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

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Anton V. Artemyev ◽  
Anatoly I. Neishtadt ◽  
Alexei. A. Vasiliev ◽  
Xiao-Jia Zhang ◽  
Didier Mourenas ◽  
...  
Keyword(s):  
Phase Space ◽  
Resonant Interaction ◽  
Relativistic Electrons ◽  
Resonance Theory ◽  
Resonant Wave ◽  
Angle Space ◽  
Long Time ◽  
Resonant Region ◽  
Whistler Mode Waves ◽  
Basic Equations

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.

Third-order resonant wave interactions under the influence of background current fields

2015 ◽  
Vol 784 ◽  
pp. 51-73 ◽  
Author(s):  
Takuji Waseda ◽  
T. Kinoshita ◽  
L. Cavaleri ◽  
A. Toffoli
Keyword(s):  
Linear Growth ◽  
Resonant Interaction ◽  
Linear Growth Rate ◽  
Spectral Evolution ◽  
Resonance Theory ◽  
Third Order ◽  
Resonant Wave ◽  
Resonance Detuning ◽  
Wave Basin ◽  
Dynamical Time

A series of experiments were conducted in a wave basin (50 m long, 10 m wide and 5 m deep) generating two waves propagating at an angle by a directional wavemaker. When the two waves were selected from a resonant triplet, an initially non-existing wave grew as the waves propagated down the tank. The linear growth rate of the resonating wave agreed well with third-order resonance theory based on Zakharov’s reduced gravity equation. Additional experiments with opposing and coflowing mean current with large temporal and spatial variations were conducted. As the flow rate increased, the linear growth was suppressed. As reproduced numerically with Zakharov’s equation, the resonant interaction saturated at time scales inversely proportional to the magnitude of the forced random resonance detuning. It is conjectured that the resonance is detuned by the variation and not by the mean of the current field due to wavelength-dependent Doppler shift and to the refraction of wave rays. Further analysis of the spectral evolution revealed that while discrete peaks appear at high frequencies as a result of dynamical cascading, a continuously saturated spectrum develops in the background as the current speed increases. Additional experiments were conducted studying the evolution of the random directional wave on a dynamical time scale under the influence of current. Due to random resonance detuning by the current, the spectral tail tended to be suppressed.

scholarly journals Conditional Entropy: A Tool to Explore the Phase Space

1999 ◽  
Vol 172 ◽  
pp. 195-209
Author(s):  
P. Cincotta ◽  
C. Simó
Keyword(s):  
Phase Space ◽  
Chaotic Motion ◽  
Conditional Entropy ◽  
Characteristic Number ◽  
Random Variable ◽  
Arc Length ◽  
Unstable Periodic Orbits ◽  
Long Time ◽  
Stable Periodic ◽  
Lyapunov Characteristic Number

AbstractIn this paper we show that the Conditional Entropy of nearby orbits may be a useful tool to explore the phase space associated to a given Hamiltonian. The arc length parameter along the orbits, instead of the time, is used as a random variable to compute the entropy. In the first part of this work we summarise the main analytical results to support this tool while, in the second part, we present numerical evidence that this technique is able to localise (stable) periodic and quasiperiodic orbits, ‘aperiodic’ orbits (chaotic motion) and unstable periodic orbits (the ‘source’ of chaotic motion). Besides, we show that this technique provides a measure of chaos which is similar to that given by the largest Lyapunov Characteristic Number. It is important to remark that this method is very simple to compute and does not require long time integrations, just realistic physical times.

Resonant wave interactions near a critical level in a stratified shear flow

1994 ◽  
Vol 269 ◽  
pp. 1-22 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Shear Flow ◽  
Critical Level ◽  
Harmonic Component ◽  
Internal Gravity Waves ◽  
Resonant Interaction ◽  
Wave Interactions ◽  
Incoming Wave ◽  
Resonant Wave ◽  
Background Density ◽  
Stratified Shear Flow

Resonant interactions between internal gravity waves propagating in a stratified shear flow are considered for the case when the background density and shear flow vary slowly with respect to the waves. In Grimshaw (1988) triad resonances were considered, and interaction equations derived for the case when the resonance conditions are met only on certain space-time surfaces, being resonance sites. Here this analysis is extended to include higher-order resonances, with the aim of studying resonant wave interactions near a critical level. It is shown that a secondary resonant interaction between two incoming waves, in which two harmonic components of one incoming wave interact with a single harmonic component of another incoming wave, produces a reflected wave. This result is shown to agree with the study of Brown & Stewartson (1980, 1982a, b) who obtained this same result by a different approach.

scholarly journals Phase Space Analysis of Pig Ear Skin Temperature during Air and Road Transport

