Beatrice Popescu Braileanu
Thesis advisor
Khomenko Shchukina
Ángel Manuel de
Vicente Garrido
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This work presents the study of wave propagation and the Rayleigh-Taylor instability in the solar
atmosphere using a two-fluid model. The solar atmosphere is strongly stratified and permeated by
magnetic fields with a complex configuration, thus creating very different regimes throughout its
layers. Of the different layers of the solar atmosphere the photosphere is the one with the highest
density and the strongest magnetic field. The high density makes the plasma collisionally coupled
and the magnetohydrodynamic (MHD) assumption valid. Because of the high collision frequencies
between different constituents: ions, free electrons and neutral particles, the plasma becomes a perfect
conductor. In mathematical terms, the non-ideal terms which appear in the generalized Ohm’s law are
very small compared to the ideal term. In the assumption of a perfectly conducting plasma, the field
lines are tied to the plasma. The corona is fully ionized, and even if the magnetic fields are weaker than
in the photosphere, the very low density of plasma makes the corona a layer dominated by the magnetic
field. Because the density decreases, the collision frequencies also decrease from the photosphere
towards the corona. In these two extreme collisional regimes, coupled and uncoupled, MHD simulations
give good results compared to the observations, but this is not the case for the chromosphere. The
solar 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 to
magnetic field dominated, and where the collisional coupling of the plasma decreases and the ionization
fraction increases. The collisional timescales between ionized and neutral atomic species become equal
or 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 this
approach 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 the
problems 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 the
single-fluid approach through a generalized Ohm’s law. However, the two-fluid approach introduces
collisional coupling terms which can lead an explicit code to become numerically unstable. For high
collision frequencies the equations become stiff. In order to ensure stability when the collisional terms
are included in an explicit scheme, the time step needed to integrate the equations in time numerically
is of order of the inverse of the collision frequency. When the collisional frequency is high, the time
step imposed is very small. This restriction can be overcome by implementing the collisional terms
implicitly. 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 compare
the numerical solutions to exact analytical solutions, for the purpose of the verification of the code
and the determination of the order of accuracy of the scheme. Afterwards, we run more realistic
simulations of fast magnetoacoustic waves in a stratified atmosphere, where we have used the VALC
model. In both cases we observe damping of the waves, more pronounced when the collision frequency
is 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, which
cannot 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 used
in the two-fluid approach, where the interaction between neutrals and charges is introduced through
the ambipolar term in the induction equation. We observed that, even if the damping of the wave is
similar 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 and
corona. We analyze the growth rate, the decoupling, the energy spectra in several simulations where
we 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 and
the corona is continuous with a characteristic length scale. In these simulations we have considered
ideal Ohm’s law (no magnetic diffusivity). We observe that the linear growth rate is considerably
smaller than in the ideal incompressible MHD case without viscosity and thermal conductivity. We
conclude 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 ideal
case without magnetic field, the compressibility increases the linear growth rate.