Thursday, July 22, 2010

equations notes

A mathematical method for inversion in atmospheric remote sensing



Analysis and synthesis of radiation pattern for the travelling wave type sources on a circular aperture (Technical report)
Asymptotic-Expansion Methods


The techniques described in the previous sections are exact methods in that the error in the numerical solution only comes from the discretization. The numerical solution approaches the exact solution as the discretization is refined. However, as the number of unknowns grows, the demand for computer memory and calculation time also grows. This prohibits these methods from being applied to high frequency problems where the size of the object is much larger than the wavelength. The methods described in this section are based on asymptotic high-frequency expansions of Maxwell's equations. They are high frequency methods that are only accurate when the dimensions of the objects being analyzing are large compared to the wavelength of the field. The asymptotic techniques introduced in the following sections include physical optics, geometrical optics, geometrical theory of diffraction, and uniform theory of diffraction.























Physical Optics

The Physical Optics (PO) approximation is a well known and efficient method for analyzing large scatters . PO reduces the cost of memory and CPU-time by performing a high frequency approximation. It is a current-based method in which the physical optics approximation is used to obtain the current density induced on a surface. The surface current density, Js, can be determined by,



(1)

where Hi and Hr represent the incident and reflected magnetic field components evaluated on the surface. is the unit vector normal to the surface. If the surface can be approximated as an infinite plane surface, then by image theory,



(2)

and Equation (1) reduces to



(3)

The electric and magnetic field radiated by the surface current on the illuminated side of the reflector can be determined by [3],



(4)

(5)

where .



Equation (3) is exact only when the surface is infinitely large. The accuracy of the approximation depends on the transverse dimensions of the reflecting surface, the radius of curvature, location of edges, and the angle of the incident field. Generally, PO works well for large, smooth surfaces with low curvature. The implicit assumption for the physical optics approximation is that the incident field is treated as a locally planar wave. Also, it assumes that the reflector surface is perfectly conducting.



It has been found that PO provides an accurate prediction of far-field patterns of reflected antennas in the main beam region and out to several side lobes [5]. The major disadvantage of PO is that the integration over the surface of the reflector may be quite complicated and time consuming when the feed is placed off-axis or the feed pattern is asymmetric [197]. Moreover, the radiation integral has to be evaluated each time the observation point is changed.



Integral equations governing radiation effects: (Notes on atomic collisions, III) (Det Kongelige Danske videnskabernes selskab. Matematiskfysiske meddelelser)


Fast and efficient evaluation of the radiation integral was proposed using a fast series approach [5], incorporating a multilevel fast multipole method [6], or decomposing the scatterer into subdomains [7]. Initially applied in the frequency domain, PO has also been extended into the time domain [8].



Geometrical Optics (Ray Optics)

Geometrical Optics (GO) [11] or geometrical optics with aperture integration (GO/AI) is a ray-based method intended for the consideration of electrically large dielectric structures in applications like the analysis of reflector antennas. In GO analysis, geometrical optics techniques (ray tracing) are used to set up equivalent currents on an aperture plane which is normal to the axis of the reflector. Then, the tangential aperture fields are constructed and used to determine the radiated fields utilizing the Fourier transform. Different formulations are obtained based on the use of aperture electric fields, magnetic fields or their combinations [10]. The advantage of the GO/AI method is that the integration over the aperture plane can be performed with equal ease for any feed pattern or feed position [4].



The relationship between GO and PO was demonstrated in [10]. It was shown that the PO integral can be represented as a summation of many Fourier transforms, such that the first few terms resemble the GO representation. Using the "extinction theorem" [3], the fields predicted by the integration of PO surface currents were shown to agree with the geometrical optics aperture fields on the aperture plane to within the local plane wave approximation. It was concluded that the accuracy obtained by the two methods is comparable.



Geometrical Theory of Diffraction

The approximations in both physical optics and geometrical optics are based on the following assumptions [3]:



•The current density is zero on the shadow side of the reflector

•The discontinuity of the current density over the rim of the reflector is neglected

•Direct radiation from the feed and aperture blockage by the feed are neglected.

