Study of ultra-high gradient wakefield excitation
by intense ultrashort laser pulses in plasma
Hideyuki Kotaki1^*, Masaki Kando1, Takatsugu Oketa1, Shinichi Masudaf,
James K. Kogaf, Shuji Kondof, Shuhei Kanazawa1, Takashi Yokoyama1,
Toru Matoba* and Kazuhisa Nakajima^*'**
*The Graduate University for Advanced Studies, Hayama, Kanagawa, 240-0193, Japan
^ Japan Atomic Energy Research Institute, Kizu, Kyoto, 619-0215, Japan
**High Energy Accelerator Research Organization, Tsukuba, Ibaraki, 305-0801, Japan
Abstract. We investigate a laser wakefield excited by intense laser pulses, and the possibility of
generating an intense bright electron source by an intense laser pulse. The coherent wakefield
excited by 2 TW, 50 fs laser pulses in a gas-jet plasma around 1018 cm~3 is measured with a
time-resolved frequency domain interferometer (FDI). The results show an accelerating wakefield
excitation of 20 GeV/m with good coherency. This is the first time-resolved measurement of laser
wakefield excitation in a gas-jet plasma. The experimental results agree with the simulation results
and linear theory. The pump-probe interferometer system of FDI will be modified to the optical
injection system as a relativistic electron beam injector. In ID particle in cell simulation we obtain
results of high quality intense electron beam generation.
INTRODUCTION
Laser-driven plasma accelerators have been conceived to be the next-generation particle
accelerators, promising ultrahigh field particle acceleration and compact size compared
with conventional accelerators[l]. In particular, it has been experimentally demonstrated
that laser wake-field acceleration (LWFA) has great potential to produce ultrahigh field
gradients excited by intense ultrashort laser pulses of the order of ~ 100 GeV/m[2]-[9].
The maximum energy gain has exceeded 100 MeV with an energy spread of ~ 100%
due to dephasing and wavebreaking effects in the self-modulated LWFA regime, where
thermal plasma electrons are accelerated[8]. The highest energy gain acceleration which
exceeded 200 MeV was observed with the injection of an electron beam at an energy
matched to the wakefield phase velocity in a fairly underdense plasma[9].
In order to control the wakefield for the laser-plasma experiments, we need to measure the amplitude and the phase of the wakefield. A direct measurement of the plasma
density oscillation can be done by means of ultrafast time-resolved frequency domain
interferometry (FDI) [10]. Several measurements have been made with FDI to demonstrate wakefield excitation by ultrashort laser pulses in an underdense plasma[9],[ll][13]. These measurements have been done for a relatively low density plasma in a gas
filled chamber using laser pulse durations around 100 fs and pump peak powers less
than 1 TW. In these measurements the pump pulses were tightly focused to enhance the
plasma wave excitation due to 2D effects. In a 2D dominant regime, where the pulse
CP634, Science of Superstrong Field Inter actions, edited by K. Nakajima and M. Deguchi
© 2002 American Institute of Physics 0-7354-0089-X/02/$ 19.00
276
width is longer than a spot size, the radial wakefield is higher than the longitudinal one.
Therefore a shorter pulse is preferable to generate a more ID coherent planar wakefield
in the higher resonant plasma density. We have developed a pump-probe frequency domain interferometer consisting of a 2 TW pump laser pulse with a duration of 50 fs at
a wavelength of 800 nm and two frequency doubled probe pulses split from the pump
pulse with a variable delay. The measurement of laser wakefields has been made in a
less 2D dominated regime to suppress radial effects [14].
Recently novel schemes which use laser triggered injection of plasma electrons into
the wakefield have been proposed as an optical injection. Presently there are three major schemes: nonlinear wavebreaking injection[15], transverse optical injection[16], and
colliding pulse optical injection[17][18]. The colliding pulse optical injection, whose
energy spread is smaller than others, uses three short laser pulses. No proof-of-principle
experiment for these schemes has been yet performed because of experimental difficulties. In the optical injection schemes, provided that the probe pulses are replaced with
the injection pulses, the FDI system will be modified to the optical injection system for
the laser wakefield. We are planning to develop an optical injection system for LWFA
to generate an ultrashort electron beam with small energy spread and low transverse
emittance. We estimate the optical injection by ID particle in cell (PIC) simulation.
