HOME work papers html 2009fermi

8.2 Overview of different comparisons performed

Two exemples of plots comparisons are presented here. Each time, three figures are presented, coresponding from left to right to step2, step3 and step1. As a result of this, the two right plots are expected to be the same, and one can happily notice that they are. The fields of step2 have most of the time a really different shape as they are expressed in the laboratory frame. Two more exemples are presented in annex E . The 3D grid used consisted in a total number of grid of 20 in each direction ( $N\ast_f$ =20), with 5 cells used for the boundary condition on each side ( $N\ast_0=5$ ). This provides reasonable results eventhough smoother curves would habe been obtained with a higher number of cells.

8.2.1 Exemple of a coin-shape cylinder

The simulation was done with the following parameters:

Table 8.1: Parameters used for the benchmarking of the rotation algorithm - exemple of a coin-shape

Parameter	Value
Distribution type	Uniform cylinder
Distribution $\sigma_x$	3 mm
Distribution $\sigma_y$	3 mm
Distribution $\sigma _z$	0.1 mm
Distribution energy $\mathcal{E}$	15 MeV
Distribution charge	-0.25 nC
Rotation axis	X
Rotation angle	$\pi/4$
3D grid used	$N\ast_0=5$ , $N\ast_f$ =20, $N\ast_2$ =32

**Figure 8.2:** Coin shape cylinder before and after rotation: canonical directions

**Figure 8.3:** Rotation algorithm - Longitudinal Field. (a) Before the rotation of the fields - (b) After the rotation of the fields - (c) Fields from a distribution not rotated
(a) (b) (c)

8.2.2 Exemple of an ellipsoid at high energy

The simulation was done with the following parameters:

Table 8.2: Parameters used for the benchmarking of the rotation algorithm - exemple of an allipsoid at high energy

Parameter	Value
Distribution type	Uniform ellipsoid
Distribution $\sigma_x$	1 mm
Distribution $\sigma_y$	1 mm
Distribution $\sigma _z$	3 mm
Distribution energy $\mathcal{E}$	100 MeV
Distribution charge	-0.25 nC
Rotation axis	X
Rotation angle	$\pi/6$
3D grid used	$N\ast_0=5$ , $N\ast f$ =20, $N\ast_2$ =32

**Figure 8.4:** Rotation algorithm - Longitudinal Field. (a) Before the rotation of the fields - (b) After the rotation of the fields - (c) Fields from a distribution not rotated
(a) (b) (c)

Emmanuel Branlard
http://emmanuel.branlard.free.fr/