Collisional broadening of nonlinear resonant wave–particle interactions

A general procedure for understanding plasma behaviour when resonant wave–particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principal results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas, narrow collisional boundary layers must be retained for resonant wave–particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear processes.

Resonant wave-filament interactions as a loss mechanism for HHFW heating and current drive

Perkins et al. PRL 2012 [1] reported unexpected power losses during High Harmonic Fast Wave (HHFW) heating and current drive in NSTX. Recently, Tierens et al [2] proposed that these losses may be attributable to surface waves on field-aligned plasma filaments, which carry power along the filaments, to be lost at the endpoints where the filaments intersect the limiters. In this work, we show that there is indeed a resonant loss mechanism associated with the excitation of these surface waves, and derive an analytic expression for the power lost to surface wave modes at each filament.

Numerical analysis of wave–structure interaction of regular waves with surface-piercing inclined plates

The Mocean wave energy converter consists of two sections, hinged at a central location, allowing the device to convert energy from the relative pitching motion of the sections. In a simplified form, the scattering problem for the device can be modelled as monochromatic waves incident upon a thin, inclined, surface-piercing plate of length $$L'$$ L ′ in a finite depth $$d'$$ d ′ of water. In this paper, the flow past such a plate is solved using a Boundary Element Method (BEM) and Computational Fluid Dynamics (CFD). While the BEM solution is based on linear potential flow theory, CFD directly solves the Navier–Stokes equations. Problems of this type are known to exhibit near-perfect reflection (indicated by a reflection coefficient $$|R|\approx 1$$ | R | ≈ 1 ) of waves at specific wavenumbers $$k'$$ k ′ . In this paper, we show that the resonant motion of the fluid induces large hydrodynamic forces on the plate. Furthermore, we argue that this low-frequency resonance resembles Helmholtz resonance, and that Mocean’s device being able to tune to these low frequencies does not act like an attenuator. For the case where the water is deep ($$d'>\lambda '/2$$ d ′ > λ ′ / 2 , where $$\lambda '=2\pi /k'$$ λ ′ = 2 π / k ′ ), we find excellent agreement between our simulations and previous semi-analytical studies on the value of the resonant wave periods in deep water. We also find excellent agreement between the excitation forces on the plate computed using the BEM model, analytical results, and CFD for large inclination angles ($$\alpha > 45^\circ $$ α > 45 ∘ ). For $$\alpha \le 15^\circ $$ α ≤ 15 ∘ , both methods show the same trend, but the CFD predicts a significantly smaller peak in the excitation force compared with BEM, which we attribute to non-linear effects such as the non-linear Froude–Krylov force

Mechanical and mathematical modeling of seismic shear vibrations of a glacial massif

В статье впервые в мире разработаны теоретические положения сдвиговых сейсмических колебаний ледникового массива. Актуальность представленных научных разработок в приложении к инженерной сейсмологии и гляциологии обусловлено тем, что в недавнее время в различных регионах нашей планеты имели место внезапные срывы с гор грандиозных масс льда, что приводило к образованию мощных гляциальных селевых потоков. Эти потоки уничтожали населенные пункты и народохозяйственные объекты с многочисленными жертвами. Все мы помним катастрофический сход ледника Колка в Геналдонском ущелье в 2002г., унесшего 125 человеческих жизней. Причиной срыва ледяных масс со своих подстилающих поверхностей примерзаний является динамическое воздействие, в качестве которого мы рассматриваем землетрясение. Цель исследования. На основе современных научных методов механики сплошных сред проведение механико-математического компьютерного моделирования колебательного процесса в ледниковом массиве, когда колебание спровоцировано гармонической сейсмической волной, упавшей на подстилающую поверхность примерзания массива. В рамках выполненного моделирования содержится постановка и решение соответствующей начально-краевой задачи. Начальными данными являются как физико-механические характеристики льда, его плотность, модуль сдвига, коэффициент внутреннего (вязкого) сопротивления, так и геометрические размеры и непризматическая конфигурация массива. Искомыми величинами в поставленной начально-краевой задаче являются перемещения и напряжения, как в самом теле массива, так и на подстилающей поверхности примерзания. Методы исследования. Составленная модель представляет собой начально-краевую задачу математической физики для дифференциального уравнения гиперболического типа, в котором один коэффициент является комплексной величиной, названной комплексным модулем сдвига согласно с гипотезой Е.С. Сорокина, а другой коэффициент является переменной величиной, зависящей от пространственной координаты. Эти два особых фактора создают трудности в аналитическом способе решения начально-краевых задач. В представленной работе найден путь решения поставленной задачи в частном случае – при экспоненциальной зависимости переменного коэффициента от пространственной координаты. Результаты работы. Получена совокупность расчётных формул для вычисления напряжений и деформаций в ледниковом массиве. Доказано утверждение о том, что низкобалльная сейсмическая околорезонансная волна может отколоть ледниковый массив от подстилающей поверхности примерзания, что приведет к образованию гляциального селевого потока Theoretical studies of seismic oscillations of the glacial massif are an urgent task in the field of engineering seismology and glaciology. This statement is confirmed if we recall the case of the sudden catastrophic collapse of the Kolka glacier in 2002, which claimed the lives of 125 human lives. Aim. Conducting a mechanical and mathematical simulation of the oscillatory process in a glacial massif, when the oscillation is triggered by a harmonic seismic wave that has fallen on the underlying surface of the frozen massif. Formulation and solution of the initial boundary value problem for calculating stresses and deformations in a glacial massif. Methods. The compiled model represents an initial boundary value problem of mathematical physics for a hyperbolic differential equation, in which one coefficient is a complex quantity called the complex shift modulus according to the hypothesis of E.S. Sorokin, and the other coefficient is a variable value depending on the spatial coordinate. These two special factors create difficulties in the analytical way of solving initial-boundary value problems. In the present paper, we find a way to solve the problem in the special case - with an exponential dependence of the variable coefficient on the spatial coordinate. Results. A set of calculation formulas for calculating stresses and deformations in the glacial massif is obtained. It is proved that a low-point seismic near-resonant wave can break off the glacial massif from the underlying freezing surface, which will lead to the formation of a glacial mudflow.

