  Two counter-propagating cool and equally dense electron beams are modelled
with particle-in-cell (PIC) simulations. The electron beam filamentation
instability is examined in one spatial dimension. The box length resolves one
pair of current filaments. A small, a medium-sized and a large filament are
considered and compared. The magnetic field amplitude at the saturation time of
the filamentation instability is proportional to the filament size. It is
demonstrated, that the force on the electrons imposed by the electrostatic
field, which develops during the nonlinear stage of the instability, oscillates
around a mean value that equals the magnetic pressure gradient force. The
forces acting on the electrons due to the electrostatic and the magnetic field
have a similar strength. The electrostatic field reduces the confining force
close to the stable equilibrium of each filament and increases it farther away.
The confining potential is not sinusoidal, as assumed by the magnetic trapping
model, and it permits an overlap of current filaments (plasmons) with an
opposite flow direction. The scaling of the saturation amplitude of the
magnetic field with the filament size observed here thus differs from that
expected from the magnetic trapping model. The latter nevertheless gives a good
estimate for the magnetic saturation amplitude. The increase of the peak
electrostatic and magnetic field amplitudes with the filament size implies,
that the electrons heat up more and that the spatial modulation of their mean
speed along the beam flow direction increases with the filament size.
