A Fast and Universal Vlasov Solver for Beam Dynamics Simulations in 3D
The Vlasov equation can describe the evolution of a particle density under the effects of electromagnetic fields and thus it is possible to describe the evolution of a charged particle beam within an accelerator beam line. The Vlasov equation forms a partial differential equation in a 6D phase space witch renders it very expensive if it is solved 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 integrated efficiently by means of numerical methods if all acting forces together with a proper initial condition are given. The beam dynamics simulation tool V-Code has been implemented at TEMF on the basis of the moment approach. In this paper the numerical model, main features and designated use cases of the V-Code will be presented.
IMPLEMENTING NEW BEAM LINE ELEMENTS INTO A MOMENT METHOD BEAM DYNAMICS CODE
Developing beam dynamics simulation tools using the moment method has advantages in terms of precision and efficiency when interests lie in average or rms dimensions of the beam, projected emittances or total energy. The moment method implemented in the V-Code solves the Vlasov equation by time integration, from an initial particle distribution represented by a discrete set of characteristic moments, accounting for all acting internal and external forces along the particle’s path. The moment method delivers highly accurate beam dynamics results within a very small CPU time. This article proposes, illustrates and validates a new beam line element (BLE) for a radio frequency quadrupole (RFQ) for insertion in the V-Code. The focus will be on the RFQ cell structure, the electric field distribution and the insertion of the field distribution in the moment code.
Influence of electric fields on friction electrification between metals and borosilicate glass
Abstract In a cylindrical geometry, electric fields were applied through the entire contact area between the sliding metal and the glass surface. The maximum electric charges developed on the metal were measured and plotted against the applied voltage producing the field. The metals were high-purity nickel and gold. The borosilicate glass was Pyrex, brand 7740. The experiments with nickel, which has a work function greater than that of the glass, were performed in 10 −7 mm Hg vacuum. The experiments with gold, with a work function smaller than that of glass, were carried out in air at atmospheric pressure. The results show that: 1. 1) There is both asymmetry and a reversed slope portion in the charge vs. voltage plot. 2. 2) For a certain range of reversing fields, the electric charge developed on the nickel is always negative and the charge on gold is always positive.