NONLINEAR PLASMA OSCILLATIONS WITH TRAPPED ELECTRONS

1966 ◽  
Vol 44 (5) ◽  
pp. 1109-1119 ◽  
Author(s):  
H. S. C. Wang
Keyword(s):  
Wave Amplitude ◽  
Periodic Potential ◽  
Low Frequency ◽  
First Integral ◽  
Stationary Wave ◽  
Wave Form ◽  
Trapped Electrons ◽  
The Poisson Equation ◽  
Maxwellian Plasma ◽  
Excessive Number

Propagation of stationary longitudinal waves in a hot (Maxwellian) plasma is investigated, when the wave amplitude, phase velocity, and electron temperature are such that the relativistic effect is negligible but trapped electrons must be taken into account. The treatment is based on an exact solution of the nonlinear collisionless Boltzmann equation compatible with the equilibrium electron distribution. The existence, propagation, and amplitude limit of a dimensionless periodic potential wave ψ are discussed in terms of the behavior of the first integral Y(ψ) of the Poisson equation. It was found that, for α = mW2/2κT (W is the wave velocity) less than a critical value αe = 0.854, no stationary wave can exist, irrespective of its amplitude. For α slightly greater than αe, wave propagation is limited to small amplitude and low frequency. As α is further increased, waves of progressively larger amplitude can also propagate; but their amplitude is limited when Y(ψ) becomes tangent to the ψ axis at ψmin because of the excessive number of electrons trapped in the wave troughs. An expression for the maximum wave amplitude as a function of α is derived and plotted. Wavelengths for different values of α and amplitude levels are computed numerically and plotted as dispersion curves. A typical example for wave form is also displayed to show the progressive distortion from pure sinusoids due to nonlinearity and the effect of trapped electrons.

Local kinetic analysis of low-frequency electrostatic modes in tokamaks

1991 ◽  
Vol 69 (2) ◽  
pp. 102-106
Author(s):  
A. Hirose
Keyword(s):  
Dispersion Relation ◽  
Kinetic Analysis ◽  
Low Frequency ◽  
Acoustic Mode ◽  
Landau Damping ◽  
Trapped Electrons ◽  
Ion Acoustic ◽  
Transit Frequency

Analysis, based on a local kinetic dispersion relation in the tokamak magnetic geometry incorporating the ion transit frequency and trapped electrons, indicates that modes with positive frequencies are predominant. Unstable "drift"-type modes can have frequencies well above the diamagnetic frequency. They have been identified as the destabilized ion acoustic mode suffering little ion Landau damping even when [Formula: see text].

scholarly journals Circulation Regimes and Low-Frequency Oscillations in the South Pacific Sector

2003 ◽  
Vol 131 (8) ◽  
pp. 1566-1576 ◽  
Author(s):  
Andrew W. Robertson ◽  
Carlos R. Mechoso
Keyword(s):  
Singular Spectrum Analysis ◽  
Low Frequency ◽  
South Pacific ◽  
Stationary Wave ◽  
Gaussian Mixture ◽  
Reanalysis Data ◽  
Oscillatory Behavior ◽  
South American ◽  
The South ◽  
Austral Spring

Abstract The characteristics of subseasonal circulation variability over the South Pacific are examined using 10-day lowpass-filtered 700-hPa geopotential height NCEP–NCAR reanalysis data. The extent to which the variability in each season is characterized by recurrent geographically fixed circulation regimes and/or oscillatory behavior is determined. Two methods of analysis (a K-means cluster analysis and a cross-validated Gaussian mixture model) both indicate three to four geographically fixed circulation regimes in austral fall, winter, and (to some extent) spring. The spatial regime structures are found to be quite similar in each season; they resemble the so-called Pacific–South American (PSA) patterns discussed in previous studies and often referred to as PSA 1 and PSA 2. Oscillatory behavior is investigated using singular spectrum analysis. This identifies a predominantly stationary wave with a period of about 40 days and a spatial structure similar to PSA 1; it is most pronounced in winter and spring and exhibits a noticeable eastward drift as it decays. The power spectrum of variability is otherwise well approximated by a red spectrum, together with enhanced broader-band 15–30-day variability. The results presented herein indicate that low-frequency variability over the South Pacific is not dominated by a propagating wave whose quadrature phases are PSA 1 and PSA 2, as hitherto described. Rather, it is found that the variability is well described by the occurrence of three to four geographically fixed circulation regimes, with a (near) 40-day oscillation that is predominantly stationary in space. The potential subseasonal predictability implied by this duality is discussed. Only during austral spring is a strong correlation found between El Niño and the frequency of occurrence of the circulation regimes.

