Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels

We present simulation results of the impulsively generated linear and non-linear Alfv\'en waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic (MHD) equations to obtain the temporal signatures of the small (linear) and large-amplitude (non-linear) Alfv\'en waves in the model atmosphere of expanding open magnetic field configuration (e.g., coronal funnels) by considering a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfv\'en waves at different heights in the coronal funnel, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfv\'en waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfv\'en waves show that they can contribute only to the plasma dynamics and heating of the funnel-like magnetic flux-tubes associated with the polar coronal holes.Comment: 16 pages of the text and 3 figure

Sequence Spaces Generated by Moduli of Smoothness

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On convolution operator in Orlicz spaces

Sin resume

Torsional Alfven Waves in Solar Magnetic Flux Tubes of Axial Symmetry

Aims: Propagation and energy transfer of torsional Alfv\'en waves in solar magnetic flux tubes of axial symmetry is studied. Methods: An analytical model of a solar magnetic flux tube of axial symmetry is developed by specifying a magnetic flux and deriving general analytical formulae for the equilibrium mass density and a gas pressure. The main advantage of this model is that it can be easily adopted to any axisymmetric magnetic structure. The model is used to simulate numerically the propagation of nonlinear Alfv\'en waves in such 2D flux tubes of axial symmetry embedded in the solar atmosphere. The waves are excited by a localized pulse in the azimuthal component of velocity and launched at the top of the solar photosphere, and they propagate through the solar chromosphere, transition region, and into the solar corona. Results: The results of our numerical simulations reveal a complex scenario of twisted magnetic field lines and flows associated with torsional Alfv\'en waves as well as energy transfer to the magnetoacoustic waves that are triggered by the Alfv\'en waves and are akin to the vertical jet flows. Alfv\'en waves experience about 5 % amplitude reflection at the transition region. Magnetic (velocity) field perturbations experience attenuation (growth) with height is agreement with analytical findings. Kinetic energy of magnetoacoustic waves consists of 25 % of the total energy of Alfv\'en waves. The energy transfer may lead to localized mass transport in the form of vertical jets, as well as to localized heating as slow magnetoacoustic waves are prone to dissipation in the inner corona.Comment: 12 pages; 12 Figures, Astron. Astrophys. (A&A); Comment : High-resolution images will be appeared with the final pape

Numerical Simulations of Torsional Alfv\'en Waves in Axisymmetric Solar Magnetic Flux Tubes

We investigate numerically Alfv\'en waves propagating along an axisymmetric and non-isothermal solar flux tube embedded in the solar atmosphere. The tube magnetic field is current-free and diverges with height, and the waves are excited by a periodic driver along the tube magnetic field lines. The main results are that the two wave variables, the velocity and magnetic field perturbations in the azimuthal direction, behave differently as a result of gradients of physical parameters along the tube. To explain these differences in the wave behavior, the time evolution of the wave variables and the resulting cutoff period for each wave variable are calculated, and used to determine regions in the solar chromosphere where strong wave reflection may occur.Comment: Submitted to Solar Physics (accepted

Translations in the exponential Orlicz space with Gaussian weight

We study the continuity of space translations on non-parametric exponential families based on the exponential Orlicz space with Gaussian reference density.Comment: Submitted to GSI 2017, Pari

Forced oscillations of coronal loops driven by external EIT waves

Aims. We study the generation of transversal oscillations in coronal loops represented as a straight thin flux tube under the effect of an external driver modelling the global coronal EIT wave. We investigate how the generated oscillations depend on the nature of the driver, and the type of interaction between the two systems. Methods. We consider the oscillations of a magnetic straight cylinder with fixed-ends under the influence of an external driver modelling the force due to the global EIT wave. Given the uncertainties related to the nature of EIT waves, we first approximate the driver by an oscillatory force in time and later by a shock with a finite width. Results. Results show that for a harmonic driver the dominant period in the generated oscillation belongs to the driver. Depending on the period of driver, compared to the natural periods of the loop, a mixture of standing modes harmonics can be initiated. In the case of a non-harmonic driver (modelling a shock wave), the generated oscillations in the loop are the natural periods only. The amplitude of oscillations is determined by the position of the driver along the tube. The full diagnosis of generated oscillations is achieved using simple numerical methods

Forced oscillations of coronal loops driven by external EIT waves

Aims. We study the generation of transversal oscillations in coronal loops represented as a straight thin flux tube under the effect of an external driver modelling the global coronal EIT wave. We investigate how the generated oscillations depend on the nature of the driver, and the type of interaction between the two systems. Methods. We consider the oscillations of a magnetic straight cylinder with fixed-ends under the influence of an external driver modelling the force due to the global EIT wave. Given the uncertainties related to the nature of EIT waves, we first approximate the driver by an oscillatory force in time and later by a shock with a finite width. Results. Results show that for a harmonic driver the dominant period in the generated oscillation belongs to the driver. Depending on the period of driver, compared to the natural periods of the loop, a mixture of standing modes harmonics can be initiated. In the case of a non-harmonic driver (modelling a shock wave), the generated oscillations in the loop are the natural periods only. The amplitude of oscillations is determined by the position of the driver along the tube. The full diagnosis of generated oscillations is achieved using simple numerical methods