JAERI-Conf 95-021

PB50
STUDY OF INFRARED FREE ELECTRON LASER OSCILLATORWITH TOHOKU LINAC
Bibo FENG, Toshiharu NAKAZATO, Masayuki OYAMADA,Shigekazu URASAW A and Tatsuya YAMAKAWA
Laboratory of Nuclear Science, Tohoku University, Sendai, Japan

Abstract
The performances of a free electron laser oscillator
based on Tohoku Linac are numerically analyzed with a
one-dimensional nonlinear theory. It is shown that theFEL can operate in wavelengths of infrared range and aradiation power of several megawatts can be obtained.
Some design parameters are discussed. The FEL basedon Linac has various applications for its advantages ofbroad spectral range, picosecond pulses and high peakpower.

(2)
whereK= eB,).. u

wavenumber,undulator parameter and YR

21tmc

the resonant energy factor given by the relation ofy~= 1 + K 2 ~ u . E, and <j>, describe, respectively, the"'r
2

1. Introduction
Since the first free electron laser (FEL) experiment
was achieved, the FEL has developed rapidly in last twodecades due to its advantageous characteristics of highpower, high efficiency and tunability of frequency 1•4l. In
FEL, a simple relationship of the radiation wavelength A,
with the undulator period A0 and electron energy factor yis A,=\12y. Thus the wavelength can be tunable bychanging the electron energy or undulator period, and theFEL, in principle, can operate in wavelength region of
millimeters to X-ray. The FEL based on a linac,
therefore, have attracted considerable interest inresearches and applications of biology, medical, materialand industry because it would be the only source capableof providing picosecond pulses of coherent radiation in
the infrared wavelengths. In this paper, a one:dimensional
nonlinear simulation mode is used to analyzed theperformances of a free electron laser oscillator with theTohoku Linac. It is shown that the FEL can operate inwavelengths of infrared range and a radiation power ofseveral megawatts can be obtained. Some design
parameters are also discussed.
2. FEL Equations
We consider that an electron beam transforms in aplanar undulator with constant parameter and exchanges
its energy with the radiation fields. For simplifying, we
consider one-dimensional case and use the approximate
condition of the slowly-varying field amplitude and phase.
The longitudinal motion of electrons (averaged over theundulator period) is described by the Lorentz factor yand the electron phase 'I' as 5 ·6)field amplitude and initial phase with respect to theelectron. J0 and J 1 are the Bessel functions of first kind.
The evolution equation for the radiation field with theelectron is described by Maxwell equations, where themoving electrons is used as transverse current density.
Assuming the condition of the slowly varying fieldamplitude and phase approximation, the evolution ofradiation field amplitude is governed by the following
complex partial differential equation,[JoC~l-Jl(~)J(exp(iiJrl: (3)'aa +J:.aa lE-2iKJ,.
E YRzct

0

where E=E,exp(i<j>,) is the complex field. The bracket( ···) indicates the average over all the electrons in a
volume V. J. describes current density of moving
electrons.
The Eqs.(l) and (2) describe the evolution of theelectron energy and phase. The Eq. (3) describes theevolution of radiation field amplitude, in space and time,
due to the interaction with electron beam. Theseequations are a set of self-consistent FEL equations fromwhich the general time-dependent, saturated behavior of
the radiation field can be described by numericallyintegrating these motion equations of the electrons andthe radiation field.
3. Numerical simulation
We focus our interest in the important case of an freeelectron laser oscillator with a linac. Because of thelimitation of electron beam current in linac, the gain in
the FEL is small for single pass of electron pulse and it
usually operates as an oscillator. The radiation-389-JAERI-Conf 95-021

electromagnetic wave, reflected by the two mirrors, thenback to the entrance of the undulator, can be repeatedly
amplified. The length of the cavity must be taken to keep
the electron bunch and radiation pulse synchronizing
when they enter the undulator field. Using theself-consistent one-dimensional FEL theory5>, theperformances of the infrared FEL oscillator with Tohoku
Linac are analyzed numerically.
The initial distribution of electrons in a bunch isassumed to have parabolic form in space and random
form in energy. According to the operation conditions ofTohoku Linac, an electron beam with energy of 32 MeV,energy spread of 0.5% are taken. The bunch length of 1.2mm, beam cross area of 2x2 mm 2 and peak bunch currentof 10 A are supposed, corresponding to current density of
2.5 106 Nm 2• The period and field amplitude ofundulatoris 4.0 em and 0.268 T, respectively, so the undulator
parameter K approximately equates to unit. The total
length of undulator is 240 em with respect to 60 periods.
The cavity length Lc must be chosen to satisfy thesynchronization condition nLb=2Lc, where ~ is thedistance between two electron bunches. The totalreflectance of the cavity is assumed as 98%. The FELparameters are summarized in Table 1.

