Transverse Waves In Simulated Coronal Loops:Their Potential In Coronal Heating And Seismology

As one of the most important problems in astrophysics,the coronal heating problem still awaits a definitive answer.To indisputably solve the coronal heating problem,two aspects should be clarified,namely the source and the dissipation of energy.The study on heating mechanisms in coronal loops,themost conspicuous magnetic structure in the solar corona,is widely seen as the key to solve the heating problem in the magnetically closed corona.More and more observations have revealed that active region loops undergo kink oscillations.As the only mode that can induce the transverse displacementof a coronal loop,kink oscillations can be excited by the random motions at photospheric footpoints of active region loops.Such random motions can injectenergy into the loop system from their footpoints.Ithas been generally accepted that the kinetic energy of the photospheric motions can readily account for the energy source required for coronal heating.Then the other aspect should be addressed,namely,how the energy dissipates to heat the corona.Since the Reynolds and magnetic Reynolds numbers are huge for the typical corona,the energy carried by collective modes are noteasy to dissipate through resistive or viscous mechanism unless small spatial scales can be generated.Kink and Alfven oscillations play an important role in generating small scales in wave-based heating mechanisms.Alfven modes have the ability to carry a large amount of energy,which can dissipate through phase mixing.During their propagation in non-uniform structures,the Alfven modes become more and more out of phase due to the difference of Alfven speeds between differentmagnetic surfaces.Thus strong gradients in the transverse velocity and magnetic field perturbations can be induced.Then the wave energy dissipates at such small scales.As for kink oscillations,their apparent damping is usually attributed to resonant absorption,whereby the collectiveenergy is transferred to localized Alfven modes atthe inhomogeneous layer near the loop boundary.Then the energy associated with kink oscillations dissipates at small scales through the subsequent phase-mixed Alfven modes.In addition,recent numerical studies revealed that kink oscillations in coronal loops can induce the Kelvin-Helmholtz Instability(KHI),thereby generating small-scale vortices that are then helpful for dissipating the wave energy.The first two chapters in the results part of this thesis show our modelling efforts on wave-based heating mechanisms.In Chapter 2,we consider the oscillations in a magnetic cylinder with different footpointdrivers,namely a kink driver,an Alfven driver,and a,combination of the two.In previous studies,Alfven modes usually derive from the resonant kink oscillations.In Chapter 2,we first consider kink and Alfven oscillations simultaneously and examine their influence on energy dissipation.As a.result,the KHI develops in loop regions in all three models.The averaged internal energy and temperature has larger increase in the loop with a mixed footpointdriver,which means thatthis model is more efficient in energy dissipation when compared with the other two models.This means thatthe KHI acts as a agent to dissipate energy in both Alfven and kink oscillations.Furthermore,our forward-modeling efforts indicate that neither Alfven oscillations nor the generated fine-scale structures can be adequately resolved given the spatial resolution of available instruments.This means that although difficultto measure,Alfven oscillations resulting from footpoint swirling motions are likely to be present in coronal loops.And when Alfven oscillations do exist together with kink oscillations,enhanced heating is expected when compared with the cases where only an individual type of drivers is presentIn Chapter 3,we go a,further step to examine how the multi-strandedness influence the wave energy dissipation,given that more and more observations suggested that coronal loops should be multi-stranded.To reveal the wave heating effects,we modelled a multi-stranded active region loop with a mixed kink and Alfven footpoint driver,as well as a.density equivalent monolithic loop for comparison.Depositing the same energy flux into the multi-stranded loop and the monolithic loop,we find a rapid increase in the averaged internal energy and temperature in the multi-stranded loopmeaning that the multi-stranded loop is more efficientin initiating the dissipation process.In addition,the temperature profile in the multi-stranded loop agrees with the previous predictions and observations.Thus the multi-strandedness of loops should be considered in wave-based heating mechanism studies,given our results and the observational facts that the coronal loops should be multi-stranded.Recent spectroscopic observations showed that the cross-sections of active region loops are unlikely to be perfectly circular.In Chapter 4.we first examine transverse oscillations in magnetic tubes with elliptical cross-sections by taking advantage of three dimensional numerical simulations.Given the lack of rotational symmetry of the considered equilibria,we distinguish between two independent polarizations,one in the direction of the major axis and the other along the minor one.Our dynamical analysis reveals that resonant absorption and phase mixing still works well in such kind of elliptical cross-sectional loops,meaning that resonantabsorption and phase mixing are robustin generating small scales.Meanwhile,this hints that the heating mechanisms in circular cross-sectional loops are likely to apply to elliptical loops as well.By examining the damping curves at loop axis,we find that both polarizations undergo a Gaussian damping profile and then an exponential damping profile for loops with both circular cross-sections and elliptical cross-sections.Furthermore,we also examine the dependence of oscillation periods and damping rates on polarizations,the flattening of cross-sections,as well as on the density ratio between the internal and external media.Based on such a property,a new seismology scheme can be proposed to infer the above physical parameters in typical active region loops.