Weibel Instability Growth Rate Research Articles

Weibel instability in the field of a short laser pulse

The growth rate of Weibel instability in a plasma interacting with a high-frequency pulse with a duration less or comparable with the electron mean free time is determined. The growth rate is shown to decrease with decreasing pulse duration. It is found that instability can develop after the short pulse is switched off and the generated magnetic field no longer affects electron motion in the high-frequency field.

Laser pulse reflection by anisotropic plasma

The effect of anomalous amplification of test laser pulse reflected by a nonequilibrium plasma formed under atom ionization by a strong pulse of circularly polarized wave is described. It is shown that the gain in radiation intensity may reach ten orders of magnitude. The most effective amplification takes place for frequencies comparable with the Weibel instability growth rate.

On the stability analysis of electromagnetic waves along the external magnetic field in a magnetized microwave-produced plasma

The stability of a plasma produced due to the interaction of a high-frequency, circularly polarized microwave (MW) field with a dilute neutral gas is investigated in the presence of an axial external magnetic field. Here the investigation is extended for excited electromagnetic waves, which propagate parallel to the external magnetic field, in the short and long wavelength limits. It is shown that the unstable Weibel mode grows under the competition of MW and external magnetic fields. However, increasing the MW field amplitude increases the Weibel instability growth rate, and the instability disappears with a sufficiently strong magnetic field. It has already been revealed that the Weibel mode oscillates very slowly on time (ℜ(ω) ≪ ωpe) in a magnetized plasma, in contrast to the case of a non-magnetized plasma where that mode does not oscillate. The numerical calculations indicate that a different unstable mode is generated during the plasma production. This unstable mode is resonant (ℜ(ω) > ℑ(ωmax), where ℑ(ωmax) denotes the maximum imaginary part of the mode frequency), oscillates very fast (ℜ(ω) > ωpe) and has a large increment compared with the Weibel mode. Furthermore, a low-frequency Alfvén mode spectrum analysis predicts that the Alfvén mode velocity increases slightly for such and anisotropic plasma. The analytical and numerical results are in good agreement for a weakly magnetized plasma in the long wavelength limit.

Streaming instabilities of intense charged particle beams propagating along a solenoidal magnetic field in a background plasma

Streaming instabilities of intense charged particle beams propagating along a solenoidal magnetic field in a background plasma are studied analytically and numerically. It is shown that the growth rate of the electromagnetic Weibel instability is modified by a relatively weak solenoidal magnetic field such that ωce>βbωpe, where ωce is the electron gyrofrequency, ωpe is the electron plasma frequency, and βb is the ion-beam velocity relative to the speed of light. Moreover, the Weibel instability is limited to very small propagation angles and long longitudinal wavelengths satisfying k∥2⪡k⊥2 and c2k∥2⪡ωpb2ωpi2∕(ωpb2+ωpi2), where ωpb and ωpi are the plasma frequencies of the beam ions and the background plasma ions, respectively. For shorter longitudinal wavelengths, the electrostatic lower-hybrid instability becomes dominant. In this paper, the growth rates of various electrostatic beam-plasma instabilities and the electromagnetic Weibel instability are compared, and the space-time development of the modified two-stream instability is studied in detail and compared with numerical simulations.

Cumulative effect of the Weibel-type instabilities in symmetric counterstreaming plasmas with kappa anisotropies

Counterstreaming plasma structures are ubiquitous in laboratory experiments and astrophysical systems, and they are investigated either to prevent unstable modes arising in beam-plasma experiments or to prove the existence of large scale magnetic fields in astrophysical objects. Filamentation instability arises in a counterstreaming plasma and is responsible for the magnetization of the plasma. A filamentationally unstable mode is described by assuming two symmetric counterstreaming plasmas, each with an isotropic Lorentzian (kappa) distribution. In this case, the filamentation instability growth rate can reach a maximum value markedly larger than that for a plasma with a Maxwellian distribution function. This behavior is opposite to what was observed for the Weibel instability growth rate in a bi-kappa plasma, which is always smaller than that obtained for a bi-Maxwellian plasma. The approach is further generalized for a counterstreaming plasma with a bi-kappa temperature anisotropy. In this case, the filamentation instability growth rate is enhanced by the Weibel effect when the plasma is hotter in the streaming direction, and the growth rate becomes even larger. These effects significantly improve the efficiency of the magnetic field generation, and provide further support for the potential role of the Weibel-type instabilities in the fast magnetization scenarios.