Both PO and GO ignore the edge diffractions which are highly dependent on the whether the edges of the reflector are flared, sharp, absorber lined or serrated. Thus, they cannot accurately predict the far fields beyond the first few side lobes. For predicting the patterns more accurately in all regions, geometrical diffraction techniques are required.



As an extension of GO, the Geometrical Theory of Diffraction (GTD) overcomes the limitations of GO by introducing a diffraction mechanism [12]. The diffracted field is determined at the points on the surface where there is a discontinuity in the incident and reflected field. The value of the diffracted field is evaluated at these points with the aid of an appropriate diffraction coefficient. Usually, the coefficient is determined from asymptotic solutions of simple boundary-value problems with so called canonical geometries, such as a conducting wedge, cylinder or sphere. Since the solutions of these canonical problems are known, the object under investigation can be partitioned into smaller components, so that each component represents a canonical geometry. The ultimate solution is a superposition of the contributions from each component [2].



Two major advantages of GTD over other high frequency asymptotic techniques are that it provides insight into the radiation and scattering mechanisms from the various parts of the structure, and it can yield more accurate results. The method has attracted increasing attention; especially for applications to reflector antennas [13-18]. Unfortunately, GTD fails in the transition region adjacent to the shadow boundary, at caustics (points through which all the rays of a wave pass), or in close proximity to the surface of the scatterer. In these zones, the field cannot be treated as a plane wave. Thus, ray techniques become invalid. To deal with this problem, a number of alternative approaches have been proposed: uniform solutions [20-21], methods for dealing with caustic curves [22-24], physical theory of diffraction (PTD) [25], and the spectral theory of diffraction (STD) [26-27]. A comprehensive introduction to these methods can be found in [19].



Uniform Theory of Diffraction

The Uniform Theory of Diffraction (UTD) is a uniform version of the geometrical theory of diffraction. It was initially proposed [28] to deal with the problem that GTD produces inaccurate results at the shadow boundaries. The uniform theory of diffraction approximates near electromagnetic fields as quasi-optical and uses ray diffraction to determine diffraction coefficients for each diffracting object-source combination. These coefficients are then used to calculate the field strength and phase for each direction away from the diffracting point.



References

[1] W. V. T. Rusch and P. D. Potter, Analysis of Reflector Antennas, New York: Academic, 1970, pp. 92-93.



[2] C. A. Balanis, Antenna Theory Analysis and Design, Third edition, John Wiley & Sons, Inc., 2005.



[3] A. D. Yaghjian, "Equivalence of surface current and aperture field integrations for reflector antennas," IEEE Trans. Antennas Propagat., vol. 32, no. 12, Dec. 1984.



[4] J. F. Kauffman, W. F. Croswell, and L. J. Jowers, "Analysis of the radiation patterns of reflector antennas," IEEE Trans. Antennas Propagat., vol. 24, no. 1, pp. 53-65, Jan. 1976.



[5] Y. Rahmat-Samii and V. Galindo, "Shaped reflector antenna analysis using the Jacobi-Bessel series," IEEE Trans. Antennas Propagat., vol. 28, pp. 425-435, July 1980.



[6] T. F. Eibert, "Modeling and design of offset parabolic reflector antennas using physical optics and multilevel fast multipole method accelerated method of moments," Multi-optic Conference, 2006. INMIC '06, IEEE, pp. 377-382, Dec. 2006.



[7] A. Boag, "A fast physical optics (FPO) algorithm for high frequency scattering," IEEE Trans. Antenna Propagat., vol. 52, no. 1, Jan. 2004.



[8] E. Y. Sun and W. V. T. Rusch, "Time-domain physical-optics," IEEE Trans. Antennas Propagat., vol. 42, pp. 9-15, Jan. 1994.



[9] R. Mittra, Y. Rahmat-Samii, V. Galindo-Israel, R. Norman, "An efficient technique for the computation of vector secondary patterns of offset reflectors," IEEE Trans. Antennas Propagat., vol. 27, pp. 294-304, May 1979.



[10] Y. Rahmat-Samii. "A comparison between go/aperture-field and physical optics methods for offset reflectors," IEEE Trans. Antennas and Propagat., vol. 32, pp. 301-306, Mar. 1984.



