Patent Number: 055770908
Section: description

DETAILED DESCRIPTION The ELMO experiments form a basis for calculating x-ray flux incident on an imaginary surface lying within a hot electron plasma annulus of the x-ray device of the present invention. However, the present invention departs from the ELMO work by replacing hydrogen (Z=1) as the fill gas with xenon (Z=54) to take advantage of the bremsstrahlung power scaling with Z.sup.2 (see Equation 1). Preferably, the present invention utilizes one of the noble gases (xenon, helium, neon, argon). For computational convenience and simplicity, it is assumed that the hot electrons are distributed uniformly throughout a well defined annular geometry. This calculation, although not rigorous, provides an order of magnitude estimate of the radiant flux levels of the device of the present invention as an x-ray source. The results of this calculation compare favorably to the dosage required for pasteurization and sterilization of various food products. It should be noted that thick target x-rays, produced by scattered ring electrons striking the sidewalls, x-ray emission from electron-atom collisions in the gas, and x-rays penetrating the irradiated food product are excluded from this estimation, making the results of the calculation a very conservative estimate of the radiation levels expected from the device of the present invention. Referring to FIG. 4, a sharp boundary model is assumed for a hot electron plasma annulus having inner and outer radii R.sub.1, R.sub.2, respectively. The x-ray power incident per unit area on an imaginary cylindrical surface of radius a (where a&lt;R.sub.1 &lt;R.sub.2) is calculated. The origin of the cylindrical coordinate system r,.theta.,z is taken at the right-hand side on the axis of the annulus as shown in FIG. 5. A truncated section of annulus is shown by solid lines in FIG. 5, while the remainder of the annulus is indicated by dotted lines. The truncated section is constructed by tangents drawn at the radius a, perpendicular to the z-axis. The angle of incidence .phi. is defined by an outward normal to the cylindrical surface drawn at the point a,0,-l, and a line of sight from an elementary volume of plasma rdrd.theta.dz within the truncated annulus. Radiation emitted from the truncated plasma volume, passes through the cylindrical surface at a,0,-l with an angle of incidence .phi. lying in a range of 0&lt;.phi.&lt;90.degree., while radiation from all other plasma regions, .phi.&gt;90.degree., pass through the surface from the interior side. The radiation incident from the interior is neglected under the assumption that it is absorbed by material contained within a radius a. Inspection of FIGS. 4 and 5 reveal the following relations: EQU r.sub.1.sup.2 =r.sup.2 +a.sup.2 -2arCos.theta., Equation 3 EQU R.sup.2 =(z+l).sup.2 +r.sub.1.sup.2 =(z+l).sup.2 +r.sup.2 +a.sup.2 -2arCos.theta., Equation 4 where l is the distance along the z-axis from the edge of the annulus to the irradiated area, and the cosine of the angle of incidence Cos.phi. at the point a,0,-l is: ##EQU1## The limits of integration are also obtained from FIGS. 4 and 5: The angle .theta. varies over the range, ##EQU2## while the radius r varies from R.sub.1 .ltoreq.r.ltoreq.R.sub.2 and z varies from 0.ltoreq.z.ltoreq.L. Continuing the calculation of radiant flux emitted as bremsstrahlung from the annulus, the radiant flux or power dP.sub.s radiated by an elementary plasma volume within the annulus is EQU dP.sub.s =wrdrd.theta.dz, Equation 6 where the radiated power density w is defined by Equation 1. It is assumed that the radiation is distributed uniformly over a solid angle of 4.pi. steradians. This assumption is not quite correct, for the direction of radiation emitted by energetic electrons will be influenced by the distribution of the energetic electron velocities with respect to the magnetic field and the orientation of the magnetic field within the annulus. These effects tend to increase the x-ray emission in the direction of the axis, i.e., toward the imaginary surfce defined by the radius a, and tend to reduce the x-ray power emitted from adjacent parts of the annulus that would otherwise contribute to the radiant flux through the surface at the point a,0,-l. These effects are expected to offset one another, and for this order of magnitude estimation, they can be neglected without serious loss of accuracy. Under these assumptions, the radiant intensity of the x-rays I, or radiant flux per unit solid angle is calculated as, ##EQU3## With the elementary plasma volume at the apex, the solid angle d.OMEGA. subtended by the surface area dA on the imaginary surface at the point a,0,-l is, ##EQU4## and the bremsstrahlung power intercepted by this area is ##EQU5## Whereby, the irradiance or radiated power per unit area ##EQU6## incident at the reference point from the elementary plasma volume is ##EQU7## Substituting the expressions for R and Cos.phi. and integrating over the radiating source (i.e., the plasma annulus) yields the total bremsstrahlung power per unit area incident at the point a,0,-l radiated by the truncated annulus, is ##EQU8## where, ##EQU9## The factor of 2 in front of the integral is due to symmetry in the integration over .theta. as it is performed only from .theta..sub.1 to 0. As a quantitative example, consider a hot electron plasma annulus in the device of the present invention with dimensions R.sub.1 =0.5 m, R.sub.2 =0.6 m, and l=1 m. We take an imaginary cylindrical surface with a radius a=0.2 m, coaxial with the annulus, and calculate the incident power per unit area, i.e., the x-ray irradiance, incident on this surface for a background plasma density n.sub.i =5.times.10.sup.18 m.sup.