skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Space-Charge Effects in the Current-Filamentation or Weibel Instability

Abstract

We consider how an unmagnetized plasma responds to an incoming flux of energetic electrons. We assume a return current is present and allow for the incoming electrons to have a different transverse temperature than the return current. To analyze this configuration we present a nonrelativistic theory of the current-filamentation or Weibel instability for rigorously current-neutral and nonseparable distribution functions, f{sub 0}(p{sub x},p{sub y},p{sub z}){ne}f{sub x}(p{sub x})f{sub y}(p{sub y})f{sub z}(p{sub z}). We find that such distribution functions lead to lower growth rates because of space-charge forces that arise when the forward-going electrons pinch to a lesser degree than the colder, backward-flowing electrons. We verify the growth rate, range of unstable wave numbers, and the formation of the density filaments using particle-in-cell simulations.

Authors:
 [1];  [2]; ;  [3];  [1];  [4]; ; ;  [5]
  1. Department of Electrical Engineering, University of California, Los Angeles, California 90095 (United States)
  2. Departments of Mechanical Engineering and Physics and Astronomy, University of Rochester, Rochester, New York 14623, USA and Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623 (United States)
  3. Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States)
  4. (United States)
  5. GoLP/Centro de Fisica dos Plasmas, Instituto Superior Tecnico, 1049-001 Lisbon (Portugal)
Publication Date:
OSTI Identifier:
20777088
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevLett.96.105002; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; DISTRIBUTION FUNCTIONS; ELECTRON TEMPERATURE; ION TEMPERATURE; NEUTRAL CURRENTS; PLASMA; PLASMA DENSITY; PLASMA INSTABILITY; PLASMA SIMULATION; SPACE CHARGE; TAIL ELECTRONS

Citation Formats

Tzoufras, M., Ren, C., Tsung, F.S., Tonge, J.W., Mori, W.B., Department of Physics and Astronomy, University of California, Los Angeles, California 90095, Fiore, M., Fonseca, R.A., and Silva, L.O. Space-Charge Effects in the Current-Filamentation or Weibel Instability. United States: N. p., 2006. Web. doi:10.1103/PhysRevLett.96.105002.
Tzoufras, M., Ren, C., Tsung, F.S., Tonge, J.W., Mori, W.B., Department of Physics and Astronomy, University of California, Los Angeles, California 90095, Fiore, M., Fonseca, R.A., & Silva, L.O. Space-Charge Effects in the Current-Filamentation or Weibel Instability. United States. doi:10.1103/PhysRevLett.96.105002.
Tzoufras, M., Ren, C., Tsung, F.S., Tonge, J.W., Mori, W.B., Department of Physics and Astronomy, University of California, Los Angeles, California 90095, Fiore, M., Fonseca, R.A., and Silva, L.O. Fri . "Space-Charge Effects in the Current-Filamentation or Weibel Instability". United States. doi:10.1103/PhysRevLett.96.105002.
@article{osti_20777088,
title = {Space-Charge Effects in the Current-Filamentation or Weibel Instability},
author = {Tzoufras, M. and Ren, C. and Tsung, F.S. and Tonge, J.W. and Mori, W.B. and Department of Physics and Astronomy, University of California, Los Angeles, California 90095 and Fiore, M. and Fonseca, R.A. and Silva, L.O.},
abstractNote = {We consider how an unmagnetized plasma responds to an incoming flux of energetic electrons. We assume a return current is present and allow for the incoming electrons to have a different transverse temperature than the return current. To analyze this configuration we present a nonrelativistic theory of the current-filamentation or Weibel instability for rigorously current-neutral and nonseparable distribution functions, f{sub 0}(p{sub x},p{sub y},p{sub z}){ne}f{sub x}(p{sub x})f{sub y}(p{sub y})f{sub z}(p{sub z}). We find that such distribution functions lead to lower growth rates because of space-charge forces that arise when the forward-going electrons pinch to a lesser degree than the colder, backward-flowing electrons. We verify the growth rate, range of unstable wave numbers, and the formation of the density filaments using particle-in-cell simulations.},
doi = {10.1103/PhysRevLett.96.105002},
journal = {Physical Review Letters},
number = 10,
volume = 96,
place = {United States},
year = {Fri Mar 17 00:00:00 EST 2006},
month = {Fri Mar 17 00:00:00 EST 2006}
}
  • Fast relativistic particles generated by an ultra strong laser pulse interacting with an overdense plasma, are the source of strong quasi-static magnetic fields. The physical mechanism underlying this process is known as the current filamentation (Weibel) instability which is an electromagnetic instability driven by the electron momentum anisotropy. Here we investigate the development of this instability in the fluid, relativistic, collisionless regime in the case of beams with a finite transverse size. We show that the development of a spatially resonant mode plays a key role in determining the kind of magnetic structure generated during the evolution of the instability.
  • High intensity laser-plasma interactions accelerate electrons to suprathermal velocities. Their current is neutralized by an induced cold electron return current. These inter-penetrating and anti-parallel currents are subject to electrostatic and electromagnetic instability. Two analytical models for electron transport are used to predict the growth rates of the linear electromagnetic beam-Weibel filamentation instability in both near-term laser-solid experiments as well as in future fast-ignition experiments. Specifications and calculations of the relevant physical parameters are made. Both models predict that instability growth is significant for the fast-ignition case. Instability development in near-term experiments is also significant, but with a greater difference betweenmore » the models' predictions at low densities.« less
  • We present three-dimensional, fully relativistic, fluid simulations of the dynamics of inhomogeneous counter streaming beams with the aim of understanding the magnetic structures that can be expected to form as a consequence of the development of the so-called Weibel instability. Ringlike structures in the transverse direction are generated as a consequence of the development of a spatially resonant mode. We describe the structures generated by beams of equal initial density and velocity and by a fast, less dense beam compensated by a slower, denser beam. We consider these two cases as schematic models of a laser produced beam propagating inmore » a plasma with nearly equal density and in a plasma much denser than the injected beam.« less
  • We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell simulations of the ion Weibel instability. The derived approximatemore » analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass.« less
  • Weibel-type filamentation instability was observed in the interaction of two counter streaming laser ablated plasma flows, which were supersonic, collisionless, and closely relevant to astrophysical conditions. The plasma flows were created by irradiating a pair of oppositely standing plastic (CH) foils with 1ns-pulsed laser beams of total energy of 1.7 kJ in two laser spots. Finally, with characteristics diagnosed in experiments, the calculated features of Weibel-type filaments are in good agreement with measurements.