Electrostatic Accelerator FELs have the capacity to generate long pulses of tens microseconds and more, that in principle can be elongated indefinitely (CW operation). This allows the generation of very coherent radiation. The fundamental linewidth is extremely narrow [1], and in practice the spectral width is limited by the pulse duration (Fourier transform limit) and e-beam stability. Practical problems such as the accelerator terminal voltage drop due to a non-ideal electron beam transport may reduce the length of the radiation pulse and hence create a limiting factor for coherence measurement. The current status of the Israeli Tandem Electrostatic Accelerator FEL allows the generation of pulses of tens microseconds duration. It has been operated recently past saturation, and produces single mode coherent radiation of relative linewidth ~Δf/f=10-5 at frequencies near 100GHz. A clear frequency chirp is observed during pulses of tens of microseconds (0.1-1 MHz/mS), and is directly proportional to the voltage drop rate of the High-Voltage terminal. We will report experimental studies of the spectral linewidth and chirp characteristics of the radiation, along with theory and numerical simulations, carried out using space-frequency model [2], matching the experimental data.

Quantum and free-electron lasers (FELs) are based on distributed interactions between electromagnetic radiation and gain media. In an amplifier configuration, a forward wave is amplified while propagating in a polarized medium. Formulating a coupled mode theory for excitation of both forward and backward waves, we identify conditions for phase matching, leading to efficient excitation of backward wave without any mechanism of feedback or resonator assembly. The excitations of incident and reflected waves are described by a set of coupled differential equations expressed in the frequency domain. The induced polarization is given in terms of an electronic susceptibility tensor. In quantum lasers the interaction is described by two first order differential equations, while in high-gain free-electron lasers, the differential equations are of the third order each. Analytical solutions of reflectance and transmittance for both quantum lasers and FELs are presented. It is found that when the solutions become infinite, the device operates as an oscillator, producing radiation at the output with no field at its input, entirely without any localized or distributed feedback.