Here, we present the laser wakefield excited by the intense laser pulse and the generation of the high quality relativistic electron beam. In section II the gas density measurements of the neutral gas and the laser wakefield measurement is described. In section
III we present the simulation of the optical injection by using anomalous blueshift and a
pump-probe mechanism, and in section IV conclusions are presented.
OBSERVATION OF LASER WAKEFIELD
Measurement of gas density distribution
The gas density was measured with a Mach-Zehnder interferometer as shown in
Fig. 1. A gas-jet nozzle with an orifice diameter of 0.8 mm is placed inside a vacuum
chamber evacuated to 10~5 Torr. The interferogram is captured with a charge-coupleddevice (CCD) camera with an image intensifer. The opening duration of the gas-jet valve
was 2 ms and the gate time of the CCD camera was 5 jtis. The distribution of the gas
density can be calculated from the phase shift.
Figure 2 shows a contour plot of the He gas density distribution at a backing pressure
of 30 atm with a 1.6 ms delay. From measurements of nitrogen gas, it is found that
the gas density distribution is uniform 1.5 mm from the gas-jet nozzle. Since the gas
density is inversely proportional to the square of the distance from the nozzle and linearly
proportional to the backing pressure, the neutral gas density of He gas is « 3.6 x 1017
cm~3 at the pump laser focus with a backing pressure of 10 atm.
277
Beam Splitter
FIGURE 1. A schematic of the Mach-Zehnder interferometer for measurement of the gas density
distribution of the gas-jet.
1.2 ~
1.0 ~
1
0<g
I
0.6,
\
"
0.4 «
0.2 »
-0,5
0.0
r [mm]
FIGURE 2. A contour map of the gas density distribution of He gas at a backing pressure of 30 atm
with a delay time of 1.6 ms.
Measurement of wakefields
An intense ultrashort laser pulse produces a fully ionized plasma through optical field
ionization on ultrafast time scales of the order of femtoseconds and excites electron
density oscillations in the plasma behind the laser pulse. This plasma density oscillation
can be measured by the frequency domain interferometry technique[10] [14].
The experimental setup of the FDI is shown in Fig. 3. The multi-TW 10 Hz Ti: sapphire
laser pulse at a wavelength of 800 nm with a maximum energy of 135 ml and a duration
of 52 fs (FWHM) is split into two beams. The reflected beam (80 %) is used as the
pump pulse and the transmitted beam as the probe beam. The pump and probe pulses
are focused by an off-axis parabolic mirror with a focal length of 15 cm. The focal
spot images taken with a CCD camera show that the pump focused intensity profile is
approximately a Gaussian distribution with a rms radius (at l/e) <Jr = 8.9 jum, while
the probe beam radius is <jrpr = 3 jum and centered on the pump beam. The peak
278
pump intensity is 8.4 x 1017 W/cm2 (a0 ~ 0.6), producing fully ionized He gas in the
focal region. The probe beam is separated from the pump beam with a dichroic beam
splitter after passing through the plasma and guided through an optical fiber into the
spectrometer to analyze the interferograms. A part of the probe beam is sent directly
to the spectrometer to make the reference fringes. The spectrometer is a Czerny-Turner
type with a focal length of 1.33 m and a grating of 1800 gr/mm. The spectral resolution is
0.06 A. The phase shift at each position was obtained by averaging 50 shots of the phase
shift data to reduce pulse-to-pulse fluctuations. The gas jet was operated at a backing
pressure of 10 atm for He gas. The pump pulse was focused 1.5 mm below the end
of the nozzle where a fully ionized plasma was expected with an electron density of
7.2 x 1017 cm~3 from the neutral gas density measurements.
