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Title: Propagation of a cloud of hot electrons through a plasma in the presence of Langmuir scattering by ambient density fluctuations

Abstract

Gas-dynamic theory is generalized to incorporate the effects of beam-driven Langmuir waves scattering off ambient density fluctuations, and the consequent effects on the propagation of a cloud of hot electrons in an inhomogeneous plasma. Assuming Langmuir scattering as the limit of nonlinear three-wave interactions with fluctuations that are weak, low-frequency, long-wavelength ion-sound waves, the net effect of scattering is equivalent to effective damping of the Langmuir waves. Under the assumption of self-similarity in the evolution of the beam and Langmuir wave distribution functions, gas-dynamic theory shows that the effects of Langmuir scattering on the beam distribution are equivalent to a perturbation in the injection profile of the beam. Analytical expressions are obtained for the height of the plateau of the beam distribution function, wave spectral number density, total wave and particle energy density, and the beam number density. The main results of gas-dynamic theory are then compared with simulation results from numerical solutions of quasilinear equations. The relaxation of the beam in velocity space is retarded in the presence of density fluctuations and the magnitude of the upper velocity boundary is less than that in the absence of fluctuations. There are four different regimes for the height of the plateau,more » corresponding to different stages of relaxation of the beam in velocity space. Moreover, Langmuir scattering results in transfer of electrons from moderate velocity to low velocity; this effect produces an enhancement in the beam number density at small distances near the injection site and a corresponding decrease at large distances. There are sharp decreases in the profiles of the beam and total wave energy densities, which are related to dissipation of energy at large phase velocities. Due to a slower velocity space diffusion of the beam distribution in the presence of scattering effects, the spatial width of the beam is reduced while its mean velocity of propagation increases slightly.« less

Authors:
; ; ; ; ;  [1];  [2];  [3];  [4];  [5];  [3]
  1. School of Physics, University of Sydney, NSW 2006, Sydney (Australia)
  2. (Iran, Islamic Republic of) and Physics Department, Faculty of Science, Sahand University of Technology, 51335-1996 Tabriz (Iran)
  3. (Australia)
  4. (Iran, Islamic Republic of) and Faculty of Physics, Tabriz University, Tabriz 51664 (Iran)
  5. (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
20960114
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 1; Other Information: DOI: 10.1063/1.2423253; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BEAM-PLASMA SYSTEMS; DISTRIBUTION FUNCTIONS; ELECTRON BEAMS; ELECTRON TRANSFER; ELECTRONS; ENERGY DENSITY; FLUCTUATIONS; INHOMOGENEOUS PLASMA; ION ACOUSTIC WAVES; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; PHASE VELOCITY; PLASMA DENSITY; PLASMA SIMULATION; SCATTERING; SOUND WAVES