10' 1~

10'2~

10' 3,.,u 10' ~4c.!!!

~

10'5u=
w 10'5 ~10'7 ~

10'"
1o·•
100

0200

300

400

Pass Number

Fig.l The Efficiency vs. pass number.

c"iii<!l10"'

1o- 2 ,_____J._

Table 1. The parameters of FEL oscillator
with Tohoku Linac.

__L._..L__L___.,L___L_

100

0200

___L_

300

_J400

Pass Number

Fig.2 The gain vs. pass number.
Accelerator
Type
Macropulse length
Macropulse repetition rate
Micropulse length
Macropulse repetition rate
Beam energy
Energy spread
Emittance
Macropulse current
Average current

Linac
3 !JS300Hz
3-4 ps2856 MHz
20-60 MeV
0.5%
45 mm mrad100-200 rnA
150 J..!A

1000
800~·;;;
c~"iii.!.!

a_600
400

02000Wiggler
TypePeriod
Number of periods
Wiggler parameter
Wiggler field

Planar permanent
4cm
60
1-20.268 TCavity
LengthMirror reflectance, M1M23m
99.9%
98.0%

Coherent Radiation
Wavelength
Power'---~L--L--L--~-~--~~-40-30-20-100102030

Normalized Frequency

Fig.3 Optical intensity vs. normalized frequency.

2 104010°~~~\~-"-'--'--'--'

10 J..IID-5MW-2-1.5-1-0.500.5

Normalized DistanceFig.4 Optical intensity vs. normalized distance.

-390-JAERI-Conf 95-021

Some typical numerical simulation results are shown
from figure 1 to 3. Figs. 1 and 2 show the relationshipof efficiency and gain of radiation field with theoscillation numbers of radiation pulse between thecavities. As shown in Fig.l, the efficiency of FEL
oscillator increases exponentially from noise under thepass number of 100. After that it gradually reaches tosaturation with a value of one percent. In the case ofelectron energy of 32 MeV, peak current of 10 A andassuming that the energies loss in electrons are transferred
totally to the radiation field, the laser output peak powerof several megawatt can be obtained, corresponding toaverage radiation power of several ten kilowatt. The gainof the FEL oscillator decreases approximately to the total
loss of the cavity at saturation, shown in Fig.2.
Fig.3 shows the dependence of optical pulse intensitywith the distance of (z-ct)/N0 ~, where the distance ismeasured as a relative point in the moving optical fieldand normalized the slip length N.~. From Fig.4 we cansee that the optical gain in the front part of the laser pulse
are relatively low, where is in the absence of electrons
due to the effective of slippage. Thus, in practically, theelectron pulses should be put enter the undulator slightly
earlier than laser pulses in FEL experiments.
The optical spectrum at saturated regimes is shown inFig.4, where the frequency, or more precisely
wavenumber, is normalized as N.~(k-kR). We can see
from this figure that the optical pulse gains in a relatively
wide spectrum and shifted down far from its .resonancevalue because of the low-energy electrons.
4. Conclusions
Based on above discussion and the operating
parameters of Tohoku Linac, it is possible to realize an
infrared free electron laser oscillator with this accelerator.
The parameters of the FEL are summarized in Table 1.
The FEL may be operating in the wavelength of infrared
regime and reach to the peak power of several, megawatt.
References
1. L.R. Elias, et al., Phys. Rev. Lett., 36, 717 (1976).
2. D.A.G. Deacon, et al., Phys. Rev. Lett., 38, 892(1977).
3. I. B. Drobyazko, et al., Proc. 11th Int. Conf. on FEL,Naples, FL, Aug 28- Sep 2, 1989.
4. T. J. Orzechowski, et al., Phys. Rev.Lett.54, 889(1985).
5. C. A. Brau, Free-Electron Lasers, (Academic Press,
New York, 1990).
6. N.M. Kroll, et al., IEEE J. Quantum Electron, QE-17,1463(1981).

-391-