Experimental Determination of Electron-impact Rotational Excitation Rate Coefficients for CH$^+$

CH$^+$ has been detected in space and laboratory plasmas. Interpretation of the observed spectrum relies, in part, on radiative transfer models built on a knowledge of the relevant excitation and de-excitation processes, such as inelastic collisions with electrons. Here we present merged beams experiments of CH$^+$ with the recently implemented electron cooler at the Cryogenic Storage Ring (CSR) in Heidelberg. This experimental setup facilitates low (meV) collision energy measurements to study inelastic electron-ion collisions. We combined the collision measurements with near-threshold photodissociation to probe the populations of the lowest rotational states of the stored CH$^+$. Using a velocity-matched or slightly detuned electron beam, we can, for the first time, experimentally determine electron-impact rotational excitation and de-excitation merged beams rate coefficients for a molecular ion. Here we will present our first results.