-3, with ring electron density n.sub.e =0.1 n.sub.i, and an electron temperature T.sub.e =2 MeV in the rings. The results of integrating Equation 11 in watts per square meter incident at the cylindrical surface is plotted as a function of position l along the axis in FIG. 6. As expected, the irradiance is distributed symmetrically about the middle of the cylindrical axis. The x-ray irradiance ranges from about 2.4 kw/m.sup.2 at the ends of the 0.2 m radius cylindrical surface to greater than 4 kw/m.sup.2 at the center. To compare dose rates obtainable from the x-ray device of the present invention with dose rates available from conventional food irradiation facilities, the calculated irradiance values must be converted to exposure rates, i.e., from watts/m.sup.2 to Rad/s. The American Institute of Physics Handbook gives the exposure-to-fluence conversion in air as ##EQU10## where the photon energy E is in MeV. Assuming that the average energy of x-ray photon emission from the plasma is equal to the average energy of the electrons in the annulus, i.e., the electron temperature T.sub.e =2 MeV, then, the average number of photons/s for an incident radiant flux of 1 w/m.sup.2 is ##EQU11## where, T.sub.e is in MeV. Dividing Equation 13 by Equation 12 and cancelling out the photon energy gives a conversion factor of ##EQU12## Now, referring to the plot in FIG. 6, an object placed in the radiation field within an imaginary surface of radius a=0.2 m will be subjected to a dose rate of about 700 roentgen/s at the ends of the axis to about 1,170 roentgen/s at the middle of the axis of the device of the present invention. Conversion from exposure in roentgens to absorbed dose in Rads for an equivalent energy fluence on the medium, is obtained through the use of the following relation as discussed in T. N. Padikal, "Medical Physics," A Physicist's Desk Reference; Second Edition of Physics Vade Mecum, H. L. Anderson, editor in chief, page 227, American Institute of Physics, 1989. ##EQU13## where X is the exposure in roentgens, D.sub.H2O is the dose absorbed in Rads by a medium which has a mass energy absorption coefficient (.mu..sub.en /.rho.).sub.H2O equivalent to that of water. The values of the absorption coefficient (.mu..sub.en /.rho.) for air and water are 2.342.times.10.sup.-3 and 2.604.times.10.sup.-3 m.sup.2 /kg, respectively, for a mean photon energy of 2 MeV. Evaluating the term in the brackets results in a factor of 0.966 multiplying the exposure X in roentgens to obtain the dose in Rads absorbed by a water-like material. The overall conversion factor from w/m.sup.2 to Rads/s is 0.281 Rads/s/w/m.sup.2. Continuous dose rates of 668 Rad/s at the ends and 1,139 Rad/s at the middle of the axis of the x-ray device of the present invention are obtained as a result of the calculation. The total bremsstrahlung power radiated by the annulus in the device of the present invention is obtained by evaluating the power density w for the chosen parameters and forming its product with the volume of the annulus. Using the parameters specified above and Equation 1, the total bremsstrahlung power radiated by the annulus is 54 kw for background plasma density of 5.times.10.sup.18 m.sup.-3. The range of usable background plasma densities in the x-ray device of the present invention is determined by the plasma frequency f.sub.p, i.e., the cutoff frequency for electromagnetic propagation through a plasma. The plasma frequency f.sub.p is given by, ##EQU14## where n.sub.c is the critical density for cutoff of electromagnetic wave propagation through the plasma, e is the electronic charge, m.sub.e is the electron mass, and e.sub.0 is the permittivity of free-space. If the background plasma density exceeds the critical density value, microwave power cannot penetrate to the resonant region of the mirror field, so that ECH and hot electron production ceases. The relation between cutoff plasma frequency as a function of density, Equation 16 is plotted in FIG. 7. Referring to FIG. 7, high power tubes, generating microwave frequencies of 9 GHz to 90 GHZ, are required to operate an x-ray device of the present invention with background plasma densities over a range from 10.sup.18 to 10.sup.20 m.sup.-3. As discussed hereinafter, the maximum plasma density in the x-ray device of the present invention will not exceed n.sub.i &lt;5.times.10.sup.19 m.sup.