- #1

IonReactor

- 8

- 1

, as being a fluid so that the equation of motion for each species (after some approximations and assumptions) is

$$0≈−n_{\sigma}q_{\sigma}∇ϕ−∇P_{\sigma}$$

where ##P_{\sigma}=κT_{\sigma}n_{\sigma}## which because we assumed that the temperature is spatially uniform gives us

$$0≈−n_{\sigma}q_{\sigma}∇ϕ−κT_{\sigma}∇n_{\sigma}$$

But didn't we also assume that ##n_{\sigma}## was also spatially uniform? Why then are we taking a gradient of it?

It seems to me like what we have done is write an operator ##−q_{\sigma}∇ϕ−κT_{\sigma}∇## and used it to look for homogeneous solutions of the species density but I am still confused as to why we are taking a gradient of a quantity that we assumed to be spatially uniform and I hope that one of you good people will have some insight