JAERI-Conf 95-021

PB46
A NOVEL TECHNIQUE FOR CONSTRUCTINGA PLASMA MICRO-UNDULATOR
AND A COMPACT SOFT X-RAY SOURCETakashi IKEHATA, Yasuo SUZUKI t, Ryohji NAGAI t, Yoshiro SADAMOTO t,Naoyuki SATO, and Hiroshi MASE

Department of Electric and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, JapantDepartment of Reactor Engineering, Japan Atomic Energy Research Institute, Tokai, Ibaraki, Japan+Institute of Natural Science, Joetsu Institute of Education, Joetsu, Niigata, JapanAbstract
The plasma micro-undulator is a compact lightsource in which a relativistic electron beam radiates
in an oscillating electric field of the rippled ion-spacecharge instead of an oscillating magnetic field of conventional undulators. In the present paper, we propose a new method of creating the plasma microundulator: a combined technique of laser interference
and resonant photoionization, where the pitch anddensity of plasma ripples have been controlled separately by a laser alone. A preliminary design of theundulator with the pitch of 10-100 JLm, the numberof ripples of 10G-1000 and the undulator constant of
0.1-1.0 has been discussed.
1. Introduction
There has been a considerable attention to develop
a compact free electron laser (FEL) since it has many
advantages over conventional lasers, such as high output power and brightness, high conversion efficiency,
tunability over wide range of wavelength and long life,
all of which are quite important for applications. In
general, FEL consists of a magnetic undulator and a
Fabry-Perot optical resonator. In the magnetic undulator, permanent magnets whose polality changes
alternately are aligned periodically.When a relativistic electron beam is injected into the undulator along
the axis, it experiences a transversely oscillating force
and emits an intense electromagnetic radiation along
the beam path.
The wavelength of the undulator radiation /1/ isgiven by2Au- ( 1 +K)
A=2r22

2. Principle
Figure 1 explains the principle /4/. A wellcollimated laser beam at wavelength AL (wavenumberk = 27r / AL) and intensity 10 is divided into two halfintensity beams by a half mirror A and a full mirror
B. These beams interfere at the intersection with angle ¢ and create optical fringes. As is well known, thetotal intensity becomes
I = 10 [1 + cos ( 2kx sin~)] ,(3)(1)
and the pitch of fringes is given by the formula:where A is the wavelength of radiation, Au is thewavelength of undulator (pitch of magnets), 1 =(1 - ~: )- 1 / 2 is the relativistic factor and K is theundulator constant defined as

K = ecBoA~ = 93.4Au(m)Bo(T).
27rmocenergy. Since it has been difficult to make Au much
shorter than 10mm due to demagnetization of permanent magnets, a large accelerator has been required
inevitably to obtain shorter-wavelength radiations extending to visible or uv region.
Recently, an alternative concept, a plasma microundulator has been reported /2,3/, where a relativistic electron beam has been injected obliquely into
one-dimensional, plasma-density ripples. The electrons then experience a transversely oscillating electrostatic force (induced by the periodic ion-spacecharge distribution) during propagation in the ripples and emit undulation radiation. The plasma
micro-undulator has a potential of an extremely compact and short-wavelength FEL which is rather difficult by conventinal magnetic undulators. This paper proposes a new scheme for the formation of
the plasma micro-undulator: a laser-interference,resonant-photoionization scheme using a coherent,tunable laser. In particular, we discuss a preliminary
design of the undulator with Au = 1G-100 JLm, thenumber of ripples, N =100-1000, K = 0.1-1.0.

