Matrix formalism for current-independent optics design

Matrix formalism has been a powerful tool for beam optics designs. It not only facilitates computations but also plays an important role in formulating various design concepts. Here we extend the standard matrix formalism for the purpose of designing an optics that transports space-charge-dominated intense beam. Furthermore, we explore the concept of current-independent optics, which can be useful for systems such as high-brightness injectors and space-charge-dominated rings. Our discussion here is preliminary and limited to axisymmetric systems.