Diffusion in a slab

Diffusion in a slab refers to the process of the net movement of particles or molecules from an area of high concentration to an area of low concentration within a flat, slab-like region. This process occurs due to random thermal motion of particles and is governed by Fick's laws of diffusion.

We have the continuity equation is

where flux of jth species,

For quasi neutrality of plasma

Γi = Γe - Γ

Putting this in equation 2, we get

Γj = - Da ∇n .....4

with the value of equation 4, equation 1 becomes

∂n/∂t - Da ∇²n = 0

∂n/∂t = Da ∇²n ......5

which is Diffusion equation

This can be solved by method of separation of variables so let

Using this in equation 5

S ∂n/∂t = naT ∇²n ......7

LHS is the function of time and RHS is function of space alone, they must be equal to some constant.

1/T ∂T/ ∂t= - 1/ 𝜏 = Da/ S . ∇²S

∂T/ ∂t = -T/𝜏

The boundary condition are S=0 at x = L. At x=0, S must have a maximum.

Since term can be

Hence complete solution is

Diffusion in a plasma slab has important implications in various plasma physics phenomena and technological applications. It affects the transport of charged particles within plasma devices, such as plasma reactors, plasma thrusters, and fusion devices. Understanding and controlling diffusion processes in plasmas are crucial for optimizing plasma performance, controlling plasma composition, and designing plasma-based technologies.

This note is a part of the Physics Repository.