We have investigated motional heating of laser-cooled Be-9(+) ions held in
radio-frequency (Paul) traps. We have measured heating rates in a variety o
f traps with different geometries, electrode materials, and characteristic
sizes. The results show that heating is due to electric-field noise from th
e trap electrodes that exerts a stochastic fluctuating force on the ion. Th
e scaling of the heating rate with trap size is much stronger than that exp
ected from a spatially uniform noise source on the electrodes (such as John
son noise from external circuits), indicating that a microscopic uncorrelat
ed noise source on the electrodes (such as fluctuating patch-potential fiel
ds) is a more likely candidate for the source of heating.