A measurement campaign was performed for characterizing the neutron ambient dose equivalent, H*(10), in selected positions at ISA, Aarhus, Denmark, around the ASTRID and ASTRID2 storage rings. The neutron stray radiation field is characterized here by very intense radiation bursts with a low repetition rate, which result in a comparatively low average H*(10) rate. As a consequence, devices specifically conceived for operating in pulsed neutron fields must be employed for efficiently measuring in this radiation environment, in order to avoid severe underestimations of the H*(10) rate. The measurements were performed with the ELSE NUCLEAR LUPIN 5401 BF3-NP rem counter, a detector characterized by an innovative working principle that is not affected by dead time losses. This allowed characterizing both the H*(10) and the time structure of the radiation field in the pre-selected positions.