Evolución de la arquitectura penitenciaria

By using a non-uniform grid, the simulation domain size can be significantly de- creased, reducing simulation time and memory requirements. The RF solver execution time improves rather linearly with a decrease in the number of cells in the domain. The particle solver execution inherits little to no benefit to a decrease in simulation

domain size. This is because each particle still requires calculations, and a reduction in the number of cells does not reduce calculations done on each particle. In this model, a reduction of the domain size by half improves RF simulations without particles by about half. This same domain size reduction on simulations with particles reduces simulation times by about 20%.

The non-uniform grid implementation allows for the cell size to change in the same direction. For example, one can change dX as a function of x but not as a function of y. The implementation of the grid is performed using 2 vectors: sectionBreaks and deltaAtBreaks. The user defines the cell size at various points, and the program alters the cell sizes in between those points smoothly. The sec- tionBreaks vector defines the spatial location where the mesh size is defined. The deltaAtBreaks vector defines the cell size at the points defined by the sectionBreaks. For example, with sectionBreaks=_{[ 0.0 1.0 ]} and deltaAtBreaks=_{[ 0.01 0.1 ]} the cell size at 0.0 m is 0.01 m and at 1.0 m is 0.1 m. The cell size in between 0.0 m

and 1.0 m is varied smoothly. The cell sizes defined by sectionBreaks is a strict constraint, and if the algorithm cannot vary the cell sizes to match the defined cell sizes, an error is generated. The cell sizes and number of cells in between the defined points is unknown to the user until after running the simulation, which makes any BCs defined by cell coordinates difficult. If the user wants to abruptly change the cell size from one cell to the next, two delta entries are used at the same point where the desired point is. For example, with sectionBreaks=_{[ 0.0 0.5 0.5 1.0 ]} and deltaAtBreaks=_{[ 0.01 0.01 0.1 0.1 ]}, the cell size is0.01in between0.0to0.5

and 0.1between 0.5 and 1.0. One should note that geometric features should not lie directly on cell coordinates because inconsistent geometry results. The grid should be slightly shifted off the geometry. This approach does not affect the simulation but

allows for more consistent results.

Different updaters than the ones used for a uniform grid are required to solve the EM fields. Instead of using Ampere and Faraday updaters, CoordProd updaters are used. These are more generic solvers where the user manually defines the functions. In this case the functions are identical to the ones used in Ampere and Faraday. Dey-Mittra implementation cannot be used with this solver.

The use of a Non-Uniform grid also limits the type of particle emitters available. Only RandDensSrc types of emitters were available at the time of use. Because it is not a xvLoaderEmitter type, the emitted current could not be monitored via the emitted current history diagnostic.

Many of the history diagnostics cannot be used with a non-uniform grid including Psuedopotential and B-Loop. These diagnostics can be created via the use of other histories and some post processing. For example, the psuedopotential can be acquired by using the electric field on line diagnostic and integrating along the line in post processing. This approach requires more hard drive space due to the fact that multiple data points are needed at each time step via the EFieldOnLine diagnostic rather than just one number per time step using psuedopotential.

The implementation in the model uses abrupt changes for the cell sizes. A top down (normal toy) view of the grid of a generic CFA model is shown in Fig. 5.13. In

x, the region overlapping the meander line is two cells thick, and the region between adjacent lines is also two cells thick. In z, the edges where the meander line runs parallel to x, the grid size is Wsw/2, and in the middle the grid size is increased to

>3Wsw. The side view (normal to Z) of a generic CFA model is shown in Fig 5.14. The dielectric is 2 cells thick, and this resolution extends into the coaxial cable; the line is 2 cells thick as the sizes are interpolated to match the size in the interaction

region, and the grid size in the interaction region can be significantly increased. This implementation reduced the number of cells by 4 times. The CoordProdSolver is inherently slower than the uniform solver, but because of the reduction of cells, a net speedup was observed. The RF solver time acquired a 3x speedup from this domain reduction. The particle solver, however, showed no improvement, and so the total speedup was only about 50%.

Figure 5.13: Vsim non-uniform mesh on the X-Z plane. The green section is the meander line, red is the ground plane, The white circles are the space between the inner and outer conductor of the coaxial cable, and the black lines are the mesh. In X, regions which coincide with the circuit is 2 cells wide and regions between the circuit is 2 cells wide. In Z, the circuit region is 2 cells wide, but in the center, the length of the cells is increased.

Figure 5.14: Vsim non-uniform mesh on the Y-X plane. The green section is the meander line, red is the ground plane, The white circles are the space between the inner and outer conductor of the coaxial cable, and the black lines are the mesh. In X, regions which coincide with the circuit is 2 cells wide and regions between the circuit is 2 cells wide. In Z, the circuit region is 2 cells wide, but in the center, the length of the cells is increased.

The RF simulations with the non-uniform model showed good agreement with the uniform model. But the simulations with particles showed an anomaly. At the locations of a change in cell size, a charge accumulation was observed. The electric fields at these points acquired a DC bias. The longer the simulation time, the more charge accumulation was observed. Fig 5.15 shows the x-component along x of an electric field fieldOnLine diagnostic, which shows the charge accumulation. From Gauss’s Law, the electric field shows charge accumulation, in the absence of RF fields, by a changing electric field. The CFA simulation was run for 200.0 ns with particles and RF, and then the RF and the electron source were turned off. The electric field in Fig. 5.15 is obtained 200.0 ns after the electron source and RF are turned off. After there were no particles and no RF, except for some tiny stray fields, the electric field should be close to zero. Note that in Fig. 5.15, from x = 0−2.0 cm the electric field increases smoothly, and for x > 2.0 cm the electric field varies periodically. For perspective, the periodic variations are larger than the electric field created by the RF

field alone. The large periodic variations in the electric field are thought to be caused by the cell size changes. This, surprisingly, did not affect the overall performance of the device, and the input and output powers matched fairly well with the uniform implementation. Even with the relatively good agreement in the powers, the huge charge accumulation casts doubt on the results, so the non-uniform implementation was dropped. x [cm] Electric Field E x [V/m] -1000 0 1000 2000 3000 4000 0.0 2.5 5.0 7.5 10.0

Figure 5.15: E-field diagnostic showing the charge accumulation in the non-uniform grid model.