On the Origin of the Slow Speed Solar Wind: Helium Abundance Variations

The First Ionization Potential (FIP) effect is the by now well known enhancement in abundance over photospheric values of Fe and other elements with first ionization potential below about 10 eV observed in the solar corona and slow speed solar wind. In our model, this fractionation is achieved by means of the ponderomotive force, arising as Alfv\'en waves propagate through or reflect from steep density gradients in the solar chromosphere. This is also the region where low FIP elements are ionized, and high FIP elements are largely neutral leading to the fractionation as ions interact with the waves but neutrals do not. Helium, the element with the highest FIP and consequently the last to remain neutral as one moves upwards can be depleted in such models. Here, we investigate this depletion for varying loop lengths and magnetic field strengths. Variations in this depletion arise as the concentration of the ponderomotive force at the top of the chromosphere varies in response to Alfv\'en wave frequency with respect to the resonant frequency of the overlying coronal loop, the magnetic field, and possibly also the loop length. We find that stronger depletions of He are obtained for weaker magnetic field, at frequencies close to or just above the loop resonance. These results may have relevance to observed variations of the slow wind solar He abundance with wind speed, with slower slow speed solar wind having a stronger depletion of He.Comment: 28 pages, 12 figures, accepted to Ap

Non-WKB Models of the FIP Effect: The Role of Slow Mode Waves

A model for element abundance fractionation between the solar chromosphere and corona is further developed. The ponderomotive force due to Alfven waves propagating through, or reflecting from the chromosphere in solar conditions generally accelerates chromospheric ions, but not neutrals, into the corona. This gives rise to what has become known as the First Ionization Potential (FIP) Effect. We incorporate new physical processes into the model. The chromospheric ionization balance is improved, and the effect of different approximations is discussed. We also treat the parametric generation of slow mode waves by the parallel propagating Alfven waves. This is also an effect of the ponderomotive force, arising from the periodic variation of the magnetic pressure driving an acoustic mode, which adds to the background longitudinal pressure. This can have subtle effects on the fractionation, rendering it quasi-mass independent in the lower regions of the chromosphere. We also briefly discuss the change in the fractionation with Alfven wave frequency, relative to the frequency of the overlying coronal loop resonance.Comment: 32 pages, 8 figures, accepted by Ap

Oracle-order Recovery Performance of Greedy Pursuits with Replacement against General Perturbations

Applying the theory of compressive sensing in practice always takes different kinds of perturbations into consideration. In this paper, the recovery performance of greedy pursuits with replacement for sparse recovery is analyzed when both the measurement vector and the sensing matrix are contaminated with additive perturbations. Specifically, greedy pursuits with replacement include three algorithms, compressive sampling matching pursuit (CoSaMP), subspace pursuit (SP), and iterative hard thresholding (IHT), where the support estimation is evaluated and updated in each iteration. Based on restricted isometry property, a unified form of the error bounds of these recovery algorithms is derived under general perturbations for compressible signals. The results reveal that the recovery performance is stable against both perturbations. In addition, these bounds are compared with that of oracle recovery--- least squares solution with the locations of some largest entries in magnitude known a priori. The comparison shows that the error bounds of these algorithms only differ in coefficients from the lower bound of oracle recovery for some certain signal and perturbations, as reveals that oracle-order recovery performance of greedy pursuits with replacement is guaranteed. Numerical simulations are performed to verify the conclusions.Comment: 27 pages, 4 figures, 5 table

The Convergence Guarantees of a Non-convex Approach for Sparse Recovery

In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial solution to the global optimum. This paper aims to provide performance guarantees of a non-convex approach for sparse recovery. Specifically, the concept of weak convexity is incorporated into a class of sparsity-inducing penalties to characterize the non-convexity. Borrowing the idea of the projected subgradient method, an algorithm is proposed to solve the non-convex optimization problem. In addition, a uniform approximate projection is adopted in the projection step to make this algorithm computationally tractable for large scale problems. The convergence analysis is provided in the noisy scenario. It is shown that if the non-convexity of the penalty is below a threshold (which is in inverse proportion to the distance between the initial solution and the sparse signal), the recovered solution has recovery error linear in both the step size and the noise term. Numerical simulations are implemented to test the performance of the proposed approach and verify the theoretical analysis.Comment: 33 pages, 7 figure