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Beam‐plasma interaction in randomly inhomogeneous plasmas and statistical properties of small‐amplitude Langmuir waves in the solar wind and electron foreshock

Identifieur interne : 009201 ( Main/Exploration ); précédent : 009200; suivant : 009202

Beam‐plasma interaction in randomly inhomogeneous plasmas and statistical properties of small‐amplitude Langmuir waves in the solar wind and electron foreshock

Auteurs : V. V. Krasnoselskikh [France] ; V. V. Lobzin [France] ; K. Musatenko [France] ; J. Soucek [République tchèque] ; J. S. Pickett [États-Unis] ; I. H. Cairns [Australie]

Source :

RBID : ISTEX:AB59685298F9E5662A9D6717EF2164D52E1E1F5F

Descripteurs français

English descriptors

Abstract

A numerical model for wave propagation in an unstable plasma with inhomogeneities is developed. This model describes the linear interaction of Langmuir wave packets with an electron beam and takes into account the angular diffusion of the wave vector due to wave scattering on small‐amplitude density fluctuations, as well as suppression of the instability caused by the removal of the wave from the resonance with particles during crossing density perturbations of relatively large amplitude. Using this model, the evolution of the wave packets in inhomogeneous plasmas with an electron beam is studied. To analyze data obtained both in space experiments and numerical modeling, a Pearson technique was used to classify the spectral density distributions. It was shown that both experimental distributions obtained within the Earth's foreshock aboard the CLUSTER spacecraft and model distributions for the logarithm of wave intensity belong to Pearson type IV rather than normal. The main reason for deviations of empirical distributions from the normal one is that the effective number of regions where the waves grow is not very large and, as a consequence, the central limit theorem fails to be true under the typical conditions for the Earth's electron foreshock. For large amplitudes, it is suggested that power law tails can result from variations of wave amplitudes due to changes of group velocity in the inhomogeneous plasma, in particular due to reflection of waves from inhomogeneities.