The Evolution of Research on Abundances of Solar Energetic Particles

Sixty years of study of energetic particle abundances have made a major contribution to our understanding of the physics of solar energetic particles (SEPs) or solar cosmic rays. An early surprise was the observation in small SEP events of huge enhancements in the isotope 3He from resonant wave–particle interactions, and the subsequent observation of accompanying enhancements of heavy ions, later found to increase 1000-fold as a steep power of the mass-to-charge ratio A/Q, right across the elements from H to Pb. These “impulsive” SEP events have been related to magnetic reconnection on open field lines in solar jets; similar processes occur on closed loops in flares, but those SEPs are trapped and dissipate their energy in heat and light. After early controversy, it was established that particles in the large “gradual” SEP events are accelerated at shock waves driven by wide, fast coronal mass ejections (CMEs) that expand broadly. On average, gradual SEP events give us a measure of element abundances in the solar corona, which differ from those in the photosphere as a classic function of the first ionization potential (FIP) of the elements, distinguishing ions and neutrals. Departures from the average in gradual SEPs are also power laws in A/Q, and fits of this dependence can determine Q values and thus estimate source plasma temperatures. Complications arise when shock waves reaccelerate residual ions from the impulsive events, but excess protons and the extent of abundance variations help to resolve these processes. Yet, specific questions about SEP abundances remain.

Near-inertial dissipation due to stratified flow over abyssal topography

Linear theory for steady stratified flow over topography sets the range for topographic wavenumbers over which freely propagating internal waves are generated, and the radiation and breaking of these waves contribute to energy dissipation away from the ocean bottom. However, previous numerical work demonstrated that dissipation rates can be enhanced by flow over large scale topographies with wavenumbers outside of the lee wave radiative range. We conduct idealized 3D numerical simulations of steady stratified flow over 1D topography in a rotating domain and quantify vertical distribution of kinetic energy dissipation. We vary two parameters: the first determines whether the topographic obstacle is within the lee wave radiative range and the second, proportional to the topographic height, measures the degree of flow non-linearity. For certain combinations of topographic width and height, breaking occurs in pulses every inertial period, such that kinetic energy dissipation develops inertial periodicity. In these simulations, kinetic energy dissipation rates are also enhanced in the interior of the domain. In the radiative regime the inertial motions arise due to resonant wave-wave interactions. In the small wavenumber non-radiative regime, instabilities downstream of the obstacle can facilitate the generation and propagation of non-linearly forced inertial motions, especially as topographic height increase. In our simulations, dissipation rates for tall and wide non-radiative topography are comparable to those of radiative topography, even away from the bottom, which is relevant to the ocean where the topographic spectrum is such that wider abyssal hills also tend to be taller.

Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography

Seiches and resonances are two closely related phenomena that can cause damage to coastal areas. Seiches that occur in a basin at a distinct period named the resonant period may generate resonance when a wave induced by external forces enters the basin and has the same period as the seiches. Studying this period has become essential if we want to understand the resonance better. Thus, in this paper, we derive the resonant period in various shapes of semi-closed basin using the shallow water equations. The equations are then solved analytically using the separation of variables method and numerically using the finite volume method on staggered grid to discover the resonant period for each basin. To validate the numerical scheme, we compare its results against the analytical resonant periods, resulting in a very small error for each basin, suggesting that the numerical model is quite reliable in the estimation of the analytical resonant period. Further, resonant wave profiles are also observed. It is revealed that, in the coupled rectangular basin, the maximum wave elevation is disproportionate to the ratio of the length of the basin, while, in the trapezoidal basin, the ratio of the depth of the basin has no significant impact on the maximum wave elevation.

Long-term dynamics driven by resonant wave–particle interactions: from Hamiltonian resonance theory to phase space mapping

In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant trajectory analysis and then generalize them into a map in the energy/pitch-angle space. The main advances of this approach are the possibility of considering effects of many resonances and to simulate the evolution of the resonant particle ensemble on long time ranges. For illustrative purposes we consider the system with resonant relativistic electrons and field-aligned whistler-mode waves. The simulation results show that the electron phase space density within the resonant region is flattened with reduction of gradients. This evolution is much faster than the predictions of quasi-linear theory. We discuss further applications of the proposed approach and possible ways for its generalization.

Statistical EMIC diffusion models calculated by averaging observation specific diffusion coefficients

<p>Electromagnetic ion cyclotron (EMIC) waves play an important role in relativistic electron losses in the radiation belts through diffusion via resonant wave-particle interactions. We present a new statistical model of electron diffusion by EMIC waves calculated, using Van Allen Probe observations, by averaging observation specific diffusion coefficients. The resulting diffusion coefficients therefore capture a wider range of wave-particle interactions than previous average models which are calculated using average observations. These calculations, and their role in radiation belt simulations, are then compared against existing diffusion models. The new diffusion coefficients are found to significantly improve the agreement between the calculated decay of relativistic electrons and Van Allen Probes data.</p><p> </p>