Patent Number: 047633441
Section: description

DETAILED DESCRIPTION OF THE INVENTION Shown in FIG. 1 is a foil stack typically constructed of thermally conductive metal rings 1 which support thin high-density foils 2, having a thickness l.sub.2 of moderate atomic number, typically between 15 and 60. Foils of higher Z (Z&gt;60) such as gold and tungsten may be used if extremely hard X-ray bremsstrahlung contamination of the transition radiation spectrum does not matter. The thickness of the foils typically ranges between 1 and 10 microns depending on the type of material used and the electron beam energy; however, this range is not intended to be restrictive. The formula for the minimum single foil thickness l.sub.2 is obtained from A. N. Chu et al. "Transition radiation as a source of X-rays," J. Appl. Phys. vol 51, pp. 1290-1293, March 1980. ##EQU6## where .gamma.=E/E.sub.o, is the electron beam energy, E.sub.o is the electron rest energy, .omega. is the X-ray photon frequency, .lambda. is the X-ray photon wavelength (.lambda.=2.pi.c/.omega.), and .omega..sub.p is the plasma frequency of the foil material. The foil thickness need not be exact, and can vary as much as 10 to 30% thinner than shown in the above equation without resulting in a large decreaes in photon emission from the foils. Hence as a preferred design criterion l.sub.2 should be greater than the thickness ##EQU7## The rings that hold the foils are held together firmly, for example with bolts 3 or other fastening devices and the rings are preferably water cooled. The foil stack itself typically resides in a vacuum in chamber 4 or in a gas of relatively low X-ray absorption. The thickness of the rings are such that they are rigid and provide adequate support for the thin foils, the rings typically being constructed of stainless steel or copper and having an optimum minimum thickness l.sub.1 where: ##EQU8## for a vacuum, or: ##EQU9## for a gas of plasma frequency .omega..sub.pg. Typical values for l.sub.1 range from 1 to 10 mm. The thickness of the rings determines the separation of the foils which is a key factor in the production of the X-ray photon flux at proper energy. Values of l.sub.1 much less than the value given in the thickness formulas (50% or less) results in a marked decrease in the photon flux so that 50% is considered a practical minimum. Hence, as design criterion the two above equations for l.sub.1 are multiplied by 0.5. X-ray photons are produced when a well-collimated energetic electron beam 5 strikes the foil stack. As shown in FIG. 1, the electron beam is usually normal to the foil stack but this not necessary and can vary up to almost 90 degrees (angle with respect to the normal to the surface of the foil). The number of photons emitted per unit frequency per electron per interface integrated over all angles is given by the transition radiation equation: ##EQU10## where b=(.gamma..omega..sub.p /.omega.).sup.2, .gamma.=E/E.sub.o, E is electron beam energy, E.sub.o is the rest energy (0.511 MeV) and .omega..sub.p is the plasma frequency of the foil material. The plasma frequency, .omega..sub.p is related to the foil density as follows: ##EQU11## where A is the atomic weight of the foil material, m.sub.e is the electron mass, .rho. is the density of the foil material, N.sub.o is Avogadro's number, and e is the electron charge. The plasma frequency is seen to vary as .rho..sup.1/2. As can be seen from the transition radiation equation, at b.sup.2 &lt;1 or .omega.&gt;.gamma..omega..sub.p =E.omega..sub.p /E.sub.o, the intensity drops rapidly to very small values. Thus .omega..sub.c =.gamma..omega..sub.p can be viewed as a "cutoff" frequency above which the photon flux is too small to use. In order to reduce construction costs and operational costs to an acceptable level, it is important to reduce the electron beam energy below 2 GeV since the principal cost of a source is the accelerator itself. This can be accomplished by using high density foils such as gold, stainless steel, and copper. With these foils, X-rays can be produced using electron-beam energies from 25 to 500 MeV. This can be seen from the "cutoff" frequency relation. Since .omega.&lt;E.omega..sub.p /E.sub.o is required for good photon production, the electron beam energy is chosen to satisfy the following inequality: ##EQU12## where the formula for the plasma frequency has been substituted. As can be seen from this inequality, one can minimize E by going to foils of high density, .rho.. The electron beam energy is selected to be large enough so that the cutoff inequality holds but the energy is kept to a reasonable value in order to minimize the expense of the accelerator, e.g. 25 to 500 MeV. The number of foils, M, that can be used in stack 1 is limited only by the absorption in the foils themselves. To determine M, note that since the photon production is known to vary as (1-exp(-M.mu.l.sub.2), larger values of M&gt;2/.mu.l.sub.2 will result in a saturation value for photon production (see A. N. Chu et al., "Transition radiation as a source of X-rays," J. Appl. Phys. vol 51, pp. 1290-1293, March 1980). Therefore, as an optimum if M is chosen to be approximately 2/.mu.l.sub.2, the flux will be maximized. In practice this typically is between 10 and 100 foils. As a practical matter choosing M at 50% of the optimum results in only a small reduction in photon flux. So acceptable design criterion for M is M.gtoreq.(0.5)2/.mu.l.sub.2. The total photon flux can be further increased by designing the foil stack just below the k-shell photoabsorption frequency of the foil material. At the low frequency side of the k-shell-photoabsorption edge there is a dramatic decrease in photon absorption. For example, as shown in FIG. 2 for iron there is a sudden change in absorption at 7 keV. Thus a source can be designed with its peak photon production at the k-edge of the foil material. Given the k-edge frequency of the foil material and its plasma frequency, one picks a minimum electron beam energy for photon production from the condition that E&gt;E.sub.o .omega./.omega..sub.p, where .omega. is the k-edge photon frequency. The optimum foil thickness is then calculated from the thickness equation, and the number of foils calculated from the condition M.perspectiveto.2/.mu.l.sub.2, where .mu. is the lowest absorption value at the k-edge. As a design criterion, the foil thickness l.sub.2 is chosen to be: ##EQU13## since the photon production is somewhat insensitive to the foil thickness. However, the photon production is sensitive to the k-edge frequency. To choose a proper number of foils, the absorption coefficient is obtained at a frequency .omega.