Experimental Observation of Radiation from
Cerenkov Wakes in a Magnetized Plasma
Noboru Yugami, Takeshi Higashiguchi*, Davoud Dorranian, Hiroaki Ito and
Yasushi Nishida
Dep. of Energy and Environmental Science, Graduate School of Utsunomiya University
7-1-2 Yoto, Utsunomiya Tochigi, Japan,
* Dep. of Electrical and Electronic Engineering, Miyazaki University,
1-1 Gakuen Kibanadai Nishi, Miyazaki, Miyazaki 889—2192, Japan
Abstract A proof-of-principle experiment demonstrates the generation of the radiation
from the Cerenkov wake excited by a ultra short and ultra high power pulse laser in a perpendicularly magnetized plasma. The frequency of the radiation is in the millimeter range(up to
200 GHz). The intensity of the radiation is proportional to the magnetic field intensity as the
theory expected. Polarization of the emitted radiation is also detected. The difference in the
frequency of the emitted radiation between the experiments and theory can be explained by
the electron oscillation under the electric field created by ions in the focal regeion.
1
Introduction
In the last decade, the phenomena of frequency up-shift of electromagnetic waves and
the generation of short pulse radiation have been experimentally [1] and theoretically investigated [2]. Photon acceleration using a relativistic ionization front has been studied by
Mori [3]. In this scheme, the ionization front propagating relativistic velocity (~ c) interacts with a counter-propagating electromagnetic wave (probe wave) and the frequency of
the probe electromagnetic wave is up-shifted. This phenomenon takes place not only at the
overdense ionization front but also at the underdense ionization front. The ionization front
generated by laser has successfully interacted with an existing microwave and its frequency
increased from 35 GHz to over 170 GHz [4,5]. Mori et al have shown that the frequency upshift occurs by the interaction between a static electric field and an ionization front [6]. This
means a direct electromagnetic wave generation from the static electric field. Lai et al have
reported this phenomenon using a high-power short-pulse glass laser system and observed
emitted radiation in the microwave region [7].
Recently Yoshii et al. have proposed new mechanism in which the short electromagnetic
pulse is radiated by the interaction between a laser wake field or short electron bunch and
a static magnetic field [8]. In the magnetized plasma, the wake field has both electrostatic
and electromagnetic component. Furthermore, the magnetized wake field has nonzero group
velocity. This enables the wake to propagate through the plasma and couples radiation into
the vacuum. This phenomenon is called Cerenkov wake and the emitted frequency of the
radiation is expected to be close to the plasma frequency when the laser is irradiated in the
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
341
underdense plasma. The theory expects the production of GHz to THz radiation at power
approaching GW level by using the wake field excited by the current laser system and appropriate magnetic field.
In this paper, we report, to our best knowledge, the first proof-of-principle experiment
demonstrating the generation of the radiation from the Cerenkov wake excited by an ultra
short and ultra high power pulse laser in a perpendicularly magnetized plasma.
2 Theory of Cerenkov wake
The geometry of the radiation scheme demonstrated here is simple. A short pulse of ultra
high power laser beam propagates in the z direction and a dc magnetic field exists in the y
direction. After the propagation of the laser pulse, the wake field is excited behind it and
couples with the magnetic field and the radiation is generated. To understand the expected
radiation, we consider the dispersion relation diagram of the electromagnetic wave in the
magnetized plasma. In the unmagnetized plasma, the dispersion relationship for the electromagnetic wave, a)2 = a)2p + c2k2 can not couple with the disturbance which propagates with
the velocity, vg, where cop and vg are the plasma frequency and the group velocity of the laser
pulse in the plasma and vg is less than the speed of light c. However, the addition of the
applied magnetic field alters the scenario. In the magnetized plasma, two branches(lower and
higher of the extraordinary (XO) mode) appear in the dispersion relationship of the electromagnetic wave. The intersection of the lower dispersion curve and the disturbance excited
by the laser beam(o> = vgk) shows the excitation of the radiation. In the underdense plasma,
vg « c, the intersection appears at aj « cop. Therefore, resultant radiation of frequency of
a) « o)p is expected. Here, the group velocity of the radiation is Vg = doj/dk = (o%/afyc,
where coc = eBo/mc is the cyclotron frequency of the electron and co^ is the upper hybrid
frequency defined as o)2h = o)2p + o%. In this case, according to the Cerenkov condition, the
almost of the radiation power is emitted in the forward direction, i.e. z direction.
