The aim of the project is to investigate spontaneous symmetry breaking in non-adiabatic phase transitions (Kibble-Zurek processes). A long and narrow annular Josephson tunnel junction is subjected to repeated thermal quenches through the normal-superconducting transition. The quench rate is varied over 4 orders of magnitude. After the quench the result of the spontaneous production of topological defects, trapped fluxons, is unambiguously observed as zero-field steps in the DC I-V characteristic of the junction. A power-law scaling behavior of trapping probability versus quench rate is found with a critical exponent of 0.5 (within experimental error). The main experimental challenges are to generate many identical quenches with accurate cooling rate, to automate data analysis and acquisition, and to suppress external magnetic fields and noise by passive magnetic shielding and compensation.