A specified source of radiation may either be given as (1) a specified incident distribution in space, energy, angle, and time or (2) as a known source of radiation that is emitting a specified amount of radiation as a function of time, space, energy, and angle. Although it is possible to show that these are mathematically equivalent [CdHP], the actual implementation of these ``sources'' into a Monte Carlo code will depend on which type of source is being examined.
In order to specify an incident flux of particles on a surface, one needs to determine the following quantities:
,
,
that the incident particle is traveling, and
that the particle is incident on the surface.
For simplicity, let us assume that the incident radiation is monoenergetic at
energy 
, and it is monodirectional, traveling down the 
-axis.
Let us assume that the surface that is being irradiated is in the 
-
plane, ranging over 
and 
.
In this case, one typically knows the number of particles incident on the
boundary per unit area of boundary, as a function of time, position on the
boundary, energy, and angle. For example, consider
a beam of monoenergetic particles
incident normally and uniformly on the negative ``'' surface of a ``brick''
of edges 
, 
, and 
, corresponding to the three coordinate axes
, , and .
In this case, there are 
particles incident per unit area per unit time
on the slab, and they are all travelling perpendicular to the surface of the
slab.
To start a particle in a Monte Carlo simulation, the source module would sample
a position on the incoming surface of the
brick.
Nuclear engineers working in reactor physics and radiation shielding areas generally employ the concept of neutron ``flux'' to describe the amount of radiation, while other disciplines employ a ``density'' or ``intensity'' to describe what is in essence a very similar quantity. However, since the Monte Carlo simulation is a direct analog of the physical application, how these terms relate to a real application will be apparent after a few examples.