Weibel Instability Growth Rate Research Articles

Analytical expression of Weibel electromagnetic instability growth rate in strongly coupled quantum plasma

The Weibel instability is one of the basic beam-plasma electromagnetic instabilities which plays an important role in the energy traveling mechanism of relativistic electrons generated by the laser-plasma interaction in the Inertial Confinement Fusion Plasma. In this paper, the Weibel instability is investigated in strongly coupled quantum plasmas, considering the Kappa distribution function for beam-plasma particles. An analytical expression is derived for the Weibel instability growth rate as the quantum and temperature anisotropy parameters for different values of the spectral index, k, under the low-frequency wave condition. The obtained results show that in the limit of low-frequency wave, the growth rate of instability decreases by increasing quantum parameter, and increases by increasing the values of special index and the temperature anisotropy parameter.

Effect of nonlinear saturation of electromagnetic instability on the viscosity of the inertial fusion fuel

One of the interesting topics of recent research is the study of the Weibel electromagnetic instability growth rate in the interaction of high-intensity lasers with the dense plasma of fusion fuel pellets. In this paper, the effect of stresses caused by laser ponderomotive force on the growth rate of Weibel instability in the nonlinear phase is investigated. The growth of the nonlinear phase of Weibel instability growth rate, which is the saturation phase of Weibel instability, in the presence of stress leads to viscosity turbulence. The results show that the coefficient of reduction of fuel viscosity in the presence of the stress flow is about 0.0014 due to the anomalous transfer mechanism caused by the nonlinear growth of the Weibel instability.

Stream instabilities in optical-field ionization of a monatomic dilute neutral gas in fully relativistic regime

Stream instabilities arising from anisotropic electron velocity distribution function (EVDF) are discussed in the optical-field ionization mechanism of a monatomic dilute gas by a circularly polarized laser beam in a fully relativistic regime. It is shown that a relativistically rotating electron beam is derived by a circularly polarized laser field with (p_z>p_perp). We show that the following ionization and before collisions thermalize the electrons, the plasma undergoes Buneman and Weibel instabilities. The Weibel and Buneman modes are co-propagating with k normal to the streaming direction. The theoretical results reveal that for the threshold of the relativistic regime (a_0approx 1), instabilities are aperiodic and grow independently. However, by increasing the laser intensity for a_0>1, two instabilities are coupled. The coupling process increased the growth rate of Weibel instability, while the Buneman instability experienced a decrement in its growth rate. For more intense laser radiation, both instabilities are broken into different oscillatory and aperiodic modes.

Theoretical and computational studies of the Weibel instability in several beam–plasma interaction configurations

The Weibel instability is investigated theoretically and numerically under three scenarios: counterstreaming electron beams in background plasma, an electron–positron beam and an electron–proton beam in background plasma. These models occur widely in laboratory and astrophysical environments. The Weibel instability growth rates are determined numerically from the corresponding cold-fluid dispersion relations, which are confirmed with two-dimensional particle-in-cell simulations. The maximum growth rates for the counterstreaming beams in background plasma are an order of magnitude smaller than the maximum growth rates for the beams cases in the same range of density ratios and beam energies. The maximum growth rate for the electron–positron beam case is shown to be at most a factor $\sqrt {2}$ greater than the electron–proton beam case with similar dispersion behaviours. A non-monotonic relation is found between the maximum Weibel instability growth rates and the electron–positron beam energy, suggesting that increasing beam energies does not entail an increase in the Weibel instability growth rate.

Effect of shear stress on collisional electromagnetic modes in the fast ignition

In the present work, the effect of the shear stress and collision within the turbulent plasma of the fuel fusion on the Weibel instability growth rate is explored using a kinetic model. The collisions are responsible for taking energy from the plasma electromagnetic wave and hence stop the wave from growing further in the fusion fuel plasma. It is found that the minimum value of the stress rate threshold for the purely transversal mode is greater than that of the transverse-longitudinal coupled mode. For product purely transverse mode, the growth rate is more as compared to the transverse-longitudinal coupled mode. The presence of the collisions has a negative effect on the Weibel instability growth rate. At small wavelengths limit, an increase in collision frequency decreases the growth rate of the Weibel instability, and for a product in the transverse-longitudinal coupled mode, the growth rate is more as compared to the purely transverse mode. In the case of large wavelengths, only for purely transverse modes, decreasing by 57% collision frequency leads to about 0.087% decrement in the maximum of the Weibel instability growth and for a product the purely transverse mode, the growth rate is more as compared to the transverse-longitudinal coupled mode.

