calculation but with varying projected velocities at distances $d(\theta)>L_{12}$ along the shock surfaces away from the symmetry axis. Here, $L_{12}$ is the time-dependent minimum distance between the colliding shocks. For each position determined by $d(\theta)$ for $0<\theta<90^0$ we calculate the non-linear particle distribution using the projected speeds $V_w \cos\theta$ and $V_\mathrm{snr} \cos\Phi$ as parallel flow speeds. That is, we assume the wind and the SNR shocks are locally plane with converging parallel flows set by the projected speeds.

For this approximation, we use the bow shock wind model of @wilkin96 for $R(\theta)$ and $V_w$, assume the SNR shock is spherical, and restrict our calculations to $3$ arc surfaces: $0-30^0$, $30-60^0$, $60-90^0$ which produce accelerated particle densities with the weights $0.84$, $0.15$ and $0.01$, respectively. Then the weighted CR distribution function is used to calculate the [$\gamma$-ray]{} and neutrino emissivities both in the accelerator (see §\[sec:trap\]) and in the surrounding ISM from the CRs escaped the accelerator (see §\[sec:esc\]).

![Model predictions of [$\gamma$-rays]{}  (solid curves) and neutrinos (dashed curves) from [$p\!-\!p$]{}-interactions calculated in a CSF source of age $400$yr. The dotted curve is the inverse Compton emission from primary and secondary electrons accelerated directly in this source. The extreme upward curvature 