Url:
DOI: 10.1029/2006JA012212


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Le document en format XML

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<term>Amplitude distribution</term>
<term>Angular diffusion</term>
<term>Angular width</term>
<term>Astrophys</term>
<term>Atmospheric physics</term>
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<term>Blue line</term>
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<term>Clumpy langmuir waves</term>
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<term>Corresponding thresholds</term>
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<term>Density fluctuations</term>
<term>Density perturbation</term>
<term>Density perturbations</term>
<term>Different factors</term>
<term>Different values</term>
<term>Differential equation</term>
<term>Diffusion</term>
<term>Diffusion coefficient</term>
<term>Diffusion effect</term>
<term>Dimensionless parameters</term>
<term>Distribution function</term>
<term>Earth</term>
<term>Effective growth rate</term>
<term>Effective number</term>
<term>Electric field</term>
<term>Electron beam</term>
<term>Electron foreshock</term>
<term>Electrostatic wave</term>
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<term>Empirical distributions</term>
<term>Error function</term>
<term>Experimental data</term>
<term>Finite regions</term>
<term>First test</term>
<term>Fluctuation</term>
<term>Foreshock</term>
<term>Foreshock boundary</term>
<term>Foreshock langmuir waves</term>
<term>Frequency range</term>
<term>General case</term>
<term>Geophys</term>
<term>Green curve</term>
<term>Green line</term>
<term>Group velocity</term>
<term>Growth rate</term>
<term>Gurnett</term>
<term>High frequencies</term>
<term>Impulse rate</term>
<term>Inhomogeneity</term>
<term>Inhomogeneous</term>
<term>Inhomogeneous plasma</term>
<term>Inhomogeneous plasmas</term>
<term>Instability</term>
<term>Integral equation</term>
<term>Intense langmuir waves</term>
<term>Intensive studies</term>
<term>Interplanetary medium</term>
<term>Isee propagation experiment</term>
<term>Kellogg</term>
<term>Krasnoselskikh</term>
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<term>Langmuir wave amplitudes</term>
<term>Langmuir wave packets</term>
<term>Langmuir waves</term>
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<term>Large amplitudes</term>
<term>Lett</term>
<term>Linear interaction</term>
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<term>Maximum likelihood</term>
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<term>Middle panels</term>
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<term>Moment technique</term>
<term>Nimp</term>
<term>Nonlinear</term>
<term>Nonlinear processes</term>
<term>Normal distribution</term>
<term>Normal distributions</term>
<term>Null hypothesis</term>
<term>Numerical model</term>
<term>Numerical modeling</term>
<term>Numerical simulations</term>
<term>Other hand</term>
<term>Packet</term>
<term>Parameter</term>
<term>Pearson curves</term>
<term>Pearson diagram</term>
<term>Pearson distributions</term>
<term>Pearson parameters</term>
<term>Pearson technique</term>
<term>Pearson type</term>
<term>Plasma</term>
<term>Plasma density</term>
<term>Plasma density profile</term>
<term>Plasma inhomogeneities</term>
<term>Plasma oscillations</term>
<term>Plasma waves</term>
<term>Positive growth rate</term>
<term>Present paper</term>
<term>Previous section</term>
<term>Probability density function</term>
<term>Probability distribution</term>
<term>Probability distributions</term>
<term>Radio sources</term>
<term>Random density inhomogeneities</term>
<term>Random inhomogeneities</term>
<term>Relative role</term>
<term>Shot noise</term>
<term>Significance level</term>
<term>Similar problem</term>
<term>Simulation</term>
<term>Small ratios</term>
<term>Solar physics</term>
<term>Solar radio bursts</term>
<term>Solar wind</term>
<term>Spacecraft</term>
<term>Spatial evolution</term>
<term>Spatial scales</term>
<term>Spatial variations</term>
<term>Spectral density</term>
<term>Spectral density distributions</term>
<term>Spectral energy density</term>
<term>Statistical ensemble</term>
<term>Statistical properties</term>
<term>Statistical scatter</term>
<term>Stochastic</term>
<term>Stochastic growth</term>
<term>Stochastic growth theory</term>
<term>Stochastic process</term>
<term>Stochastic wave growth</term>
<term>Terrestrial electron foreshock</term>
<term>Typical conditions</term>
<term>Typical value</term>
<term>Unstable plasma</term>
<term>Upstream shock wave</term>
<term>Wave</term>
<term>Wave amplitude</term>
<term>Wave amplitudes</term>
<term>Wave energies</term>
<term>Wave energy</term>
<term>Wave energy density</term>
<term>Wave intensity</term>
<term>Wave numbers</term>
<term>Wave packet</term>
<term>Wave packets</term>
<term>Wave propagation</term>
<term>Wave spectra</term>
<term>Wave statistics</term>
<term>Wave vector</term>
<term>amplitude</term>
<term>digital simulation</term>
<term>experimental studies</term>
<term>inhomogeneity</term>
<term>instability</term>
<term>numerical models</term>
<term>particles</term>
<term>resonance</term>
<term>solar wind</term>
<term>wave scattering</term>
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<term>Amplitude</term>
<term>Densité spectrale</term>
<term>Diffusion onde</term>
<term>Diffusion(transport)</term>
<term>Distribution densité</term>
<term>Etude expérimentale</term>
<term>Faisceau électronique</term>
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<term>Instabilité</term>
<term>Interaction faisceau plasma</term>
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<term>Perturbation densité</term>
<term>Planète Terre</term>
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<term>Propagation onde</term>
