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tokens: engine half-opening angle θ 0 = 0.2 (denoted as SJ0.2-EH). The jet engine parameter values for these three models are listed in Table 3 . Table 3 Jet Engine Parameters Note. L 0 and τ 0 represent jet engine power and average jet engine duration, respectively. The energy-to-mass ratio η 0 and injected Lorentz factor γ 0 are set to the same value for all of the jet engine models. θ 0 is the half-opening angle of the injected jet engines. To better interpret the role of each fluid component, we use three passive scalars X i to track the mass fraction of each individual component filling the cells. The subscript i labels each individual component: 1 for a stellar progenitor, 2 for ISM material, and 3 for jet engine material. Initially, X 1 ( X 2 ) is set to 1(0) inside the progenitor and 0(1) in the ISM. Three auxiliary equations are solved accordingly (Duffell MacFadyen 2013 ):The conserved mass for each component () is updated based on the density flux through the cell boundary and the addition of source term (for the injection of jet engine material). Dividing the individual conserved mass M i by the total conserved mass () gives us the new primitive passive scalar X i . 4.2. Dynamical Details of the FTD Jet Simulation 4.2.1. Launch of the Jet Engine Figure 6 shows the early evolution of the jet engine flow upon injection. The ram pressure generates a bow shock. Dense stellar material gets pushed to the side, forming a cocoon that confines the engine outflow. A high-density wedge of stellar material develops at the head of the jet. It shreds jet engine materials from the head. These engine materials curl back, forming vortexes. These vortexes then detach from the jet and get swept backward relative to jet propagation. This vortex shedding phenomena is, generally speaking, similar to that found in previous simulations (Scheck et al. 2002 ; Mizuta et al. 2004 ; Morsony et al. 2007 ). The speed of the jet head keeps increasing and soon exceeds the local sound speed (at the time t = 1.5s, the Lorentz factor of the head of the jet is ∼2, as shown in Figure 6 ). The backflow becomes quasi-straight to the main jet (Mizuta et al. 2010 ). At early times, the bow shock has a narrow head and a wide tail. When it approaches the surface, the jet head expands in the low-density envelope, as shown in the next subsection (see also, e.g., Zhang et al. 2003 , 2004b ). We use spherical coordinate to conduct simulations. As jets propagate outward, the width of the cell increases. The features of the inner part of the jet (close to pole) may not be fully resolved. We resolve the relativistic shell in the radial direction via the previously described AMR scheme. As the ultra-relativistic jet shell penetrates the progenitor, the stellar material that lies on top of the jet easily gets pushed aside. No strong “plug” instability has been seen (Lazzati et al. 2010 ; Mizuta Ioka 2013 ; Gottlieb et al. 2018a ; Xie et al. 2018 ). Figure 6. Early time snapshots of jet