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.

In the Israeli Electrostatic Accelerator FEL, the distance between the accelerator's end and the wiggler's entrance is about 2.1 m, and 1.4 MeV electron beam is transported through this space using four similar quadrupoles (FODO-channel). The transfer matrix method (ABCD matrix method) was used for simulating the beam transport, a set of programs is written in the several programming languages (MATHEMATICA, MATLAB, MATCAD, MAPLE) and reasonable agreement is demonstrated between experimental results and simulations. Comparison of ABCD matrix method with the direct "numerical experiments" using EGUN, ELOP, and GPT programs with and without taking into account the space-charge effects showed the agreement to be good enough as well. Also the inverse problem of finding emittance of the electron beam at the S1 screen position (before FODO-channel), by using the spot image at S2 screen position (after FODO-channel) as function of quad currents, is considered. Spot and beam at both screens are described as tilted eellipses with diameters and orientation angle of which being found by STB (Spot-to-Beam) procedure, and trace-ellipse transformation is used to found emittance at S1 position.

We describe the interactive "STB" (spot_to_beam) MATHEMATICA procedure for a) approximating the spot image at the screen as ellipse, b) getting five parameters of the elliptic beam (two diameters, center coordinates, and orientation angle). The basic idea is to "map" the reference holes at screen onto the X-Y plane normal to the beam direction (Z-axis). All distortions of the image, e.g., due to camera-screen disposition can be, in principle, taken into account,assuming that the hole positions at screen and the orientation of the screen are known. With the non-linear LMS fitting, the "curved-coordinate-system" of the holes at image is transferred to the Cartesian coordinate system at XY-plane. Then the fitting ellipse is found in this latter system, by solving the system of N linear equations for 5 unknown parameters of beam ellipse, where N>5 is a number of reference points on edge of spot image. The examples of the real measurements at various screens will be demonstrated. The accuracy of beam diameters is about .1 mm depending on quality of picture and the perator's experience. The procedure is to be used in the routine measurements in the Israeli FEL.