Changes between Version 7 and Version 8 of theory_Eng

Timestamp:

Feb 17, 2025, 8:02:31 AM (19 months ago)

Author:

Yifeng Zheng

Comment:

--

theory_Eng

@@ -6 +6 @@
 == ISSDE Basic Algorithm
 * Splitting Method
-The equations that ISSDE mainly requires to be solved are \\
+The equations that ISSDE mainly requires to be solved are [[FootNote(Yifeng Zheng et al. 2021 Chin. Phys. B 30 095201)]]\\
 [[math(\begin{equation}\begin{cases}\frac{\mathrm{d}\mathbf{x}}{\mathrm{d}t} & =\mathbf{v}\ ,\\ \frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} & =\frac{q}{m}\mathbf{E}+\frac{q}{m}\mathbf{v}\times\mathbf{B}+\mathbf{a}_{c}\ ,\end{cases}\end{equation})]] \\
 where [[math(\mathbf{a}_{c})]] is the acceleration caused by the Coulomb collision. According to splitting method, the equation can be regarded as a vector field [[math(\boldsymbol{F}(\boldsymbol{x},\boldsymbol{v}))]] \\
@@ -22 +22 @@
 [[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}\ .)]]\\
 
-* Volumn-preserving algorithm
+* Volumn-preserving algorithm[[FootNote(Yang He et al. 2015 Phys. Plasma 22 124503)]]
 * Quasi-Newton Method
+
+[[FootNote]]
+
 == Physical Process Calculated by ISSDE
 * Fast ion trajectory