3
Experiments
Figure 1 shows the experimental setup and measurement system for the observation of
the emitted radiation from the Cerenkov wake. The dc magnetic field in the y direction is
generated by the permanent magnet and its field strength is varied from 0 to 6 kG. A 10
Hz Ti:Sapphire laser beam at a wavelength of 800 nm, with a maximum energy of 100 mJ
and a duration of 100 fs [full width at half maximum(FWHM)], is used for the wake field
generation. The laser beam is focused by a f / 5 lens at the region where the static magnetic
field is applied. The focal spot diameter is less than 20 //m and its maximum intensity is in
the order of 1017 W/cm2.
After the vacuum chamber is evacuated by a turbomolecular pump below 10~5 Torr, it is
statically filled with nitrogen or argon gas, as a working gas and the maximum pressure was
342
Window
Magnet
Pairs
Ma
net Pairs
II
9
—P!
A-^l" *Laser
Laser Pulse
Pulse
IF7
Lens:
Lens: f = 150
150 mm
Window
Window
X_
Grating
Grating
Radiation
7
Beam Damp
z
Receiver
y
Intensity (normalized units)
Fig.l : Experimental setup
Fig.1
1
0.8
0.6
200 ps
0.4
0.2
0
-2
-1
-1
o0
1
1
2
Time (ns)
Fig. 2 :: Typical Waveform of radiation
Torr. When
When the
the high
high intensity
intensity laser
laser beam
beam is
is focused,
focused, the ionization by tunnel ionization
11 Torr.
process is
is expected
expected to occur.
process
In order
order to
to measure
measure the
the emitted
emitted radiation,
radiation, we
we used
In
used two
two methods;
methods; one
one was
was the
the combination
combination
of
the
waveguide
and
horn
antenna
for
temporal
evolution
of
radiation
waveform,
of the waveguide and horn antenna for temporal evolution of radiation waveform, other
otherisisthe
the
spectrum
measurement
using
the
grating
with
15
0.5
cm
grooves
and
blazed
with
30
spectrum measurement using the grating with 15 0.5 cm grooves and blazed with 30 degrees
degrees
angle. In
In the
the both
both experiments,
experiments, the
the radiation
angle.
radiation was
was detected
detected by
by aa crystal
crystal detector.
detector. The
The angle
angle
between
an
emitting
horn
antenna
and
a
receiving
one
is
kept
constant
while
the
between an emitting horn antenna and a receiving one is kept constant while the grating
grating isis
rotated.
rotated.
Figure 22 shows
shows the
the typical
typical output
output signal
signal with
Figure
with the
the duration
duration of
of 200
200 ps(FWHM).
ps(FWHM). Here,
Here, the
the
microwave
detection
system
consists
of
31.4
GHz
waveguide
and
horn
antenna
combinamicrowave detection system consists of 31.4 GHz waveguide and horn antenna combination with
with the
the microwave
microwave detector
detector of
of time-resolution
time-resolution of
100 ps
tion
of 100
ps displayed
displayed on
on the
the oscilloscope
oscilloscope
(Tektronix type
type ;; TDS-694C)
TDS-694C) with
with the
the analog
analog frequency
(Tektronix
frequency band
band width
width of
of 33 GHz.