-3, so that microwave tubes with frequencies &lt;60 GHz will suffice for operation. Gyrotron tubes which generate &gt;200 kw over the specified microwave frequency range are available from the Microwave Power Tube Division of Varian Associates in Palo Alto, Calif. As a result of Department of Energy (DOE) investments in high-power microwave tubes, sources operable at frequencies of 28, 56, 90, and 140 GHz with nominal output powers of 200 kw are commercially available. Additionally, the magnitudes of magnetic fields that cause electron gyration about a field line to resonant with a microwave frequency from 9 to 90 GHz is 0.32 to 3.2 T (3.2 to 32 kgauss), respectively. The magnetic field for electron cyclotron resonance at 56 GHz is .congruent.2.0 T. As magnitudes of the resonant magnetic fields required are relatively modest, and the coil geometry is a simple solenoid, suitable electromagnetic coils are readily obtainable from commercial fabricators. The bremsstrahlung radiated power is dependent on the annular plasma density. The results of integrating Equation 11 for three values of background plasma densities, n.sub.i =5.times.10.sup.18, 10.sup.19, and 5.times.10.sup.19 m.sup.-3 with all other plasma parameters and dimensions remaining the same as the previous calculation, is plotted in FIG. 8. Here, the calculated peak values of radiant flux at the mid point of the axis are 4, 16, and 400 kw/m.sup.2 for background plasma densities n.sub.i of 5.times.10.sup.18, 10.sup.19, and 5.times.10.sup.19 m.sup.-3, respectively. The values of peak radiant flux, given above, correspond to dose rates of about 1.16, 4.54, and 116 kRad/s under the assumption that the mass energy adsorption coefficient of food products is equivalent to the mass energy adsorption coefficient of water. Thus, increasing the annulus plasma density significantly alters the radiated bremsstrahlung power output from the x-ray device of the present invention over a wide range. FIG. 9 is a schematic representation of the x-ray device of the present invention. The device 10 of the present invention includes two electromagnetic coils 12 that, when energized, provide the magnetic mirror field required to confine the plasma, as discussed above. The electromagnetic coils 12, preferably, are capable of producing a magnetic field having a magnitude in the range of 0.32 to 3.2T (3.2 to 32 kgauss). Device 10 includes a vacuum chamber 14 suitable for confining a gas 20. Preferably, the gas utilized in the present invention is one of the noble gases such as xenon (Xe), helium (He), neon (Ne) or argon (Ar). The chamber wall 16 is formed of a material that will pass x-rays, and may be made of steel, for example. Wall 16 is provided with a terminal 18 for microwave heating of the gas 20. The terminal 18 is connected to a microwave source 22. Microwave source 22 will preferably be capable of operating at frequencies in the range of 9 GHz to 90 GHz with a nominal output power of about 200 kw. As discussed above, the microwave frequency is chosen to be resonant with the second harmonic of the electron cyclotron frequency of particular regions of the mirror field. Heating of the gas 20 in this manner gives rise to the annular plasma structure shown as 24 in FIG. 9, as confined by the mirror magnetic field. In the present invention, the background plasma density n.sub.i in chamber 14 is preferably in the range of 10.sup.18 to 10.sup.20 electrons/m.sup.3, with the annular plasma density n.sub.e =0.1n.sub.i. The electron temperature Te in the annular plasma is preferably about 2 MeV. Chamber wall 16 includes a central cylinder 26 with interior opening 28 that is open on both ends to the surrounding air. The device 10 of the present invention includes a support 32 for supporting and locating the product 30 proximate to the chamber 14 for receiving x-rays radiating therefrom. Support 32 may be stationary, or preferably mobile, as shown in the embodiment of FIG. 9, in which support 32 includes a conveyor 34 for moving the product 30 through opening 28 in cylinder 26. This annular geometry shown in FIG. 9 is particularly well suited to irradiating food products moving through cylinder 26, as these products will be completely encircled by the radiating media. While the present invention is particularly effective in irradiating food products, it is applicable to any product where irradiation is desired. FIG. 10 illustrates an embodiment of the present invention in which a plurality of chambers 14 are arranged coaxially in series and each is connected to a microwave source 22. In certain applications, a plurality of microwave sources may be used. The arrangement of FIG. 10 increases the throughput capacity of the device. Further, this arrangement permits certain electromagnetic coils 12A to be shared between chambers 14. This reduces the number of coils required for n chambers from 2n to n+1, which results in capital savings. Radiation from chambers 14 is directed not only radially inward toward central opening 28 but also radially outward. In the embodiments of FIGS. 9 and 10, this outward