Citation Formats

Foroutan, G. R., Robinson, P. A., Sobhanian, S., Moslehi-Fard, M., Li, B., Cairns, I. H., Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha, School of Physics, University of Sydney, NSW 2006, Sydney, Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha, Faculty of Physics, Tabriz University, Tabriz 51664, and School of Physics, University of Sydney, NSW 2006, Sydney. Propagation of a cloud of hot electrons through a plasma in the presence of Langmuir scattering by ambient density fluctuations. United States: N. p., 2007. Web. doi:10.1063/1.2423253.
Foroutan, G. R., Robinson, P. A., Sobhanian, S., Moslehi-Fard, M., Li, B., Cairns, I. H., Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha, School of Physics, University of Sydney, NSW 2006, Sydney, Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha, Faculty of Physics, Tabriz University, Tabriz 51664, & School of Physics, University of Sydney, NSW 2006, Sydney. Propagation of a cloud of hot electrons through a plasma in the presence of Langmuir scattering by ambient density fluctuations. United States. doi:10.1063/1.2423253.
Foroutan, G. R., Robinson, P. A., Sobhanian, S., Moslehi-Fard, M., Li, B., Cairns, I. H., Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha, School of Physics, University of Sydney, NSW 2006, Sydney, Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha, Faculty of Physics, Tabriz University, Tabriz 51664, and School of Physics, University of Sydney, NSW 2006, Sydney. Mon . "Propagation of a cloud of hot electrons through a plasma in the presence of Langmuir scattering by ambient density fluctuations". United States. doi:10.1063/1.2423253.
@article{osti_20960114,
title = {Propagation of a cloud of hot electrons through a plasma in the presence of Langmuir scattering by ambient density fluctuations},
author = {Foroutan, G. R. and Robinson, P. A. and Sobhanian, S. and Moslehi-Fard, M. and Li, B. and Cairns, I. H. and Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha and School of Physics, University of Sydney, NSW 2006, Sydney and Research Institute for Astronomy and Astrophysics of Maragha, P.O. Box 55134-441 Maragha and Faculty of Physics, Tabriz University, Tabriz 51664 and School of Physics, University of Sydney, NSW 2006, Sydney},
abstractNote = {Gas-dynamic theory is generalized to incorporate the effects of beam-driven Langmuir waves scattering off ambient density fluctuations, and the consequent effects on the propagation of a cloud of hot electrons in an inhomogeneous plasma. Assuming Langmuir scattering as the limit of nonlinear three-wave interactions with fluctuations that are weak, low-frequency, long-wavelength ion-sound waves, the net effect of scattering is equivalent to effective damping of the Langmuir waves. Under the assumption of self-similarity in the evolution of the beam and Langmuir wave distribution functions, gas-dynamic theory shows that the effects of Langmuir scattering on the beam distribution are equivalent to a perturbation in the injection profile of the beam. Analytical expressions are obtained for the height of the plateau of the beam distribution function, wave spectral number density, total wave and particle energy density, and the beam number density. The main results of gas-dynamic theory are then compared with simulation results from numerical solutions of quasilinear equations. The relaxation of the beam in velocity space is retarded in the presence of density fluctuations and the magnitude of the upper velocity boundary is less than that in the absence of fluctuations. There are four different regimes for the height of the plateau, corresponding to different stages of relaxation of the beam in velocity space. Moreover, Langmuir scattering results in transfer of electrons from moderate velocity to low velocity; this effect produces an enhancement in the beam number density at small distances near the injection site and a corresponding decrease at large distances. There are sharp decreases in the profiles of the beam and total wave energy densities, which are related to dissipation of energy at large phase velocities. Due to a slower velocity space diffusion of the beam distribution in the presence of scattering effects, the spatial width of the beam is reduced while its mean velocity of propagation increases slightly.},
doi = {10.1063/1.2423253},
journal = {Physics of Plasmas},
number = 1,
volume = 14,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • The propagation of a cloud of hot electrons through a plasma and the generation of Langmuir waves are investigated in the presence of an externally applied uniform electric field. Using numerical simulations of the quasilinear equations the evolution of the electron distribution function and the spectral density of Langmuir waves are monitored in coordinate and velocity space. It is found that the Langmuir waves are enhanced in the presence of the electric field and the distribution functions of the beam and Langmuir waves diffuse toward large velocities. The overall self-similar characteristic of the system is preserved in the presence ofmore » the electric field. The average beam velocity is no longer constant and increases with time along its trajectory, but the acceleration is much less than that of free streaming particles. The beam number density plateaus in coordinate space and large scale, small amplitude fluctuations develop on the top of this plateau. The level of the fluctuations depends on the strength of the electric field. We also investigated the influence of the external electric field on the evolution of gas-dynamical parameters such as the height of the plateau in the beam distribution function in velocity space, its upper velocity boundary, and the local velocity spread of the beam. Due to the finite quasilinear relaxation time and spatial inhomogeneity of the electron beam, different parts of the beam are in different states of relaxation. In the region of partial relaxation the plateau is specified by both upper and lower velocity boundaries. The upper boundary of plateau increases linearly with the strength of the electric field but the lower boundary is independent of it. Contrary to the free streaming of a beam in an electric field or quasilinear relaxation in the absence of the electric field, the local velocity spread of the beam increases during its propagation. Some of the electrons at the back of the beam are also transferred by the electric field to its front, so that the height of plateau increases at large distan0009c.« less
