In an attempt to improve the predictions for the particle dynamics in the ESS linac the idea of parametrizing the field by expanding it in trigonometric functions have been concieved. The field parametrization is suitable for the high and medium beta cavities, with possible extension to the spoke cavities. The expectations of the model is that it will accurately be able to describe particles that are far from the synchronous particle in both the transversal and longitudinal directions, and to be able to do this in a fast and reliable way. The work that has been done so far has been part of a master thesis supervised by Emanuele Laface, in cooperation with Mamad Eshraqi.