A New Self-Consistent Unbounded Magnetic Field 3-D FE Computation for Electron Guns

Optimization of multistage depressed collectors using fem and parallel algorithm MeTEO

“…Several methods can be used for solving this coupled problem, but the only one suitable for an optimization framework is the particle-in-cell (PIC) steady-state approach: in PIC the beam is represented by a reasonable number of macro-particle and its motion is obtained by integrating dynamic equations, the self-consistent electric field E is the solution of a Poisson equation, including space-charge density as source, while the self-consistent magnetic field B can be calculated from the field equations for the magnetic vector potential, including the beam current density as a source term (Coco et al, 2010). The tracing of the electrons' trajectories, the space charge distribution and the solution of electromagnetic problem are iteratively performed until the convergence is obtained when the "distance" between two consecutive solutions is less than a user-specified end-iteration tolerance: in this situation, a fixed point for the solution is approached and electromagnetic field distributions can be assumed self-consistent.…”

“…The tracing of the electrons' trajectories, the space charge distribution and the solution of electromagnetic problem are iteratively performed until the convergence is obtained when the "distance" between two consecutive solutions is less than a user-specified end-iteration tolerance: in this situation, a fixed point for the solution is approached and electromagnetic field distributions can be assumed self-consistent. The detailed description of the PIC steady-state FE analysis of MDC can be found in Coco et al (2007Coco et al ( , 2010 and in references within these. Clearly after the solution of the self-consistent problem the FE simulator must compute in COMPEL 32,6 a post-processing phase the current recovered by each electrode and also the back-streaming current (due to secondary electrons emitted by electrodes' surface) in order to evaluate the total power recovered and the collector efficiency.…”

TWT magnetic focusing structure optimization by parallel evolutionary algorithm

“…The coupled electromagnetic‐motional problem inside collector region is governed by the Vlasov equation, coupled with Maxwell equations (Coco et al , 2010). This system of equations considers on one hand the function distribution of charged particles, solution of the motion equation (Vlasov equation) under the effect of electromagnetic field, and on the other hand the self‐consistent electromagnetic field, solution of the Maxwell equations, whose source terms are the charged particles themselves: in other words the electromagnetic field has as sources the charged particles, which move according to the electromagnetic field strength.…”

“…By following this steady‐state approach and using FE discretization the resulting discrete problem consists of three sets of equations: the first is an FE linear algebraic system regarding the spatial distribution of the unknown electric scalar potential values originated by a nodal formulation of the Poisson problem, the second is an FE linear algebraic system regarding the spatial distribution of the unknown magnetic vector potential A, originated by an edge element formulation of the curl‐curl magnetostatic problem; the other regards the computation of trajectories for all the discrete particles used in the model. This algorithm in its most basic form is shown in Figure 1, and consists of a main loop starting with the solve/update fields step (Coco et al , 2010). Once the fields are solved, the particle tracking algorithm begins: in this steady‐state model, particles (launched according to an emission rule or injection rule) advanced until each of them encountered a boundary.…”

Neural-FEM approach for the analysis of hysteretic materials in unbounded domain

“…The boundary conditions on the fictitious boundary are initially guessed and successively updated according to the solution obtained in the previous iteration step. This treatment of boundlessness closely follows an analogous approach, successfully used for the solution of uncoupled electromagnetic problems in unbounded domains (Coco and Laudani, 2002;Coco et al, 2010). An application to a 2.5-D geometry is presented in order to illustrate the whole procedure.…”