A note on the formation of Debye potential well in current-carrying plasmas

1971 ◽  
Vol 6 (1) ◽  
pp. 223-228 ◽  
Author(s):  
J. R. Kan
Keyword(s):  
Thermal Equilibrium ◽  
Resonant Interaction ◽  
Landau Damping ◽  
Potential Well ◽  
Direction Parallel ◽  
Debye Potential ◽  
Collective Interaction ◽  
Test Charge ◽  
Net Flux ◽  
The Waves

The field of a test charge at rest in a plasma is known to be shielded via the collective interaction between the test charge and the particles of the plasma. In a thermal equilibrium plasma, the shielded potential has a spatial variation of the Debye form exp (— r)/r. In this note we will show that, in a collisionless current-carrying plasma, the potential profile along the radial direction parallel to the current changes from the Debye form to a potential well form, and causes a reversal of the ele ctric field of the test charge. The formation of the Debye potential well is attributed to the resonant interaction between the particles and the waves stationary in the test charge frame when the net flux of charged particles is different from zero. This is the same type of resonant interaction which leads to the well-known Landau damping (Landau 1946).

An experimental investigation of resonant interaction of a rectangular jet with a flat plate

2015 ◽  
Vol 779 ◽  
pp. 751-775 ◽  
Author(s):  
K. B. M. Q. Zaman ◽  
A. F. Fagan ◽  
J. E. Bridges ◽  
C. A. Brown
Keyword(s):  
Mach Number ◽  
Flat Plate ◽  
Cross Section ◽  
Leading Edge ◽  
Resonant Interaction ◽  
Trailing Edge ◽  
Resonant Condition ◽  
Direction Parallel ◽  
Rectangular Jet ◽  
Axis Switching

The interaction between an 8:1 aspect ratio rectangular jet and a flat plate, placed parallel to the jet, is addressed in this study. At high subsonic conditions and for certain relative locations of the plate, a resonance takes place with accompanying audible tones. Even when the tone is not audible the sound pressure level spectra are often marked by conspicuous peaks. The frequencies of these peaks, as functions of the plate’s length, its location relative to the jet as well as jet Mach number, are studied in an effort to understand the flow mechanism. It is demonstrated that the tones are not due to a simple feedback between the nozzle exit and the plate’s trailing edge; the leading edge also comes into play in determining the frequency. With parametric variation, it is found that there is an order in the most energetic spectral peaks; their frequencies cluster in distinct bands. The lowest frequency band is explained by an acoustic feedback involving diffraction at the plate’s leading edge. Under the resonant condition, a periodic flapping motion of the jet column is seen when viewed in a direction parallel to the plate. Phase-averaged Mach number data on a cross-stream plane near the plate’s trailing edge illustrate that the jet cross-section goes through large contortions within the period of the tone. Farther downstream a clear ‘axis switching’ takes place for the time-averaged cross-section of the jet that does not occur otherwise for a non-resonant condition.

scholarly journals Asymptotic Analysis of Nonlinear Resonance Interaction of Capillary Waves of Arbitrary Symmetry on Moving Charged Jet at Multimode Initial Deformation

2021 ◽  
Vol 57 (3) ◽  
pp. 72-82
Author(s):  
S. Shiryaeva ◽  
Keyword(s):  
Surface Tension ◽  
Nonlinear Resonance ◽  
Radial Electric Field ◽  
Resonant Interaction ◽  
Capillary Waves ◽  
Initial Deformation ◽  
Physical Parameters ◽  
Dimensionless Amplitude ◽  
Material Environment ◽  
The Waves

The problem of research of a nonlinear resonance between capillary waves on a surface of the charged jet at multimode initial deformation moving regarding the material environment is considered. It is shown in analytical asymptotic calculations of the second order on the dimensionless amplitude of oscillations that on a surface of a jet an internal nonlinear resonant interaction of capillary waves of any symmetry, both degenerate and secondary combinational, takes place. Positions of resonances depend on physical parameters of the system: the values of the coefficient of a surface tension and of the radial electric field at a surface of a jet, the velocity of its movement regarding the material environment, the values of the wave and azimuthal numbers of the interacting waves, a range of the waves defining initial deformation.

