We present systematic analysis of the spatio-temporal evolution of sources of hard X-ray (HXR) pulsations in solar flares. We concentrate on disk flares whose impulsive phase are accompanied by a series of more than three successive peaks (pulsations) of HXR emission detected in the RHESSI 50-100 keV energy channel with 4-second time cadence. 29 such flares observed from February 2002 to June 2015 with characteristic time differences between successive peaks P ≈ 8 − 270 s are studied. The main observational result of the analysis is that sources of HXR pulsations in all flares are not stationary, they demonstrate apparent movements/displacements in parental active regions from pulsation to pulsation. The flares can be subdivided into two main groups depending on the character of dynamics of HXR sources. The group-1 consists of 16 flares (55%) with the systematic dynamics of the HXR sources from pulsation to pulsation with respect to a magnetic polarity inversion line (MPIL), which has simple extended trace on the photosphere. The group-2 consists of 13 flares (45%) I.V. Zimovets ivanzim@iki.rssi.ru with more chaotic displacements of the HXR sources with respect to an MPIL having more complicated structure, and sometimes several MPILs are presented in parental active regions of such flares. Based on the observations we conclude that the mechanism of the flare HXR pulsations (at least with time differences of the considered range) is related to successive triggering of flare energy release process in different magnetic loops (or bundles of loops) of parental active regions. Group-1 flare regions consist of loops stacked into magnetic arcades extended along MPILs. Group-2 flare regions have more complicated magnetic structures and loops are arranged more chaotically and randomly there. We also found that at least 14 (88%) group-1 flares and 11 (85%) group-2 flares are accompanied by coronal mass ejections (CMEs), i.e. the absolute majority of the flares studied are eruptive events. This gives a strong indication that eruptive processes play important role in generation of HXR pulsations in flares. We suggest that an erupting flux rope can act as a trigger of flare energy release. Its successive interaction with different loops of a parental active region can lead to apparent motion of HXR sources and to a series of HXR pulsations. However, the exact mechanism responsible for the generation of pulsations remains unclear and requires more detailed investigation.

Numerical methods for solving the inverse problem of determining solar flaring loop physical parameters are sought and developed. This problem can be solved by fitting theoretically calculated radio emission characteristics (the flux or the degree of circular polarization) to the observed characteristics. Such a fitting is reduced to the solution of a system of equations with the observed and theoretically calculated radio emission characteristics on the right and left hand sides, respectively. The genetic algorithm method, which demonstrated good accuracy and calculation time when five parameters of a model flaring loop were recov ered, has been used in fitting. After testing this method on the model sources, an algorithm was used to recover four parameters of the real flaring loop using the Nobeyama Radioheliograph data.

The 5 July 2012 solar flare (11:39 -11:49 UT) with an increasing millimeter spectrum between 93 and 140 GHz is considered. We use space and ground-based observations in X-ray, extreme ultraviolet, microwave, and millimeter wave ranges obtained with the Reuven Ramaty High-Energy Solar Spectroscopic Imager, Solar Dynamics Observatory (SDO), Geostationary Operat ional E nvironmental Satellite, Radio Solar Telescope Network, and Bauman Moscow State Technical University millimeter radio telescope RT-7.5. The main parameters of thermal and accelerated electrons were determined through Xray spectral fitting assuming the homogeneous thermal source and thick-target model. From the data of the Atmospheric Imaging Assembly/SDO and differential emission measure calculations it is shown that the thermal coronal plasma gives a negligible contribution to the millimeter flare emission. Model calculations suggest that the observed increase of millimeter spectral flux with frequency is determined by gyrosynchrotron emission of high-energy ($\gtrsim 300$