Parameter rays for the exponential family

We investigate the set of parameters $\kappa \in \text{C}$ for which the singular orbit $(0,e^{\kappa },\mathrm{.}\mathrm{.}\mathrm{.})$ of $E_{\kappa }(z):=\exp (z+\kappa )$ converges to $\mathrm{\infty }$. These parameters are organized in smooth curves in parameter space called \emph{parameter rays}.