Fundamental and Harmonic Microbunching Measurements in a High-Gain, Self-amplified, Spontaneous Emission Free-Electron Laser

The self-amplified, spontaneous emission free-electron laser (SASE FEL) gain process is a collective instability which induces microbunching in the electron beam. Microbunching approaching unity at the fundamental FEL wavelength (845 nm), and its second harmonic, have been measured at the VISA FEL, at or near saturation. These measurements, which use the beam's coherent transition radiation (CTR) spectrum, are compared to the predictions of FEL simulations. Comparison of shot-by-shot SASE and CTR signals firmly establishes the role of SASE in the development of microbunching harmonics. PACS numbers: 41.60.Cr, 41.60.Ap, 41.85.Ja Submitted to Physical Review Letters Significant progress has been recently achieved in the worldwide effort of Self Amplified Spontaneous Emission Free Electron Laser (SASE FEL) R&D; saturation [13] and nonlinear harmonic radiation [4-5] have been observed from the near infrared to UV wavelengths. A signature of the FEL is the microbunching of the longitudinal electron beam distribution with a periodicity of the FEL’s fundamental wavelength. For current SASE FEL’s, the microbunch spacing can now be below 100 nm [3], which is the shortest structure yet imparted to laboratory electron beams. By measuring the degree to which the electron beam is microbunched, important microscopic properties of the SASE radiation system can be determined. In the current measurements, we have a tightly microbunched system, a characteristic of the FEL saturation, in which case the microbunching structure contains rich harmonics. Observations were first made on fundamental SASE FEL microbunching using coherent transition radiation (CTR) [6-7] and later on an FEL oscillator using other methods [8]. In this letter, the first direct experimental observation of the correlation between the SASE FEL output and electron beam longitudinal microbunching (determined by CTR) is presented. We will also discuss the first measurement of harmonic microbunching in a SASE FEL. Bunching factors for both the fundamental, b1 , and second harmonic, b2 , are experimentally characterized and compared with computer simulation. The technique presented in this letter provides another independent verification that the fundamental microbunching drives both the SASE FEL gain mechanism and nonlinear harmonic generation. We begin by reviewing the basic physics of the SASE FEL. An intense relativistic electron beam propagating through a periodic magnetic undulator may undergo a radiation-producing interaction termed the SASE FEL instability [9]. This instability proceeds by generating light at the FEL’s resonant wavelength, lr, n=1 (the fundamental given by Eq. 1 below), and allows the beam to microbunch at the same wavelength. This process has positive feedback, as microbunching stimulates more coherent radiation production. As this process evolves and the electron beam continues to microbunch further, the coherence of the radiated field increases, and the SASE power grows exponentially through the undulator, P μ P0 exp(z / Lg ) . Here, P0 is usually taken as the coherent fraction of the spontaneous radiation in the first field gain length, z is the distance along the undulator, and Lg is the power gain length. When the exponential growth in radiated power ends (levels off), the FEL is in a state termed saturation [10]. At saturation, the beam is most strongly microbunched, and further coherent power generation is mitigated. As saturation is approached, the modulation of the beam current becomes deep and non-sinusoidal, with significant higher harmonic content. Thus the onset of saturation should be accompanied by the generation of harmonics, both in the FEL light that is generated [9-12], and the microbunching of the electron beam distribution. The wavelengths at which the electron beam is microbunched, lmb , are given by lmb,n = lr ,n = lu 2g n 1 + K 2 2 Ê Ë Á ˆ ̄ ̃ (1) where lu is the undulator period, g is the electron beam energy, K is the undulator parameter, and n=1,2,3... is the harmonic number with n=1 as the fundamental mode. Near saturation, most of the electrons in the beam are densely packed in a narrow region, much shorter than the fundamental period, lmb,1 = lr ,1 . This dense packing implies the existence of harmonics in the longitudinal distribution [10]. Further, this harmonic microbunching will generate radiation at the same wavelength, lr, n , although because of the nature of the radiative process in a planar undulator FEL, odd harmonic radiation production is favored [12]. Because the higher harmonic SASE process is driven by the fundamental microbunching, it is termed nonlinear harmonic radiation. The growth of the nonlinear harmonic radiation starts later in the undulator compared to that of the fundamental, as the fundamental must have considerable gain before the harmonic microbunching can develop. Experimental observation of nonlinear harmonic radiation on the VISA FEL has been reported in an earlier publication [4] The theory of CTR and its use for longitudinal microbunching measurements of electron beams has been extensively studied [6-7,13-14]. The most common model of this process describes transition radiation (TR) approximately as an annihilation (or creation) of an electron with its image charge at the conductor/vacuum interface. A more physical picture of the process, known as the virtual photon, or Weizsacker-Williams method [15] can also be used to give the same predictions concerning CTR microbunching [14]. In addition, this theory has been bench-marked with experiment [67]. We now quantify our model for measuring the microbunching. A useful form of the electron beam charge distribution at the exit of a SASE FEL is r(x , y,z) = eN exp x 2 2s x 2 y 2s y 2 z 2sz 2 Ê