=.omega..sub.o such that .omega..sub.k -.epsilon.&lt;.omega..sub.o &lt;.omega..sub.k where .epsilon.=0.35 .omega..sub.k and .omega..sub.k is the k-edge frequency. This design criterion then recognizes the variability available in the number of foils. An added benefit of designing the foil stack at the k-edge is that the photon energy spectrum will be narrowed due to the sudden change in X-ray absorption. Such a more monochromatic source is often desired in many experimental situations, for example in angiography and microscopy. This case is illustrated in FIG. 3 for the soft X-ray region using aluminum, whose k edge is at 1.56 keV. The increases in absorption above the k edge results in a narrower energy spectrum that would otherwise be observed. Similar results are expected in the moderate to hard X-ray region. It is also important to understand that the cone of X-ray emission for high-density foils is different from the low-density case, and results in a decrease in the number of photons per unit solid angle. Hence, careful design of the foil thickness and density is important. Without elastic scattering of the electrons with the foil atoms, the X-ray emission from single or multiple interfaces is in a tight forward cone with an apex angle of .theta.=1/.gamma., and width .DELTA..theta.=1/.gamma., where .gamma.=(1-.beta..sup.2).sup.-1/2. For example, a 300-MeV-electron beam would produce angles .theta..perspectiveto..DELTA..theta..perspectiveto.1.6 mr. In general, this is true for low density foils; however, for the high desity foils considered here, the elastic scattering of the incoming electrons with the foil atoms results in a larger divergence of the exiting photon beam, and, hence, a decrease in photon density. Although photons are emitted at an angle of 1/.gamma. relative to the individual electron trajectories, divergence of the electrons, .DELTA..theta..sub.s, results in an increase in the apex angle of the cone of emission: EQU .theta.=(1/.gamma..sup.2 +.DELTA..theta..sub.s.sup.2).sup.1/2(14) where the scattering is given by the scattering formula to be: ##EQU14## where E is the electron beam energy in MeV, and X.sub.o is the radiation length of the foil material (X.sub.o =0.5 cm for copper), see V. L. Highland, "Some practical remarks on multiple scattering," Nucl. Instrum. Meth., vol. 129, pp. 497-499 (1975). Further complications in the development of a lower cost source of X-rays results from bremsstrahlung radiation, since bremstrahlung is also generated in the foils. For practical reasons, such as X-ray mirror damage and extremely hard X-ray contamination of possible experiments, this radiation should often be minimized. Assuming complete screening of the nuclear charge (valid for the frequency interval of those photons for which n.omega.&lt;&lt;E, where E is the electron beam energy), one obtains the double differential radiation cross section for relativistic bremsstrahlung: ##EQU15## where n.sub.o is the number of atoms per cubic centimeter, Z is the atomic number, and .theta. is the angle between the electron beam line and the observation point. In the prior art, bremsstrahlung was small because foils having low Z, and low density were used exclusively. However, since bremsstrahlung varies roughly as Z.sup.2 when high density foils are used, the amount of bremsstrahlung can be large. However, the bremsstrahlung emission can be minimized by selecting foils of high density with only moderate atomic number. For example, for the case of 33 keV photon generation, stainless steel (Z=26) or copper (Z=29) foils are a better choice than tungsten (Z=74) or gold foils (Z=79). However, if relatively low energy accelerators are used, and a relatively high photon energy desired, these high density and large atomic number materials can be used provided that the extremely energetic photons from bremsstrahlung are not detremental to the desired use of the X-rays source. As shown in the experimental results illustrated in FIG. 4, gold foils can be used and produce a bremsstrahlung background of approximately half that of the transition radiation. Subtracting the background from the measured flux results in the transition-radiation flux which can be compare to the theoretical photon flux. This favorable comparison is illustrated in FIG. 5. In another experiment stacks of stainless steel and copper have been shown to achieve a better ratio of transition radiation to bremsstrahlung radiation. The number of counts from a single 250-.mu.m foil and from forty 8.5-.mu.m stainless-steel-foils are presented in FIG. 6. The appearance of the large background is due to spurious radiation generated upstream of the foils. Subtracting these two spectra results in transition-radiation flux. Knowing the absolute magnitude of the charge that produced the flux, one can calculate the number of photons per unit bandwidth per electron, (photons/keV-electron). This is plotted as a scale on the right-hand side of FIGS. 7 and 8. In both cases the radiation at the peak is higher than expected from theoretical calculations (20% higher for copper and 30% for stainless steel). This high result is probably due to a low estimate on the number of electrons generated per pulse and not to any deviation from theory. The same experiment was performed with a 400-MeV beam. The results using a stainless steel stack are presented in FIG. 9. Only the relative number of counts was measured for this case. Similar results were obtained. These experiments prove that hard (30 keV) X rays can be generated from 100- to 500-MeV-electron beams using high density foils, and that transition radiation is a viable source for medical imaging such as angiography. Clearly for lower energy X-rays, lower electron source energies can be used and a practical cut off at the present time appears to be about 25 MeV.