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Description  |
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BACKGROUND OF THE INVENTION
This invention relates to a method for the determination of the density
distribution of gas phase constituents in a plasma. The term "plasma" as
employed in the instant application means an ionized gas which contains
equal numbers of ions and electrons.
In particular the invention relates to a method for the determination of
the density distribution of gas phase constituents of a plasma existing in
an operating discharge lamp.
The method of the invention is particularly useful for the determination of
the density distribution of mercury (H.sub.3) present in the plasma of an
operating high pressure metal vapor discharge lamp.
The determination of the density distribution of the gas phase species in a
plasma is important in understanding the chemistry of the plasma and
thereby enhances the ability to improve the quality of the plasma.
Also, in many types of plasmas present in high density discharge lamps, the
temperature distribution in such plasmas may be readily determined from
its density distribution by the use of the gas laws. Knowledge of the
temperature distribution in a plasma is also highly useful in
understanding the chemistry of the plasma.
The density distribution of species in the plasma existing in an operating
discharge lamp particularly a high pressure metal vapor discharge lamp,
affects its efficacy, color rendition and useful life.
Thus, knowledge of the density distribution of the species present in a
discharge lamp plasma is a key to the optimization of the design of the
lamp. Additionally, the temperature distribution of the plasma which
critically affects the operation of the lamp, may also readily be
determined from the density distribution by employing the gas laws.
Attempts have been made to measure the temperature distribution in the
plasma in a discharge lamp by means of optical methods.
These methods, such as described in H.S. Rothwell, Jr. et al J. IES Oct.
1980, pp. 40-46 and J. F. Waymouth, Electric Discharge Lamps, First
Edition, M.I.T. Press, Cambridge, Mass., 1978, pp. 155 and 160-165 rely on
an analysis of the emission spectra produced by operating lamps. These
methods suffer from the defects of being undesirably slow and of being
based on an assumption (among others) that the plasma in the operating
lamp is axially symmetric. However, this assumption is not correct when
the lamp is operated in a horizontal position.
In addition, by use of optical means it is not possible to obtain the
temperature of the plasma near the wall of the plasma-containing tube but
only in the luminous region of the arc.
BRIEF SUMMARY OF THE INVENTION
An object of the invention is to provide an improved method for determining
the density distribution of species in a plasma. This and other objects of
this invention will be apparent from the description that follows.
According to the invention a new and novel method of determining the
density distribution in a plasma comprises scanning a cross section of the
plasma with an X-ray computerized tomographic scanner (CAT scanner) to
determine the attenuation of x-radiation along a plurality of lines in the
scanned section of the plasma and generating and recording a series of
transmitted intensity values. Such values can be obtained at different
angular displacements of the X-ray beam relative to the plasma. By use of
tomographic reconstruction algorithms it is possible to transform the
values so obtained into a map of density at points within the scanned
cross section.
BRIEF DESCRIPTION OF THE DRAWING
In the drawing:
FIG. 1 is a schematic of a horizontally oriented high intensity discharge
(HID) lamp positioned in a CAT scanner employed in carrying out the method
of the invention,
FIGS. 2, 3 and 4 are photographs of reconstructed images obtained from a
display of the CAT scanner during various stages of operation of the HID
lamp.
DETAILED DESCRIPTION OF THE INVENTION
The use of an absorption of a beam of X-rays passing along the axis of a
carbon arc in air to determine the gas density and from that the
temperature on the arc axis is described in von Engel and Steinbeck,
Siemens-Veroff 10, 155 (1931). Application of this method to an Hg arc is
described in Kenty and Karash, Phys. Rev. 60, 66 (1941) and Phys. Rev. 78,
625 (1950). These methods are limited to providing information only of the
axial temperature and density and additionally require specifically
designed arc tube constructions to perform the measurements.
By employing the CAT scanner according to the method of the invention it is
possible to obtain gas density and temperature profiles within a desired
cross-sectional area of a plasma and particular of the plasma present in a
high pressure discharge lamp. By use of a CAT scanner according to the
method of the invention the following two fundamental advantages over the
previous attempts to employ X-ray methods for lamp diagnostics are
achieved:
1. The method can be applied to ordinary commercial lamps without
modification. This is important because one cannot modify the geometry of
such lamps without significantly affecting their operating
characteristics.
