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In weak magnetic fields (⁠|$\lesssim 50 \, \mbox{G}$|⁠), parallel and perpendicular viscosities, mainly from neutrals, may exceed magnetic diffusivities (Ohm, Hall, and ambipolar) in the middle and upper chromospheres. Ion-driven gyroviscosity may dominate in the upper chromosphere and transition region. In strong fields (⁠|$\gtrsim 100\, \mbox{G}$|⁠), viscosities primarily exceed diffusivities in the upper chromosphere and transition region. Parallel and perpendicular viscosities, being similar in magnitude, dampen waves and potentially compete with ambipolar diffusion in plasma heating, potentially inhibiting Hall and ambipolar instabilities when equal. The perpendicular viscosity tensor has two components, |$\nu _1$| and |$\nu _2$|⁠ , which differ slightly and show weak dependence on ion magnetization. Their differences, combined with shear, may destabilize waves, though magnetic diffusion introduces a cut-off for this instability. In configurations with a magnetic field |${\boldsymbol B}$| having vertical (⁠|$b_z=B_z/|{\boldsymbol B}|$|⁠) and azimuthal (⁠|$b_y=B_y/|{\boldsymbol B}|$|⁠) components, and a wavevector |${\boldsymbol k}$| with radial (⁠|$\hat{k}_x=k_x/|{\boldsymbol k}|$|⁠) and vertical (⁠|$\hat{k}_z=k_z/|{\boldsymbol k}|$|⁠) components, parallel viscosity, and Hall diffusion can generate the viscous-Hall instability. Gyroviscosity further destabilizes waves in the upper regions. These findings indicate that the solar atmosphere may experience various viscous instabilities, revealing complex interactions between viscosity, magnetic fields, and plasma dynamics across different atmospheric regions. [ABSTRACT FROM AUTHOR]

The dynamics of the partially ionized solar atmosphere is controlled by the frequent collisions and charge exchange between the predominant neutral hydrogen atoms and charged ions. At signal frequencies below or of the order of either of the collision or charge exchange frequencies, the magnetic stress is felt by both the charged and neutral particles simultaneously. The resulting neutral-mass loading of the ions leads to the rescaling of the effective ion-cyclotron frequency (it becomes the Hall frequency), and the resultant effective Larmor radius becomes of the order of few kms. Thus, the finite Larmor radius effect that manifests as the ion and neutral pressure stress tensors operates over macroscopic scales. Whereas parallel and perpendicular (with respect to the magnetic field) viscous momentum transport competes with the Ohm and Hall diffusion of the magnetic field in the photosphere–chromosphere, the gyroviscous effect becomes important only in the transition region between the chromosphere and corona, where it competes with the ambipolar diffusion. The wave propagation in the gyroviscous effect-dominated medium depends on the plasma β (a ratio of the thermal and magnetic energies). The abundance of free energy makes gyro waves unstable with the onset condition exactly opposite of the Hall instability. However, the maximum growth rate is identical to the Hall instability. For a flow gradient of |${\sim} 0.1 \, \mbox{s}^{-1}$|⁠ , the instability growth time is 1 min. Thus, the transition region may become subject to this fast-growing gyroviscous instability. [ABSTRACT FROM AUTHOR]

In the solar photosphere-chromosphere region where SB 1 sb ~ SB 2 sb ~ SB P sb the dispersion relation is same as equation (39) of PW22. Errata, addenda, Sun: atmosphere, photosphere, MHD, plasmas, waves, chromosphere Keywords: errata; addenda; Sun: atmosphere; photosphere; chromosphere; MHD; plasmas; waves EN errata addenda Sun: atmosphere photosphere chromosphere MHD plasmas waves 2754 2755 2 05/18/23 20230620 NES 230620 The paper 'The non-ideal finite Larmor radius effect in the solar atmosphere' was published in MNRAS, 513, 1842-1857 (Pandey & Wardle [1]; hereafter PW22). [Extracted from the article]

The properties of surface waves in a partially ionized, compressible magnetized plasma slab are investigated in this work. The waves are affected by the non-ideal magnetohydrodynamic (MHD) effects which causes finite drift of the magnetic field in the medium. When the magnetic field drift is ignored, the characteristics of the wave propagation in a partially ionized plasma fluid is similar to the fully ionized ideal MHD except now the propagation properties depend on the fractional ionization as well as on the compressibility of the medium. The phase velocity of the sausage and kink waves increases marginally (by a few per cent) due to the compressibility of the medium in both ideal as well as Hall-diffusion-dominated regimes. However, unlike ideal regime, only waves below certain cut-off frequency can propagate in the medium in Hall dominated regime. This cut-off for a thin slab has a weak dependence on the plasma beta whereas for thick slab no such dependence exists. More importantly, since the cut-off is introduced by the Hall diffusion, the fractional ionization of the medium is more important than the plasma compressibility in determining such a cut-off. Therefore, for both compressible as well incompressible medium, the surface modes of shorter wavelength are permitted with increasing ionization in the medium. We discuss the relevance of these results in the context of solar photosphere–chromosphere. [ABSTRACT FROM AUTHOR]

