RT info:eu-repo/semantics/doctoralThesis
T1 Simulations of the solar chromosphere in the two-fluid approximation
A1 Popescu Braileanu, Beatrice
A2 Programa de Doctorado en Astrofísica
K1 FISICA SOLAR
AB This work presents the study of wave propagation and the Rayleigh-Taylor instability in the solaratmosphere using a two-fluid model. The solar atmosphere is strongly stratified and permeated bymagnetic fields with a complex configuration, thus creating very different regimes throughout itslayers. Of the different layers of the solar atmosphere the photosphere is the one with the highestdensity and the strongest magnetic field. The high density makes the plasma collisionally coupledand the magnetohydrodynamic (MHD) assumption valid. Because of the high collision frequenciesbetween different constituents: ions, free electrons and neutral particles, the plasma becomes a perfectconductor. In mathematical terms, the non-ideal terms which appear in the generalized Ohm’s law arevery small compared to the ideal term. In the assumption of a perfectly conducting plasma, the fieldlines are tied to the plasma. The corona is fully ionized, and even if the magnetic fields are weaker thanin the photosphere, the very low density of plasma makes the corona a layer dominated by the magneticfield. Because the density decreases, the collision frequencies also decrease from the photospheretowards the corona. In these two extreme collisional regimes, coupled and uncoupled, MHD simulationsgive good results compared to the observations, but this is not the case for the chromosphere. Thesolar chromosphere is a complex and dynamic layer located between the photosphere and the corona.It is a transition layer where the properties of plasma change abruptly from gas pressure dominated tomagnetic field dominated, and where the collisional coupling of the plasma decreases and the ionizationfraction increases. The collisional timescales between ionized and neutral atomic species become equalor larger than the hydrodynamic timescale causing partial decoupling between charges and neutrals.Therefore, classical MHD approach is not valid in the chromosphere. A suitable alternative for thisapproach is a two-fluid model, numerically implemented in this work.The complexity of the solar atmosphere does not allow to solve the equations analytically, and theproblems are solved numerically using simulations. We have extended the non-ideal single-fluid code,Mancha3D, to simultaneously treat neutral and ionized plasma components in the two-fluid approach.The Mancha3D code uses an explicit scheme which has a series of advantages in the case of large-scale parallel simulations in 3D domains. The partial ionization effects are taken into account in thesingle-fluid approach through a generalized Ohm’s law. However, the two-fluid approach introducescollisional coupling terms which can lead an explicit code to become numerically unstable. For highcollision frequencies the equations become stiff. In order to ensure stability when the collisional termsare included in an explicit scheme, the time step needed to integrate the equations in time numericallyis of order of the inverse of the collision frequency. When the collisional frequency is high, the timestep imposed is very small. This restriction can be overcome by implementing the collisional termsimplicitly. In our newly developed code we treat such terms implicitly in a semi implicit scheme.We perform tests of acoustic and Alfvén waves in a uniform atmosphere, where we can comparethe numerical solutions to exact analytical solutions, for the purpose of the verification of the codeand the determination of the order of accuracy of the scheme. Afterwards, we run more realisticsimulations of fast magnetoacoustic waves in a stratified atmosphere, where we have used the VALCmodel. In both cases we observe damping of the waves, more pronounced when the collision frequencyis similar to the wave frequency. These results are consistent with results present in the literature.When the amplitude is large enough, an additional mechanism of damping can be observed, whichcannot be predicted by an analytical solution, but it can be shown through numerical simulations.We have performed a simulation using the MHD model, with a setup corresponding to the setup usedin the two-fluid approach, where the interaction between neutrals and charges is introduced throughthe ambipolar term in the induction equation. We observed that, even if the damping of the wave issimilar in the two cases, the increase in temperature is several times smaller in the MHD case.In the last part we study Rayleigh-Taylor instability at the interface between a solar prominence andcorona. We analyze the growth rate, the decoupling, the energy spectra in several simulations wherewe want to study the effect of the elastic and inelastic collisions, viscosity and thermal conductivity,compressibility, density contrast, initial perturbation, and the background magnetic field on the devel-opment of the instability in a non uniform medium where the transition between the prominence andthe corona is continuous with a characteristic length scale. In these simulations we have consideredideal Ohm’s law (no magnetic diffusivity). We observe that the linear growth rate is considerablysmaller than in the ideal incompressible MHD case without viscosity and thermal conductivity. Weconclude that the ion-neutral collisions, the viscosity and thermal conductivity have a stabilizing ef-fect. The magnetic field also inhibits the instability. For our equilibrium configuration, in the idealcase without magnetic field, the compressibility increases the linear growth rate.
YR 2020
FD 2020
LK http://riull.ull.es/xmlui/handle/915/24487
UL http://riull.ull.es/xmlui/handle/915/24487
LA en
DS Repositorio institucional de la Universidad de La Laguna
RD 29-may-2024