Photocurrent measurements have been performed on a quantum cascade detector structure under strong magnetic field applied parallel to the growth axis. The photocurrent shows oscillations as a function of B. In order to describe that behavior, we have developed a rate equation model. The interpretation of the experimental data supports the idea that an elastic scattering contribution plays a central role in the behavior of those structures. We present a calculation of electron lifetime versus magnetic field which suggests that impurities scattering in the active region is the limiting factor. These experiments lead to a better understanding of these complex structures and give key parameters to optimize them further.