Observations and simulations of foreshock waves during magnetic clouds

2020 ◽  
Author(s):  
Lucile Turc ◽  
Owen Roberts ◽  
Martin Archer ◽  
Minna Palmroth ◽  
Markus Battarbee ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Wave Field ◽  
Geomagnetic Storms ◽  
Wave Activity ◽  
Bow Shock ◽  
Magnetic Clouds ◽  
Direction Parallel ◽  
High Magnetic Field Strength ◽  
The Waves

<p>The foreshock is a region of intense wave activity, situated upstream of the quasi-parallel sector of the terrestrial bow shock. The most common type of waves in the Earth's ion foreshock are quasi-monochromatic fast magnetosonic waves with a period of about 30 s. In this study, we investigate how the foreshock wave field is modified when magnetic clouds, a subset of coronal mass ejections driving the most intense geomagnetic storms, interact with near-Earth space. Using observations from the Cluster constellation, we find that the average period of the fast magnetosonic waves is significantly shorter than the typical 30 s during magnetic clouds, due to the high magnetic field strength inside those structures, consistent with previous works. We also show that the quasi-monochromatic waves are replaced by a superposition of waves at different frequencies. Numerical simulations performed with the hybrid-Vlasov model Vlasiator consistently show that an enhanced upstream magnetic field results in less monochromatic wave activity in the foreshock. The global view of the foreshock wave field provided by the simulation further reveals that the waves are significantly smaller during magnetic clouds, both in the direction parallel and perpendicular to the wave vector. We estimate the transverse extent of the waves using a multi-spacecraft analysis technique and find a good agreement between the numerical simulations and the spacecraft measurements. This suggests that the foreshock wave field is structured over smaller scales during magnetic clouds. These modifications of the foreshock wave properties are likely to affect the regions downstream - the bow shock, the magnetosheath and possibly the magnetosphere - as foreshock waves are advected earthward by the solar wind.</p>

Two-sensor microtremor SPAC method: potential utility of imaginary spectrum components

2019 ◽  
Author(s):  
Ikuo Cho
Keyword(s):  
Imaginary Part ◽  
Quality Data ◽  
Potential Utility ◽  
Coefficient Estimates ◽  
Direction Parallel ◽  
Seismic Arrays ◽  
Site Field ◽  
Relative Errors ◽  
The Waves ◽  
Array Axis

Summary We build a model of discretization errors, known as directional aliasing, to theoretically evaluate how biases in the microtremor spatial autocorrelation (SPAC) coefficient, or the real part of the SPAC spectrum of microtremor analysis, are related to the magnitudes of the imaginary part when a seismic array of only two sensors is used. By using this model, we investigate the potential utility of the imaginary spectrum component as an indicator of applicability of the two-sensor SPAC method to the field of microtremors generated at an observation site. Field data of microtremors from compact seismic arrays (1–15 m) are used to test the model. It is found that, when the imaginary components are very large in magnitude (where the threshold depends on the rk, the array radius times the wavenumber), the field of microtremors is dominated by waves arriving from a single direction parallel to the array axis and the SPAC coefficients tend to be underestimated in small rk ranges (i.e. rk < 3.8; the range considered throughout this study). In the present study, which is based on the observations of 400 microtremor arrays, the underestimates seldom exceeded 30 per cent. The SPAC coefficient estimates could be corrected in that case by using information on the imaginary part. When the imaginary components are very modest in magnitude, by contrast, there are two possible scenarios: either (i) the waves are arriving predominantly from a single direction perpendicular to the array axis and the SPAC coefficients are wildly overestimated (i.e. there was a small percentage of low-quality data, with relative errors exceeding +50 per cent, based on the observed data analyses), or (ii) the wavefield is close to isotropic and the SPAC coefficients are unbiased (i.e. 70–90 per cent of all observed data fell within the relative error range of ±20 per cent). It is difficult in that case to have SPAC coefficient estimates corrected by using information on the imaginary part alone.