  • The effects of plasma inhomogeneities on the propagation of a cloud of hot electrons through a cold background plasma and generation of Langmuir waves are investigated using numerical simulations of the quasilinear equations. It is found that in a plasma with decreasing density the quasilinear relaxation of the electron distribution in velocity space is accelerated and the levels of the generated Langmuir waves are enhanced. The magnitude of the induced emission rate is increased and its maximum value moves to lower velocities. Due to density gradient the height of plateau shows an increase at small distances and a corresponding decreasemore » at large distances. It is also found that in a plasma with decreasing temperature, the relaxation of the beam is retarded, the spectral density of Langmuir waves is broadened, and the height of the plateau decreases below its value in a uniform plasma. In the presence of both density and temperature gradients, at given position, the height and upper boundary of the plateau and the level of Langmuir waves are all increased at small velocities. The spatial expansion of the beam is increased by the plasma inhomogeneities, but its average velocity of propagation decreases. Initially, at a given position, the velocity at the upper boundary of the plateau is smaller in the presence of the density gradient than in the uniform plasma but the reverse is true at longer times. Due to temperature gradient, at large times and small distances, the upper boundary of the plateau is increased above its value in the uniform plasma. Because of fast relaxation, the value of the lower boundary of the plateau in the plasma with decreasing density is always less than its value in the uniform plasma. It is found that the local velocity of the beam decreases when the density gradient is present. The local velocity spread of the beam remains unchanged during the propagation of the beam in the uniform plasma, but increases in the presence of inhomogeneities.« less
  • The generation of beam-driven Langmuir waves and the propagation of an electron beam in the presence of ambient density fluctuations are numerically studied using quasilinear calculations in one spatial dimension. The random spatiotemporal density fluctuations are driven externally as ion-sound-like turbulence. The effects of Langmuir wave scattering off density inhomogeneities in three spatial dimensions are represented through effective damping of the Langmuir waves, and are included in the quasilinear model. The numerical results are explored for illustrative parameters, and Langmuir wave field statistics are compared with stochastic growth theory (SGT) predictions. Due to the combined effects of quasilinear interaction withmore » the beam and scattering off density fluctuations, the Langmuir waves show burstiness and the levels are generally lower than when the density is homogeneous, qualitatively consistent with previous predictions. Apart from early evolution, the average beam speed is approximately the same as in the homogeneous case, but relaxation of the beam is significantly retarded. Both features are in qualitative agreement with earlier predictions. Moreover, the beam distribution function displays relatively smooth variations, which implies that the burstiness in the wave levels originates predominantly from the randomness in the damping rate due to density perturbations, rather than from the stochasticity in the beam growth rate. The statistics of the Langmuir wave field show good agreement with SGT predictions, thus indicating the beam-Langmuir wave system is in a SGT state. Furthermore, variations of the density fluctuation parameters are found to affect the evolution of both beam and Langmuir waves.« less
  • The dynamics of a beam of hot electrons traveling through a cold plasma and the generation of Langmuir waves are investigated in the presence of a nonthermal tail of electrons in the background distribution function. Using quasilinear simulations, it is shown that in the presence of the nonthermal electrons, the relaxation of the beam distribution function in velocity space is retarded and the Langmuir waves are strongly damped at low velocities. The average velocity of beam propagation is almost constant but its magnitude is larger in the presence of nonthermal electrons than their absence. It is found that the self-similaritymore » of the system is preserved in the presence of nonthermal electrons. The effects of nonthermal electrons on the evolution of gas-dynamical parameters of the beam, including the height of plateau in the beam distribution function, its upper and lower velocity boundaries, and beam velocity width, are also studied. It is found that initially the values of the upper and lower velocity boundaries are almost unaltered, but at large times the lower (upper) boundary velocity is larger (smaller) in the presence of nonthermal electrons than without the nonthermal electrons.« less
  • Stimulated Raman scattering of a laser in plasmas with energetic drifting electrons was investigated by analyzing the growth of interacting waves during the Raman scattering process. The Langmuir wave and scattered electromagnetic sideband wave grow initially and are dampened after attaining a maximum level that indicates a periodic exchange of energy between the pump wave and the daughter waves. The presence of energetic drifting electrons in the laser-produced plasma influences the stimulated Raman scattering process. The plasma wave generated by Raman scattering may be influenced by the energetic electrons, which enhance the growth rate of the instability. Our results showmore » that the presence of energetic (hot) drifting electrons in a plasma has an important effect on the evolution of the interacting waves. This phenomenon is modeled via two-dimensional particle-in-cell simulations of the propagation and interaction of the laser under Raman instability.« less