Prediction of solar flares is an important task in solar physics. The occurrence of solar flares is highly dependent on the structure and the topology of solar magnetic fields. A new method for predicting large (M and X class) flares is presented, which uses machine learning methods applied to the Zernike moments of magnetograms observed by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) for a period of six years from 2 June 2010 to 1 August 2016. Magnetic field images consisting of the radial component of the magnetic field are converted to finite sets of Zernike moments and fed to the Support Vector Machine (SVM) classifier.Zernike moments have the capability to elicit unique features from any 2-D image, which may allow more accurate classification. The results indicate whether an arbitrary active region has the potential to produce at least one large flare. We show that ALL AUTHORS AND AFFILIATIONS

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A 2.5D numerical model of magnetoacoustic-Alfvén linear mode conversions in the partially ionised low solar atmosphere induced by the Hall effect is surveyed, varying magnetic field strength and inclination, and wave frequency and horizontal wave number. It is found that only the magnetic component of wave energy is subject to Hall-mediated conversions to Alfvén wave-energy via a process of polarisation rotation. This strongly boosts direct mode conversion between slow magnetoacoustic and Alfvén waves in the quiet low chromosphere, even at mHz frequencies. However, fast waves there, which are predominantly acoustic in nature, are only subject to Hall- induced conversion via an indirect two-step process: (i) a geometry-induced fast-slow transformation near the Alfvén-acoustic equipartition height zeq; and (ii) Hall-rotation of the fast wave in z > zeq. Thus, for the two-stage process to yield upgoing Alfvén waves, zeq must lie below or within the Hall-effective window 0 ≲ z ≲ 700 km. Magnetic field strengths over 100 G are required to achieve this. Since the potency of this Hall effect varies inversely with the field strength but directly with the wave frequency, only frequencies above about 100 mHz are significantly affected by the two-stage process. Increasing magnetic field inclination θ generally strengthens the Hall convertibility, but the horizontal wavenumber kx has little effect. The direct and indirect Hall mechanisms both have implications for the ability of MHD waves excited at the photosphere to reach the upper chromosphere, and by implication the corona.

A 2.5D numerical model of magnetoacoustic-Alfvén linear mode conversions in the partially ionised low solar atmosphere induced by the Hall effect is surveyed, varying magnetic field strength and inclination, and wave frequency and horizontal wave number. It is found that only the magnetic component of wave energy is subject to Hall-mediated conversions to Alfvén wave-energy via a process of polarisation rotation. This strongly boosts direct mode conversion between slow magnetoacoustic and Alfvén waves in the quiet low chromosphere, even at mHz frequencies. However, fast waves there, which are predominantly acoustic in nature, are only subject to Hall-induced conversion via an indirect two-step process: (i) a geometry-induced fast-slow transformation near the Alfvén-acoustic equipartition height 𝑧 eq ; and (ii) Hall-rotation of the fast wave in 𝑧 > 𝑧 eq . Thus, for the two-stage process to yield upgoing Alfvén waves, 𝑧 eq must lie below or within the Hall-effective window 0 𝑧 700 km. Magnetic field strengths over 100 G are required to achieve this. Since the potency of this Hall effect varies inversely with the field strength but directly with the wave frequency, only frequencies above about 100 mHz are significantly affected by the two-stage process. Increasing magnetic field inclination 𝜃 generally strengthens the Hall convertibility, but the horizontal wavenumber 𝑘 𝑥 has little effect. The direct and indirect Hall mechanisms both have implications for the ability of MHD waves excited at the photosphere to reach the upper chromosphere, and by implication the corona.