Weibel instability induced by kinetic stimulated Raman scattering in unmagnetized and magnetized plasmas

The kinetic stimulated Raman scattering (SRS) is found to result in significant Weibel-generated magnetic fields via 2D particle-in-cell simulations. During the high-intensity laser pulse, the daughter electron plasma waves of SRS heat the electrons effectively and lead to anisotropy in the velocity space. This anisotropy results in the development of a quasi-static magnetic field near the laser speckle, and the growth rate has been discussed. The results show that the kinetic SRS can lead to an averaged magnetic field of more than 10 T, which can be an important magnetic field source in laser-plasma experiments. Besides, the energy of the Weibel-field undergoes an oscillatory rise with the SRS bursts and can be stable after cutting off the laser. Moreover, in the magnetized plasmas, the application of a longitudinal magnetic field enhances the SRS, but interestingly, it significantly reduces the growth rate of Weibel instability. Simulation results also indicate that a small transverse magnetic field can evidently change the motion of the hot electrons, which dramatically destroys the symmetry of the SRS and the Weibel-generated magnetic fields.

Study of Coulomb collisional effects on the propagation of electromagnetic waves in a turbulent plasma

AbstractThe presence of Weibel instability in laser‐irradiated fuel could be detrimental to the process of ablative implosion, which is necessary for achieving thermonuclear fusion reactions. In this paper, the effect of the Coulomb collisional within the turbulent plasma on the Weibel instability growth rate has been investigated for linear and circular polarization. The results indicate that the Weibel instability growth rate at circular polarization near the ignition centre of the fuel fusion (collisional plasma) is about 105 times higher than the collisional Weibel instability growth rate at linear polarization. The Weibel instability growth rate is observed near the critical density of the fuel fusion (collisionless plasma) at linear polarization and enhancement near the foot of the heat in front of the fuel fusion. By increasing the steps of the density gradient plasma in the low‐density corona, electromagnetic instability occurs at a higher stress flow. Therefore, the deposition condition of electron beam energy in circular polarization of turbulent plasma can be shifted to the fuel core for suitable ignition.

The effect of dust grains on the Weibel instability in presence of large amplitude electrostatic waves

Theoretical investigations on the effect of dust charge fluctuations on Weibel instability in a plasma, with an electron beam in the presence of large amplitude electrostatic Langmuir waves, have been performed. It is observed that the dust charge fluctuations enhance the growth rate of electromagnetic (EM) perturbations. An increase in the electron to ion temperature ratio amplifies the EM perturbations, leading to an enhanced magnetic field due to Weibel instability. It has been found that the growth rate of Weibel instability strongly depends on the dust grain size for different values of ion to electron density ratio δm. Moreover, the electron to ion temperature ratio also destabilizes the Weibel instability.

The effect of shear flow and the density gradient on the Weibel instability growth rate in the dense plasma

Shear stress effect has been often neglected in calculation of the Weibel instability growth rate in laser-plasma interactions. In the present work, the role of the shear stress in the Weibel instability growth rate in the dense plasma with density gradient is explored. By increasing the density gradient, the shear stress threshold is increasing and the range of the propagation angles of growing modes is limited. Therefore, by increasing steps of the density gradient plasma near the relativistic electron beam-emitting region, the Weibel instability occurs at a higher stress flow. Calculations show that the minimum value of the stress rate threshold for linear polarization is greater than that of circular polarization. The Wiebel instability growth rate for linear polarization is 18.3 times circular polarization. One sees that for increasing stress and density gradient effects, there are smaller maximal growth rates for the range of the propagation angles of growing modes π2<θmin<π and 3π2<θmin<2π in circular polarized plasma and for kcωp<4 in linear polarized plasma. Therefore, the shear stress and density gradient tend to stabilize the Weibel instability for kcωp<4 in linear polarized plasma. Also, the shear stress and density gradient tend to stabilize the Weibel instability for the range of the propagation angles of growing modes π2<θmin<π and 3π2<θmin<2π in circular polarized plasma.

Effect of collisions on Weibel instability with anisotropic electron distributions

