TH1IOdn  —  Vlasov, Vlasov/Maxwell, Maxwell/Lorentz   (03-Sep-09   08:10—09:50)

Paper Title Page
TH1IODN01 A Fast and Universal Vlasov Solver for Beam Dynamics Simulations in 3D 208
 
  • S. Franke, W. Ackermann, T. Weiland
    TEMF, TU Darmstadt, Darmstadt
 
 

The Vlasov equation describes the evolution of a particle density under the effects of electromagnetic fields. It is derived from the fact that the volume occupied by a given number of particles in the 6D phase space remains constant when only long-range interaction as for example Coulomb forces are relevant and other particle collisions can be neglected. Because this is the case for typical charged particle beams in accelerators, the Vlasov equation can be used to describe their evolution within the whole beam line. This equation is a partial differential equation in 6D and thus it is very expensive to solve it via classical methods. A more efficient approach consists in representing the particle distribution function by a discrete set of characteristic moments. For each moment a time evolution equation can be stated. These ordinary differential equations can then be evaluated efficiently by means of time integration methods if all considered forces and a proper initial condition are known. The beam dynamics simulation tool V-Code implemented at TEMF utilizes this approach. In this paper the numerical model, main features and designated use cases of the V-Code will be presented.

 
TH1IODN04 Discretizing Transient Curent Densities in the Maxwell Equations 212
 
  • D.A. White, M.L. Stowell
    LLNL, Livermore, California
 
 

The Finite Difference Time Domain (FDTD) method and the related Time Domain Finite Element Method (TDFEM) are routinely used for simulation of RF and microwave structures. In traditional FDTD and TDFEM algorithms the electric field E is associated with the mesh edges, and the magnetic flux density B is associated with mesh faces. It can be shown that when using this traditional discretization , projection of an arbitrary current density J(x,t) onto the computational mesh can be problematic. We developed and tested a new discretization that uses electric flux density D and magnetic field H as the fundamental quantities, with the D-field on mesh faces and the H-field on mesh edges. The electric current density J is associated with mesh faces, and charge is associated with mesh elements. When combined with the Particle In Cell (PIC) approach of representing J(x,t) by discrete macroparticles that transport through the mesh, the resulting algorithm conserves charge in the discrete sense, exactly, independent of the mesh resolution h. This new algorithm has been applied to unstructured mesh simulations of charged particle transport in laser target chambers with great success.