Detailed Description of the Collision Frequency in the Solar Atmosphere

Abstract

This work aims to provide an accurate description and calculations of collision frequencies in conditions relevant to the solar atmosphere. To do so, we focus on the detailed description of the collision frequency in the solar atmosphere based on a classical formalism with Chapman–Cowling collision integrals, as described by Zhdanov. These collision integrals allow linking the macroscopic transport fluxes of multifluid models to the kinetic scales involved in the Boltzmann equations. In this context, the collision frequencies are computed accurately while being consistent at the kinetic level. We calculate the collision frequencies based on this formalism and compare them with approaches commonly used in the literature for conditions typical of the solar atmosphere. To calculate the collision frequencies, we focus on the collision integral data provided by Bruno et al., which is based on a multicomponent hydrogen–helium mixture used for conditions typical for the atmosphere of Jupiter. We perform a comparison with the classical formalism of Vranjes & Krstic and Leake & Linton. We highlight the differences obtained in the distribution of the cross sections as functions of the temperature. Then, we quantify the disparities obtained in numerical simulations of a 2.5D solar atmosphere by calculating collision frequencies and ambipolar diffusion. This strategy allows us to validate and assess the accuracy of these collision frequencies for conditions typical of the solar atmosphere.

Two-fluid numerical model of chromospheric heating and plasma outflows in a quiet-Sun

“…with σ kl = σ lk being the collisional cross-section for k-and l-species for which its classical values of σ in = σ ei = 1.4 × 10 −19 m 2 and σ en = 2 × 10 −19 m 2 are chosen from Vranjes & Krstic (2013). See Wargnier et al (2022) for recently derived expressions for collision frequencies.…”

Chromospheric Heating from Local Magnetic Growth and Ambipolar Diffusion under Nonequilibrium Conditions

“…However, it is also inversely proportional to the ion-neutral collision frequency. This decreases drastically with height as the density drops (not shown here; see also Wargnier et al 2022).…”

Multifluid Simulations of Upper-chromospheric Magnetic Reconnection with Helium–Hydrogen Mixture

“…The fact that the decoupling between He and H + is stronger than that of other interactions is attributed to the collisional frequencies that involve neutral helium species, which are much smaller by more than 2 orders of magnitude than all the other collisional frequencies, as shown in Table 2 (for the initial conditions). These differences are attributed to the magnitude of the collision integrals at the kinetic level that leads to smaller collisional frequencies, as described with further details in Wargnier et al (2022). This effect leads to slower velocities for neutral helium species with respect to H + , as illustrated in panel (D) of Figure 3 and panel (C) of Figure 4.…”

“…The drift between H and H + is higher in the MFMS model than in the TF model because the collisional frequency associated with H-H + interactions is smaller in the former than in the latter. As shown in Wargnier et al (2022), the collisional frequencies are calculated from the products of (1) the collision integral associated with H-H + interaction, (2) H and H + number densities, and (3) thermal speed associated with H-H + interaction. In our chosen conditions, the number densities of H and H + in the MFMS model are smaller than those in the TF model due to the presence of helium species.…”

“…Note that Equation (5) does not include the term associated with the difference in heat fluxes between species, as described by Hansteen et al (1997) or in the 13N moment model of Zhdanov (2002). The collision frequencies , col a a n ¢ ¢   are described in detail in Wargnier et al (2022). In this context, the collisional frequencies are consistent with the definition given by Zhdanov (2002) in the context of the 13-N moment model for multicomponent plasmas, calculated from generalized Chapman-Cowling collision integrals.…”