The critical current in high-Tc materials is strongly reduced by a mag
netic field. We studied this dependency for tubular YBCO samples. We f
ind an exponential drop as the field is increased from zero up to some
tens of oersted. This behavior was already observed by others, howeve
r little work has been done in this direction. We define what we call
the 'exponential critical state' of HTSC and compare the prediction fo
r the magnetization with experimental data. Furthermore, the 'Kim crit
ical state' is obtained as the small field limit.