free electron laser one would like a repetition rate of the electron bunch to be of the order of the light round trip time in the optical cavity this allows for the build up of radiation in the laser cavity and generates a very narrow line of the laser emission it is possible but not demonstrated experimentally that very short pulses with a large time interval between pulses large compared to the pulse duration have the same breakdown characteristics as a single isolated pulse in other words after the application of a single pulse there are mechanisms that allow the structure to u201c remember u201d previous application of high field in general the u201c memory u201d of the system should be limited to the lifetime of excited stated in the x ray range plus some low probability effects like plasma recombination with light emission in vacuum and the existence of metastable states in the residual gas the slowest longest memory mechanism could be due to the presence of heavy ions of very low almost thermal energy these ions may extract electrons from the metallic surfaces this u201c permanence u201d time can be as long as a few microseconds construction of a pulse train in accordance with the present invention a general mathematical theorem states that any continuous periodic function can be represented by a sum of orthogonal periodic functions each periodic function with an appropriate coefficient an example of this expansion is the sine or cosine fourier series viz f ue8a0 t u2211 k ue89e a k ue89e sin ue89e.