APPLIED PHYSICS LETTERS 90, 011502 共2007兲
Thomson scattering diagnostics of the plasma generated in a hollow anode
with a ferroelectric plasma source
D. Yarmolich, V. Vekselman, J. Z. Gleizer, Y. Hadas, J. Felsteiner, and Ya. E. Krasika兲
Physics Department, Technion, 32000 Haifa, Israel
共Received 31 October 2006; accepted 27 November 2006; published online 2 January 2007兲
Thomson scattering of a laser beam was applied to study the plasma parameters inside a hollow
anode having a ferroelectric plasma source incorporated in it. This method allowed avoiding
difficulties related to spectroscopical measurements in the case of unknown electron energy
distribution. It was found that the electron density and energy of the ferroelectric plasma
are ⬃1015 cm−3 and 艋5 eV, respectively, and the density of the hollow anode bulk plasma
is ⬃6 ⫻ 1013 cm−3. Applying an accelerating pulse for electron extraction from the bulk plasma
leads to an increase in the electron density and energy of the ferroelectric plasma up to
6 ⫻ 1016 cm−3 and 艋20 eV, respectively. © 2007 American Institute of Physics.
关DOI: 10.1063/1.2426886兴
Ferroelectric plasma source1 共FPS兲 has been used for
different applications, namely, as an electron source for generation of high-current electron beams,2,3 triggering of gaseous switches,4 microwave generation,5 ion acceleration,6
microthruster7 propulsion, and for heavy ion beam charge
neutralization.8 Also, recent experiments9–11 have shown that
using FPS one can ignite and sustain a hollow-anode 共HA兲
discharge with current amplitude of 艋1.5 kA and pulse duration of ⬃20 ␮s at pressure of 艋5 ⫻ 10−5 Torr. This FPSassisted HA plasma source served as a cathode in a diode
generating electron beam with amplitude of ⬃1 kA and electron energy of ⬃200 keV. A common important feature for
all these applications is the FPS surface plasma which is
generated at the ferroelectric surface under the application of
a driving pulse. However, the parameters of this plasma require additional research. Indeed, the analysis of spectroscopic data10 concerning plasma parameters required a preassumption of the electron energy distribution 共EED兲 which
is difficult to measure in non-Maxwellian plasma.11
The use of Thomson scattering allows one to avoid the
above drawback of the spectroscopic measurements and to
determine the plasma EED and density by analyzing the
scattered light spectrum and intensity.12,13 A pulsed
neodymium-doped yttrium aluminium garnet laser permits
application of this method for a plasma with density down to
ne ⬇ 5 ⫻ 1013 cm−3. Here let us note that in the case of
ne 艋 1017 cm−3 the light scattering due to collective plasma
effects is negligibly small.13 Thus one can describe light scattering in such plasma as Thomson light scattering by free
electrons. Here the electrons may have an arbitrary EED
which results in spectral broadening of the scattered photons
due to the Compton or inverse Compton effects. For a single
scattering the dependence of the photon frequency shift ⌬␻
on the electron momentum p is14
⌬␻ = −
c␻关p · 共n̂ − n̂⬘兲兴 + ប␻2共1 − n̂ · n̂⬘兲
mc2关1 + 共ប␻/mc2兲共1 + n̂ · n̂⬘兲 − p · n̂/mc兴
,
ity, and ប␻ is the incident photon energy. Thus, analysis of
the spectrally resolved scattered light allows one to obtain
the EED. In the case of an absolute scattered light intensity
calibration, one obtains also the plasma electron density.
The experimental setup used in the present research was
similar to the one described in Ref. 11. Namely, a HA with
incorporated seven identical FPSs was used. The application
of a driving pulse 共⬃2 kV, ⬃200 ns兲 caused plasma formation at each FPS front surface. Electron and ion flows emitted from the plasma initiated the HA bulk plasma discharge
by means of an additional pulse generator 共艋7 kV, 20 ␮s兲.
During the HA discharge, the FPS plasma was selfconsistently formed at the front surfaces of the FPSs. An
accelerating pulse 共⬃200 kV, ⬃300 ns兲 applied with a time
delay ␶d ⬵ 15 ␮s with respect to the beginning of the FPS
driving pulse caused extraction of electrons from the HA
plasma through the HA output grid.
To make available an optical access to the plasma, longitudinal slots were prepared in the HA electrode. The laser
beam 共SureLite laser, ␭ = 5320 Å, 0.2 J, and 8 ns兲 was collimated and focused at a distance of either d ⬵ 3 mm or
d ⬵ 5 mm from the central FPS front surface 共see Fig. 1兲.
