The recently developed Doppler spectroscopy diagnostic has been used to evaluate the height of the ambipolar potential barrier forming in the gas dynamic trap (GDT) plasma between the central cell and the region with a large magnetic expansion ratio beyond the mirror. The diagnostic technique based on the gas jet charge exchange target, allowed to measure the potential profile along the line of sight covering the radial range from the axis to the limiter. The on-axis potential drop was found to be 2.6 ÷ 3.1 in units of the central plane electron temperature, which supports the existing theoretical understanding of suppression of electron thermal conductivity in the GDT expander.