Theoretical study of a high-extraction efficiency undulator for a free electron laser oscillator☆

Abstract Theoretical issues in designing a high-extraction efficiency undulator for a free electron laser oscillator are discussed. Assuming that an undulator system consists of a prebuncher undulator and a main undulator separated by a drift, design criteria of the untapered prebuncher are studied. The main undulator is designed parabolically tapered in wave number from no taper to a 30% taper. A small signal gain is enhanced at the low taper section, and the large signal gain is enhanced at the high taper section. To optimize the operation of this prebuncher system, electron dynamics in phase space from the prebuncher to the main undulator is studied. To demonstrate the advantage of having the prebuncher, comparisons of the extraction efficiency and the gain are performed between the prebuncher system and the system with the prebuncher removed. The optimized prebuncher system is then tested for the sideband instability with more complex one-dimensional FEL codes that assume a finite electron pulse and a finite laser pulse length. The electron beam emittance requirement is studied using a three-dimensional FEL simulation code.