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Register a new userNonlinear growth of firehose and mirror fluctuations in turbulent galaxy-cluster plasmas
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Added by
Alexander Schekochihin
Publication date
2008
fields
Physics
and research's language is
English
Authors
A. A. Schekochihin
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In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, dB/B ~ 1, on a timescale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.
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Hybrid-kinetic numerical simulations of firehose and mirror instabilities in a collisionless plasma are performed in which pressure anisotropy is driven as the magnetic field is changed by a persistent linear shear $S$. For a decreasing field, it is found that mostly oblique firehose fluctuations grow at ion Larmor scales and saturate with energies $sim$$S^{1/2}$; the pressure anisotropy is pinned at the stability threshold by particle scattering off microscale fluctuations. In contrast, nonlinear mirror fluctuations are large compared to the ion Larmor scale and grow secularly in time; marginality is maintained by an increasing population of resonant particles trapped in magnetic mirrors. After one shear time, saturated order-unity magnetic mirrors are formed and particles scatter off their sharp edges. Both instabilities drive sub-ion-Larmor--scale fluctuations, which appear to be kinetic-Alfv{e}n-wave turbulence. Our results impact theories of momentum and heat transport in astrophysical and space plasmas, in which the stretching of a magnetic field by shear is a generic process.
The selfgenerated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that the firehose and the ordinary-mode instabilities can develop under the same conditions, confusing the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron temperature anisotropy $T_parallel > T_perp$, where $parallel$ and $perp$ denote directions with respect to the local mean magnetic field. In addition to the previous comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, paying particular attention to the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For larger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding the ones of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the small $beta [< 1]$ regimes, here it is rigorously shown that only the large $beta [> 1]$ regimes are susceptible to these instabilities.
Using hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfvenic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfv{e}nic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale critical balance between their characteristic linear and nonlinear frequencies. Once the temperature anisotropy is sufficiently negative, the plasma becomes unstable to kinetic firehose instabilities, which excite rapidly growing magnetic fluctuations at ion-Larmor scales. The consequent pitch-angle scattering of particles maintains the temperature anisotropy near marginal stability, even as the turbulent plasma continues to expand. The resulting evolution of parallel and perpendicular temperatures does not satisfy double-adiabatic conservation laws, but is described accurately by a simple model that includes anomalous scattering. Our results have implications for understanding the complex interplay between macro- and micro-scale physics in various hot, dilute, astrophysical plasmas, and offer predictions concerning power spectra, residual energy, ion-Larmor-scale spectral breaks, and non-Maxwellian features in ion distribution functions that may be tested by measurements taken in high-beta regions of the solar wind.
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