Nonlinear dynamics of the firehose instability in a magnetic dipole geotail

Abstract

[1] The nonlinear dynamics of the firehose instability provides a possible explanation for the onset of the magnetic fluctuations associated with bursty bulk flows and substorms. Magnetic fluctuations called Pi2 geomagnetic pulsations are associated with bursty flows in the geotail plasma, where the plasma pressure exceeds the magnetic pressure. These strong magnetic fluctuations are often associated with substorms and start a few minutes before the arrival of the dipolarization pulse. Motivated by these observations, we have derived a nonlinear partial differential equation and developed an initial value code to investigate the firehose anisotropy-driven turbulence in the Earth's geotail. We show that Hall MHD and dispersive ion kinetic effects limit the range of unstable parallel wavenumbers and determine the frequency spectrum of the turbulence. Nonlinear saturation is caused by the nonlinear weakening at large magnetic field line distortions of the destabilizing magnetic curvature force driven by the pressure anisotropy.

Parallel proton fire hose instability in gyrotropic Hall MHD model

“…To counterbalance the nonlinear instability resistivity and/or viscosity however need be included in both MHD and Hall MHD calculations (in particular, the diffusion term ( η / μ 0 )∇ 2 is added in and the viscous term ν ∇ 2 is added in ). The incorporation of resistivity/viscosity in the fluid model of nonlinear instability which may be attributed to the kinetic effects such as lower‐hybrid drift instability is physically necessary to achieve nonlinear saturation as was also shown recently by Horton et al [2004b] in their study of fire hose driven turbulence in a magnetic dipole geotail geometry.…”

“…The solitary structures however become less pronounced as time progresses in the Hall MHD model while they may sustain in the MHD model. Note that soliton‐like magnetic structures though not reported in the earlier studies of hybrid simulations have also been found in the fluid simulation for nonlinear fire hose instability in a dipole geometry for certain parameter values [ Horton et al , 2004b]. As shown in Figure 5, substantial noncoplanar components of the magnetic field B y and flow velocity v y comparable to B z and v z may develop as a result of Hall current and B z and v z may exhibit bipolar feature of a few ion inertial lengths in the middle and ending portions of the simulation domain.…”

“…The growth curve shown in Figure 1 exhibits parabola shape with maximum growth rate γ m = ω ci ( α − 1) occurring at intermediate wavelengths λ i k m = which is similar to the result obtained from solving the kinetic dispersion relation for right‐hand polarized whistler mode numerically [see, e.g., Quest and Shapiro , 1996, Figure 2]. In fact the kinetic counterparts, γ m = (2/ β ∥ i ) ω ci ( α − 1) and λ i k m = (2/ β ∥ i ), derived from the kinetic dispersion assuming ω < ω ci and neglecting the Hall term as compared to the finite Larmor radius (FLR) term [e.g., Stix , 1992; Horton et al , 2004b], are in analogy with the Hall MHD expressions which is not restricted to the condition of ω < ω ci (though physically the model may no longer be representative at this frequency). The result that the growth rates derived from the kinetic model are in general smaller than those based on the Hall MHD model implies that for high β plasma FLR is important in stabilizing the parallel fire hose instability.…”

“…In this paper the linear stability and nonlinear evolutions of fire hose instabilities are examined within the framework of gyrotropic Hall MHD theory by retaining the ion inertia but neglecting the electron inertia in the generalized Ohm's law. Since the oblique propagation may involve also the new fire hose instability which is compressible and may be more sensitive to the choice of energy equations in the fluid model, as a first attempt the present study will focus on the parallel fire hose instability which has recently been studied in connection with expanding solar wind [e.g., Matteini et al , 2006] and magnetic fluctuations in the magnetosphere [ Horton et al, 2004a, 2004b]. The results based on gyrotropic Hall MHD model are complementary to the previous studies of fire hose instability using the hybrid particle simulations [ Quest and Shapiro , 1996; Gary et al , 1998] and to our earlier MHD results [ Wang and Hau , 2003] (hereafter referred to as paper 1).…”

Localized magnetic field structures and their boundaries in the near-Sun solar wind from Parker Solar Probe measurements

“…It was shown that due to it here may grow two types of waves: the shear incompressible Alfvén waves and compressible Alfvén waves. These instabilities were studied in detail by many authors in different versions of Chew-Goldberg-Low (CGL) MHD and kinetic approximations (Shapiro & Shevchenko 1964;Kennel & Sagdeev 1967a,b;Kennel & Scarf 1968;Berezin & Sagdeev 1969;Berezin 1972;Berezin & Vshivkov 1976;Gary 1993;Quest & Shapiro 1996;Gary et al 1998;Horton et al 2004). Statistical studies of the radial evolution of the solar wind from 0.3 to 1.0 AU showed that the ion distribution often consists of a core and a beam with relative velocity of the order of Alfvén speed (Marsch et al 1982a;Marsch 2012).…”