On approximative linear Boltzmann transport equation for charged particles
2018 ◽
Vol 28
(14)
◽
pp. 2905-2939
Keyword(s):
We present results on existence and positivity of solutions for a linear Boltzmann transport equation used for example in radiotherapy applications and more generally in charged particle transports. Therein, some differential cross-sections, that is, kernels of collision integral operators, may become hyper-singular. These collision operators need to be approximated for analytical and numerical treatments. Here, we present an approximation leading to pseudo-differential operators. The final approximation, for which the existence and positivity of solutions is shown, is an integro-partial differential operator which is known as Continuous Slowing Down Approximation (CSDA).
1974 ◽
Vol 11
(6)
◽
pp. 441-456
◽
Keyword(s):
2014 ◽
Vol 185
(6)
◽
pp. 1747-1758
◽
2013 ◽
Vol 12
(2)
◽
pp. 168-173
◽
2008 ◽
Vol 35
(6)
◽
pp. 1098-1108
◽
2018 ◽
Vol 777
◽
pp. 421-425
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