GHz. The
The applied
applied
_1.2
&
c
1 S(5 GHz' ' '199 GHz' -i
(270 mTorr)M(80 mTorr);
i
| 0.6
179 GHz
(40 mTorr) |
&
104 GHz
I 0.2
0
r
50
116 GHz
°11
-W'A* . . i jflgj . .*u • ?^- ± 1
100
150
200
250
Frequency (GHz)
Fig. 3 : Spectrum of radiation
magnetic field is 6 kG and gas pressure of nitrogen is 270 mTorr.
The radiation duration, r, is estimated by the damping of wake filed, when the damping is
strong. In the case of weak damping, however, the duration is defined by the cycles of the
wake field in the plasma, N, and the group velocity of the radiation, Vg, in the plasma, i.e., [8]
2nNc
-L.
c <
(1)
where Lp is the length of plasma. In our experiments, the plasma is weakly magnetized,
0.01, i.e. a?p
, this equation is approximately written as,
(2)
In our experimental conditions, the time-scale of the damping of the wake field may be estimated in the order of 10 ps and the length of the plasma, Lp will be given by the order of
the Rayleigh length ZR [9]. The estimated Rayleigh length by the optical parameters of our
experiments is 1.6 mm and the expected pulse duration of the radiation is calculated to be
700 ps. Although the experimental value is in the same order of the theoretical one, precise
density measurement is required for our future experiments.
Figure 3 shows the frequency spectrum of the radiation measured at nitrogen pressures
of 60, 120 and 270 mTorr(denoted by solid circles) and argon pressures of 40 and 80
mTorr(denoted by open circles), leading to center frequencies of 104 and 116 GHz(in the
m = 1 order) and 179, 195 and 199 GHz (in the m = 2 order). Intensity is normalized by
the maximum value of each gas. The incident wave is s-polarized and the signal is observed
in the m = 1 and m = 2 reflection orders of the grating spectrometer. In this experiment,
frequencies under 120 GHz are observed in the m = 1 order and frequencies from 120 to 240
344
1.2
1
0.8
0.6
0.4
0.2
-90
-60
-30
0
30
60
90
Angle (degrees)
Fig. 4 : Polarization of Radiation
GHz are observed in the m = 2 order. The crystal detector of response in flat under 250 GHz
and decays over 250 GHz. We observed radiation signal in higher gas pressure, however,
we cannot determine the frequency of the radiation. Higher signal intensity is observed at
higher gas pressure. This is expected from ID unmagnetized plasma theory [10] that the
excitation of strong longitudinal electric field of the wake filed is expected. Plasma density
corresponding to the frequency of 200 GHz is 4.9 x 1014 cm"3. Nitrogen gas is expected
to be 5 times ionized by the laser pulse, that is, the plasma density of 4.5 x 1016 cm"3 is
expected. Therefore the detected frequency of the radiation to is approximately cop/5. We
will explain this discrepancy bellow.
The emitted radiation is expected to be polarized in the x direction, i.e. vertical to the
dc magnetic field. The polarization is measured by rotating the microwave horn antenna
around the z axis. The signal is detected by the 31.4 GHz cut-off waveguide and the horn
antenna. Figure 4 shows the relationship between the electric field of the emitted microwave
and the angle of the antenna. The each data is normalized by the maximum value at 9 = 0
degree. Here, the gas pressure of nitrogen is 270 mTorr and the static magnetic field is 6 kG.
The polarization angle of zero degree meets with the x direction. The solid line indicates
the electric field distribution cos2 0 which is assumed that the tiny dipole antenna with a
current propagates in the z direction. As the electric field of electromagnetic (EM) wave is
proportional to cos 0, the observed signal intensity should be proportional to cos2 0, because
the crystal detector detects the power of the EM wave. The data is fairy good agreement
with the assumption. Therefore, these data mean that the observed radiation is emitted by the
Cerenkov wake.
The direction of the emitted radiation is also measured(not shown here). The distribution
angle of radiation is ±5 degree in the forward direction. Therefore the Cerenkov radiation
condition is satisfied.
