Download 2. PRINCIPLES OF OPERATION 2.1. Operation principle

the electrons, they will start to oscillate with
different frequencies because the gyrotron
frequency depends on the energy of the
electron. Hence the electron beam will form
phase bunches. For a small mismatch, when the
frequency of the electron oscillations is slightly
smaller than the frequency of the radiation
field, this bunch is formed in the decelerating
phase. Therefore, the bunch will give its energy
to the radiation field. The wavelength of the
generated radiation depends inversely on the
magnetic field strength. Technical limitations
on magnets limits the frequency to about 40
GHz when magnets at room temperature are
used. Superconducting magnets are required
to go to shorter wavelengths. Harmonic
operation is also possible but the efficiency is
much poorer for harmonics above the second.
Nevertheless, the Gyrotron has been operated
at sub-millimetre wavelengths and is capable
of generating an average power of close to a
megaWatt at millimetre wavelengths. The
tunability of these devices is limited.
The Gyrotron was one of the first devices
which used induced Bremsstrahlung to avoid
the restriction on the transverse dimension of
the interaction space, and therefore it is capable
of generating radiation at higher frequencies
and higher power levels. As the operating
frequency is determined by the strength of
the magnetic field used, the (superconducting)
magnets will eventually limit the maximum
obtainable frequencies. New schemes were
required to reach higher frequencies. It was
recognised that the Doppler effect can be
used to increase the operating frequency of
electron beam based radiation sources.13 The
first study making use of this Doppler shift
was done on an electron beam moving through
a static periodic magnetic field produced
by the so called undulator or wiggler.14 The
term Free-Electron Laser (FEL) for these
devices was introduced by Madey.15 At present
time, free-electron lasers have operated over
a considerable part of the electromagnetic
spectrum, from about 1 m wavelength16 down
to about 13 nm17.
2. PRINCIPLES OF OPERATION
2.1. Operation principle
In an FEL, electrons emit coherent radiation as
in a conventional laser. In a conventional laser
radiation is produced by a transition between
bound states of the electrons in the lasing
medium, whereas in an FEL it is produced
by free streaming electrons. Therefore the
radiation wavelength can span a much larger
range compared to conventional lasers as, in
a quantum mechanical picture, the electrons
radiate by transitions between energy levels in
the continuum. In principle, the description of
the FEL should require a quantum mechanical
description. However, except for the start-up
phase, the process can be completely described
by classical (electromagnetic) theory.
A large variety of FELs exist. They can
be distinguished not only with respect to
accelerator type but also with respect to
interaction mechanism. The latter can be
divided into Cerenkov FEL, Smith-Purcell
FEL and undulator FEL. These concepts are
shown in fig. 1. In this figure, b=v/c, c is the
speed of light in vacuum and v is the velocity
of the electrons, v=|v|, and g is the relativistic
factor, g2 = (1-b2). The total energy of the
electron is given by gmc2. The description in
this paper will focus on undulator FELs. The
other two devices are similar in many aspects.
The radiation is produced by an interaction
between three elements: an electron beam,
an electromagnetic wave with wavelength l
travelling in the same direction as the electrons
and a periodic magnetic field with period lu.
The periodic magnetic field, or undulator field,
induces a wiggling motion on the electrons.
The acceleration associated with this motion
produces the radiation. Therefore when
the electrons pass through the undulator
incoherent radiation is produced. This is the
mechanism employed in synchrotron light
sources. In order to produce coherent radiation
by stimulated emission it is necessary for the
electron beam to form coherent bunches.
Bunching is possible when a light wave copropagates with the electron beam through
the undulator as the spatial variations of the
Figure 1. Overview of different FEL
mechanisms: undulator FEL (a), SmithPurcell FEL (b) and Cerenkov FEL (c)
together with the tuning characteristic
(l is the radiation wavelength and g is
related to the beam energy).