A. A. Solov’EV

We estimated the relative location of the solar rotation axis and the magnetic axis of the solar dipole, which were defined as centers of polar coronal holes. We used observations of polar coronal hole data, which were originally obtained with Solar Dynamic Observatory (SDO) spacecraft. To calculate the tilt of the magnetic axis relative to the rotation axis of the Sun, an empirical method for the estimation of the coronal hole centers is proposed. As a result, it was found that these axes do not coincide. The average deviation of the magnetic dipole axis from the rotation axis is ∼5 degrees of latitude. Using the wavelet transform method, it was found that the magnetic axis rotates around the rotation axis with a main period of 15–16 days. This period is related to the sector structure of the global magnetic field in the polar zones of the Sun.

In this paper, we show that inside the magnetic force tube formed by the open field of the coronal hole (CH), the magnetic field (MF) decreases with the distance from the Sun according to the inverse square law. In the study, we select such time periods when there were no active formations on the solar disk, with the exception of CHs (period 2006–2009, the minimum phase of the 23rd activity cycle). The main result of the study, the inverse square law, was obtained by comparing the duration of the CH passage through the central meridian with the duration of the increase in the SW velocity caused by these CHs in the Earth’s orbit. The ratio of the two indicated time intervals turns out to be very close to unity. The data from SOHO (Solar and Heliospheric Observatory), GGS WIND (Global Geospace Science Program WIND), and ACE (Advanced Composition Explorer) spacecraft were used. A special computer program was used to digitize the CH coordinates on daily EIT images at the λ195 Å (SOHO) line and calculate the CH areas in the sector affecting the SW parameters (ellipse 0.6R_o by 0.3R_o). Based on the inverse square law, MF (~2 G) and the particle flux density (~1.2 × 10¹³ particles/s cm²) on the solar surface at the base of 15 studied CHs were calculated using the SW parameters near the Earth’s orbit.

The main property of magnetic flux ropes in plasma is the shielding of electric currents. The second important property of force-free ropes is the need for external pressure, which prevents the loop from lateral expansion. With allowance for these factors, we calculated a force-free filament structure, in which the magnetic field on the axis significantly exceeds the external one. When a magnetic loop emerges into the rarefied solar atmosphere, the external pressure continuously drops, and at some limiting value, the longitudinal magnetic field of the loop turns to zero at the surface of the change of a sign of electric currents. This leads to a break in the azimuthal current on it and serves as a trigger for the excitation of plasma instability, the appearance of abnormal resistance with subsequent flare energy release and the generation of super-dreicer electric fields in elements of the thin magnetic structure with a diameter of ~100 km. Such fields can accelerate charged particles to hundreds of MeV on a path of several thousand km. The quasi-periodic mode of flare energy release in such a magnetic flux rope is discussed and a mechanism for ejection of accelerated particles from a loop magnetic trap upon entering the heliosphere is proposed.

We investigate the properties of a double horizontal magnetic filament, uniform in length and located in the solar atmosphere in an external uniform magnetic field. A specific feature of current screening in this magnetic configuration is that the currents do not form a coaxial structure, like in a single magnetic bundle, but are located in two close parallel bands, so the total current in the double filament is zero. Such filaments do not tend to merge during lateral contact into a single magnetic structure. The equilibrium distributions of the plasma density and electric current density in the filament are calculated and the possibilities are shown for the electric current density in the filament to reach critical values at which “anomalous resistance” occurs due to the development of current ion–acoustic instability. The anomalous resistance turns out to be much larger than the usual Coulomb resistance. The following values have been found: the scale of the dissipation region, the electric field strength in it, which significantly exceeds the Dreiser value, and the possible energy of accelerated charged particles (up to hundreds of MeV).

Thirty-five stable single sunspots of sufficiently regular round shapes were studied to determine the vertical magnetic field strength at the sunspot umbra–penumbra (UP) boundary and the degree of inclination of the total field vector at this boundary. A new data tool (SDO/hmi) called Space-weather HMI Active Region Patches (SHARPs) was used. Four different methods have been used to determine the UP boundary, including Otsu’s mathematical method (Otsu, 1979). It is shown that there is no single value of the vertical component of the field at the UP boundary that is universal for spots of all sizes and field strengths. The value of 1867 G found earlier by Jurčák, (2011) was not confirmed either by our data or by the data of other authors (Schmassmann, et al., 2018; Loptien et al., 2020). We obtained the UP border, 〈Bver〉, of ~1.6 kg with a fairly large dispersion. It is important to note that the inclination of the total field vector γ remains almost constant at this boundary with very small dispersion (SD ~ 1.5–2.5 deg). This gives grounds to believe that this quantity determines the transition of the spot plasma to the magnetoconvection regime.

A new class of force-free solutions for a horizontal magnetic filament with a circular cross-section is found, in which the magnetic field strength on the axis significantly (up to 2–3 orders of magnitude and more) exceeds the strength of the longitudinal external field that keeps the rope from lateral expansion. A weak transverse field leads to a small deviation from the force-free field structure and results in a density deficit and an increase in temperature on the rope axis. The possibility of a flare release of magnetic energy is shown when critical values ​​of the longitudinal electric current density in the filament are reached at which ‘anomalous resistance’ occurs, caused by the development of the current ion-sound plasma instability. It turns out to be much larger than the usual Coulomb resistance. The following values are determined: the scale of the current dissipation region, the electric field strength in it, which significantly exceeds the Dreicer value, and the possible energy of accelerated charged particles (up to hundreds of MeV). The critical density of the longitudinal current at which the plasma turbulence is excited does not depend on the presence of a super-strong field on the flux-rope axis, so that the current density depends only on the electron concentration, temperature, and anomalous conductivity. However, super-strong magnetic fields can manifest themselves in the fact that, in their presence, the excitation of plasma instabilities can occur at sufficiently high electron concentrations. This effect may explain the large number of accelerated particles sometimes observed in solar flares.

We considered coronal holes as a manifestation of the large-scale magnetic field of the Sun. The main goal of this work was to study the variations in the largest areas and longitudinal widths of solar coronal holes observed daily in the polar and mid-latitude zones on a time scale of 984 days. Statistical methods of fast Fourier transform (FFT), wavelet transform, and empirical mode decomposition (EMD) were used to detect periodicity in the variations of the considered parameters. Long-term variations in the daily measured areas and longitudinal widths of the largest solar coronal holes with periods of 8–9, 13–15, and 26–29 days were detected in three zones of the Sun: polar (north and south) and equatorial. The obtained periods are most clearly visible at the equatorial zone. In the polar zones the period of 8–9 days has a weak amplitude. We interpreted variations with periods of 8–9, 13–15, and 26–29 days as a rotation of the six-, four-, and two-sector structure of the large-scale solar magnetic field.

The properties of an axisymmetric magnetohydrostatic configuration resembling a laboratory tokamak in its geometry are investigated. On the Sun this structure is located horizontally in an external magnetic field that is assumed to be uniform and vertical, a nondistorting external hydrostatic medium—the solar atmosphere. We calculate the equilibrium plasma density, pressure, and electric current distributions inside such a system and show the possibilities for the accumulation of magnetic energy and its flare release when the critical electric current densities are reached on the magnetic axis of the toroid. The scale of the current dissipation region, the electric field strength in it exceeding considerably the Dreicer one, and the energies of accelerated charged particles (up to a hundred MeV) are estimated.