bi-Maxwellian Plasma Research Articles

Global model analysis of negative ion generation in low-pressure inductively coupled hydrogen plasmas with bi-Maxwellian electron energy distributions

A global model was developed to investigate the densities of negative ions and the other species in a low-pressure inductively coupled hydrogen plasma with a bi-Maxwellian electron energy distribution. Compared to a Maxwellian plasma, bi-Maxwellian plasmas have higher populations of low-energy electrons and highly vibrationally excited hydrogen molecules that are generated efficiently by high-energy electrons. This leads to a higher reaction rate of the dissociative electron attachment responsible for negative ion production. The model indicated that the bi-Maxwellian electron energy distribution at low pressures is favorable for the creation of negative ions. In addition, the electron temperature, electron density, and negative ion density calculated using the model were compared with the experimental data. In the low-pressure regime, the model results of the bi-Maxwellian electron energy distributions agreed well quantitatively with the experimental measurements, unlike those of the assumed Maxwellian electron energy distributions that had discrepancies.

The instability condition of the aperiodic ordinary mode for new scalings of the counterstreaming parameters

The aperiodic ordinary (O-) mode instability in homogeneous and collisionless plasmas with kinetic anisotropies has recently received renewed attention due to its potential application in the solar wind, as well as for equal-mass plasmas. The present paper revisits the marginal instability condition of the O-mode derived from the electromagnetic linear dispersion equation for waves propagating perpendicular to the background magnetic field. For a counterstreaming bi-Maxwellian plasma system, this condition is found to be significantly affected by the streaming parameters. New functional dependencies (not studied before) of the counterstreaming parameters on the magnetic field and the other plasma parameters lead to new conditions of this instability for the both equal mass and electron-proton plasmas.

Marginal instability threshold condition of the aperiodic ordinary mode in equal-mass plasmas

The purely growing ordinary (O) mode instability for counter-streaming bi-Maxwellian plasma particle distribution functions has recently received renewed attention due to its importance for the solar wind plasma. Here, the analytical marginal instability condition is derived for magnetized plasmas consisting of equal-mass charged particles, distributed in counter-streams with equal temperatures. The equal-mass composition assumption enormously facilitates the theoretical analysis due to the equality of the values of the electron and positron (positive and negative ion) plasma and gyrofrequencies. The existence of a new instability domain of the O-mode at small plasma beta values is confirmed, when the parallel counter-stream free energy exceeds the perpendicular bi-Maxwellian free energy.

Silicon drift detector based X-ray spectroscopy diagnostic system for the study of non-thermal electrons at Aditya tokamak

Silicon drift detector based X-ray spectrometer diagnostic was developed to study the non-thermal electron for Aditya tokamak plasma. The diagnostic was mounted on a radial mid plane port at the Aditya. The objective of diagnostic includes the estimation of the non-thermal electron temperature for the ohmically heated plasma. Bi-Maxwellian plasma model was adopted for the temperature estimation. Along with that the study of high Z impurity line radiation from the ECR pre-ionization experiments was also aimed. The performance and first experimental results from the new X-ray spectrometer system are presented.

On the marginal instability threshold condition of the aperiodic ordinary mode

The purely growing ordinary (O) mode instability has recently received renewed attention owing to its potential applicability to the solar wind plasma. Here, an analytical marginal instability condition is derived for counter-streaming bi-Maxwellian plasma particle distribution functions. The derived marginal instability condition as a function of the temperature anisotropy and plasma beta agrees remarkably well with the numerically determined instability condition. The existence of a new instability domain of the O-mode at small plasma beta values is confirmed with the leading A∝β∥−1-dependence, if the counter-stream parameter Pe exceeds a critical value. At small plasma beta values at large enough counter-stream parameter, the O-mode also operates for temperature anisotropies A = T⊥/T∥ > 1 even larger than unity, as the parallel counter-stream free energy exceeds the perpendicular bi-Maxwellian free energy.

Solar wind kinetic instabilities at small plasma betas

The ordinary perpendicular mode of drifting bi-Maxwellian plasma particle distributions with and without temperature anisotropy can provide aperiodic instabilities. These instabilities occur if the perpendicular thermal energy is much smaller than the streaming energy. This provides instabilities at small parallel plasma betas β∥<1 and temperature anisotropies A < 1. In this regime, the solar wind is unstable, which cannot be explained so far. To clarify if the ordinary perpendicular mode can be responsible for this instability, here we compare measurements in the solar wind with the instability provided by this mode.

