M-Class Solar Flares in Solar Cycles 23 and 24: Properties and Space Weather Relevance

A comprehensive statistical analysis on the properties and accompanied phenomena of all M-class solar flares (as measured in soft X-rays) in the last two solar cycles (1996–2019) is presented here with a focus on their space weather potential. The information about the parent active region and the underlying sunspot (Hale) type is collected for each case, where possible, in order to identify photospheric precondition as precursors for the solar flare eruption or confinement. Associations with coronal mass ejections, solar energetic particles, and interplanetary radio emissions are also evaluated and discussed as possible proxies for flare eruption and subsequent space weather relevance. The results show that the majority (∼80%) of the analyzed M-class flares are of β, β-γ, and β-γ-δ magnetic field configuration. The M-class population of flares is accompanied by CMEs in 41% of the cases and about half of the flare sample has been associated with radio emission from electron beams. A much lower association (≲10%) is obtained with shock wave radio signatures and energetic particles. Furthermore, a parametric scheme is proposed in terms of occurrence rates between M-class flares and a variety of accompanied solar phenomena as a function of flare sub-classes or magnetic type. This study confirms the well-known reduced but inevitable space weather importance of M-class flares.

Ion current optimization in a magnetron with tunable magnetic field configuration

The response of the ion current in the substrate region to the magnetic system configuration of a circular magnetron was studied during direct current sputtering of aluminum target. The unbalancing degree induced by changing of magnets’ positions was modelled with finite element methods. The ion saturation current in the substrate region showed more than twofold variation with unbalancing degree in the range 0.6–1.2. The dependence was non-monotonic, and the system was optimized to maximize the substrate ion current. The Langmuir probe diagnostics showed plasma density ~ 1016 m−3 in the optimized magnetic configuration.

An adjoint method for determining the sensitivity of island size to magnetic field variations

An adjoint method to calculate the gradient of island width in stellarators is presented and applied to a set of magnetic field configurations. The underlying method for calculation of the island width is that of Cary & Hanson (Phys. Fluids B, vol. 3, issue 4, 1991, pp. 1006–1014) (with a minor modification), and requires that the residue of the island centre be small. Therefore, the gradient of the residue is calculated in addition. Both the island width and the gradient calculations are verified using an analytical magnetic field configuration introduced by Reiman & Greenside (Comput. Phys. Commun., vol. 43, issue 1, 1986, pp. 157–167). The method is also applied to the calculation of the shape gradient of the width of a magnetic island in a National Compact Stellarator Experiment (NCSX) vacuum configuration with respect to positions on a coil. A gradient-based optimization is applied to a magnetic field configuration studied by Hanson & Cary (Phys. Fluids, vol. 27, issue 4, 1984, pp. 767–769) to minimize stochasticity by adding perturbations to a pair of helical coils. Although only vacuum magnetic fields and an analytical magnetic field model are considered in this work, the adjoint calculation of the island width gradient could also be applied to a magnetohydrodynamic (MHD) equilibrium if the derivative of the magnetic field, with respect to the equilibrium parameters, is known. Using the island width gradient calculation presented here, more general gradient-based optimization methods can be applied to design stellarators with small magnetic islands. Moreover, the sensitivity of the island size may itself be optimized to ensure that coil tolerances, with respect to island size, are kept as high as possible.