Geodesic
A grid-projectional method of self-consistent electron beams simulation
Matematičeskoe modelirovanie, Tome 14 (2002) no. 12, pp. 85-97

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Using the Galekin technique the authors developed a numerical algorithm appropriate to the simulation of high-energy relativistic electron beams, propagation in technological devices. The essence of the algorithm is the direct solution of the Vlasov–Maxwell system by means of it's approximation using a fixed mesh in a phase spase. The set of discrete models pertinent to 1D, 1,5D, 2D problem formulations is considered and corresponding conservative grid-projectional numerical schemes are constructed and investigated. Some numerical results are given which show good accuracy of the developed algorithms. The algorithm for simulation of beams propagating through objects of complex geometry is constructed via finite-element approximations on triangular unstructured boundary-fitted meshes. 
@article{MM_2002_14_12_a7,
     author = {V. A. Gasilov and E. L. Kartasheva and O. G. Olkhovskaya},
     title = {A grid-projectional method of self-consistent electron beams simulation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {85--97},
     publisher = {mathdoc},
     volume = {14},
     number = {12},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_12_a7/}
}
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V. A. Gasilov; E. L. Kartasheva; O. G. Olkhovskaya. A grid-projectional method of self-consistent electron beams simulation. Matematičeskoe modelirovanie, Tome 14 (2002) no. 12, pp. 85-97. http://geodesic.mathdoc.fr/item/MM_2002_14_12_a7/