Quasi-linear heating and acceleration in bi-Maxwellian plasmas

Quasi-linear acceleration and heating rates are derived for drifting bi-Maxwellian distribution functions in a general nonrelativistic case for arbitrary wave vectors, propagation angles, and growth/damping rates. The heating rates in a proton-electron plasma due to ion-cyclotron/kinetic Alfvén and mirror waves for a wide range of wavelengths, directions of propagation, and growth or damping rates are explicitly computed.

Whistler instability in a semi-relativistic bi-Maxwellian plasma

Employing linearized Vlasov-Maxwell system, the Weibel instability embedded in an ambient magnetic field is discussed for a semi-relativistic bi-Maxwellian distribution hoping such a scenario occurs in some relativistic environments e.g., gamma-ray burst sources and relativistic jet sources, supernovae, and galactic cosmic rays where the perpendicular temperature is much dominated over the parallel . The dispersion relations are analyzed analytically along with the graphical representation and the estimates of the growth rate are presented along with the instability threshold condition in the limiting cases i.e., xi<=1 (resonant case) and xi>>1 (non-resonant case). It is observed that the relativistic effect suppresses the instability and also lowers the threshold for the instability to set in. The ambient magnetic field contribution to instability appears only in non-resonant case resulting in reduction of growth rate. However, the effect of the ambient magnetic field is diminished as we go from the weak relativistic regime to the highly relativistic one. We also note that the ambient magnetic field generates real oscillations and the reletivistic effect reduces these oscillations. Further for field free case i.e., B0=0, the growth rates for Weibel instabilities are also presented in a semi-relativistic bi- Maxwellian plasma for both the limiting cases.

Inertial Alfven waves in an inhomogeneous bi-Maxwellian plasma

Abstract The Vlasov kinetic equation is solved using gyrokinetic theory and the dielectric tensor for non-relativistic, magnetized, bi-Maxwellian plasmas is calculated. A generalized dispersion relation for kinetic Alfven waves is derived taking into account the density inhomogeneity and temperature anisotropy. The modified dispersion relation thus obtained is then used to examine the propagation characteristics of the kinetic Alfven waves in the inertial regime. The importance of density inhomogeneity and temperature anisotropy for Solar corona is highlighted. The growth rate of the inertial Alfven wave proves that density inhomogeneity acts as a source of free energy.

Towards a complete parametrization of the ordinary-mode electromagnetic instability in counterstreaming plasmas. II. Ion effects

The linear marginal instability analysis of the ordinary perpendicular mode instability of drifting bi-Maxwellian plasma particle distributions with and without temperature anisotropy is extended by including the modifications of heavier ion species. For general values of the temperature anisotropy, the streaming velocity, and the parallel plasma beta, accurate marginal stability conditions are derived, which enable a better understanding of the interplay of counterstreaming and temperature anisotropy.

Towards a complete parametrization of the ordinary-mode electromagnetic instability in counterstreaming plasmas. I. Minimizing ion dynamics

The ordinary mode instability can be driven by drifting bi-Maxwellian plasma particle distributions with and without temperature anisotropy. Here, the linear instability analysis is generalized for realistic settings, when the plasma streams are magnetized and hot enough. The new parametrization proposed in this study enables a better understanding of the interplay of counterstreaming and temperature anisotropy, providing the derivation of new regimes of the ordinary mode instability. Accurate analytical forms are derived for the instability conditions for general values of the temperature anisotropy, the streaming velocity, and the parallel plasma beta. To keep the analysis straightforward, the role of ions is minimized.

Extended Tonks–Langmuir-type model with non-Boltzmann-distributed electrons and cold ion sources