345
40i i • • • i • • • i '
30
i
Exp.
1,20
°" 10
w
0
2
4
6
8
Magnetic field strength (KG)
10
Fig. 5: Radiation Power vs. Magnetic field
The theory gives the output power p of the emitted radiation
^ r2 fe) fr'
(3)
where Ez and F is the longitudinal electric field of the excited wake field and the damping
factor of the radiation at the plasma-vacuum boundary, respectively [8]. The longitudinal
wake field can be estimated from the ID unmagnetized plasma theory and its value is calculated to be 2.0 x 105 V/cm. The damping factor F is calculated when a linear plasma density
with a ramp length of L is assumed, and is given as F = eaLa)plc, where a is called damping
coefficient which is a function of a)cla)p. Figure 5 shows the output power of the radiation
as a function of the applied dc magnetic field. The power of vertical axis is in arbitrary unit,
because whole of the measurement system is not calibrated to the power of the radiation. The
circles with error bars and dotted line indicate the experimental results and the theoretical
value given by above model which takes the damping phenomena at the boundary into account. The length L is assumed to be 2 mm in our experiments. The dependence of the output
power on the dc magnetic field is in good agreement on the theory. The detail of structures
in the data cannot be explained so far. Even if no magnetic field is applied, weak signal is
detected. This might be caused by the radiation due to nonlinear current which has been
reported by Hamster et al [11].
The theory predicts that the frequency of emitted radiation is equal to the plasma
frequency(o> ~ a)p\ however, the frequency of the radiation in the experiments is much
lower than that of expected value(o> ~ a)p/5) as stated above. This discrepancy can be
explained by the taking the radial oscillation of electrons into account. At the focal region of
laser beam, the extreme ponderomotive force on the plasma can expel the plasma electrons
and remaining immovable ions create the radial electric field. The electron obeys the
equation of motion,
2
ffir
A
2w
m—2 = -4nn0e —,
dt
r
346
where w is focal radii of laser beam. In our experimental condition, the skin depth c/a)p
is lager than the spot size, therefore, the electric field can influence outside of the plasma
column and electrons oscillate by this electric field. The frequency of the electron oscillation
can be obtained by the integration of the above equation,
where VQSC is the maximum oscillation velocity of electron which is initially accelerated by
laser ponderomotive force. Finally, we can obtain the scale equation,
^Kv~Jp
y
osc.
where 2nfp = a)p. This formula indicates the frequency of the oscillation is proportional to
the focal size of laser beam. Numerical calculation using our experimental values result that
the emitted frequency of radiation is a)p/5 ~ a)p/4. The detail PIC simulation results will be
published in anywhere. [12]
Further work is required to obtain the plasma density along the laser propagation and the
electric field of the longitudinal wake field. In higher density experiments, higher frequency
radiation is expected. Therefore, a direct measurement of the radiation electric field will be
required for the precise frequency measurement by using such as EO(electro-optical) sampling method. Use of supersonic gas jet valve may be appropriate for the creation of the
sharp boundary plasma-vacuum interface and highly efficient extraction of the radiation energy from the plasma to vacuum.
We have verified the physical mechanism of generation of radiation from Cerenkov wake
field. In the present experiment, the maximum radiation frequency of 200 GHz is detected
by varying the gas pressure. The relative power of the signal is measured to scale with the
square of the dc magnetic field strength. The results support the potentiality of developing
high-power, tunable and short pulse coherent radiation source with the frequency ranging
from microwave to THz radiation.
Acknowledgments
A part of the present work was supported by a Grant-in-Aid for Scientific Research from the
Ministry of Education, Science, Sports and Culture, Japan. One of the authors (T. H.) is also
grateful to the JSPS Research Fellowships for Young Scientists. We also are grateful to Cooperative Research Center, and Satellite Venture Business Laboratory (SVBL) of Utsunomiya
University for providing us the laser system.
347
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