2. The method provides a means for directly obtaining spatially localized
density and temperature information within the arc tube. This localized
information, which is important in the area of lamp diagnostics, cannot be
readily obtained by other means.
In carrying out the method of the invention the arc tube of an operating
discharge lamp is positioned within the CAT scanner so that the plane of
X-rays defined by the CAT scanner coincides with the plane of the lamp in
which the density is to be measured. Thus, if the lamp is horizontally
positioned and one is interested in measuring the density profile of the
cross sectional plane in the middle of the lamp, the CAT scanner is
positioned so that a vertical X-ray scan is performed through that plane.
In the case of a high pressure Hg lamp, the X-ray intensity measured by
each detector of the CAT scanner will be
I.sub.T =I.sub.o exp (- .sub.1 .alpha.(x, y,z)dl)
where I.sub.o is the initial intensity of the X-ray beam, I.sub.T is the
intensity at the detector, 1 is the path length of the X-ray beam,
.alpha.(x,y,z) is the absorption coefficient at position (x,y,z) and the
integration is performed along the path of the X-ray beam. For atomic or
molecular absorption .alpha.(x,y,z)=n(x,y,z).sigma.(E), where .sigma.(E)
is the absorption cross-section for that species at an X-ray energy E and
n(x,y,z) is the corresponding species density. As is seen, under fixed
experimental conditions, the absorption coefficient is directly related to
the species density being measured. In the case of a high pressure Hg lamp
the dominant gas phase species during the operation of the lamp is Hg and
the small amount of the inert gas present to initiate the discharge does
not contribute in any significant extent to the X-ray absorption compared
with that contributed to by the Hg.
In the method of the invention data consisting of transmitted X-ray
intensity measurements along many different lines within a desired plane
in the lamp and measured by an array of detector elements of the CAT
scanner is fed into a computer portion of the CAT scanner where a
reconstruction algorithm appropriate to the scan geometry is employed to
generate a series of density values each value corresponding to a point in
the scanned section of the lamp. The generated series of density values is
fed to a display portion for example a cathode ray tube where an image
consisting of a matrix of pixels to each of which is ascribed a numerical
value corresponding to the absorption coefficient of the X-ray image at a
particular point and thereby the gas phase density of a point in the tube
associated with the pixel.
By this method a qualitative density scale of a cross-section of the plasma
in the tube is obtained.
The numerical values obtained can be absolutely calibrated to known
densities by repeating the measurements with a Hg filled vessel containing
an excess of mercury and heated to a known temperature. Under these
conditions the vapor pressure is determined by the temperature of the
liquid and the temperature can readily be measured. By measuring the gas
volume of the vessel and by use of the gas laws the density can readily
calculated. In this manner each pixel value can be associated with an
absolute value of mercury density.
Upon obtaining the density profile, the spatially resolved temperature
profile T(x,y,z) can be obtained by the use of the gas law:
T(x,y,z)=P/kn(x,y,z) where P is the pressure within the arc tube of the
lamp and k is the Boltzmann constant.
Since the absolute value of the pressure within the tube is not known it is
necessary to calibrate the temperature at one point to absolutely
determine the temperature within the profile. This is generally done by
measuring the arc tube wall temperature with a pyrometer.
The magnitude of the X-ray absorption generally scales as .sup.2, where
is the atomic number of the elements. Thus Hg has as a much higher
absorption cross section than Na. As the position of the characteristic
absorption edges are different for different elements these edges can be
used to discriminate between elements where a number of elements are
present in a plasma in which each makes measurable contributions to the
absorption, as will be illustrated below.
While the method of the invention is applicable to the measurement of any
gas phase plasma species which exhibits sufficient X-ray absorption, as a
practical matter it is most useful for measurement of discharge lamps such
as high pressure mercury lamps, metal halide lamps and high pressure
sodium lamps.
High pressure mercury lamps are filled with mercury and several tens of
Torr of a rare-earth starting gas. Generally only mercury will contribute
to the measurable absorption.
