The paper quantitatively describes the photoelectron effective temperature
evolution and the spontaneous magnetic field amplification in plasmas produ
ced under atomic tunnel ionization. It is demonstrated the possibility of t
he generation and of the substantial amplification of magnetic fields both
with a laser pulse having duration t(p) much smaller, equal or larger than
the inverse electron collision frequency t(c). It is shown that with t(p) g
reater than or similar to t(c), thanks to an anisotropic electron heating d
ue to the inverse bremsstrahlung absorption of the strong laser radiation,
the magnetic field amplification is almost an order of magnitude greater th
an it is in the case t(p) much less than t(c). It is also treated the case
of a simultaneous full tunnel ionization of two atomic levels, founding a m
agnetic field amplification smaller than that obtained for the case when th
e ionization comes from one atomic level only.