radiation can be taken advantage of by circulating the products 30 on a conveyor system, for example, that makes several passes within a shielded room housing the x-ray devices 10. In this manner, the products 30, e.g. food products, receive a large x-ray dose prior to entering the central opening 28 in the device(s) and thereby reduces the time required in central region 28 for adequate exposure. Another embodiment of the present invention, shown in FIG. 11, takes further advantage of such outward radiation and eliminates the need for a central channel with a support or conveyor located therein. In such embodiment, the devices 10 are arranged in an array which could take any suitable form such as a rectangle or square (as shown). Such array surrounds central open area 36. Located within open area 36 is support 32 for locating the product(s) 30 proximately to x-ray devices 10 of the present invention. Support 32 may be stationary and may simply comprise a floor area, or may be movable, such as an elevator that lifts/lowers a pallet of food products 30 into/out of central open area 36. With reference again to FIG. 9 and assuming the platform 32 includes a conveyor 34, the previous calculations can be used to calculate the total dose D received by a cylindrical object passing through x-ray device 10 with a plasma annulus 24 of length L at a constant velocity V. Converting the results of the calculations plotted in FIG. 6 to Rads/s, the dose rate R(z) is modeled as a parabolic function of the distance x along the axis as EQU R(z)=-1,799(z-0.5).sup.2 +1,139, Equation 17 and this equation is plotted as a function of axial position in FIG. 12. For comparison, the curve appearing in FIG. 6 (after conversion to Rads/s) is also replotted in FIG. 12. The parabolic fit is very good as is seen in the graph. The analytical model is a convenient means of calculating the total dose D received by a cylindrical object transiting a plasma annulus 24 of length L at a constant velocity v. Assuming that only radiation directly entering the cylindrical surface is absorbed, i.e., neglecting the radiation incident on the circular ends and that penetrating through the product, e.g. food, the dose absorbed at an axial position z and radius r is given by the product of the rate of absorbed dose R(z) multiplied by the time dt spent at the position r,z. Since a point on the surface is moving at a constant velocity v, the time dt=dz/v, and by symmetry, dD(z)=2.pi.r R(z)dz/v is the dose absorbed through the elemental surface d.sigma.=2.pi.r dz. The total dose D in Rads absorbed by the cylindrical object is calculated by integrating Equation 17 along the z axis, i.e., ##EQU15## Using the device parameters from earlier calculations, i.e., L=1 m, and the radius of the imaginary surface a=0.2 m, the total dose received D is plotted as a function of velocity v.sub.i in FIG. 13. The products will receive a total dose better than 10 to 60 kRads (100 to 600 Gy) moving through x-ray device 10 at a speed of 0.1 to 0.02 m/s, (corresponding to a transit time of 10 to 50 s) respectively. This calculation does not include bremsstrahlung generated by the impact of energetic electrons on the walls 16 of device 10, so that this is a minimum dosage calculation. Additionally, dose rates absorbed by the product, e.g. food, are controlled by the amount of microwave power put into device 10 and the transsit time of the product through device 10. Thus, dosage may be lowered by lowering the microwave power input, or passing the products 30 through device 10 at higher speeds. The radiated power from x-ray device 10 of the present invention is consistent with achieving a high throughput of irradiated food products when compared to x-ray dosages required to perform food preservation treatments. The annular geometry of the x-ray device of the present invention (FIGS. 9 and 10) is highly amenable to irradiating products moving through the device, especially food products, as these products will be completely encircled by the radiating media. Operating a plurality of devices in series (FIG. 10) increases product throughput and results in certain capital savings. Arrangement of the x-ray devices in an array (FIG. 11) permits irradiation of large products. The calculated estimates of radiant flux of the present invention are conservative and do not take into account several factors that enhance x-ray intensity. These factors include the thick target bremsstrahlung from the side walls and the bremsstrahlung collisions with unionized gas atoms and electrons. Inclusion of these factors may increase the dose rates an order of magnitude over the calculated values, and accordingly, reduce the required exposure time by the same factor. While the present invention has been described in terms of preferred embodiments, various changes and modifications will become apparent to those having skill in the pertinent art. All such modifications and enhancements are intended to fall within the scope and spirit of the present invention, limited only by the following claims.