Laser Physics and Nonlinear Optics
Department of Science & Technology

Cerenkov Free Electron Laser (FEL)

Content

	Research description
	Experimental setup
	References

Free-Electron Lasers (FEL) form a class of lasers that produce coherent light by converting kinetic energy of a (highly) relativistic electron beam into radiation energy. Usually an undulator is used to provide coupling between the electron beam and radiation field, such that the action of the resulting ponderomotive force, results in bunching of the electrons on the scale of the radiation wavelength. This bunching meganism is responsible for the coherent genereation and amplification of the radiation field at the expense of the average electron energy. However, bunching of the electrons will only take place if the ponderomotive force changes slowly over macroscopic distances, i.e. the relative slippage of the electrons with respect to the force must be small over a macroscopic distance. This phase matching results in a resonance condition that relates the radiation frequency to the electron energy (or electron velocity) and makes the laser continously tuneable by varying the electron velocity. The wavelength scales inversely proportional to electron beam energy squared and high energy electron beams are required to generated short wavelengths (of the order of a few GeV to generate nanometer wavelengths)

A Cerenkov FEL uses a different mechanism to couple the electron beam to the radiation field. Here use is made of the modified dispersion properties of the radiation wave when a cylindrical waveguide is lined with a dielectric material (see figure 1).

	figure 1. Schematic view of a lined cylindrical waveguide and the TM01 mode used in a Cerenkov Free-Electron Laser.

The electron beam moves with a normalised velocity β=v/c, where c is the speed of light in vacuum, through the inner part of the waveguide that contains no material. For sufficiently high frequency, the radiation field is concentrated in the dielectric liner and has an evanescent component in the vacuum region of the waveguide. Consequently, the radiation field has a phase velocity that is less than the speed of light in vacuum and the electron velocity can be made equal to this phase velocity. Due to the waveguide, modes exists with a longitundinal electric field that will bunch the electrons in a similar way as the ponderomotive force in the undulator based FEL. The bunching will be at the scale of the radiation wavelength and again coherent amplification of the radiation wave takes place. Because of the different dispersion characteristics of the wave propagation in a Cerenkov FEL compared to an undulator based FEL, one finds that the Cerenkov FEL has a different tuning characteristic, i.e., the wavelength decreases with decreasing electron beam energy.
In this research programme we are studying a low energy (maximum 100 keV) Cerenkov FEL that will operate around a design frequency of 50 GHz. Note that to design an undulator based FEL to operate at the same frequency, an electron beam energy is required that is about an order of magnitude higher. As in a Cerenkof FEL the electrons interact with the evanescent part of the radiation wave, it is necessary that the evanescent part does not decay too quickly with the distance from the inner surface of the liner. This limits the maximum operating frequency of the Cerenkov FEL. The study includes generation and acceleration of the electron beam, beam transport through the lined section, the Cerenkov FEL instability, tunability and phase stability of the generated radiation and finally a study to improve the overall system efficiency by recovery of the electron beam energy in the spent electron beam.

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Experimental set-up

The general design parameters are given in table 1 and a general overview of the current state of the system is shown in figure 2.

	figure 2. Overview of our miniature Cerenkov Free-Electron Laser. Shown are the electron gun (on the left side), the interaction region surrounded by a solenoid and the outcoupler (middle). Also shown are the Faraday cup (middle) that is used for diagnostics on the electron beam and the housing for a depressed collector that will be installed at a later stage and will be used for cw operation and increased efficiency (right side).

A gridded thermionic electron gun is used as the source for the electron beam and is similar to the ones used in traveling wave tubes (TWTs). The gun provides a current of up to 800 mA at a beam energy of 9.45 keV. Post acceleration is used to increase the energy up to the working range of 60 to 100 keV. The beam current of 800 mA is not sufficient to saturate the laser in a single pass within a reasonable distance. Therefore the laser is configured as an oscillator. A maximum liner length of 25 cm was chosen based upon numerical simulations of the output power as a function of liner length and total reflectivity of the cavity. Figure 3 shows an example of results of such a computer simualtion.

	figure 3. Calculated performance of the miniature Cerenkov FEL. Shown is the max output power and the required reflection coefficient to obtain that output power. Also shown is the dissipated power in the dielectric liner as a consequency the liner material having a non-zero tan Δ.

The radiation is separated from the electron beam by the outcoupler that extracts the radiation at right angles with respect to the propagation direction of the electron beam. The outcoupler also convert the waveguide geometery from cylindrical to the standard rectangular shape (WR19). The outcoupler is also designed to provide the required feedback for the oscillator and therefore acts also as the downstream mirror.
The expected tuning characteristics of the CFEL is shown in figure 4 for a liner material with a dielectric constant β_r of 5.8, an inner radius R_d of 1.5 mm and for different values of the thickness of the liner. This figure shows that a tuning range of 40 to 60 GHz can be obtained for different values of the liner thickness d_β. Optimisation of gain and dissipated power in the liner will eventually determine the thickness of the liner to be used in the laser.

	figure 4. Calculated operating frequency of the miniature Cerenkov FEL as a function of the total accelerating voltage and with the thickness of the liner dβ as a parameter.

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References:

H.P.Freund and T.M. Antonse, Jr, Principles of Free-electron Lasers, Chapman & Hall, 1996.
T.C. Marshall, Free electron lasers, Maxmillan Publishing, 1985.
Brau C.A., Free electron lasers, Academic Press, INC., 1990.
H. P. Freund and A.K. Ganguly, Nonlinear analysis of the Cerenkov maser, Phys. Fluids B 2 (10) 1990.
E.P. Garate and J.E. Walsh, The Cerenkov Maser at Millimeter Wavelengths, IEEE Transactions on Plasma Science, Volume PS-13, No. 6, December 1985.

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This research is funded in part by the EU, contract G5RD-CT-2001-00546.