Question

Set up a differential equation of ionizing emission in gas environment that gives the relation between number of ions and time.

Answer 1

Let we have a gas environment and q is the number of positive (negative)
ions
that appear every second.
Suppose at moment t there are n ions. As
positive and negative ions join,
their number decreases in rate proportional
to n^2 every second.
Then the differential equation is the
following:

dn / dt = q - a*n^2,

where a is a constant that depends
on gas environment characteristics.