“…Then, time averagely, the pressure of the jet coincides with that of the cocoon due to the confinement of the jet by the cocoon. The internal energy and mass of the cocoon garnered through the reverse shock during the jet injection time, t, thus are estimated, when all the physical quantities characterizing the jet, such as jet radius, density, pressure, velocity, and Lorentz factor, are treated as the "temporally averaged" values, as follows: (Martí et al 1997;Bromberg et al 2011;Perucho et al 2017), where subscripts j and c stand for the jet and cocoon respectively. Here, V c is the volume of the cocoon, r j is the jet radius, h := 1 + ΓP/(Γ − 1)ρc 2 is the dimensionless specific enthalpy and v h is the propagation velocity of the jet head.…”