AbstractA general formalism for calculating the potential distribution Φ(z) in the quasineutral region of a new class of plane Tonks–Langmuir (TL)-type bounded-plasma-system (BPS) models differing from the well-known ‘classical’ TL model (Tonks, L. and Langmuir, I. 1929 A general theory of the plasma of an arc. Phys. Rev. 34, 876) by allowing for arbitrary (but still cold) ion sources and arbitrary electron distributions is developed. With individual particles usually undergoing microscopic collision/sink/source (CSS) events, extensive use is made here of the basic kinetic-theory concept of ‘CSS-free trajectories’ (i.e., the characteristics of the kinetic equation). Two types of electron populations, occupying the ‘type-t’ and ‘type-p’ domains of electron phase space, are distinguished. By definition, the type-t and type-p domains are made up of phase points lying on type-t (‘trapped’) CSS-free trajectories (not intersecting the walls and closing on themselves) and type-p (‘passing’) ones (starting at one of the walls and ending at the other). This work being the first step, it is assumed that ε ≡ λD/l → 0+ (where λD and l are a typical Debye length and a typical ionization length respectively) so that the system exhibits a finite quasineutral ‘plasma’ region and two infinitesimally thin ‘sheath’ regions associated with the ‘sheath-edge singularities’ | dΦ/dz|z→±zs → ∞. The potential in the plasma region is required to satisfy a plasma equation (quasineutrality condition) of the form ni {Φ} =ne (Φ), where the electron density ne (Φ) is given and the ion density ni {Φ} is expressed in terms of trajectory integrals of the ion kinetic equation, with the ions produced by electron-impact ionization of cold neutrals. While previous TL-type models were characterized by electrons diffusing under the influence of frequent collisions with the neutral background particles and approximated by Maxwellian (Riemann, K.-U. 2006 Plasma-sheath transition in the kinetic Tonks–Langmuir model. Phys. Plasmas 13, 063508) or bi-Maxwellian (Godyak, V. A. et al. 1995 Tonks–Langmuir problem for a bi-Maxwellian plasma. IEEE Trans. Plasma Sci. 23, 728) electron velocity distribution functions (VDFs), which satisfy the zero-CSS-term (Vlasov) kinetic equation and imply zero electron currents, we here propose a more general class of electron VDFs allowing, in an approximate manner, for non-zero CSS terms and finite electron currents inside the plasma region. The sheath-edge and floating-wall potentials are calculated by balancing the ion and electron current densities at sheath-edge singularities. In a first detailed application, the type-t and type-p electron VDFs are assumed to be ‘inner’ and ‘outer’ cut-off Maxwellians respectively, with different amplitudes and ‘formal’ temperatures, implying the perfectly CSS-free limit. For the special case of equal type-t and type-p electron VDF amplitudes and formal temperatures, the classical Boltzmann distribution for electrons is formally retrieved. Special cases with other amplitude and formal-temperature ratios show significant deviations from the classical case.

On the mirror instability in the presence of electron temperature anisotropy

Computation of the mirror instability growth rate in an ion-electron bi-Maxwellian plasma is revisited, starting from the low-frequency kinetic theory. The role of the electron finite Larmor radius (FLR) effects on the instability quenching is shown to possibly be dominant, even near threshold where the smallest unstable scales significantly exceed the electron gyroscale. Validation of the results by comparison with predictions of the fully kinetic whamp software is also presented. The influence of the electron temperatures on the ion FLR effects very near threshold, where the electron kinetic effects are negligible, is also pointed out.

Effect of Temperature Anisotropy on Various Modes and Instabilities for a Magnetized Non-relativistic Bi-Maxwellian Plasma

Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those modes whose magnetic-field perturbations are perpendicular to the ambient magnetic field, i.e., B 1 $\bot $ B 0, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them (i.e., the whistler mode, pure Alfvén mode, firehose instability, and whistler instability), and the O-mode are affected by thermal anisotropies, since they satisfy the required condition $\mathbf{B}_{1}\bot \mathbf{B}_{0}$ . By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfvén waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations. The threshold conditions for different instabilities are also obtained.

Ion-cyclotron instability in current-carrying Lorentzian (kappa) and Maxwellian plasmas with anisotropic temperatures: A comparative study

Current-driven electrostatic ion-cyclotron instability has so far been studied for Maxwellian plasma with isotropic and anisotropic temperatures. Since satellite-measured particle velocity distributions in space are often better modeled by the generalized Lorentzian (kappa) distributions and since temperature anisotropy is quite common in space plasmas, theoretical analysis of the current-driven, electrostatic ion-cyclotron instability is carried out in this paper for electron-proton plasma with anisotropic temperatures, where the particle parallel velocity distributions are modeled by kappa distributions and the perpendicular velocity distributions are modeled by Maxwellian distributions. Stability properties of the excited ion cyclotron modes and, in particular, their dependence on electron to ion temperature ratio and ion temperature anisotropy are presented in more detail. For comparison, the corresponding results for bi-Maxwellian plasma are also presented. Although the stability properties of the ion cyclotron modes in the two types of plasmas are qualitatively similar, significant quantitative differences can arise depending on the values of κe and κi. The comparative study is based on the numerical solutions of the respective linear dispersion relations. Quasilinear estimates of the resonant ion heating rates due to ion-cyclotron turbulence in the two types of plasma are also presented for comparison.

Spontaneously growing, weakly propagating, transverse fluctuations in anisotropic magnetized thermal plasmas

A new dispersion formalism describing the weakly propagating, transverse fluctuations with wave vectors (k⃗∥B⃗) parallel to the uniform background magnetic field B⃗ in an anisotropic bi-Maxwellian magnetized electron-proton plasma is presented. Different transverse right-handed or left-handed polarized modes can be excited, which are the whistler Weibel-like modes and the electron and proton firehose modes. Analytic instability threshold conditions are derived in terms of the combined temperature anisotropy A=T⊥/T∥, the parallel plasma beta β∥=8πnekBT∥/B2, and the electron plasma frequency phase speed w=ωp,e/(kc).

