The current density relaxation equation on account for the derivative
of the ac external field has been derived. The effective attempt time
for ac response, t(eff)(ac), differs from that obtained under the cond
ition of the static magnetic field by Blatter et al. The current relax
ation equations under different models of the effective pinning potent
ial have been obtained and discussed. In very short time window, say 1
0(-5) - 10(-3) s, we have found that the current density of the Hg0.69
Pb0.31Ba2Ca2Cu3O8+delta superconductor has nonlogarithmic relaxation c
haracteristic behaviour. This characteristic nicely agrees with the co
llective pinning model. Furthermore, we also introduce and consider th
e dependence of t(eff)(ac) in the current relaxation study, and the ef
fect of the t(eff)(ac) on the study of current relaxation has been dis
cussed.