Metal halide lamps are filled with mercury and small quantities of a metal
halide salts as well as rare-earth starting gases. Again the dominant
species is mercury and followed by a much lesser amount of iodine. Since
iodine also is a high element it may contribute to a small but
measurable absorption depending upon the sensitivity of the detection and
electronics in the CAT scanner used. It is possible to distinguish between
mercury and iodine by doing measurements at X-ray energies on either side
of a characteristic absorption edge. The species whose absorption edge is
bracketed by the two energies will exhibit distinctly different absorption
at those energies while the other species will show little change in
absorption at the two energies.
The absorption of the species which shows little change in absorption can
be subtracted out as a "constant" background, leaving absorption signals
which are due only to the one species whose absorption edge occurs between
the two measurement energies.
The metal species and the inert starting gas present in the metal halide
lamps are too low in atomic number and these species are too low in
abundance relative to mercury to contribute to the measured absorption.
High pressure sodium lamps are filled with a small amount of inert starting
gas and a mercury/sodium amalgam. Mercury is the most abundant species and
the only species to contribute appreciably to the measured absorption. The
atomic number of sodium is too low to allow the sodium to contribute
appreciably to the measured absorption.
The invention will now be described in greater detail with reference to the
drawing, FIG. 1 of which is a schematic of a high pressure arc lamp
operating in a horizontal position and positioned in a CAT scanner to
provide a scan through a vertical cross-section of the lamp. For this
determination the arc tube of a standard 400 W sodium/scandium metal
halide discharge lamp 1 was positioned so as to operate horizontally
within a commercial CAT scanner comprising an X-ray source 2, a detector
array 3 both rotatable along a desired plane of the lamp, a computer 4 for
generating a series of density values from the corresponding measurements
of attenuation of X-radiation as determined by the detector array 3,
interface electronics 5 for electronically conditioning the signal output
of the detector array 3 to make it compatible for the computer 4, and a
recorder 6 for recording this series of density values comprising a
cathode ray tube (not shown) for recording and displaying an image
corresponding to the series of density values.
For measuring the density of the plasma in the lamp during operation the
arc tube was removed from the outer envelope and the current return wire
was removed and rerouted so as to be outside of the X-ray beam. This was
done so that the only object intersecting the X-ray beam was the arc tube
itself. This was carried out to avoid possible image artifacts from being
produced by the reconstruction algorithm.
The arc tube 1 was oriented horizontally within the CAT scanner thus
allowing vertical sections to be studied. The peak energy in the X-ray
pulse was set at 100 kev, corresponding to an average energy of 50-60 kev.
FIG. 2 shows a photograph of the screen image on the cathode ray tube
screen of the recorder 6 of a vertical section taken through the arc tube
when the arc tube is cold. Here the only species in the gas phase is a
small amount of argon gas (35 Torr) present to initiate the discharge.
This quantity of gas does not contribute to any appreciable X-ray
absorption. It should be noted that in this figure no X-ray absorption at
all is recorded.
FIG. 3 is a photograph of the screen image for the same vertical section
after the discharge has been turned on and the arc tube has been allowed
to come to the equilibrium operating condition. At this point the mercury
fill in the tube is fully vaporized. As will be noted there is a variation
in the degree of greyness of the image which variation corresponds to the
amount of gas phase absorption, the darker the area the greater the degree
of gas phase absorption. The absorption is asymmetrical as is indicated by
the fact that the image is darker in the lower part of the arc tube. This
is due to the fact that there is more mercury in the lower part of the arc
tube than in the upper part due to convection effects.
FIG. 4 is a photograph of an image of the scan taken immediately after
power to the arc tube was removed. At this point the tube is hot, the arc
is extinguished, the temperature gradient produced by the arc has rapidly
dissipated and the density distribution is at a relatively uniform value
throughout the volume. This shown by the almost uniform nature of the
image within the tube. In these photographs a greyness scale R is present
to the right of the image.
Besides being displayed on a cathode ray tube screen the image may be
photographically recorded using any of the well known photosensitive
materials.
While the present invention has been described with references to
particular embodiments thereof, it will be understood that numerous
modifications can be made by those skilled in the art without actually
departing from the scope of the invention.
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