Alfvenic modes in a bi-Maxwellian electron-ion plasma

Employing linearized Vlasov–Maxwell system, we derive a generalized dielectric tensor for a magnetized nonrelativistic bi-Maxwellian electron-ion plasma. Assuming low frequency waves in a low β plasma, a new dispersion relation describing oblique propagation of the Alfvenic modes is determined, incorporating the temperature anisotropies of both the electrons and ions and their finite Larmor radii effects. From the resulting dispersion relation for kinetic Alfven waves, analytical expressions are determined for both the kinetic (vt∥i⪡ω/k∥⪡vt∥e and me/mi⪡β⪡1) and the inertial (ω/k∥⪢vt∥e,i and β⪡me/mi) regimes. We observe that in both cases, the Alfvenic modes stand modified due to the acoustic effect arising from the temperature anisotropy, which may enhance or reduce the Alfven speed depending on the strength and signature of the anisotropies. A number of special cases are also retrieved under appropriate conditions.

LINEAR THEORY OF WEAKLY AMPLIFIED, PARALLEL PROPAGATING, TRANSVERSE TEMPERATURE-ANISOTROPY INSTABILITIES IN MAGNETIZED THERMAL PLASMAS

A rigorous analytical study of the dispersion relations of weakly amplified transverse fluctuations with wave vectors ($\vec{k}\parallel \vec{B}$) parallel to the uniform background magnetic field $\vec{B}$ in an anisotropic bi-Maxwellian magnetized electron-proton plasma is presented. We determine the conditions for which the weakly amplified LH-handed polarized Alfven-proton-cyclotron and RH-handed polarized Alfven-Whistler-electron-cyclotron branches can be excited. The results of our instability study are applied to the observed solar wind magnetic turbulence. The Alfvenic instability diagram explains well the main characteristic properties of the observed solar wind fluctuations. Especially, the observed confinement limits at small parallel plasma beta values are explained.

IMPLICATIONS OF A NON-MODAL LINEAR THEORY FOR THE MARGINAL STABILITY STATE AND THE DISSIPATION OF FLUCTUATIONS IN THE SOLAR WIND

The non-modal approach for a linearized system differs from a normal mode analysis by following the temporal evolution of some perturbed equilibria, and therefore includes transient effects. We employ a non-modal approach for studying the stability of a bi-Maxwellian magnetized plasma using the Landau fluid model, which we briefly describe. We show that bi-Maxwellian stable equilibria can support transient growth of some physical quantities, and we study how these transients behave when an equilibrium approaches its marginally stable condition. This is relevant to anisotropic plasma, that are often observed in the solar wind with a temperature anisotropy close to values that can trigger a kinetic instability. The results obtained with a non-modal approach are relevant to a re-examination of the concept of linear marginal stability. Moreover, we discuss the topic of the dissipation of turbulent fluctuations, suggesting that the non-modal approach should be included in future studies.

Linear Theory of Temperature Anisotropy Instabilities in Magnetized Thermal Pair Plasmas

A rigorous study of the dispersion relations of weakly amplified and weakly propagating transverse fluctuations with wave vectors ( � k � � B ) parallel to the uniform background magnetic field B in an anisotropic bi-Maxwellian magnetized pair plasma is presented. Earlier work, based on the weakly-amplified limit, is extended to the case of weakly propagating solutions, which includes in particular aperiodic fluctuations, by the appropriate Taylor expansion of the plasma dispersion function. It is shown that six different transverse right-handed (RH) and left-handed (LH) polarized modes can be excited whose dispersion relations and instability threshold conditions are derived. The existence and instability conditions are derived in terms of the combined temperature anisotropy A = T� / T� , the parallel plasma beta � =8 � nekBT� / B 2 and the electron plasma frequency phase speed w = p,e /( kc) . The pair Alfven and cyclotron instabilities are the only two weakly amplified solutions, whereas the four weakly propagating solutions are the mirror, firehose, cool magnetized Weibel and cyctronic fluctuations, respectively. The four weakly propagating solutions are aperiodic with vanishing real phase speeds R =0 if the plasma positrons and electrons have the same temperature anisotropy. The mirror and cool magnetized Weibel fluctuations reduce to the known hot and cool Weibel instabilities in the limit of an unmagnetized plasma.