The current of secondary electrons emanating from the specimen 14 in an ESEM is amplified by an avalanche-like ionization of the molecules 41 of the gas atmosphere. However, in order to achieve an adequate number of successive ionizations, a comparatively high voltage is required at the detector electrode 30 and, because of the risk of electric breakdowns, the distance between the specimen and the detector may not be smaller than a comparatively large minimum distance. Consequently, the number of successive ionizations is limited and hence also the current amplification. In order to achieve a higher amplification, the invention proposes the application of an additional magnetic field B in the ionization space. The path length of the secondary electrons is thus substantially increased so that a significantly larger number of ionizations takes place and hence a higher amplification is achieved.