For neutrals $n$ :

$\begin{eqnarray*} \frac{\delta \gamma_n^{\parallel}}{\delta t} &=& t_n \sum_{m \ne n} \nu_{nm}A^{m0p}_{nm}(\frac{C_m}{C_n} u_m - u_n)\frac{1}{t_n^{\parallel\frac{3}{2}}}\\ &+& t_n \sum_j \nu_{nj}A^{c0p}_{nj}(\frac{C_j}{C_n} u_j - u_n)\frac{1}{t_n^{\parallel\frac{3}{2}}}\\ &+& t_n \nu_{ne}A^{c0p}_{ne}(\frac{1 }{C_n} U_e - u_n)\frac{1}{t_n^{\parallel\frac{3}{2}}}\\ &+& \sum_{m \ne n} \nu_{nm}\left( D^{n1pt}_{nm} \frac{t_n^{\perp \frac{3}{2}}}{t_n^{\parallel \frac{3}{2}}} \gamma_n^{\perp }+ D^{n4pt}_{nm}\frac{C_m}{C_n} \frac{t_m^{\perp \frac{3}{2}}}{t_m^{\parallel \frac{3}{2}}} \gamma_m^{\perp }+ D^{n1pp}_{nm} \gamma_n^{\parallel }+ D^{n4pp}_{nm}\frac{C_m}{C_n} \frac{t_m^{\parallel \frac{3}{2}}}{t_m^{\parallel \frac{3}{2}}} \gamma_m^{\parallel }\right)\\ &+& \sum_j \nu_{nj}\left( D^{m1pt}_{nj} \frac{t_n^{\perp \frac{3}{2}}}{t_n^{\parallel \frac{3}{2}}} \gamma_n^{\perp }+ D^{m4pt}_{nj}\frac{C_j}{C_n} \frac{t_j^{\perp \frac{3}{2}}}{t_j^{\parallel \frac{3}{2}}} \gamma_j^{\perp }+ D^{m1pp}_{nj} \gamma_n^{\parallel }+ D^{m4pp}_{nj}\frac{C_j}{C_n} \frac{t_j^{\parallel \frac{3}{2}}}{t_j^{\parallel \frac{3}{2}}} \gamma_j^{\parallel }\right)\\ &+& \nu_{nn}\left( D^{n1pt}_{nn} \frac{t_n^{\perp \frac{3}{2}}}{t_n^{\parallel \frac{3}{2}}} \gamma_n^{\perp }+ D^{n4pt}_{nn} \frac{t_n^{\perp \frac{3}{2}}}{t_n^{\parallel \frac{3}{2}}} \gamma_n^{\perp }+ D^{n1pp}_{nn} \gamma_n^{\parallel }+ D^{n4pp}_{nn} \gamma_n^{\parallel }\right)\\ &+& \nu_{ne}\left( D^{m1pt}_{ne} \frac{t_n^{\perp \frac{3}{2}}}{t_n^{\parallel \frac{3}{2}}} \gamma_n^{\perp }+ D^{m4pt}_{ne}\frac{C_e}{C_n} \frac{t_e^{\perp \frac{3}{2}}}{t_e^{\parallel \frac{3}{2}}} \gamma_e^{\perp }+ D^{m1pp}_{ne} \gamma_n^{\parallel }+ D^{m4pp}_{ne}\frac{C_e}{C_n} \frac{t_e^{\parallel \frac{3}{2}}}{t_e^{\parallel \frac{3}{2}}} \gamma_e^{\parallel }\right)\\ &-& \left.3t_n^{\parallel}\frac{\delta u_n}{\delta t}\frac{1}{t_n^{\parallel\frac{3}{2}}}\right]\\ \end{eqnarray*}$

