Changes between Version 6 and Version 7 of theory_Eng

Timestamp:

Feb 17, 2025, 7:35:17 AM (19 months ago)

Author:

Yifeng Zheng

Comment:

--

theory_Eng

@@ -19 +19 @@
 The main purpose is that for the deterministic parts, which are [[math(\boldsymbol{\phi}_t ^{F_1},\ \boldsymbol{\phi}_t ^{F_2},\ \boldsymbol{\phi}_t ^{F_3})]], we can use the volume-preserving algorithm to calculte, while the Coulomb collision part, which is [[math(\boldsymbol{\phi}_t ^{F_4})]], still uses the Newton-Raphson method or the quasi-Newton method for calculation. In order to construct a second-order algorithm of implicit midpoint similar to Boris algorithm, we can use such a combination\\
 [[math(\boldsymbol{G}_h ^2=\boldsymbol{\phi}_{h/2} ^{F_1}\circ \boldsymbol{\phi}_{h/2} ^{F_2} \circ \boldsymbol{\phi}_{h/2} ^{F_4} \circ \boldsymbol{\phi}_{h} ^{F_3} \circ \boldsymbol{\phi}_{h/2} ^{F_4}\circ \boldsymbol{\phi}_{h/2} ^{F_2} \circ \boldsymbol{\phi}_{h/2} ^{F_1}\ .)]]\\
-The calculate each part separately. When there is no collision, it reduces to the normal Boris algorithm as\\
+Then calculate each part separately. When there is no collision, it reduces to the normal Boris algorithm as\\
 [[math(\boldsymbol{G}_h ^2=\boldsymbol{\phi}_{h/2} ^{F_1}\circ \boldsymbol{\phi}_{h/2} ^{F_2} \circ \boldsymbol{\phi}_{h} ^{F_3} \circ \boldsymbol{\phi}_{h/2} ^{F_2} \circ \boldsymbol{\phi}_{h/2} ^{F_1}\ .)]]\\