The dynamics of the partially ionized solar photosphere and chromosphere can be described by a set of equations that are structurally similar to the magnetohydrodynamic equations, except now the magnetic field is no longer frozen in the fluid but slips through it due to non-ideal magnetohydrodynamic effects which are manifested as Ohm, ambipolar and Hall diffusion. Macroscopic gas motions are widespread throughout the solar atmosphere and shearing motions couple to the non-ideal effects, destabilizing low-frequency fluctuations in the medium. The origin of this non-ideal magnetohydrodynamic instability lies in the collisional coupling of the neutral particles to the magnetized plasma in the presence of a sheared background flow. Unsurprisingly, the maximum growth rate and most unstable wavenumber depend on the flow gradient and ambient diffusivities.The orientation of the magnetic field, velocity shears and perturbation wavevector play a crucial role in assisting the instability. When the magnetic field and wavevector are both vertical, ambipolar and Ohm diffusion can be combined as Pedersen diffusion and cause only damping; in this case only Hall drift in tandem with shear flow drives the instability. However, for non-vertical fields and oblique wavevectors, both ambipolar diffusion and Hall drift are destabilizing.We investigate the stability of magnetic elements in the network and internetwork regions. The shear scale is not yet observationally determined, but assuming a typical shear flow gradient of ∼0.1 s−1 we show that the magnetic diffusion shear instability grows on a time-scale of 1 min. Thus, it is plausible that network–internetwork magnetic elements are subject to this fast growing, diffusive shear instability, which could play an important role in driving low-frequency turbulence in the plasma in the solar photosphere and chromosphere. [ABSTRACT FROM AUTHOR]

ABSTRACT The magnetic network, which consists of vertical flux tubes located in intergranular lanes, is dominated by Hall drift in the photosphere-lower chromosphere region (≲ 1 Mm). In the internetwork regions with weak magnetic field, Hall drift dominates above 0.25 Mm in the photosphere and below 2.5 Mm in the chromosphere. Although Hall drift does not cause any dissipation in the ambient plasma, it can destabilize the flux tubes and magnetic elements in the presence of azimuthal shear flow. The physical mechanism of this instability is quite simple. The shear flow twists the radial magnetic field and generates an azimuthal field. Then, torsional oscillations of the azimuthal field, in turn, generate the radial field, completing feedback loop. The maximum growth rate of Hall instability is proportional to the absolute value of the shear gradient, and it is dependent on the ambient diffusivity. The diffusivity also determines the most unstable wavelength, which is smaller for weaker fields. We apply the results of a local stability analysis to the network and internetwork magnetic elements and show that the maximum growth rate for a kiloGauss field occurs around 0.5 Mm and decreases with increasing altitude. However, for a 120-G field, the maximum growth rate remains almost constant in the entire photosphere-lower chromosphere, except in a small region closer to the surface. For a shear flow gradient ∼0.1 s−1, the Hall growth time is about 1 min near the photospheric footpoint. Therefore, network and internetwork regions with an intense field in the presence of shear flow are likely to be unstable in the photosphere. The weak field internetwork regions could be unstable in the entire photosphere-chromosphere. Thus, Hall instability can play an important role in generating low-frequency turbulence, which can heat the chromosphere. [ABSTRACT FROM AUTHOR]

The solar photosphere is a partially ionized medium with collisions between electrons, various metallic ions and neutral hydrogen playing an important role in the momentum and energy transport in the medium. Furthermore, the number of neutral hydrogen atoms could be as large as 104 times the number of plasma particles in the lower photosphere. The non-ideal magnetohydrodynamic (MHD) effects, namely Ohm, ambipolar and Hall diffusion, can play an important role in the photosphere. We demonstrate that Hall is an important non-ideal MHD effect in the solar photosphere and show that the Hall effect can significantly affect the excitation and propagation of the waves in the medium. We also demonstrate that the non-ideal Hall-dominated inhomogeneous medium can become parametrically unstable, and it could have important ramifications for the photosphere and chromosphere of the Sun. The analysis hints at the possibility of the solar photosphere becoming parametrically unstable against the linear fluctuations. [ABSTRACT FROM AUTHOR]

The Hall effect arises in a plasma when electrons are able to drift with the magnetic field but ions cannot. In a fully ionized plasma this occurs for frequencies between the ion and electron cyclotron frequencies because of the larger ion inertia. Typically this frequency range lies well above the frequencies of interest (such as the dynamical frequency of the system under consideration) and can be ignored. In a weakly ionized medium, however, the Hall effect arises through a different mechanism – neutral collisions preferentially decouple ions from the magnetic field. This typically occurs at much lower frequencies and the Hall effect may play an important role in the dynamics of weakly ionized systems such as the Earth's ionosphere and protoplanetary discs. To clarify the relationship between these mechanisms we develop an approximate single-fluid description of a partially ionized plasma that becomes exact in the fully ionized and weakly ionized limits. Our treatment includes the effects of ohmic, ambipolar and Hall diffusion. We show that the Hall effect is relevant to the dynamics of a partially ionized medium when the dynamical frequency exceeds the ratio of ion to bulk mass density times the ion-cyclotron frequency, i.e. the Hall frequency. The corresponding length-scale is inversely proportional to the ion to bulk mass density ratio as well as to the ion-Hall beta parameter. In a weakly ionized medium, the critical frequency becomes small enough that Hall magnetohydrodynamics (MHD) is an accurate representation of the dynamics. More generally, ohmic and ambipolar diffusion may also be important. We show that both ambipolar and Hall diffusion depend upon the fractional ionization of the medium. However, unlike ambipolar diffusion, Hall diffusion may also be important in the high fractional ionization limit. The wave properties of a partially ionized medium are investigated in the ambipolar and Hall limits. We show that in the ambipolar regime wave damping is dependent on both fractional ionization and ion–neutral collision frequencies. In the Hall regime, since the frequency of a whistler wave is inversely proportional to the fractional ionization, and bounded by the ion–neutral collision frequency it will play an important role in the Earth's ionosphere, solar photosphere and astrophysical discs. [ABSTRACT FROM AUTHOR]