When the Viking satellite crossed the auroral acceleration region, where the electron density is supposed to be less than a few particles per cubic centimeter, a strong spin modulation of the signal of a positively biased Langmuir probe was observed. This spin modulation is better correlated with the angle of the antenna to the geomagnetic field than with the angle to the Sun. A simple model based on the photoelectron orbits in a spherically symmetric electric field, in the presence of a uniform magnetic field, gives the right phase and amplitude of the extrema. In addition, it shows that the perturbation could be negligible when the antenna is perpendicular to the magnetic field, provided that the photoelectron sources are far enough from the magnetic field lines connected to the probe (about 2 Larmor radii). As a consequence, we deduce important information for the design of experiments devoted to very low density measurements, and we show that the magnetic field may be a crucial parameter for the study of the exchange of photoelectrons between parts of a satellite. The most important results of this study is to facilitate the probe density measurements inside the acceleration structures. It is shown that in these regions the cold plasma density is depleted, with a density of thermal electrons below 5 cm-3 at altitudes between 6500 km and 8500 km. When auroral kilometers radiation (AKR) is generated inside such structures, the density of thermal electrons can be below 1 cm-3. The edges of the structure are sharply defined, and the gradient scale can be as low as 1.4 km. This is the first time that density measurements of thermal electron have been realized inside clearly identified AKR sources, with appropriate resolution. ¿American Geophysical Union 1992