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@article{1828357, author = {Stopka, Jan}, article_location = {Amsterdam}, article_number = {217}, keywords = {Trajectory displacement; Multi-beam electron microscope; Coulomb interactions; Slice method; Electron optics}, issn = {0304-3991}, journal = {Ultramicroscopy}, title = {Analytical formulae for trajectory displacement in electron beam and generalized slice method}, url = {https://doi.org/10.1016/j.ultramic.2020.113050}, year = {2020} }
TY - JOUR ID - 1828357 AU - Stopka, Jan PY - 2020 TI - Analytical formulae for trajectory displacement in electron beam and generalized slice method JF - Ultramicroscopy IS - 217 PB - Elsevier SN - 03043991 KW - Trajectory displacement KW - Multi-beam electron microscope KW - Coulomb interactions KW - Slice method KW - Electron optics UR - https://doi.org/10.1016/j.ultramic.2020.113050 N2 - Trajectory displacement due to statistical Coulomb interactions can play a major role in determining the performance of a charged particle beam system. Accurate estimation of the trajectory displacement is thus an important part of the design procedure of such an optical system. Traditionally, there are three approaches to determine the trajectory displacement: Monte Carlo simulation, the slice method, where trajectory displacement is integrated along the beam length and finally a full analytical formula describing transparently the dependence of the trajectory displacement on the parameters of the system. The latter two were developed thoroughly by Jansen and Jiang. We revise Jansen’s slice method and the derivation of the integral formulae in Holtzmark and pencil-beam regimes. We show the integral formula fails to give accurate results in case a transition between the regimes occurs and we derive a new analytical expression unifying the Holtzmark and pencil-beam regime into a single formula. Furthermore, we generalize the slice method for arbitrary beam trajectory, hugely increasing its accuracy for non-ideal systems. ER -
STOPKA, Jan. Analytical formulae for trajectory displacement in electron beam and generalized slice method. \textit{Ultramicroscopy}. Amsterdam: Elsevier, 2020, č.~217. ISSN~0304-3991.
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