  Escape of $\alpha$-particles from a burning or an ignited burning
deuterium-tritium (DT) fuel with temperature up to more than tens keV is very
important in inertial confinement fusion, which can significantly influence not
only the hot spot dynamics and the energy gain but also the shielding design in
fusion devices. In this paper, we study the $\alpha $-particle escape from a
burning or an ignited burning DT fuel by considering the modifications
including the $\alpha $-particle stopping by both DT ions and electrons with
their Maxwellian average stopping weights, the relativity effect on electron
distribution, and the modified Coulomb logarithm of the DT-$\alpha $ particle
collisions. As a result of our studies, the escape-effect from our modified
model is obviously stronger than those from the traditional models. A fitted
expression is presented to calculate the escape factor in a DT fuel, which can
be applied to a burning fuel with temperatures of 1 to 150 keV and areal
densities of 0.04 to 3 g/cm$^2$ with an accuracy within $\pm0.02$. Finally, we
discuss the $\alpha $-particle escape-effect on the hot-spot dynamics and the
thermonuclear energy gain by comparing the results with escape factors from
different models.