scholarly journals Acoustic Emission Wavelet Analysis of Filament Wound Composite Tube Fatigue Damage Process

2015 ◽  
Vol 9 (1) ◽  
pp. 214-219 ◽  
Author(s):  
Su Hua ◽  
Chang Cheng
Keyword(s):  
Acoustic Emission ◽  
Wavelet Transform ◽  
Fatigue Damage ◽  
Frequency Band ◽  
Low Frequency ◽  
High Signal ◽  
Wave Form ◽  
Radial Compression ◽  
Time Frequency ◽  
Emission Signal

This paper performed a radial compression fatigue test on glass fiber winding composite tubes, collected acoustic emission signals at different fatigue damages stages, used time frequency analysis techniques for modern wavelet transform, and analyzed the wave form and frequency characteristics of fatigue damaged acoustic emission signals. Three main frequency bands of acoustic emission signal had been identified: 80-160 kHz (low frequency band), 160-300 kHz (middle frequency band), and over 300kHz (high frequency band), corresponding to the three basic damage modes: the fragmentation of matrix resin, the layered damage of fiber and matrix, and the fracture of cellosilk respectively. The usage of wavelet transform enabled the separation of fatigue damaged acoustic emission signals from interference wave, and the access to characteristics of high signal-noise-ratio fatigue damage.

scholarly journals Classical soft graviton theorem rewritten

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Biswajit Sahoo ◽  
Ashoke Sen
Keyword(s):  
Low Frequency ◽  
Constant Term ◽  
Wave Form ◽  
Null Infinity ◽  
Final State ◽  
Massless Particles ◽  
Retarded Time ◽  
Hard Particles ◽  
State Radiation ◽  
Large Impact Parameter

Abstract Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u2, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u2 term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u2 terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

scholarly journals Dynamics of Eddy-Driven Low-Frequency Dipole Modes. Part III: Meridional Displacement of Westerly Jet Anomalies during Two Phases of NAO

2007 ◽  
Vol 64 (9) ◽  
pp. 3232-3248 ◽  
Author(s):  
Dehai Luo ◽  
Tingting Gong ◽  
Yina Diao
Keyword(s):  
Theoretical Model ◽  
Storm Track ◽  
Low Frequency ◽  
Stationary Wave ◽  
Negative Phase ◽  
Stationary Waves ◽  
The North ◽  
Westerly Jet ◽  
Two Phases ◽  
The North Atlantic Oscillation

Abstract In this paper, the north–south variability of westerly jet anomalies during the two phases of the North Atlantic Oscillation (NAO) is examined in a theoretical model. It is found that the north–south variability of the zonal mean westerly anomaly results from the interaction between the eddy-driven anomalous stationary waves with a dipole meridional structure (NAO anomalies) and topographically induced climatological stationary waves with a monopole structure, which is dependent upon the phase of the NAO. The westerly jet anomaly tends to shift northward during the positive NAO phase but southward during the negative phase. Synoptic-scale eddies tend to maintain westerly jet anomalies through the excitation of NAO anomalies, but the climatological stationary wave and its position relative to the eddy-driven anomalous stationary wave appear to dominate the north–south shift of westerly jet anomalies. On the other hand, it is shown that when the climatological stationary wave ridge is located downstream of the eddy-driven anomalous stationary wave, the storm track modulated by the NAO pattern splits into two branches for the negative phase, in which the northern branch is generally stronger than the southern one. However, the southern one can be dominant as the relative position between anomalous and climatological stationary waves is within a moderate range. The storm track for the positive phase tends to drift northeastward when there is a phase difference between the NAO anomaly and climatological stationary wave ridge downstream. Thus, it appears that the relationship between the NAO jets and storm tracks can be clearly seen from the present theoretical model.

scholarly journals Boltzmann electron PIC simulation of the E-sail effect

2015 ◽  
Vol 33 (12) ◽  
pp. 1507-1512 ◽  
Author(s):  
P. Janhunen
Keyword(s):  
Solar Wind ◽  
Hybrid Simulation ◽  
Space Propulsion ◽  
Electron Population ◽  
Trapped Electrons ◽  
Pic Simulation ◽  
Particle In Cell ◽  
The Poisson Equation ◽  
New Type ◽  
The One

