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Radiation measurements in the new tandem accelerator FEL

The measurements of both spontaneous and stimulated emissions of radiation in the newly configured Israeli EA-FEL are made for the first time. The radiation at the W-band was measured and characterized. The results match the predictions of our earlier theoretical modeling and calculations.


Introduction
The Israeli electrostatic accelerator FEL (EA-FEL) is based on a 6 MeV EN-Tandem Van de Graaff accelerator, which was originally used as an ion accelerator for nuclear physics experiments [1]. The scheme employs straight geometry for the electron beam transport, where the electron gun and the collector are installed outside of the accelerator region. Lasing was reported in a previous configuration, where radiation was transmitted through the accelerator tubes with 40dB attenuation [2,3].
In the present version of the FEL, which was relocated to Ariel, the millimeter-wave radiation generated in the resonator is separated from the electron beam by means of a perforated Talbot effect reflector [4,5]. A quasi-optic delivery system transmits the out-coupled power through a window in the pressurized gas accelerator tank. The basic parameters of the FEL are summarized in Table 1. The acceleration voltage is set to be E k = 1.4 M eV in order to tune the frequency of the FEL radiation to the W-band near 100 GHz.
In the following sections, we present an analysis and the results of spontaneous and stimulated emissions measurements carried out recently.

Spontaneous emission in a resonator
Random electron distribution in the e-beam causes fluctuations in current density, identified as shot noise in the beam current. Electrons passing through a magnetic undulator emit a partially coherent radiation, which is called undulator synchrotron radiation. The electromagnetic fields excited by each electron add incoherently, resulting in a spontaneous emission with generated power spectral density [6]: where P sp (L W ) is the expected value of the spontaneous emission power, τ sp = Table 1 Parameters of the tandem electrostatic accelerator FEL Accelerator Electron beam energy: T =7% Total round-trip reflectivity: R=65% is the detuning parameter (V z0 is the axial velocity of the accelerated electrons and V g is the group velocity of the generated radiation). The spontaneous emission null-to-null bandwidth is approximately 2/τ sp = 2(f 0 /N W ). In a FEL, utilizing a magneto-static planar wiggler, the total power of the spontaneous emission is given by: where Z ≈ 2πf µ 0 /k z is the mode impedance, and I 0 is the DC beam current. The expected value of the total spontaneous emission power generated inside the cavity is about P sp (L W )/I 0 = 60 µW A −1 . The calculated spectrum of the spontaneous emission power of the Israeli EA-FEL, has a null-to-null bandwidth of 18 GHz. At the resonator output, the spontaneous emission spectrum generated inside the resonator is modified by a Fabry-Perot spectral transferfunction [7]: where L c is the resonator (round-trip) length, R is the total power reflectivity of the cavity, T is the power transmission of the out-coupler and k z (f ) is the axial wavenumber of the waveguide mode.  Fig. 1.
The noise equivalent bandwidth is defined as the bandwidth of an ideal band-pass filter producing the same noise power at its output. The noise equivalent bandwidth of a single resonant longitudinal mode is B = (π/2)FWHM ≈ 12.2 MHz. Consequently, the spontaneous emission power of mode m is given by: The typical bandwidth of the generated spontaneous emission power spectrum (1) is 1/τ sp ≈ 9 GHz. The number of longitudinal modes within the spontaneous emission bandwidth is then N modes = (1/τ sp )(1/FSR ≈ 80. Thus the total spontaneous emission power measured at the output of the resonator is given as follows: Using equation (2), we expect up to P out sp (L w ) ≈ 120 µW spontaneous emission power to be generated inside the resonator. From (5), the power emitted from the resonator out-coupler is reduced to P out sp ≈ 24 µW. The attenuation of the wave-guiding system, delivering the power from the resonator, located inside the highvoltage terminal, to the measurement apparatus is 10dB. Consequently, the spontaneous emission power expected at the detector sight is 2.4 µW. The traces shown in Fig. 2 Figure 1. Spontaneous emission power spectrum at resonator output (for I 0 = 1 A).

Stimulated emission
In the present operation regime of the FEL, the efficiency of energy extraction from the electron beam is given in terms of the number of wiggler's periods N w by the approximate formula η ext ≈ 1/2N W = 2.5 %. The stimulated radiation power generated inside the resonator at steady state is given as follows: where ∆P ≈ 35 kW for a beam current of I 0 = 1 A. The resulted power obtained from the outcoupler is given as follows: and evaluated to be P o ut = 7 kW. Considering the attenuation of the transmission system, 700 W is expected at the detector. Fig. 3 shows recent measurement of 150 W radiation power at the end of the optical transmission line in the measurement room. We note that in the present preliminary experiments, only a fraction of the cathode current was transported through the wiggler, and no beam circulation (transport up to the collector) was achieved. The charging of the terminal caused voltage drop of the terminal of 125 kV during the pulse duration. Evidently, the FEL had not yet reached saturation because the radiation mode built inside the resonator went out of synchronism with the beam before reaching saturation.