2019 ◽  
Vol 9 (24) ◽  
pp. 5527
Author(s):  
Miguel Garrido-Izard ◽  
Eva-Cristina Correa ◽  
José-María Requejo ◽  
Morris Villarroel ◽  
Belén Diezma
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Skin Temperature ◽  
Road Transport ◽  
Thermal Data ◽  
Intercontinental Transport ◽  
Long Time ◽  
65 H ◽  
Thermal Variability ◽  
Space Phase

High or variable ambient temperature can affect thermal regulation in livestock, but few studies have studied thermal variability during air and road transport, partly due to the lack of tools to compare thermal data from a long time series over periods of different duration. In this study, we recorded the ear skin temperature (EST) of 11 Duroc breeder pigs (7 females and 4 males) during commercial intercontinental transport from Canada to Spain, which included both road and aircraft travel and lasted 65 h. The EST was measured using a logger placed inside the left ear. Phase space diagrams EST, that is EST time series vs. itself delayed in time, were used to quantify the variability of the time-temperature series based on the areas that included all the points in the phase space. Phase space areas were significantly higher for all the animals during air travel, almost doubling that of road transport. Using the phase spaces, we identified an event during air transport that lasted 57 min, leading to a general decrease in EST by 8 °C, with respect to the average EST (34.1 °C). We also found that thermal variability was more stable in males (F = 20.81, p = 0.0014), which were also older and heavier.

Substorm Injections as a Source of Relativistic Electrons in Earth’s Outer Radiation Belt

2020 ◽  
Author(s):  
Drew Turner ◽  
Ian Cohen ◽  
Kareem Sorathia ◽  
Sasha Ukhorskiy ◽  
Geoff Reeves ◽  
...  
Keyword(s):  
Phase Space ◽  
Plasma Sheet ◽  
Radiation Belt ◽  
Energetic Electron ◽  
Local Source ◽  
Relativistic Electrons ◽  
Phase Space Density ◽  
Outer Radiation Belt ◽  
Space Density ◽  
Van Allen Probes

<p>Earth’s magnetotail plasma sheet plays a crucial role in the variability of Earth’s outer electron radiation belt. Typically, injections of energetic electrons from Earth’s magnetotail into the outer radiation belt and inner magnetosphere during periods of substorm activity are not observed exceeding ~300 keV.  Consistent with that, phase space density radial distributions of electrons typically indicate that for electrons below ~300 keV, there is a source of electrons in the plasma sheet while for electrons with energies above that, there is a local source within the outer radiation belt itself.  However, here we ask the question: is this always the case or can the plasma sheet provide a direct source of relativistic (> ~500 keV) electrons into Earth’s outer radiation belt via substorm injection? Using phase space density analysis for fixed values of electron first and second adiabatic invariants, we use energetic electron data from NASA’s Van Allen Probes and Magnetospheric Multiscale (MMS) missions during periods in which MMS observed energetic electron injections in the plasma sheet while Van Allen Probes concurrently observed injections into the outer radiation belt. We report on cases that indicate there was a sufficient source of up to >1 MeV electrons in the electron injections in the plasma sheet as observed by MMS, yet Van Allen Probes did not see those energies injected inside of geosynchronous orbit.  From global insight with recent test-particle simulations in global, dynamic magnetospheric fields, we offer an explanation for why the highest-energy electrons might not be able to inject into the outer belt even while the lower energy (< ~300 keV) electrons do. Two other intriguing points that we will discuss concerning these results are: i) what acceleration mechanism is capable of producing such abundance of relativistic electrons at such large radial distances (X-GSE < -10 RE) in Earth’s magnetotail? and ii) during what conditions (if any) might injections of relativistic electrons be able to penetrate into the outer belt?</p>

Nonlinear wave interactions in a collisionless space and time dependent warm fluid plasma

1982 ◽  
Vol 28 (2) ◽  
pp. 215-232 ◽  
Author(s):  
Jonas Larsson
Keyword(s):  
Mathematical Structure ◽  
Time Dependent ◽  
Current Response ◽  
Wave Interactions ◽  
Coupled Mode ◽  
Space And Time ◽  
Resonant Wave ◽  
Isotropic Pressure ◽  
Arbitrary Space ◽  
Basic Equations

Expressions for the current response operators of first and second order are calculated for a fluid plasma with isotropic pressure terms. The unperturbed state is an arbitrary space and time dependent solution of the basic equations. The response operators are given in a form which shows explicitly the mathematical structure behind the approximate conservation of wave energy in resonant wave interactions. The coefficients in the coupled mode equations are expressed in terms of these response operators.

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