Electric field analysis in a cold-ion source using Stark spectroscopy of Rydberg atoms

We analyze electric fields in ion sources generated by quasi-continuous photo-ionization of cold Rb atoms trapped in the focal spot of a near-concentric, in-vacuum cavity for 1064-nm laser light. Ion streams are extracted with an external electric field, ${\bf{F}}$. Stark effects of Rb 57$F$ and of nearby high-angular-momentum Rydberg levels, which exhibit large, linear Stark shifts, are employed to study the net electric-field probability distribution within the ion-source region over an extraction-field range of $0<F<0.35$ V/cm. For $F=0$, we also investigate ion-field-induced Stark spectra of the 60$P_{1/2}$-state, which exhibits a (lesser) quadratic electric-field response that affords a simplified electric-field analysis. Experimental Rydberg spectra are compared with theoretical Stark spectra, which are weighed with net electric-field distributions obtained from classical ion-trajectory simulations that include Coulomb interactions. Experiments and models agree well. At small $F$ and high ion source rates, the field approximately follows a Holtsmark distribution, and the ion streams are degraded by the Coulomb micro-fields. With increasing $F$ and at lower ion source rates, the fields become narrowly distributed around ${\bf{F}}$, resulting in directional ion streams that are less degraded by micro-fields. Our results are of interest for monitoring cold-ion sources for focused-ion-beam applications, where Coulomb interactions are of concern, and for studies of electric fields in cold plasmas.