...  ...  @@ 556,8 +556,8 @@ E1=0, E2=0, 


....



+



.TRACE 3D and _OPAL_ comparison: SBEND without edge angles,



image:figures/Benchmarks/SBEND_noEdge_Env.png[width=350]



image:figures/Benchmarks/SBEND_noEdge_Emi.png[width=350]



image:figures/Benchmarks/SBEND_noEdge_Env.png[width=340]



image:figures/Benchmarks/SBEND_noEdge_Emi.png[width=340]



+



A good overall agreement has been found between the two codes in term of



beam size and emittance. The different behavior inside the bending

...  ...  @@ 572,8 +572,8 @@ E1=10*Pi/180.0, E2=5* Pi/180.0, 


....



+



.TRACE 3D and _OPAL_ comparison: SBEND with edge angles



image:figures/Benchmarks/SBEND_Edges_Env.png[width=350]



image:figures/Benchmarks/SBEND_Edges_Emi.png[width=350]



image:figures/Benchmarks/SBEND_Edges_Env.png[width=340]



image:figures/Benchmarks/SBEND_Edges_Emi.png[width=340]



+



Even in this case, a good overall agreement has been found between the



two codes in term of beam size and emittance.

...  ...  @@ 613,8 +613,8 @@ E1=0, E2=0, 


....



+



.TRACE 3D and _OPAL_ comparison: SBEND with field index and default field map



image:figures/Benchmarks/FI_SBEND_FMDef_Env_T2.png[width=350]



image:figures/Benchmarks/FI_SBEND_FMDef_Emi_T2.png[width=350]



image:figures/Benchmarks/FI_SBEND_FMDef_Env_T2.png[width=340]



image:figures/Benchmarks/FI_SBEND_FMDef_Emi_T2.png[width=340]



+



Concerning the emittances and vertical beam size, a perfect agreement



has been found, instead a defocusing effect appears in the horizontal

...  ...  @@ 625,8 +625,8 @@ which the fringe field extension has been changed in the thin lens 


approximation.



+



.TRACE 3D and _OPAL_ comparison: SBEND with field index and test field map



image:figures/Benchmarks/FI_SBEND_FMTest_Env_T2.png[width=350]



image:figures/Benchmarks/FI_SBEND_FMTest_Emit_T2.png[width=350]



image:figures/Benchmarks/FI_SBEND_FMTest_Env_T2.png[width=340]



image:figures/Benchmarks/FI_SBEND_FMTest_Emit_T2.png[width=340]






[[ssec:T3DtoOPAL]]



From TRACE 3D to _OPALt_

...  ...  @@ 875,8 +875,7 @@ with 


latexmath:[\epsilon_x(x, P_x) = \sqrt{\langle x^2 \rangle \langle P_x^2\rangle  \langle xP_x \rangle^2}]



where latexmath:[P_x = \beta\gamma x'], not the tracelike emittance



which is calculated as



latexmath:[\epsilon_x(x, x') = \beta\gamma\sqrt{\langle x^2 \rangle \langle x'^2 \rangle  \langle xx' \rangle^2}]






latexmath:[\epsilon_x (x, x') = \beta \gamma \sqrt{\langle x^2 \rangle \langle x'^{2} \rangle  \langle xx' \rangle^2}]



[prstab2003]. In Figure [plotemitcsron], a tracelike horizontal



emittance is also calcualted for the _OPAL_ output beam distributions.



Like the ELEGANT result, this tracelike emittance doesn’t grow in the

...  ...  