  An evolution of the electron distribution function in the beam-plasma system
with the return current is computed numerically for different parameters. The
X-ray bremsstrahlung corresponding to such an electron distribution is
calculated and the directivity of the X-ray emission is studied. For
computations of the electron distribution functions we used a 3-D
particle-in-cell electromagnetic code. The directivity of the X-ray emission
was calculated using the angle-dependent electron-ion bremsstrahlung
cross-section. It was found that the resulting electron distribution function
depends on the magnetic field assumed along the electron beam propagation
direction. For small magnetic fields the electron distribution function becomes
broad in the direction perpendicular to the beam propagation due to the Weibel
instability and the return current is formed by the electrons in a broad and
shifted bulk of the distribution. On the other hand, for stronger magnetic
fields the distribution is more extended in the beam-propagation direction and
the return current is formed by the electrons in the extended distribution
tail. In all cases, the anisotropy of the electron distribution decreases
rapidly due to fast collisionless processes. However, the magnetic field
reduces this anisotropy decrease. The X-ray directivity shows the same trend
and it is always closer to the isotropic case than that in a simple beaming
model.