Abstract. The solar wind electric sail (E-sail) is a planned in-space propulsion device that uses the natural solar wind momentum flux for spacecraft propulsion with the help of long, charged, centrifugally stretched tethers. The problem of accurately predicting the E-sail thrust is still somewhat open, however, due to a possible electron population trapped by the tether. Here we develop a new type of particle-in-cell (PIC) simulation for predicting E-sail thrust. In the new simulation, electrons are modelled as a fluid, hence resembling hybrid simulation, but in contrast to normal hybrid simulation, the Poisson equation is used as in normal PIC to calculate the self-consistent electrostatic field. For electron-repulsive parts of the potential, the Boltzmann relation is used. For electron-attractive parts of the potential we employ a power law which contains a parameter that can be used to control the number of trapped electrons. We perform a set of runs varying the parameter and select the one with the smallest number of trapped electrons which still behaves in a physically meaningful way in the sense of producing not more than one solar wind ion deflection shock upstream of the tether. By this prescription we obtain thrust per tether length values that are in line with earlier estimates, although somewhat smaller. We conclude that the Boltzmann PIC simulation is a new tool for simulating the E-sail thrust. This tool enables us to calculate solutions rapidly and allows to easily study different scenarios for trapped electrons.

Period doubling of azimuthal oscillations on a non-neutral magnetized electron column

1985 ◽  
Vol 33 (1) ◽  
pp. 59-69 ◽  
Author(s):  
R. W. Boswell ◽  
M. J. Giles
Keyword(s):  
Electron Beam ◽  
Low Frequency ◽  
Period Doubling ◽  
Wave Form ◽  
Low Density ◽  
Slow Mode ◽  
Good Qualitative Agreement ◽  
Rigid Rotator ◽  
Perturbation Amplitude ◽  
Beam Experiment

We investigate the low-frequency azimuthal oscillations on a non-neutral magnetized electron column of very low density. A perturbation analysis of the slow mode of the rigid rotator equilibrium is developed to illustrate the nature of large-amplitude fundamental-mode oscillations. The results of this theoretical analysis show two important characteristics: firstly, as the perturbation amplitude is increased the wave form ceases to be purely sinusoidal and shows period doubling. Secondly, above a certain threshold, all harmonics of the wave grow and the wave breaks. The results of the former are compared with a simple electron beam experiment and are found to be in good qualitative agreement.

scholarly journals Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
M. W. Kunz ◽  
A. A. Schekochihin ◽  
C. H. K. Chen ◽  
I. G. Abel ◽  
S. C. Cowley
Keyword(s):  
Solar Wind ◽  
Free Energy ◽  
Distribution Function ◽  
Low Frequency ◽  
Energetic Cost ◽  
Astrophysical Plasmas ◽  
Order Unity ◽  
Quantitative Measurements ◽  
Maxwellian Plasma ◽  
Field Lines

A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihinet al.,Astrophys. J. Suppl. Ser., vol. 182, 2009, pp. 310–377) to the case where the mean distribution function of the plasma is pressure-anisotropic and different ion species are allowed to drift with respect to each other – a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas such as the intracluster medium. Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g. the Alfvén ratio) are order-unity modified compared to the more commonly considered Maxwellian case, and so a quantitative theory is developed to support quantitative measurements now possible in the solar wind. Beyond these order-unity corrections, the main physical feature of low-frequency plasma turbulence survives the generalisation to non-Maxwellian distributions: Alfvénic and compressive fluctuations are energetically decoupled, with the latter passively advected by the former; the Alfvénic cascade is fluid, satisfying RMHD equations (with the Alfvén speed modified by pressure anisotropy and species drifts), whereas the compressive cascade is kinetic and subject to collisionless damping (and for a bi-Maxwellian plasma splits into three independent collisionless cascades). Secondly, the organising principle of this turbulence is elucidated in the form of a conservation law for the appropriately generalised kinetic free energy. It is shown that non-Maxwellian features in the distribution function reduce the rate of phase mixing and the efficacy of magnetic stresses, and that these changes influence the partitioning of free energy amongst the various cascade channels. As the firehose or mirror instability thresholds are approached, the dynamics of the plasma are modified so as to reduce the energetic cost of bending magnetic-field lines or of compressing/rarefying them. Finally, it is shown that this theory can be derived as a long-wavelength limit of non-Maxwellian slab gyrokinetics.

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