(2)

It is to be noted that A is proportional to the pitchof magnets and inversely proportional to the beam

d=~.
2sin

¥(4)

When a plume of neutral gas is introduced into thisregion, a plasma will be created by photoionization.
Since optical fringes correspond to a spatial modulation in the laser intensity and the plasma density
should increase in proportion to the laser intensity(without saturation), we can obtain plasma density-378-JAERI-Conf 95-021

ripples which are quite regular reflecting the coherence of laser. It is worth emphasizing that the pitchof ripples is controlled only by optical parameters, A£
and¢.
We have considered two photoionization schemes:
resonant ionization and tunnel ionization 15/. In resonant ionization, the laser wavelength has been tuned
to the energy level of a neutral atom. However, elements of interest have the ionization energy U; ofat least 5-10 eV (the minimum energy is 3.9 eV ofCs). So, the ionization occurs by absorbing two or
more photons. Shibata et al. 16,71 have developed
one-wavelength multi-step resonant photoionization
schemes:
Nd(U; = 5.52eV):
Gd(U; = 6.15eV):

441.96 nm
575.19 nm

two step,
three step,which use resonant metastable states. These schemes
should be most suitable for our purpose. Twowavelength schemes developed for laser isotope separation are also considered to be applicable. The
plasma created by resonant photoionization has quite
low temperature ( < 0.1 eV). This is an importantfeature because the life time of plasma ripples is predominantly limited by thermal expansion.
When a neutral atom is irradiated by an intenselaser beam of greater than 1014 W lcm 2 , its coulomb
potential barrier is strongly deformed and a boundelectron is liberated by tunnel effect. Tunnel ionization requires strong compression (focusing and bunching) of the laser pulse to achieve a high power density
above threshold. However, this leads to degradationin the periodicity of interference fringes. Therefore,
we conclude that resonant-photoioniz ation scheme ismore appropriate for our purpose.

is reasonable to assume K = 0.1-1.0. In addition, weemployed the following parameters: d = 10-100 J-Lm;
N = 10Q-1000; the length of undulator, L = N d =1 em; Nd plasma (two-step photoionization, A£ =441.96 nm). Since Lis comparable to the diameter oflaser beam, D, the effective volume of undulator, Vbecomes V:::::; L 3 = lcm 3 . From eq.(4), the interference angle ¢ required for d = lOJ-Lm and 100J-Lm are
2.5 deg and 0.25 deg, respectively (see also Fig. 2).
When a cost-effective 10 MeV (r = 21) linac is used,
we can cover wavelengths of 20-200 nm.
Finally, we examine the requirement for theplasma density and laser energy. Suzuki 181 calculated K for three types of electron beams: shortbunch (radius r0 , lengthl 0 « Au), long bunch (r 0 «Au "' lo) and uniform beam (ro, l0 < Au)· He showedthat the plasma density was proportional to KIA~and was about 2 x 10 16 cm- 3 for Au = 10J-Lm and2 x 10 14 cm- 3 for Au = lOOJ-Lm under K = 1.0. A
rough estimate of the laser energy should be given bynp VU;/rn where nP is the plasma density and 'f/L isthe efficiency of photoionization. When typical values, np = 1015 cm - 3 , V = lcm3 , U; = 5.52eV and'f/L = 0.1, we obtain 9 mJ. The latest pulse-dye-lasers
and solid-state-lasers will cover this energy without
difficulty. A schematic view of the system is shown inFig. 3.
There remain items to be further examined.
• Laser pulse length
The laser pulse length T£ must satisfy the condition:
L-c < T£ < Tr,

where Llc=30 ps. The life time of ripples, Tr is predominantly determined by thermal expansion as

3. A preliminary design

0.5dHere, we consider design parameters of the plasma
micro-undulator for a compact FEL. When plasma
density ripples are of the form:. 27r )
n = n 0 ( 1 + sm dx ,(5)an alternating force acting on a relativistic electron
beam injected at an angle () is given bynoI• ()cos() kuEo ex ku,
F = e2 n 0 cos kus · sm(7):!".
Tr::::T;+T,(8)M,For Nd plasma, Te < T; ::::: T0 (vaportemperature) :::::;
500K has been reported. This yields Tr = 30ns ford = 10J-Lm, so that eq. (7) is easily satisfied.
• Beam attenuation due to neutral collisions
Rutherford scattering is dominant. The attenuation
rate, flne I ne is estimated using the cross section of
Rutherford scattering, CJR to be:

(6)
(9)

where ku = k cos() = 27r I Au, Au = dl cos(), cos() =s · xl sx and s is the coordinate along the beam axis.
For typical()= 45 deg, it becomes Au = ,fid = 1.41d.
The performance of undulators is well characterized
by K of eq.(2). Since brightness of the undulator radiation is proportional to K 2 , small K leads to an
inefficient device, while too large K (K » 1 ; wiggler mode) causes quite large broadening in the radiation spectrum and increase in the emittance. So it

where 1 = 21(10MeV), the neutral density n 0 =3 x 1016 cm- 3 (1 Torr), L = 1cm, and scattering angleof 10- 2 rad are assumed.
• Repetition
Once the electron beam interacts with the plasma undulator, the plasma will break up. So, the repetition rate, f will be limited by the time for a plasma
with a flow velocity u 0 to traverse a distance D as-379-JAERI-Conf 95-021

f ~ u 0 / D. When u 0 ~ 1000m/s and D = 1cm, we
have f ~ 100kHz.
4. Application to a compact soft x-ray source
We showed above that a combination of a 10MeV linac and a 10-f.tm plasma undulator can generate soft X-ray radiation. However, the conventional
linac is too large to realize a table-top device. Recently, there has been a rapid progress in the development of plasma-based accelerators in which the interaction between a dense plasma and a ultra-shortpulse driver beam (laser beam or electron beam) generates strong accelerating fields of order of GeV /m.
For example, a LWA (laser-wake-field accelerator) experiment at KEK /9/ has demonstrated accelerationof electrons up to 18 MeV over a distance of 0.6 mm.
However, there has been a problem that diffraction
limits the laser-plasma-interaction distance to c::: 1r Z R(ZR : Rayleigh length) and optical guiding /10/ using
a parabolic plasma-density profile (plasma channel)
has been proposed. Our laser-interference, resonantphotoionization scheme will be useful to create plasmachannel too. Two sets of plasma density ripples created with intersection at 90 deg by four laser beams
form a bundle of square plasma channels /11/. It isclear that the density and diameter of plasma channel can be easily controlled by the laser intensity,laser wavelength and interference angle. A combinedlaser

half-mirror

system of LWA and the plasma micro-undulator isquite attractive because it has a possibility of making a table-top x-ray FEL. In the beginning, proof-ofprinciple experiments will be needed.
References/1/ H. Kitamura, Synchrotron Housya Riyou Gijutsu,
edited by T. Kohra, (Science Forum, 1989), pp.52-64 (inJapanese).
/2/ K.R.Chen, and J.M.Dawson, Phys. Rev. Lett., vol.68,
pp.29-32, 1992.
/3/ Y. Suzuki, Kakuyugo Kenkyu, vol.68, pp.488-502,
1992 (in Japanese).
/4/ T. Ikehata, Y. Suzuki eta!., JAERI-Research 95-028,pp.1-20, 1995 (in Japanese).
/5/ S. Augst et a!., Phys. Rev. Lett., vol.63, pp.22122215, 1989.
/6/ K. Ogura eta!., JAERI-M-90-162, pp.1-14, 1990 (inJapanese).
/7/ T. Shibata eta!., JAERI-M-94-025, pp.1-20, 1994 (inJapanese).
/8/ Y. Suzuki, JAERI-Research 95-009, pp.1-18, 1995 (inJapanese).
/9/ K. Nakajima et a!., Phys. Rev. Lett., vol.74 p.4428,
1995.
/10/ E. Esarey et a!., Phys. Fluids, vol.B5, p.2690, 1993.
/11/ Y. Suzuki and T. Ikehata, JAERI-Research 95-035,
pp.1-15, 1995 (in Japanese).

mirrorC~:I.=IO!lmB!

.....[VAG: 1.=1.064JlffiL_ ..... .

100::e.: 10electron beam

"0.s::£a:1~----~~«;·:96~;;;··-·r·T

lFig. 1.
Optical fringes byinterference of twolaser beams.

1.=370.94nm
0. 1 .. ""2"'3"4'5"6'"": ... '2"":i"4 56'"":.......2
10
100
Angle <jl (degree)

Fig. 2. Pitch d vs interference angle <j)TunableFig. 3.
A schematic view ofplasmamicro-undulator.

laser-380-