Figure 4 shows the results of the wakefield measurement. In the region where the
probe pulse was delayed after the pump pulse, a large amplitude density perturbation
excited by the pump pulse was detected as indicated by the phase shifts shown in
Fig. 4 (a). From the phase shift data, the period and the amplitude of the electron
density oscillation and the amplitude of the longitudinal wakefield are obtained as a
function of time delay between the pump and the probe pulses. The oscillation period
of the electron plasma wave is 130 ± 3.4 fs behind the pump. This plasma wave period
corresponds to the electron density of 7 x 1017 ± 8.5 x 1015 cm~3 in linear wakefield
theory, which is in good agreement with the electron density for the fully ionized He gas
expected from the neutral gas density measurements. The measured density perturbation
before damping is (8n/ne)m ~ 0.74 with the plasma length Lp = 1 mm. The maximum
longitudinal wakefield of 20 GV/m is deduced. These estimates are in good agreement
with the density perturbation (Sn/ne)th = 0.75 and the longitudinal wakefield of 21
GV/m calculated by linear wakefield theory.
We compare the experimental and the ID PIC simulation results. Figure 4 (b) shows
the amplitude of the longitudinal wakefields and the plasma wavelength as a function
of the plasma density. The solid line and the dotted line show the wakefield and wavelength from linear theory. Closed circles and triangles show the wakefields from the FDI
experiment and the PIC simulation. Open circles and triangles show the plasma wavelength from the FDI experiment and the PIC simulation. The experimental results and
the simulated results agree with linear theory.
GENERATION OF ELECTRON BEAMS FROM LASER-PLASMA
The wakefield excited in the gas jet has good coherency and can be used for particle
accelerators. This pump-probe interferometer system will be remade into a plasma cathode laser accelerator for high quality electron beam generation. In the plasma cathode
schemes, provided that the probe pulses are replaced with the injection pulses, the FDI
system will be modified to the optical injection system for the laser wakefield.
279
reference beam
probe beam
Delay Line 1
FIGURE 3. Experimental setup of the frequency domain interferometry. Delay line 1 adjusts the time
delay between two collinear probe pulses and delay line 2 the time delay between the pump and the probe
pulses.
1000
100
0
50
100
150
200
250
1017
300
1018
2L
g
1019
3
Time [fs]
Density [cm" ]
(a)
(b)
FIGURE 4. (a) The relative phase shift as a function of the time delay for the measurement of the
plasma density oscillation in the gas-jet operated at a backing pressure of 10 atm. (b) The amplitude of
the longitudinal wakefields and the plasma wavelength as a function of the plasma density as a function
of the plasma density. The solid line and the dotted line show the wakefield and wavelength from linear
theory. Closed circles and triangles show the wakefields from the FDI experiment and the PIC simulation.
Open circles and triangles show the plasma wavelength from the FDI experiment and the PIC simulation.
Trapping electrons in wakefields
Three laser pulses, a pump pulse for wakefield excitation and two injection pulses
for trapping the electrons in a plasma, construct a colliding optical injector[17] [18]. A
colliding pulse optical injection scheme for LWFA is proposed and analyzed that uses
280
three short laser pulses: an intense pump pulse (denoted by the subscript 0), a forward
going injection pulse (denoted by the subscript 1), and a backward going injection pulse
(denoted by the subscript 2). The frequency, wave number, and normalized intensity are
denoted by, respectively, CD-, kt, and at (i = 0,1,2). Furthermore, cOj = eo0 + Aeo (Ao) >0),
co2 — o)0, and o)0 <C Ao) <C cop are assumed such that k\ = &0 and k2 — —&0- The laser
pulse of injection 1 is the frequency up-shifted pulse by an anomalous blueshift[19]. The
pump pulse generates a fast wakefield. When the injection pulses collide, they generate
a slow ponderomotive beat wave with a phase velocity vp. The phase velocity vp is given
by
(Qi-CDi
AO)
During the time in which the two injection pulses overlap, a two-stage acceleration
process can occur; i.e., the slow beat wave injects plasma electrons into the fast wakefield
for acceleration to high energies.
Electron beam generation by colliding pulse optical injection
We simulated colliding pulse optical injection for the pump pulse laser strength
parameter of 1 and the injection pulses laser strength parameter of 0.3. The frequency of
the forward going injection pulse col is 6% blueshifted by the anomalous blueshift[19].