Nonlinear bound on unstable electrostatic fluctuation energy for non-relativistic non-neutral electron flow in a planar diode with applied magnetic field

1985 ◽  
Vol 33 (2) ◽  
pp. 157-169 ◽  
Author(s):  
Ronald C. Davidson
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Thermal Equilibrium ◽  
Maxwell Equations ◽  
Initial Conditions ◽  
Electron Flow ◽  
Reference State ◽  
Planar Diode ◽  
Net Flux ◽  
Fluctuation Energy

Global conservation constraints satisfied by the Vlasov-Maxwell equations are used to obtain a nonlinear bound on the unstable electrostatic fluctuation energy that can develop for non-relativistic non-neutral electron flow in a planar diode with an axial applied magnetic field. It is shown that the Heimholte free energy is a minimum for the thermal equilibrium reference state. The nonlinear bound on unstable fluctuation energy that can develop for general initial conditions is calculated for the case of flute perturbations with no axial dependence. To determine the lowest upper bound on fluctuation energy consistent with conservation constraints, the density, temperature and drift velocity of the reference state are chosen to minimize the nonlinear bound. The analysis assumes that the net flux of particles, momentum, and energy, vanish identically at the cathode and at the anode.

scholarly journals Damped perturbations in stellar systems: Genuine modes and Landau-damped waves

2021 ◽  
Author(s):  
E V Polyachenko ◽  
I G Shukhman ◽  
O I Borodina
Keyword(s):  
Initial Perturbation ◽  
Stability Study ◽  
Landau Damping ◽  
Complex Conjugate ◽  
Stellar Systems ◽  
Initial Value ◽  
Set Up ◽  
The Stability ◽  
The Waves ◽  
Problem Versus

Abstract This research was stimulated by the recent studies of damping solutions in dynamically stable spherical stellar systems. Using the simplest model of the homogeneous stellar medium, we discuss nontrivial features of stellar systems. Taking them into account will make it possible to correctly interpret the results obtained earlier and will help to set up decisive numerical experiments in the future. In particular, we compare the initial value problem versus the eigenvalue problem. It turns out that in the unstable regime, the Landau-damped waves can be represented as a superposition of van Kampen modes plus a discrete damped mode, usually ignored in the stability study. This mode is a solution complex conjugate to the unstable Jeans mode. In contrast, the Landau-damped waves are not genuine modes: in modes, eigenfunctions depend on time as exp ( − iωt), while the waves do not have eigenfunctions on the real v-axis at all. However, ‘eigenfunctions’ on the complex v-contours do exist. Deviations from the Landau damping are common and can be due to singularities or cut-off of the initial perturbation above some fixed value in the velocity space.

scholarly journals Nonlinear Landau Damping of Alfven Waves and the Production and Propagation of Cosmic Rays

1981 ◽  
Vol 94 ◽  
pp. 255-256
Author(s):  
R. J. Stoneham
Keyword(s):  
Cosmic Rays ◽  
Phase Speed ◽  
Alfven Waves ◽  
Magnetized Plasma ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Fermi Acceleration ◽  
Image Position ◽  
Hydromagnetic Waves ◽  
The Waves

The existence of hydromagnetic waves (waves whose frequency ω is less than the ion gyrofrequency Ωi = eB/mic) in a collisionless magnetized plasma with β, the ratio of plasma pressure to magnetic pressure, much greater than unity is required in theories for Fermi acceleration of cosmic rays by converging scattering centres at a shock front, in theories for the adiabatic cooling of cosmic rays due to trapping by plasma instabilities in an expanding supernova remnant (Kulsrud and Zweibel 1975, Schwartz and Skilling 1978) and in theories for resonant scattering of cosmic rays by hydromagnetic waves in the hot phase of the interstellar medium (Holman et al. 1979). Hydromagnetic waves may be damped by thermal ion cyclotron damping for wavenumbers k≳Ωi/vi, where vi = (Ti/mi)1/2 is the average thermal ion speed, and by linear Landau damping for non-zero angles of propagation with respect to the ambient magnetic field (Foote and Kulsrud 1979). Damping by both these processes is strong in a high-β plasma where there are many particles travelling at the phase speed of the waves. Hydromagnetic waves propagating along may be damped by nonlinear wave-particle interactions, the most important of which is thermal ion Landau damping of the beat wave of two Alfvén waves. This nonlinear process has the effect of transferring energy from the waves to the particles and can therefore be considered as a damping process for the waves.