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<term>Atmospheric physics</term>
<term>Beam speed</term>
<term>Blue curve</term>
<term>Blue line</term>
<term>Blue lines</term>
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<term>Clumpy langmuir waves</term>
<term>Cluster spacecraft</term>
<term>Corresponding data point</term>
<term>Corresponding thresholds</term>
<term>Czech republic</term>
<term>Density fluctuations</term>
<term>Density perturbations</term>
<term>Different factors</term>
<term>Different values</term>
<term>Differential equation</term>
<term>Diffusion coefficient</term>
<term>Diffusion effect</term>
<term>Dimensionless parameters</term>
<term>Distribution function</term>
<term>Effective growth rate</term>
<term>Effective number</term>
<term>Electric field</term>
<term>Electron beam</term>
<term>Electron foreshock</term>
<term>Empirical distribution</term>
<term>Empirical distributions</term>
<term>Error function</term>
<term>Experimental data</term>
<term>Finite regions</term>
<term>First test</term>
<term>Fluctuation</term>
<term>Foreshock</term>
<term>Foreshock boundary</term>
<term>Foreshock langmuir waves</term>
<term>Frequency range</term>
<term>General case</term>
<term>Geophys</term>
<term>Green curve</term>
<term>Green line</term>
<term>Group velocity</term>
<term>Growth rate</term>
<term>Gurnett</term>
<term>High frequencies</term>
<term>Impulse rate</term>
<term>Inhomogeneity</term>
<term>Inhomogeneous</term>
<term>Inhomogeneous plasma</term>
<term>Inhomogeneous plasmas</term>
<term>Instability</term>
<term>Integral equation</term>
<term>Intense langmuir waves</term>
<term>Intensive studies</term>
<term>Interplanetary medium</term>
<term>Isee propagation experiment</term>
<term>Kellogg</term>
<term>Krasnoselskikh</term>
<term>Langmuir</term>
<term>Langmuir wave amplitudes</term>
<term>Langmuir wave packets</term>
<term>Langmuir waves</term>
<term>Large amplitude</term>
<term>Large amplitudes</term>
<term>Lett</term>
<term>Linear interaction</term>
<term>Logarithm</term>
<term>Lognormal distribution</term>
<term>Magnetic field</term>
<term>Main reason</term>
<term>Maximum likelihood</term>
<term>Middle panel</term>
<term>Middle panels</term>
<term>Model distributions</term>
<term>Moment technique</term>
<term>Nimp</term>
<term>Nonlinear</term>
<term>Nonlinear processes</term>
<term>Normal distribution</term>
<term>Normal distributions</term>
<term>Null hypothesis</term>
<term>Numerical model</term>
<term>Numerical modeling</term>
<term>Numerical simulations</term>
<term>Other hand</term>
<term>Packet</term>
<term>Parameter</term>
<term>Pearson curves</term>
<term>Pearson diagram</term>
<term>Pearson distributions</term>
<term>Pearson parameters</term>
<term>Pearson technique</term>
<term>Pearson type</term>
<term>Plasma</term>
<term>Plasma density</term>
<term>Plasma density profile</term>
<term>Plasma inhomogeneities</term>
<term>Plasma oscillations</term>
<term>Plasma waves</term>
<term>Positive growth rate</term>
<term>Present paper</term>
<term>Previous section</term>
<term>Probability density function</term>
<term>Probability distribution</term>
<term>Probability distributions</term>
<term>Radio sources</term>
<term>Random density inhomogeneities</term>
<term>Random inhomogeneities</term>
<term>Relative role</term>
<term>Shot noise</term>
<term>Significance level</term>
<term>Similar problem</term>
<term>Simulation</term>
<term>Small ratios</term>
<term>Solar physics</term>
<term>Solar radio bursts</term>
<term>Solar wind</term>
<term>Spacecraft</term>
<term>Spatial evolution</term>
<term>Spatial scales</term>
<term>Spatial variations</term>
<term>Spectral density distributions</term>
<term>Spectral energy density</term>
<term>Statistical ensemble</term>
<term>Statistical properties</term>
<term>Statistical scatter</term>
<term>Stochastic</term>
<term>Stochastic growth</term>
<term>Stochastic growth theory</term>
<term>Stochastic process</term>
<term>Stochastic wave growth</term>
<term>Terrestrial electron foreshock</term>
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<term>Typical value</term>
<term>Unstable plasma</term>
<term>Wave</term>
<term>Wave amplitude</term>
<term>Wave amplitudes</term>
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<div type="abstract">A numerical model for wave propagation in an unstable plasma with inhomogeneities is developed. This model describes the linear interaction of Langmuir wave packets with an electron beam and takes into account the angular diffusion of the wave vector due to wave scattering on small‐amplitude density fluctuations, as well as suppression of the instability caused by the removal of the wave from the resonance with particles during crossing density perturbations of relatively large amplitude. Using this model, the evolution of the wave packets in inhomogeneous plasmas with an electron beam is studied. To analyze data obtained both in space experiments and numerical modeling, a Pearson technique was used to classify the spectral density distributions. It was shown that both experimental distributions obtained within the Earth's foreshock aboard the CLUSTER spacecraft and model distributions for the logarithm of wave intensity belong to Pearson type IV rather than normal. The main reason for deviations of empirical distributions from the normal one is that the effective number of regions where the waves grow is not very large and, as a consequence, the central limit theorem fails to be true under the typical conditions for the Earth's electron foreshock. For large amplitudes, it is suggested that power law tails can result from variations of wave amplitudes due to changes of group velocity in the inhomogeneous plasma, in particular due to reflection of waves from inhomogeneities.</div>
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