After passing the HA, the laser beam was absorbed by a
graphite damper placed at the bottom of the vacuum chamber. Also, black velvet sheets placed at the HA wall were
used as “viewing dampers”15 in order to decrease the parasitic laser beam scattering inside the HA and vacuum chambers. The laser beam focus 共⬃1 mm in diameter兲 was im-
共1兲
where m is the electron mass, n̂ and n̂⬘ are the incident and
scattered photon directions, respectively, c is the light veloca兲
Electronic mail: fnkrasik@physis.technion.ac.il
FIG. 1. Experimental setup 共only the central FPS is shown兲.
0003-6951/2007/90共1兲/011502/3/$23.00
90, 011502-1
© 2007 American Institute of Physics
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011502-2
Yarmolich et al.
FIG. 2. Framing spectral images of the scattered laser beam: 共a兲 driving
pulse only, 共b兲 the HA discharge prior to applying the accelerating pulse, and
共c兲 during the accelerating pulse.
aged at a 250 mm imaging Chromex spectrometer 共600
groove/ mm grating兲 input slit using an achromatic lens. The
spectrometer resolution was 1.3 Å / pixel. The spectrometer
optical axis was perpendicular to the laser beam propagation
direction and to the FPS surface normal. The laser beam
polarization was perpendicular to the FPS surface 共see Fig.
1兲. Hence, the scattered light had the same polarization as the
laser beam. At the same time, the parasitic light was randomly polarized. Thus, a polarizer which transmits only perpendicular polarized light was placed in the front of the spectrometer slit in order to increase the signal to noise ratio. The
image of the spectral line profile at the output of the spectrometer was recorded using a 4Quik05A camera with frame
duration of 20 ns.
Already the first experiments without HA discharge
when only the FPSs were ignited showed that at ␶d = 15 ␮s
and d = 3 mm there was laser beam scattering by microparticles, whose generation accompanied the ferroelectric
surface discharge.16 In Ref. 16 it was shown that the mean
microparticle size and velocity are ⬃5 ␮m and
⬃6 ⫻ 103 cm/ s, respectively. For this case, which further
will be referred as case 共a兲, an example of the spectral image
of the laser beam scattering is shown in Fig. 2共a兲. In order to
obtain the image of the laser beam, a spectrometer entrance
slit width of 0.3 mm was used. Typical spectral framing images of the scattered light obtained during the HA discharge
prior to and during the accelerating pulse are shown in
Fig. 2共b兲 关case 共b兲兴 and in Fig. 2共c兲 关case 共c兲兴, respectively.
Also, with the same experimental setup, the mean backgrounds 共the 4Quik05A camera self-background and the
Appl. Phys. Lett. 90, 011502 共2007兲
background of the plasma light emission without the laser
during and without the accelerating pulse and the laser background, i.e., without the FPS and HA discharge兲 with statistical averaging over ten shots were obtained. All the spatially
resolved spectral images were transformed to spectral curves
by vertical summing of the camera pixel intensities. These
spectral curves are shown in Fig. 3 after the subtraction of
the corresponding backgrounds.
In case 共a兲 the spectral line is not broadened or shifted
because at ␶d = 15 ␮s and d = 3 mm, ne 艋 1010 cm−3.2 Thus
the obtained spectrum is related to the laser light scattering
by the microparticles.16 In cases 共b兲 and 共c兲, the spectra of
the scattered light showed significantly different features: the
peak intensity is increased and wings appear in the spectra.
These wings are related to the Compton shifted photons
which were scattered by the plasma electrons.
The absolute calibration of the Thomson experimental
setup was carried out using the laser beam Rayleigh scattering by nitrogen gas whose pressure was changed in the range
of 0.1– 5.5 Torr. The increase in the Rayleigh scattered light
intensity SR with the increase in the nitrogen pressure by
1 Torr was used to determine the electron density ne. The
ratio of the measured light intensity obtained in the Thomson
scattering ST and the Rayleigh scattering SR at the N2 gas
density of 3.5⫻ 1016 cm−3 is13
ST
n e␴ T
=
= 3.7 ⫻ 10−13ne ,
SR 3.5 ⫻ 1016␴R
共2兲
where ␴T = 6.65⫻ 10−25cm2 共Ref. 13兲 and ␴R = 5.1
⫻ 10−27 cm2 for ␭ = 5320 Å 共Ref. 17兲 are the Thomson and
Rayleigh cross sections, respectively.
