scatterers for the same set of parameters used in Figure \[fig:fpplotsgamjet\]. For all solutions the number density of scatterers approaches zero as we near the center of the jet. We see that the average number density of scatterers within the boundary layer is lower for larger Lorentz factors.[]{data-label="fig:rhoplotsgamjet"}](Figure4.eps){width="3.5in"}

![The normalized number density of photons for the same set of $\zeta$ used in Figure \[fig:fpplotsgamjet\]. The photon number density closely follows that of the scatterers.[]{data-label="fig:hplotsgamjet"}](Figure5.eps){width="3.5in"}

![The $y$-component of the three-velocity normalized by $\sqrt{2/(9\rho'_0\kappa{z_0})}$ (see equation ) for the same set of parameters used in Figure \[fig:fpplotsgamjet\]. For positive $\tilde\alpha$, each solution is initially positive and reaches a relative maximum before approaching a negative constant, which shows that the flow expands outwards near the center of the jet and entrains ambient material far from the axis. []{data-label="fig:vyplotsgamjet"}](Figure6.eps){width="3.5in"}

Figure \[fig:fpplotsgamjet\] shows the solution for $f_{\xi}$, the normalized $z$-component of the four-velocity, for $\zeta = 4$, 10, and 25. Since $\zeta = \Gamma_jv_j(z/z_0)^{-1/4}$, these values of $\zeta$ scale approximately linearly with the Lorentz factor until $z \gg z_0$. The outflow velocity is maximized at the origin and decays as we move farther into the ambient medium. We see that the width of the boundary 