Figure 5 shows the results of the colliding pulse optical injection simulation for the
plasma density ne of 7 x 1017 cm~3. The graph on the left side shows y in phase space,
and the graph on the right side shows an energy spectrum. In the phase space graph,
the horizontal axis shows the position of the electrons. The length of 1 mm is 200
in the horizontal axis. In the energy spectrum, the vertical axis shows the number of
particles in arbitrary units, and the horizontal axis shows the normalized energy y, where
y = H/m^c2 and E is the total energy of electrons. The accelerated electrons for the
plasma density of 7 x 1017 cm"3 are shown in Fig. 6 (a). The accelerated electrons have
a pulse width of 14 fs, a peak energy of 7 MeV and an energy spread AE/E of 7%. The
accelerated electron charge becomes 26 pC when the laser spot size r is 15 jum.
The transvers J3s of the accelerated electrons are shown in Fig. 6 (b). The maximum
value is 0.019 and the angular spread of the electron is 19 mrad for a longitudinal j3 of 1.
The emittance of the accelerated electrons becomes 0.28 mm mrad when the laser spot
size r is 15 j
CONCLUSIONS
In order to investigate the laser-wakefield excited by an intense laser pulse in plasma,
we study the measurement of the laser wakefield and the optical injection by the laser
wakefield.
We made the first direct observation of coherent ultrahigh gradient wakefields excited
by an intense ultrashort laser pulse in a gas-jet plasma with a density around 7 x 1017
cm~3. The wakefield with the oscillation period of 130 fs and maximum longitudinal
281
141210-
-50
0
50
100
150
14
16
18
20
Position (200=1 mm)
FIGURE 5. Results of the three pulse optical injection simulation for the plasma density ne of 7 x
1017 cm"3 for the pump pulse laser strength parameter a0 of 1.0 and the injection pulses laser strength
parameter of 0.3. The graph on the left side are the y in the phase space, and the graph on right side are
histogram.
16.0-
15.515.014.514.013.513.0-
227.5
227.5
228.0
Posiotion (200 = 1mm)
228.0
Posiotion (200 = 1mm)
(b)
(a)
FIGURE 6. The accelerated electrons in a phase space (a) and the transverse speed of the accelerated
electrons (b) of the three pulse optical injection for the plasma density n e of 7 x 1017 cm~3 for the pump
pulse laser strength parameter aQ of 1.0 and the injection pulses laser strength parameter of 0.3.
amplitde of 20 GV/m was observed, showing fast damping in time from a few oscillation
periods to ten periods. These measured wakefield parameters are quite consistent with
the neutral gas density measurements and wakefield theory. The experimental results
are compared to a ID particle in cell (PIC) simulation. The experimental results and the
simulated results agree with linear theory.
We will develop an optical injection system for laser accelerators to generate high
quality electron beams using a gas jet and the pump-probe technique on a compact scale.
Three laser pulses, a pump pulse for a wakefield excitation and two injection pulses for
trapping the electrons in a plasma, make up a colliding optical injector. The problems
of optical injection, which are the frequency shift and the timing between the Spulses,
can be solved by the FDI system and the anomalous blueshift. For the three pulse optical
injection case, the energy spread is less than 10% at the energy of 7 MeV. The accelerated
electrons have the pulse width of 14 fs. When we make an assumption that the laser spot
radius is 15 jum, the accelerated electron charge and the emittance become 26 pC and
0.28 mm mrad, respectively.
282
ACKNOWLEDGMENTS
This work was supported by the JAERI-Kansai Advanced Photon Research Center. We
would like to thank to K. Nagashima, N. Hasegawa, K. Sukegawa, M. Suzuki, E. Yanase,
K. Yasuike, M. Nishiuchi and H. Daido for the help during the experiments.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
T. Tajima and J. M. Dawson, Phy. Rev. Lett. 43, 267 (1979).
K. Nakajima, D. Fisher, T. Kawakubo, H. Nakanishi, A. Ogata, Y. Kato, Y. Kitagawa, R. Kodama, K. Mima, H. Shiraga, K. Suzuki, K. Yamakawa, T. Zhang, Y. Sakawa, T. Shoji, Y. Nishida,
N. Yugami, M. Downer, and T. Tajima, Phy. Rev. Lett. 74, 4428 (1995).
D. Umstadter, S. -Y. Chen, A. Maksimchuk, G. Mourou, and R. Wanger, Science 273, 472 (1996).
D. Gordon, K. C. Tzeng, C. E. Clayton, A. E. Dangor, V. Malka, K. A. Marsh, A. Modena,
W. B. Mori, P. Muggli, Z. Najmudin, D. Neely, C. Danson, and C. Joshi, Phy. Rev. Lett. 80, 2133
(1998).