Using kinetic approach, the effect of electron–ion collisions on Weibel instability has been investigated for three different types of anisotropic distribution functions (i.e., bi-kappa, bi-Maxellian, and product bi-kappa). It is found that the presence of electron–ion collisions has a negative effect on the growth rate of Weibel instability. By using analytical analysis, it has been found that the growth rate of the collisional plasma becomes negative if the electron–ion collision frequency becomes higher than the growth rate of the Weibel instability for a collisionless plasma while keeping all the other parameters same. The impact of electron–ion collisions has also been studied on the temperature anisotropy parameter τ(=T⊥/T||) threshold required for making the growth rate of the Weibel instability positive for all the three distribution functions. The illustrations show that for higher spectral index κ||=κ>4, the temperature anisotropy threshold is same for all the three distribution functions; however, for lower κ||=κ<4, the threshold conditions are different for the bi-kappa as compared to those found for the other two distribution functions. The boundaries between the stable and unstable regions of bi-kappa and product bi-kappa distributions have been found in the presence of collisions. In the presence of collisions, the boundary curve for product bi-kappa is similar to that we get in the absence of collisions. However, the temperature anisotropy threshold parameters are higher for collisional plasma as compared to those obtained for the collisionless plasma. The boundary curve for bi-kappa distribution function in the presence of collisions is significantly different from the boundary curve formed in the absence of collisions. In the presence of collisions, the temperature anisotropy threshold increases very rapidly when the spectral index is <2.

The ion streaming effect on Weibel instability in the relativistic dense plasma

The Weibel instability plays an important role in stopping hot electrons and energy deposition mechanism in fast ignition of inertial fusion process. In this paper, the ion Weibel instability in counter propagating electron‐ion plasmas is investigate. The obtained results show that the growth rate of Weibel instability will be decreased about 40% with the anisotropy velocity as vxe = 2vze = 20; the ion density ratio, b = n0i1/n0i2, and density gradient, are increasing 50 and 90% respectively. The ion streaming in density gradient of dense plasma leads to increasing the Weibel instability growth rate and its amplification through ion streaming in the large wavenumber. The maximum unstable wavenumber has been decreased with decreasing the ion beam density ratio. For fixed ion density ratio, increasing 90% of the density gradient in the near of fuel plasma corona leads to reducing growth rate and unstable wavenumber about 43 and 42% respectively.

The Role of the Collisions on the Weibel Instability Growth Rate in the Fast Ignition Scenario

In this paper, the effects of Coulomb elctron-ion collisions and plasma density gradient, $$\eta$$ , on the Weibel instability in inertial confinement fusion are investigated. The results are indicative that the corrected collision of Weibel instability growth rate of the relativistic region near the corona, $$\eta >0.3$$ , increases with increasing relativistic parameter, $$\upgamma$$ . Also, near the fuel core as $$\eta$$ goes down, the corrected collisional growth rate decreases with increasing $$\upgamma$$ for $$\mathrm{{\upgamma }}<6$$ and and increases with increasing $$\upgamma$$ for $$\upgamma >6$$ . Therefore, for $$\upgamma <6$$ , the effect of collision and fuel density gradient tend to stabilize the Weibel instability in fuel core, with the Weibel growth rate below the collisionless value. Also deposition condition of relativistic electron beam energy can be shifted to the fuel core for the suitable ignition.

The density gradient effect on quantum Weibel instability

The Weibel instability plays an important role in stopping the hot electrons and energy deposition mechanism in the fast ignition of inertial fusion process. In this paper, the effects of the density gradient and degeneracy on Weibel instability growth rate are investigated. Calculations show that decreasing the density degenerate in the plasma corona, near the relativistic electron beam emitting region by 8.5% leads to a 92% reduction in the degeneracy parameter and about 90% reduction in Weibel instability growth rate. Also, decreasing the degenerate density near the fuel core by 8.5% leads to 1% reduction in the degeneracy parameter and about 8.5% reduction in Weibel instability growth rate. The Weibel instability growth rate shrinks to zero and the deposition condition of relativistic electron beam energy can be shifted to the fuel core for a suitable ignition by increasing the degeneracy parameter in the first layer of plasma corona.

The Quantum Effects Role on Weibel Instability Growth Rate in Dense Plasma

The Weibel instability is one of the basic plasma instabilities that plays an important role in stopping the hot electrons and energy deposition mechanism. In this paper, combined effect of the density gradient and quantum effects on Weibel instability growth rate is investigated. The results have shown that, by increasing the quantum parameter, for large wavelengths, the Weibel instability growth rate shrinks to zero. In the large wavelengths limit, the analysis shows that quantum effects and density gradient tend to stabilize the Weibel instability. The density perturbations have decreased the growth rate of Weibel instability in the near corona fuel,η&gt;0.1. In the small wavelengths limit, for the density gradient,η&lt;0.1, the tunneling quantum effects increase anisotropy in the phase space. The quantum tunneling effect leads to an unexpected increase in the Weibel instability growth rate.