Let us note that the increase in the intensity in case 共b兲 as
compared with case 共a兲 could be due to the increase in the
amount of microparticles. In order to avoid this uncertainty
and to obtain the EED, the averaged case 共b兲 spectrum was
normalized to the averaged case 共a兲 spectrum. Namely, the
intensities of case 共a兲 spectrum were multiplied by the ratio
of the areas of case 共b兲 and case 共a兲 spectra. Thus, the difference between the wings of case 共b兲 spectrum and the normalized case 共a兲 spectrum is due to the Compton shifted
photons. This Compton spectrum was transformed to the
EED using Eq. 共1兲 and the Rayleigh calibration
关see Fig. 4共a兲兴. Here it was assumed that the electrons possessing velocities parallel to the laser beam or to the observation directions give a major contribution to the Compton
wavelength shift. One can see that during the HA discharge,
ne ⬃ 2 ⫻ 1015 cm−3 and a major part of the plasma electrons
has energy 艋5 eV. The same analysis of the EED during the
accelerating pulse for case 共c兲 is shown in Fig. 4共b兲. In this
case ne increases up to ⬃5 ⫻ 1016 cm−3 and the major part of
plasma electrons increases its energy up to 20 eV.
It is reasonable to assume that during the first 150 ns of
the accelerating pulse, the amount of microparticles remains
FIG. 3. Spectrum of the scattered laser
beam: 共a兲 driving pulse only, 共b兲 HA
discharge prior to applying the accelerating pulse, and 共c兲 during the accelerating pulse.
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011502-3
Appl. Phys. Lett. 90, 011502 共2007兲
Yarmolich et al.
FIG. 4. HA plasma electron energy distribution: 共a兲 prior to applying the
accelerating pulse and 共b兲 during the accelerating pulse.
the same for cases 共b兲 and 共c兲. Thus the increase in the spectrum area for case 共c兲 could be explained by the increase in
ne by ⬃8 ⫻ 1016 cm−3 which agrees satisfactorily with the
previous analysis.
The same Thomson scattering experiments were carried
out at d = 15 mm where the plasma density is significantly
lower.10 To increase the system sensitivity, the width of the
spectrometer slit was increased up to 2 mm and the
4Quik05A camera magnification was set to maximum. Also,
a 150 groove/ mm spectrometer grating was installed. The
changes in the spectrometer setup resulted in spectral resolution of 5.2 Å / pixel and instrumental linewidth of 90 Å full
width at half maximum that did not allow us to observe the
Compton broadening of the scattered light spectrum. The
image was obtained as a result of summing up of 20 shots in
order to increase the resulting intensity. It was found that
microparticles already appear also at this distance when
␶d 艌 5 ␮s. With the increase in ␶d the amount of microparticles increases significantly. Thus one can conclude that a
small amount of microparticles acquires velocities up to
3 ⫻ 105 cm/ s. Analyzing only the horizontal lines of the images without the microparticle spots, it was found that the
intensity of the scattered light in cases 共b兲 and 共c兲 exceeded
the intensity in case 共a兲. The latter allows one to estimate the
HA bulk plasma density as ⬃6 ⫻ 1013 cm−3. During the ac-
celeration pulse, the statistical error in the density measurements did not permit us to confirm the density changes.
To summarize, it was shown that the application of Thomson scattering diagnostics with pulsed laser, imaging
spectrometer, and intensified framing camera allows one to
improve significantly the time and space resolutions, to avoid
difficulties related to spectroscopic data analysis in the case
of non-Maxwellian EED 共Ref. 11兲 and to obtain in a single
shot ne 艌 4 ⫻ 013 cm−3 and EED for ne 艌 1014 cm−3. It was
found that the ferroelectric surface plasma during the HA
operation is characterized by ne ⬃ 1015 cm−3 and electron energy 艋5 eV prior to applying the accelerating pulse. During
the accelerating pulse, the FPS surface plasma density increases up to ⬃共3 – 6兲 ⫻ 1016 10−3 and the electron energy
increases up to ⬃20 eV. The obtained increase in ne and in
the electron energy of the FPS plasma could be related to the
increase in the HA plasma potential10 during the accelerating
pulse. The latter leads to an increase in the energy of the HA
bulk plasma ions whose bombardment causes formation of
the surface plasma.
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