A Discussion on the early days of ionospheric research and the theory of electric and magnetic waves in the ionosphere and magnetosphere - Waves in a hot plasma

1975 ◽  
Vol 280 (1293) ◽  
pp. 95-110 ◽  
Keyword(s):  
Cyclotron Frequency ◽  
Phase Speed ◽  
Direct Application ◽  
Magnetized Plasma ◽  
Landau Damping ◽  
Unperturbed Motion ◽  
Hot Plasma ◽  
New Phenomena ◽  
The Waves ◽  
Thermal Speed

In studying wave propagation in a hot plasma, we treat the dynamics of the medium by kinetic theory rather than by continuum mechanics. The theory thus combines Maxwell’s equations with a transport equation in phase space (the Vlasov equation). An outline of the required procedure will be given. Some of the results are in close agreement with those of the fluid treatment provided the specific heat ratio is appropriately chosen. This is generally the case if the phase speed of the waves well exceeds the thermal speed of the electrons and, for a magnetized plasma, the frequency is not close to a harmonic of the cyclotron frequency. New phenomena are found if there are particles whose unperturbed motion is in resonance with the wave field. In the unmagnetized case this results in Landau damping or in instabilities, the latter being analogous to the mechanism of the laser. In the magnetized case there are, in addition, completely new modes of propagation for waves travelling approximately normal to the applied field. Many of these phenomena find direct application in ionospheric phenomena and diagnostics.

scholarly journals Nonlinear low-frequency wave aspect of foreshock density holes

2008 ◽  
Vol 26 (12) ◽  
pp. 3707-3718 ◽  
Author(s):  
N. Lin ◽  
E. Lee ◽  
F. Mozer ◽  
G. K. Parks ◽  
M. Wilber ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Plane Electromagnetic Wave ◽  
Timing Analysis ◽  
Low Frequency ◽  
Resonant Interaction ◽  
Ion Temperature ◽  
Temperature Anisotropy ◽  
Frequency Wave ◽  
Wave Nature ◽  
The Waves

Abstract. Recent observations have uncovered short-duration density holes in the Earth's foreshock region. There is evidence that the formation of density holes involves non-linear growth of fluctuations in the magnetic field and plasma density, which results in shock-like boundaries followed by a decrease in both density and magnetic field. In this study we examine in detail a few such events focusing on their low frequency wave characteristics. The propagation properties of the waves are studied using Cluster's four point observations. We found that while these density hole-structures were convected with the solar wind, in the plasma rest frame they propagated obliquely and mostly sunward. The wave amplitude grows non-linearly in the process, and the waves are circularly or elliptically polarized in the left hand sense. The phase velocities calculated from four spacecraft timing analysis are compared with the velocity estimated from δE/δB. Their agreement justifies the plane electromagnetic wave nature of the structures. Plasma conditions are found to favor firehose instabilities. Oblique Alfvén firehose instability is suggested as a possible energy source for the wave growth. Resonant interaction between ions at certain energy and the waves could reduce the ion temperature anisotropy and thus the free energy, thereby playing a stabilizing role.

On the kinetic theory of stable and weakly unstable plasma. Part 2

1969 ◽  
Vol 3 (1) ◽  
pp. 119-147 ◽  
Author(s):  
A. Rogister ◽  
C. Oberman
Keyword(s):  
Kinetic Equation ◽  
Kinetic Theory ◽  
Time Evolution ◽  
Particle Distribution ◽  
Landau Damping ◽  
Collisional Damping ◽  
Field Fluctuations ◽  
The One ◽  
The Waves ◽  
Unstable Plasma

In plasma, where collective motions are made possible by the long range of the Coulomb interaction, there is properly no general kinetic equation for the one-particle distribution function alone. In part 1, we gave the foundations of an enlarged kinetic theory of plasma where the time evolution of the electric field fluctuations Ik is considered simultaneously with the time evolution of the one-particle distribution F. Here we improve these equations in a systematic fashion to include all processes which are relevant in stable and weakly unstable plasma. More precisely, the equation for the waves now includes, besides Landau damping and Cerenkov emission, the effect of collisional damping and nonlinear Landau damping, as well as emission via particle-particle scattering (bremsstrahlung), wave-particle and wave-wave scattering. The particle kinetic equation is also improved accordingly so that we obtain a kinetic description which is uniformly valid for all plasma réegimes, if one excludes strong turbulence (for which there is at present no completely satisfactory statistical theory).

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