• W. Ackermann, T. Weiland
  TEMF, Darmstadt

The moment method model has been proven to be a valuable tool for numerical simulations of a charged particle beam transport both in accelerator design studies and in optimization of the operating parameters for an already existing beam line. On the basis of the Vlasov equation which describes a collision-less kinetic approach, the time evolution of such integral quantities like the mean or rms dimensions, the mean or rms kinetic momenta, and the total energy or energy spread for a bunched beam can be described by a set of first order non-autonomous ordinary differential equations. Application of a proper time integrator to such a system of ordinary differential equations enables then to determine the time evolution of all involved ensemble parameter under consistent initial conditions. From the vast amount of available time integration methods different versions have to be implemented and evaluated to select a proper algorithm. The computational efficiency in terms of effort and accuracy serves as a selection criterion. Among possible candidates of suited time integrators for the given set of moment equations are the explicit Runge-Kutta methods, the implicit theta methods, and the linear implicit Rosenbrock methods. Various algorithms have been implemented and tested under real-world conditions. In the paper the evaluation process is documented.