The longitudinal tracking engine of the particle accelerator simulation application PyHEADTAIL shows a heavy potential for parallelisation. For basic beam circulation, the tracking functionality with the leap-frog algorithm is extracted and compared between a sequential C and a concurrent CUDA C API implementation for 1 million revolutions. Including the sequential data I/O in both versions, a pure speedup of up to S = 100 is observed which is in the order of magnitude of what is expected from Amdahl's law. From O(100) macro-particles on the overhead of initialising the GPU CUDA device appears outweighed by the concurrent computations on the 448 available CUDA cores.