A. Modena, Z. Najmudin, A. E. Dangor, C. E. Clayton, K. A. Marsh C. Joshi, V. Malka, C. B. Darrow,
and C. Danson, IEEE Trans. Plasma Sci., 24, 289 (1996).
C. I. Moore, A. Ting, K. Krushelnick, E. Esarey, R. F. Hubbard, B. Hafizi, H. R. Burris, C. Manka,
and P. Sprangle, Phy. Rev. Lett. 79, 3909 (1997).
K. Nakajima, Nucl. Instr. and Meth. in Phys. Res. A410, 514 (1998).
T. E. Cowan, A. W. Hunt, T. W. Phillips, S. C. Wilks, M. D. Perry, C. Brown, W. Fountain,
S. Hatchett, J. Johnson, M. H. Key, T. Parnell, D. M. Pennington, R. A. Snavely, and Y. Takahashi,
Phy. Rev. Lett 84, 903 (2000).
K. Nakajima, Nucl. Instr. and Meth. in Phys. Res. A455, 140 (2000); H. Dewa, H. Ahn, H. Harano,
M. Kando, K. Kinoshita, S. Kondoh, H. Kotaki, K. Nakajima, H. Nakanishi, A. Ogata, H. Sakai,
M. Uesaka, T. Ueda, T. Watanabe, K. Yoshii, Nucl. Instr. and Meth. in Phys. Res. A410, 357 (1998);
M. Kando, H. Ahn, H. Dewa, H. Kotaki, T. Ueda, M. Uesaka, T. Watanabe, H. Nakanishi, A. Ogata
and K. Nakajima, Jpn. J. Appl. Phys. 38, 967 (1999).
E. Tokunaga, A. Terasaki, and T. Kobayashi, Opt. Lett. 17, 1131 (1992).
C. W. Siders, S. P. Le Blanc, D. Fisher, T. Tajima, and M. C. Downer, Phys. Rev. Lett. 76,3570 (1996);
C. W. Siders, S. P. Le Blanc, A. Babine, A. Stepanov, A. Sergeev, T. Tajima, and M. C. Downer, IEEE
Trans. Plasma Sci. 24, 301 (1996).
J. R. Marques, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon,
Phys. Rev. Lett. 76,3566 (1996); J. R. Marques, F. Dorchies, P. Audebert, J. P. Geindre, F. Amiranoff,
J. C. Gauthier, G. Hammoniaux, A. Antonetti, P. Chessa, P. Mori, and T. M. Antonsen Jr., Phys.
Rev. Lett. 78,3463 (1997); J. R. Marques, F. Dorchies, F. Amiranoff, P. Audebert, J. C. Gauthier,
J. P. Geindre, A. Antonetti, T. M. Antonsen Jr., P. Chessa, and P. Mori, Phys. Plasmas 5,1162 (1998).
E. Takahashi, H. Honda, E. Miura, N. Yugami, Y. Nishida, and K. Kondo, J. Phys. Soc. Jpn. 69, 3266
(2000); E. Takahashi, H. Honda, E. Miura, N. Yugami, Y. Nishida, K. Katsura, and K. Kondo, Phys.
Rev. E 62,7247 (2000).
H. Kotaki, M. Kando, T. Oketa, S. Masuda, J. K. Koga, S. Kondo, S. Kanazawa, T. Yokoyama,
T. Matoba, and K. Nakajima, Phys. Plasmas 9, 1392 (2002).
S. Bulanov, N. Naumova, F. Pegoraro, and J. Sakai, Phys. Rev. E 58, R5257 (1998).
D. Umstadter, J. K. Kirn, and E. Dodd, Phy. Rev. Lett. 76, 2073 (1996).
E. Esarey, R. F. Hubbard, W. P. Leemans, A. Ting, and P. Sprangle, Phy. Rev. Lett. 79, 2682 (1997).
C. B. Schroeder, P. B. Lee, J. S. Wurtela, E. Esarey, and W. P. Leemans, Phy. Rev. E 59,6037 (1999).
J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa,
H. Kotaki, and T. Tajima, Phys. Plasmas 7, 5223 (2000).
283