$\begin{eqnarray*} t_n\sum_{m \ne n} \nu_{nm}A^{n0p}_{nm}u_m\frac{C_m}{C_n} \frac{1}{t_n^{\parallel\frac{3}{2}}} - 3t_n^{\parallel}\sum_{m \ne n} \nu_{nm}u_m\frac{C_m}{C_n} \frac{1}{t_n^{\parallel\frac{3}{2}}} & \text{ Contribution } u_m \rightarrow \gamma_n^{\parallel}\\ t_n\sum_j \nu_{nj}A^{c0p}_{nj}u_j\frac{C_j}{C_n} \frac{1}{t_n^{\parallel\frac{3}{2}}} - 3t_n^{\parallel}\sum_j \nu_{nj}u_j\frac{C_j}{C_n} \frac{1}{t_n^{\parallel\frac{3}{2}}} & \text{ Contribution } u_j \rightarrow \gamma_n^{\parallel}\\ t_n \nu_{ne}A^{c0p}_{ne}\left(compo_i u_i + \sum_{j \ne i}compo_j u_j\frac{C_j}{C_i}\right) \frac{1}{t_n^{\parallel\frac{3}{2}}} - 3t_n^{\parallel} \nu_{ne}\left(compo_i u_i + \sum_{j \ne i}compo_j u_j\frac{C_j}{C_i}\right) \frac{1}{t_n^{\parallel\frac{3}{2}}} & \text{ Contribution } u_e \rightarrow \gamma_n^{\parallel}\\ \sum_{m \ne n} \nu_{nm}D^{n4pp}_{nm}\frac{C_m}{C_n}\frac{t_m^{\parallel\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_m^{\parallel} + \frac{3}{2}t_n^{\parallel}\sum_{m \ne n} \underbrace{D^{no}_{nm}\nu_{nm}\frac{1}{t_{nm}}}_{\text{coefnm}}\frac{C_m}{C_n}\frac{t_m^{\parallel\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_m^{\parallel} & \text{ Contribution } \gamma_m^{\parallel} \rightarrow \gamma_n^{\parallel}\\ \sum_j \nu_{nj}D^{m4pp}_{nj}\frac{C_j}{C_n}\frac{t_j^{\parallel\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_j^{\parallel} + \frac{3}{2}t_n^{\parallel}\sum_j \underbrace{D^{mo}_{nj}\nu_{nj}\frac{1}{t_{nj}}}_{\text{coefni}}\frac{C_j}{C_n}\frac{t_j^{\parallel\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_j^{\parallel} & \text{ Contribution } \gamma_j^{\parallel} \rightarrow \gamma_n^{\parallel}\\ \nu_{ne}D^{m4pp}_{ne}\frac{C_e}{C_n}\frac{t_e^{\parallel\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_e^{\parallel} + \frac{3}{2}t_n^{\parallel} \underbrace{D^{mo}_{ne}\nu_{ne}\frac{1}{t_{ne}}}_{\text{coefne}}\frac{C_e}{C_n}\frac{t_e^{\parallel\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_e^{\parallel} & \text{ Contribution } \gamma_e^{\parallel} \rightarrow \gamma_n^{\parallel}\\ \sum_{m \ne n} \nu_{nm}D^{n4pt}_{nm}\frac{C_m}{C_n}\frac{t_m^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_m^{\perp} + 3t_n^{\parallel}\sum_{m \ne n} \underbrace{D^{no}_{mn}\nu_{nm}\frac{1}{t_{nm}}}_{\text{coefnm}}\frac{C_m}{C_n}\frac{t_m^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_m^{\perp} & \text{ Contribution } \gamma_m^{\perp} \rightarrow \gamma_n^{\parallel}\\ \sum_j \nu_{nj}D^{m4pt}_{nj}\frac{C_j}{C_n}\frac{t_j^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_j^{\perp} + 3t_n^{\parallel}\sum_j \underbrace{D^{mo}_{jn}\nu_{nj}\frac{1}{t_{nj}}}_{\text{coefnj}}\frac{C_j}{C_n}\frac{t_j^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_j^{\perp} & \text{ Contribution } \gamma_j^{\perp} \rightarrow \gamma_n^{\parallel}\\ \nu_{ne}D^{m4pt}_{ne}\frac{C_e}{C_n}\frac{t_e^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_e^{\perp} + 3t_n^{\parallel} \underbrace{D^{mo}_{en}\nu_{ne}\frac{1}{t_{ne}}}_{\text{coefne}}\frac{C_e}{C_n}\frac{t_e^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_e^{\perp} & \text{ Contribution } \gamma_e^{\perp} \rightarrow \gamma_n^{\parallel}\\ \end{eqnarray*}$

Contribution $u_n \rightarrow \gamma_n^{\parallel}$ :

$-t_n\left( \underbrace{\sum_{m \ne n} \nu_{nm}A^{n0p}_{nm} }_{\text{Dn0pnun}}+ \underbrace{\sum_j \nu_{nj}A^{m0p}_{nj}+\nu_{ne}A^{m0p}_{ne} }_{\text{Dm0pnun}} \right)\frac{1}{t_n^{\parallel\frac{3}{2}}} +3t_n^{\parallel}\left(\underbrace{\sum_{m \ne n} \nu_{nm} + \sum_j \nu_{nj} + \nu_{ne}}_{\text{nuin} + \text{nuij}}\right)\frac{1}{t_n^{\parallel\frac{3}{2}}}$

Contribution $\gamma_n^{\parallel} \rightarrow \gamma_n^{\parallel}$ :

$\left( \sum_{m \ne n} \nu_{nm}D^{n1pp}_{nm} + \underbrace{ \sum_j \nu_{nj}D^{m1pp}_{nj} + \nu_{ne}D^{m1pp}_{ne} + \nu_{nn}D^{n1pp}_{nn} + \nu_{nn}D^{n4pp}_{nn}}_{\text{Dm1ppnun}} \right)\gamma_n^{\parallel} -\frac{3}{2}t_n^{\parallel}\left(\text{Dnnun} + \text{Dmnun}\right)\gamma_n^{\parallel}$

Contribution $\gamma_n^{\perp} \rightarrow \gamma_n^{\parallel}$ :

$\left( \sum_{m \ne n} \nu_{nm}D^{n1pt}_{nm} + \underbrace{ \sum_j \nu_{nj}D^{m1pt}_{nj} + \nu_{ne}D^{m1pt}_{ne} + \nu_{nn}D^{n1pt}_{nn} + \nu_{nn}D^{n4pt}_{nn}}_{\text{Dm1ptnun}} \right)\frac{t_n^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_n^{\perp} -3t_n^{\parallel}\left(\text{Dnnun} + \text{Dmnun}\right)\frac{t_n^{\perp\frac{3}{2}}}{t_n^{\parallel\frac{3}{2}}}\gamma_n^{\perp}$