Populations at a given moment can be represented by the rate equations
N
__
\
dNm/dt = / Kmn Nn + Dm = Gm (1.1)
--
n=1
The matrix Kmn will be called the relaxation matrix. Its elements give the average
number of transitions from state n to state m in an atom in a unit time interval;
the diagonal term Kmn governs the total loss of particles (per unit time) from the
state m. The quantity Dm represents the arrival of particles from the continuum.
In the case pf a plasma of simple chemical composition, it is usual to allow only
for the spontaneous radiative transitions (3) and for collisions with electrons; (4)
Kmn = Vmn Ne + Amn(m not equal to n),
N
__
\
-Kmm = / Knm + Vem Ne = Ne Vm + Am (1.2)
--
n=1
-Kmm = Km =
here, Amn is the rate at which the radiative transition n to m takes place (this
quantity is known as the Einstein coefficient), and Vmn=(sigmamn v) is the rate
of this transition as a result of inelastic collisions with electrons. In the case
of a low-temperature dense plasma with
Ne cm^-3 > 3 X 10^13 [Te eV]^3.75 (1.3)
we can ignore the radiative recombination compared with the three-particle process
(28) and can assume that Dm = Vem Ne^2 N+. The effective limit of the continuous
spectrum N is selected in such a way that its position does not affect
significantly the results of the calculations of the populations.a) General calculation methods