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scratchpad5

-              v2
+              v3
 So we can rewrite the equations as
 $\frac{\partial T}{\partial t} = \nabla \cdot \left [ n \hat{b} \left ( \kappa_\parallel T^{\lambda_\parallel} - \frac{n \kappa_\perp}{B^2} T^{\lambda_\perp} \right ) \left ( \hat{b} \cdot \nabla T \right ) + \frac{n \kappa_\perp}{B^2} T^{\lambda_perp} \nabla T \right ]$
+$\frac{\partial T}{\partial t} = \nabla \cdot \left [ n \hat{b} \left ( \kappa_\parallel T^{\lambda_\parallel} - \frac{n \kappa_\perp}{B^2} T^{\lambda_\perp} \right ) \left ( \hat{b} \cdot \nabla T \right ) + \frac{n \kappa_\perp}{B^2} T^{\lambda_\perp} \nabla T \right ]$
+or
+$\frac{\partial T}{\partial t} = \nabla \cdot \left [ n \hat{b} \left ( \frac{\kappa_\parallel}{\lambda_\parallel+1} \left ( \hat{b} \cdot \nabla T^{\lambda_\parallel+1} \right )  - \frac{n \kappa_\perp}{B^2 \left ( \lambda_\perp+1 \right )} \left ( \hat{b} \cdot \nabla T^{\lambda_\perp + 1} \right ) + \frac{n \kappa_\perp}{B^2 \left ( \lambda_\perp +1 \right )} \nabla T^{\lambda_\perp+1} ]$
 Let's first just consider the $\chi_\parallel$ term.