The Study of Thermal Conditions on Weibel Instability

Weibel electromagnetic instability has been studied analytically in relativistic plasma with high parallel temperature, where|α=(mc2/T∥)(1+p^⊥2/m2c2)1/2|≪1and while the collision effects of electron-ion scattering have also been considered. According to these conditions, an analytical expression is derived for the growth rate of the Weibel instability for a limiting case of|ζ=α/2(ω′/ck)|≪1, whereω′is the sum of the wave frequency of instability and the collision frequency of electrons with background ions. The results show that in the limiting conditionα≪1there is an unusual situation of the Weibel instability so thatT∥≫T⊥, while in the classic Weibel instabilityT∥≪T⊥. The obtained results show that the growth rate of the Weibel instability will be decreased due to an increase in the number of collisions and a decrease in the anisotropic temperature by the increasing of plasma density, while the increase of the parameterγ^⊥=(1+p^⊥2/m2c2)1/2leads to the increase of the Weibel instability growth rate.

Publisher's Note: “The effect of density gradient on the growth rate of relativistic Weibel instability” [Phys. Plasmas 21, 022707 (2014)

Publisher's Note: “The effect of density gradient on the growth rate of relativistic Weibel instability” [Phys. Plasmas <b>21</b>, 022707 (2014)

The effect of density gradient on the growth rate of relativistic Weibel instability

In this paper, the effect of density gradient on the Weibel instability growth rate is investigated. The density perturbations in the near corona fuel, where temperature anisotropy, η, is larger than the critical temperature anisotropy, ηc, (η > ηc), enhances the growth rate of Weibel instability due to the sidebands coupled with the electron oscillatory velocity. But for η < ηc, the thermal spread of the energetic electrons reduces the growth rate. Also, the growth rate can be reduced if the relativistic parameter (Lorentz factor) is sufficiently large, γ > 2. The analysis shows that relativistic effects and density gradient tend to stabilize the Weibel instability. The growth rate can be reduced by 88% by reducing η by a factor of 100 and increasing relativistic parameter by a factor of 3.

Collisional Effect on Weibel Instability with Semi-Relativistic Maxwellian Distribution Function

In this paper, the Coulomb collisional effect of electron-ion on the growth rate of Weibel instability is investigated based on the semi-relativistic Maxwellian distribution function in dense and unmagnetized plasma. An analytical expression was derived for the dispersion relation of Weibel instability for two limit cases |ξ = ω′/k‖ T‖|≫ 1 and |ξ| ≪ 1. In limit |ξ| ≫ 1 the dispersion relation only includes a real part and in limit |ξ| ≪ 1 the imaginary part of the frequency of waves' instability plays a role in the dispersion relation. In limit |ξ| ≪ 1, the two quantities μ and η, that are due to the relativistic and collisional effects, will appear in the growth rate of Weibel instability. The growth rate of Weible istability will be increased through decreasing the Coulomb collisional frequency and also increasing the temperature anisotropic parameter in strong relativistic limit.

Collisional effect on the Weibel instability in a semi-relativistic anisotropic plasma

The detailed properties of the classical electromagnetic Weibel instability in a semi-relativistic anisotropic plasma are investigated for Maxwellian distribution. In this article, the effects of one particular factor affecting the growth rate of Weibel instability, Coulomb collision effect of electrons and ions, is studied and discussed based on the equilibrium semi-relativistic Maxwellian distribution function, in a dense and unmagnetized anisotropic plasma. An analytical expression is derived for the growth rate of the Weibel instability. The two limiting cases ( $\left| \xi\right| \ll1$ and $\left| \xi\right| \gg1$ ) are considered. It is shown that in the limit $\left| \xi\right| \ll 1$ , the quantity η, which is due to the collision term, will appear in the growth and in the conditions of the rate of the Weibel instability. The quantity χ symbolizes the contribution from relativistic terms which becomes unity as we approach the non-relativistic Maxwellian case, leading to the standard Weibel instability scenario. The increasing of η leads to decreasing of the growth rate, and with the decreasing of η the growth rate will increase.

The effect of degeneracy parameter on Weibel instability in dense plasma

In this paper, the role of degeneracy parameter, in both directions parallel and perpendicular with propagation direction of the laser beam in plasma, on the growth rate of Weibel instability, is studied. Calculations show that with the temperature anisotropy, β = T∥/T⊥ = 0.2 and a 0.75 times reduction of the degeneracy parameter, the increased rate of the the Weibel instability growth rate is 72%. The degeneracy required for minimal growth rate in interaction laser plasma with a density of 1.2 × 1032m−3, is larger than 3. The reduction of temperature and the degeneracy parameter of plasma in parallel direction will also increase growth rate about 30% more than incrossing degeneracy parameter in transverse direction. With the minimum pressure costs of cold compression, subsequent degeneracy parameters, and the minimum value of electron quiver energy, we can expect growth rate of Weibel instability order 0.01.