Parallel Plasma Beta Research Articles

Modified Temperature-Anisotropy Instability Thresholds in the Solar Wind

The proton and electron temperature anisotropies in the solar wind are constrained by the instability thresholds for temperature-anisotropy-driven kinetic plasma instabilities. The modifications to the marginal instability conditions from accounting for the influence of damping connected with the collisional effects in the solar wind plasma are calculated for right- and left-handed polarized parallel propagating Alfvén waves and mirror and firehose fluctuations. These modifications provide tighter threshold constraints compared to the marginal thresholds but do not fully explain the observations at small values of the parallel plasma beta.

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).

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.

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.

Hybrid simulations of parallel and oblique electromagnetic alpha/proton instabilities in the solar wind

The linear Vlasov theory has shown that the relative flow between alpha particles and protons in the fast solar wind can excite both magnetosonic and oblique Alfven modes and the velocity threshold of the Alfven instability is lower than that of the magnetosonic instability. In this paper, hybrid simulations are performed to investigate the nonlinear evolution of parallel and oblique electromagnetic alpha/proton instabilities in the fast solar wind. The parallel proton plasma beta, defined as β∥p = 8πnpkBT∥p/B02, is set equal to 0.15, and the initial average value of the alpha/proton relative flow speed is chosen as 1.76vA (vA is the local Alfven speed). The influences of the temperature anisotropy of alpha particles (T⊥α/T∥α) and temperature anisotropy of protons (T⊥p/T∥p) on the alpha/proton instabilities are also considered. The decrease of the temperature anisotropy of alpha particles (T⊥α/T∥α) can significantly enhance the amplitude of both the magnetosonic and oblique Alfven modes and decelerate alpha particles more efficiently, while the temperature anisotropy of protons (T⊥p/T∥p) tends to reduce the amplitudes of these two modes. Moreover, in the two‐dimensional hybrid simulations the magnetosonic waves are first excited. Then the oblique Alfven waves are also excited and dominate the wave spectrum at the late stage of time evolution. The implications of our simulation results on observations in the fast solar wind are also discussed.

Limits on the core temperature anisotropy of solar wind protons

Abstract. We analyse the temperature anisotropy of the protons in the solar wind and thereby concentrate on plasma data obtained in the year 1976 of the Helios 1 and Helios 2 missions. We derive the core proton temperatures and , in the directions perpendicular and parallel to the magnetic field, as well as the core parallel plasma beta, . The data are separately analysed for two distance ranges, AU and AU, and divided into 24 bins for the plasma beta, in the range from to , and into 72 bins for the total temperature anisotropy, , which is here considered in the range from −0.9 to 0.9. The number of spectra in each bin is determined to obtain distributions. The statistical results are presented in two-dimensional histograms. For each column we define a critical upper and lower limit of the anisotropy. The resulting empirical points are compared with the known theoretical instability thresholds. The protons are found to come with increasing radial distance closer to the fire-hose instability threshold.

Magnetic spectral signatures in the terrestrial plasma depletion layer: Hybrid simulations

The electromagnetic ion cyclotron waves in the terrestrial plasma depletion layer (PDL) are characterized by three different spectral categories. They are LOW, where the ion cyclotron waves have a continuous spectrum with main power below 0.5Ωp (Ωp is the proton gyrofrequency); CON, where the main power in the continuous spectrum of the waves can extend from ∼0.1 up to 1.0Ωp; and BIF, where a diminution around 0.5Ωp occurs between two activity peaks in the spectrum. These magnetic fluctuations in the PDL are considered to be the combined effects of two types of ion cyclotron waves: proton cyclotron waves and helium cyclotron waves, which are excited by the H+ and He2+ temperature anisotropies, respectively. In this paper, with one‐dimensional (1‐D) hybrid simulations we investigate the nonlinear evolution of the ion cyclotron waves excited by the H+ and He2+ temperature anisotropies. The proton cyclotron waves with the dominant frequency (the amplitude at that frequency is largest in the spectrum) larger than 0.5Ωp are first excited, and then the helium cyclotron waves with the dominant frequency smaller than 0.5Ωp are excited. The frequencies of the proton cyclotron waves decrease in their corresponding nonlinear stage. For β∥p = 0.1 (where β∥p is the parallel proton plasma beta), the dominant frequency of the proton cyclotron waves remains around 0.62Ωp because of the He2+ absorption around the helium gyrofrequency. Therefore, after the helium cyclotron waves with the dominant frequency around 0.25Ωp are excited, there exist two activity peaks in the spectrum. At the quasi‐equilibrium stage, the amplitude of the proton cyclotron waves is very small because of the He2+ absorption, and a continuous spectrum with main power below 0.5Ωp is formed. When β∥p = 0.3, the effect of the He2+ absorption is very small and can be neglected. The frequencies of the proton cyclotron waves decrease in their nonlinear evolution. After the helium cyclotron waves are excited, their frequency band merges with that of the proton cyclotron waves and forms a continuous spectrum with main power extending above 0.5Ωp. At the quasi‐equilibrium stage, with the decrease of the frequencies of the ion cyclotron waves a continuous spectrum with main power below 0.5Ωp is formed. The relations between the three different spectral categories observed in the PDL and the spectra during the evolution of the ion cyclotron waves are also discussed. The results on the spectrum evolution of the ion cyclotron waves excited by the H+ and He2+ temperature anisotropies may help to explain the magnetic spectral signatures observed in the PDL.

Kinetic treatment of nonlinear magnetized plasma motions: General geometry and parallel waves

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is three dimensional, this very general result is used in a present paper only to focus on the parallel propagation of nonlinear Alfvén waves. The derivative nonlinear Schrödinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfvén speed, and shows that one cannot neglect parallel heat fluxes then, not even in the case of low parallel plasma beta. Finally, a truly stationary soliton solution is derived.