The thermoacoustic-to-magnetohydrodynamic energy conversion is a new and attractive option for electricity power generation and power supply aimed at deep space missions. This technology uses radioisotopes as a primary energy source that supply heat to sophisticated technology, called thermoacoustic engine. The heat introduced in thermoacoustic engine is further converted to mechanical vibrations. These vibrations are further converted to electrical power by liquid metal (sodium - Na) oscillations in a magnetic field. This technology was developed, and the prototype was constructed at the Institute of Physics, University of Latvia. It was done during the ambitious international European project with the acronym “SpaceTRIPS” (Space Thermoacoustic Radio Isotopic Power System). In this work, the further advances of this technology are presented. The main disadvantage of thermoacoustic-to-MHD energy conversion is the existence of liquid metal free surface. This is the region where gas from the thermoacoustic engine is applied to liquid metal. This interface eventually becomes unstable, resulting in chaotic splashes. It decreases the performance of the electric machine. During the first tests, it was found that a certain measures should be taken to suppress this instability. There are many options to do this. To solve this problem, it is proposed to apply an external magnetic field to the region of liquid metal free surface, to electromagnetically suppress the free surface instability. These results will be reported in the conference.