Magneto-seismology: effect of inhomogeneous magnetic field on transversal coronal loop oscillations

The extreme-ultraviolet (EUV) imagers onboard the planned Solar Dynamics Observatory (SDO) and Solar Orbiter (SO) will offer us the best chance yet of using observations of post-flare loop oscillations to probe the fine structure of the corona. Recently developed magnetohydrodynamic (MHD) wave theory has shown that the properties of loop oscillations depend on their plasma fine structure. Up to this point, many studies have concentrated solely on the effect of plasma density stratification on coronal loop oscillations. In this paper we develop MHD wave theory which models the effect of an inhomogeneous magnetic field on coronal loop oscillations. The results have the potential to be used in testing the efficacy of photospheric magnetic field extrapolations and have important implications regarding magneto-seismology of the corona

Magneto-seismology of solar atmospheric loops by means of longitudinal oscillations

There is increasingly strong observational evidence that slow magnetoacoustic modes arise in the solar atmosphere. Solar magneto-seismology is a novel tool to derive otherwise directly un-measurable properties of the solar atmosphere when magnetohydrodynamic (MHD) wave theory is compared to wave observations. Here, MHD wave theory is further developed illustrating how information about the magnetic and density structure along coronal loops can be determined by measuring the frequencies of the slow MHD oscillations. The application to observations of slow magnetoacoustic waves in coronal loops is discused.Comment: 4 pages, 2 figures, to appear in Proceedings of IAU Symp 286, Comparative Magnetic Minima, C. H. Mandrini, ed

Spatial magneto-seismology : effect of density stratification on the first harmonic amplitude profile of transversal coronal loop oscillations

Context. The new generation of extreme-ultraviolet (EUV) imagers onboard missions such as the Solar Dynamics Observatory (SDO)and Solar Orbiter (SO) will provide the most accurate spatial measurements of post-flare coronal loop oscillations yet. The amplitude profiles of these loop oscillations contain important information about plasma fine structure in the corona. Aims. We show that the position of the anti-nodes of the amplitude profile of the first harmonic of the standing fast kink wave of a coronal loop relate to the plasma density stratification of that loop. Methods. The MHD kink transversal waves of coronal loops are modelled both numerically and analytically. The numerical model implements the implicit finite element code pollux. Dispersion relations are derived and solved analytically. The results of the two methods are compared and verified. Results. Density stratification causes the anti-nodes of the first harmonic to shift towards the loop footpoints. The greater the density stratification, the larger the shift. The anti-node shift of the first harmonic of a semi-circular coronal loop with a density scale height H = 50 Mm and loop half length L = 100 Mm is approximately 5.6Mm. Shifts in the Mm range are measureable quantities providing valuable information about the subresolution structure of coronal loops. Conclusions. The measurement of the anti-node shift of the first harmonic of the standing fast kink wave of coronal loops is potentially a new tool in the field of solar magneto-seismology, providing a novel complementary method of probing plasma fine structure in the corona

Solvable rational extensions of the Morse and Kepler-Coulomb potentials

We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using Darboux-B\"acklund transformations based on unphysical regular Riccati-Schr\"odinger functions which are obtained from specific symmetries associated to the considered family of potentials

Sum rules for correlation functions of ionic mixtures in arbitrary dimension d≥2d\geq 2

The correlations in classical multi-component ionic mixtures with spatial dimension $d\geq 2$ are studied by using a restricted grand-canonical ensemble and the associated hierarchy equations for the correlation functions. Sum rules for the first few moments of the two-particle correlation function are derived and their dependence on $d$ is established. By varying $d$ continuously near $d=2$ it is shown how the sum rules for the two-dimensional mixture are related to those for mixtures at higher $d$.Comment: 19 page

Solar feature tracking in both spatial and temporal domains

A new method for automated coronal loop tracking, in both spatial and temporal domains, is presented. The reliability of this technique was tested with TRACE 171A observations. The application of this technique to a flare-induced kink-mode oscillation, revealed a 3500 km spatial periodicity which occur along the loop edge. We establish a reduction in oscillatory power, for these spatial periodicities, of 45% over a 322 s interval. We relate the reduction in oscillatory power to the physical damping of these loop-top oscillations

The Absence of Positive Energy Bound States for a Class of Nonlocal Potentials

We generalize in this paper a theorem of Titchmarsh for the positivity of Fourier sine integrals. We apply then the theorem to derive simple conditions for the absence of positive energy bound states (bound states embedded in the continuum) for the radial Schr\"odinger equation with nonlocal potentials which are superposition of a local potential and separable potentials.Comment: 23 page

Complex Periodic Potentials with a Finite Number of Band Gaps

We obtain several new results for the complex generalized associated Lame potential V(x)= a(a+1)m sn^2(y,m)+ b(b+1)m sn^2(y+K(m),m) + f(f+1)m sn^2(y+K(m)+iK'(m),m)+ g(g+1)m sn^2(y+iK'(m),m), where y = x-K(m)/2-iK'(m)/2, sn(y,m) is a Jacobi elliptic function with modulus parameter m, and there are four real parameters a,b,f,g. First, we derive two new duality relations which, when coupled with a previously obtained duality relation, permit us to relate the band edge eigenstates of the 24 potentials obtained by permutations of the four parameters a,b,f,g. Second, we pose and answer the question: how many independent potentials are there with a finite number "a" of band gaps when a,b,f,g are integers? For these potentials, we clarify the nature of the band edge eigenfunctions. We also obtain several analytic results when at least one of the four parameters is a half-integer. As a by-product, we also obtain new solutions of Heun's differential equation.Comment: 33 pages, 0 figure