蒙特卡罗方法来模拟四极阱中原子运动的参变激发现象,得到了原子温度与原子数损失随激发频率的变化关系,并进一步计算了两个共振峰处原子温度随调制时间和调制深度的变化曲线。此外,还研究了弹性碰撞速率对参变激发过程中原子温度上升的影响。这些结果对四极阱参变激发的实验有较好的参考价值。

Spectral density of first order Piecewise linear systems excited by white noise

The Fokker-Planck (FP) equation is used to develop a general method for finding the spectral density for a class of randomly excited first order systems. This class consists of systems satisfying stochastic differential equations of form ẋ + f(x) = m/Ʃ/j = 1 h_j(x)n_j(t) where f and the h_j are piecewise linear functions (not necessarily continuous), and the n_j are stationary Gaussian white noise. For such systems, it is shown how the Laplace-transformed FP equation can be solved for the transformed transition probability density. By manipulation of the FP equation and its adjoint, a formula is derived for the transformed autocorrelation function in terms of the transformed transition density. From this, the spectral density is readily obtained. The method generalizes that of Caughey and Dienes, J. Appl. Phys., 32.11.

This method is applied to 4 subclasses: (1) m = 1, h₁ = const. (forcing function excitation); (2) m = 1, h₁ = f (parametric excitation); (3) m = 2, h₁ = const., h₂ = f, n₁ and n₂ correlated; (4) the same, uncorrelated. Many special cases, especially in subclass (1), are worked through to obtain explicit formulas for the spectral density, most of which have not been obtained before. Some results are graphed.

Dealing with parametrically excited first order systems leads to two complications. There is some controversy concerning the form of the FP equation involved (see Gray and Caughey, J. Math. Phys., 44.3); and the conditions which apply at irregular points, where the second order coefficient of the FP equation vanishes, are not obvious but require use of the mathematical theory of diffusion processes developed by Feller and others. These points are discussed in the first chapter, relevant results from various sources being summarized and applied. Also discussed is the steady-state density (the limit of the transition density as t → ∞).

Helicon Mode Formation and Radio Frequency Power Deposition in a Helicon Produced Plasma

Time- and space-resolved magnetic (B-dot) probe measurements in combination with measurements of the plasma parameters were carried out to investigate the relationship between the formation and propagation of helicon modes and the radio frequency (rf) power deposition in the core of a helicon plasma. The Poynting flux and the absorbed power density are deduced from the measured rf magnetic field distribution in amplitude and phase. Special attention is devoted to the helicon absorption under linear and nonlinear conditions. The present investigations are attached to recent observations in which the nonlinear nature of the helicon wave absorption has been demonstrated by showing that the strong absorption of helicon waves is correlated with parametric excitation of electrostatic fluctuations.

On numerical simulations of a nonlinear self-excited system with two non-ideal sources

In this work, the dynamic behavior of self-synchronization and synchronization through mechanical interactions between the nonlinear self-excited oscillating system and two non-ideal sources are examined by numerical simulations. The physical model of the system vibrating consists of a non-linear spring of Duffing type and a nonlinear damping described by Rayleigh's term. This system is additional forced by two unbalanced identical direct current motors with limited power (non-ideal excitations). The present work mathematically implements the parametric excitation described by two periodically changing stiffness of Mathieu type that are switched on/off. Copyright © 2005 by ASME.

Messung des Landé-gJ-Faktors im Grundzustand von Ca + und Untersuchung des Speicherverhaltens von Elektronen in einem Penningkäfig

Ionenkäfige und speziell Penningfallen stellen sich in der Atomphysik als außergewöhnliche Werkzeuge heraus. Zum einen bieten diese 'Teilchencontainer' die Möglichkeit atomphysikalische Präzisionsmessungen durchzuführen und zum anderen stellen Penningfallen schwingungsfähige Systeme dar, in welchen nichtlineare dynamische Prozesse an gespeicherten Teilchen untersucht werden können. In einem ersten Teil der Arbeit wurde mit der in der Atomphysik bekannten Methode der optischen Mikrowellen-Doppelresonanz Spektroskopie der elektronische g-Faktor von Ca+ mit einer Genauigkeit von 4*10^{-8} zu gJ=2,00225664(9) bestimmt. g-Faktoren von Elektronen in gebundenen ionischen Systemen sind fundamentale Größen der Atomphysik, die Informationen über die atomare Wellenfunktion des zu untersuchenden Zustandes liefern. In einem zweiten Teil der Arbeit wurde hinsichtlich der Untersuchungen zur nichtlinearen Dynamik von parametrisch angeregten gespeicherten Elektronen beobachtet, dass ab bestimmten kritischen Teilchendichten in der Penningfalle die gespeicherten Elektronen kollektive Eigenschaften manifestieren. Weiterhin wurde bei der Anregung der axialen Eigenbewegung ein Schwellenverhalten der gemessenen Subharmonischen zur 2*omega_z-Resonanz beobachtet. Dieser Schwelleneffekt lässt sich mit der Existenz eines Dämpfungsmechanismus erklären, der auf die Elektronenwolke einwirkt, so dass eine Mindestamplitude der Anregung erforderlich ist, um diese Dämpfung zu überwinden. Durch Bestimmung der charakteristischen Kurven der gedämpften Mathieuschen Differentialgleichung konnte das beobachtete Phänomen theoretisch verstanden werden.

Investigation of photorefractive subharmonics in the absence of wavemixing

Using a new optical configuration free from the influence of photorefractive optical nonlinearity, we investigate the main characteristics of the spatial subharmonic K/2 excited in a Bi12SiO20 crystal by a light-intensity pattern with wave vector K and frequency O. It is shown that in a large region of intensity and applied electric field the optimum value O of the frequency corresponds to the conditions of parametric excitation of the weakly damped eigenmodes of the medium: the space-charge waves. The threshold and above-threshold characteristics of the subharmonic regime are in good agreement with the theory.

Investigation of photorefractive subharmonics in the absence of wavemixing

Using a new optical configuration free from the influence of photorefractive optical nonlinearity, we investigate the main characteristics of the spatial subharmonic K/2 excited in a Bi12SiO20 crystal by a light-intensity pattern with wave vector K and frequency O. It is shown that in a large region of intensity and applied electric field the optimum value O of the frequency corresponds to the conditions of parametric excitation of the weakly damped eigenmodes of the medium: the space-charge waves. The threshold and above-threshold characteristics of the subharmonic regime are in good agreement with the theory.

Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling

Using a new experimental geometry, we have proved for the first time that the generation of spatial subharmonic gratings in photorefractive crystals is not dependent on optical nonlinearity. We present results which confirm that the subharmonic gratings result from a parametric excitation of ultra low-frequency eigenmodes of a crystal by a time modulated fundamental grating.