Electron temperature anisotropy modeling and its effect on anisotropy-magnetic field coupling in an underdense laser heated plasma

The laser interaction with an underdense plasma leads to an anisotropic laser heating of electrons. This temperature anisotropy gradient in turn is the source of an early magnetic field, which has an important effect on the plasma evolution, due to the thermal flux reduction. We describe the temperature anisotropy by an evolution equation including the anisotropy-magnetic field coupling and observe a rather efficient magnetic field generation. However at high anisotropy levels, a small-scale instability emerges, leading to a serious problem in numerical calculations. We introduce the kinetics effects, which fix the problem by the anisotropy diffusion through the heat flux tensor. A constant-coefficient Fokker-Planck model in the 2-D geometry allows us to derive an anisotropy diffusion term. The diffusion coefficient is fitted from the kinetic theory of the collisional anisotropic (Weibel) instability growth rate. Such an anisotropy diffusion term wipes out the unphysical instability without any undesirable smoothing. This diffusion along with the viscosity term leads also to a quite good restitution of the Weibel instability growth rate and to the short wavelength cutoff, even in a weakly collisional situation. This allows us to use such a model to predict emergence the Weibel instability as well as its saturation.

Magnetic field generation in a plasma produced through atomic ionization by circularly polarized radiation

We have established the dependences of the maximum Weibel instability growth rate and the corresponding wavenumber on the degree of anisotropy in the photoelectron distribution formed through tunnel atomic ionization in the field of a circularly polarized short laser pulse. We show how the relaxation of the initial distribution of photoelectrons due to their collisions with ions affects the pattern of generation of a quasi-static magnetic field.

Eigenmodes and growth rates of relativistic current filamentation instability in a collisional plasma

I theoretically found eigenmodes and growth rates of relativistic current filamentation instability in collisional regimes, deriving a generalized dispersion relation from self-consistent beam-Maxwell equations. For symmetrically counterstreaming, fully relativistic electron currents, the collisional coupling between electrons and ions creates the unstable modes of growing oscillation and wave, which stand out for long-wavelength perturbations. In the stronger collisional regime, the growing oscillatory mode tends to be dominant for all wavelengths. In the collisionless limit, those modes vanish, while maintaining another purely growing mode that exactly coincides with a standard relativistic Weibel mode. It is also shown that the effects of electron-electron collisions and thermal spread lower the growth rate of the relativistic Weibel instability. The present mechanisms of filamentation dynamics are essential for transport of homogeneous electron beam produced by the interaction of high power laser pulses with plasma.

Weibel instability of relativistic electron flows in a laser produced plasma

The strong flows of relativistic electrons, encountered in high power short pulse laser plasma interaction, have the potential to drive Weibel instability producing short wavelength magnetic fields. The presence of a Langmuir wave couples the Weibel instability to two electrostatic wave sidebands. The density perturbations due to the sidebands couple with the oscillatory electron velocity due to the pump to produce a current that enhances the growth rate of Weibel instability. The thermal spread of the energetic (drifting) electrons, however, reduces the growth rate.

Plasma electron kinetics in a weak high-frequency field and magnetic field amplification.

We describe the linear stage of Weibel instability in a plasma heated via inverse bremsstrahlung absorption of a high-frequency, moderate intensity radiation field under conditions in which the plasma electron velocity distribution function is weakly anisotropic. We report on the possibility of a significant amplification of spontaneous magnetic fields both in the case of an electron distribution function slightly departing from a Maxwellian in the region of subthermal velocities, and in the case where the Langdon nonequilibrium distribution is formed. We show that the direct influence of collisions on the Weibel instability growth rate may be traced back to subthermal electrons, for which the effective collision frequency is large.