[11] G. A. Deschamps, "Ray techniques in electromagnetics," Proc. IEEE, vol. 60, pp. 1022-1035, Sept. 1972.



[12] J. B. Keller, "Geometrical theory of diffraction," Journal of Optical Society of America, 52(2), 1962.



[13] D. L. Hutchins, "Asymptotic series describing the diffraction of a plane wave by a two-dimensional wedge of arbitrary angle," Ph.D. Dissertation, The Ohio State University, Dept. of Electrical Engineering, 1967.



[14] C. A. Balanis and L. Peters, Jr., "Analysis of aperture radiation from an axially slotted circular conducting cylinder using GTD," IEEE Trans. Antennas Propagat., vol. 17, no. 1, pp. 93-97, Jan. 1969.



[15] G. L. James and V. Kerdemelidis, "Reflector antenna radiation pattern analysis by equivalent edge currents," IEEE Trans. Antenna Propagat., vol. 21, no. 1, pp. 19-24, Jan. 1973.



[16] C. A. Mentzer and L. Peter, Jr., "A GTD analysis of far-out sidelobes of Cassegrain antennas," IEEE Trans. Antenna Propagat., vol. 23, no. 5, pp. 702-709, Sep. 1975.



[17] P .H. Pathak and R. G. Kouyoumjian, "An analysis of the radiation from aperture on curved surfaces by the geometrical theory of diffraction," Proc. IEEE, vol. 62, no. 11, pp. 1438-1447, Nov. 1974.



[18] A. W. Rudge, "Offset-parabolic-reflector antennas: A review," Proc. IEEE, vol. 66, no. 12, pp. 1592-1618, Dec. 1978.



[19] D. P. Bouche, F. A. Molinet and R. Mittra, "Asymptotic and hybrid techniques for electromagnetic scattering," Proc. IEEE, vol. 81, no. 12, pp. 1658-1684, Dec. 1993.



[20] R. C. Kouyoumjian and P. H. Pathak, "A geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE, vol. 62, pp. 1448-1461, Nov. 1974.



[21] S. W. Lee and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propagat., vol. 24, pp. 25-34, Jan. 1976.



[22] R. W. Ziolkowski and G. A. Deschamps, "Asymptotic evaluation of high frequency fields near a caustic: An introduction to Maslov's method," Radio Sci., vol. 19, no. 4, pp. 1001-1025, Jul.-Aug. 1984.



[23] Y. Kravtsov and Y. Orlov, "Caustics, catastrophes and wave fields," Sov. Phys.-Usp., vol. 26, pp. 1039-1058, Dec. 1983.



[24] H. Ikuno and L. B. Felsen, "Complex ray interpretation of reflection from concave-convex surfaces," IEEE Trans. Antennas Propagat., vol. 36, pp. 1206-1211, 1988.



[25] P. Y. Ufimtsev, "Elementary edge waves and the physical theory of diffraction," Electromagnetics, vol. 11, pp. 125-160, 1991.



[26] R. Mittra, Y Rahmat-Samii, and W. L. Ko, "Spectral theory of diffraction," Appl. Phys., vol. 10, pp. 1-13, 1976.



[27] Y. Rahmat-Samii and R. Mittra, "A spectral domain interpretation of high-frequency diffraction phenomena," IEEE Trans. Antennas Propagat., vol. 25, pp. 676-687, Sept. 1977.



[28] R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE, vol. 62, pp. 1448-1461, Nov. 1974.

Thursday, July 8, 2010

FREQUENCY CONTROL

Filing date: Nov 17, 1960

Issue date: Sep 1962









Sept. 4, 1962 E. w. Herold 3,052,614



FREQUENCY CONTROL OF RF HEATING OF GASEOUS PLASMA Filed Nov. 17, 1960







3,052,614



Patented Sept. 4, 1962



3,052,614



FREQUENCY CONTROL OF RF HEATING



OF GASEOUS PLASMA



Edward W. Heroid, Atherton, Calif., assignor, by mesne assignments, to the United States of America as represented by the United States Atomic Energy Commission Filed Nor. 17, I960, Ser. No. 70,016 2 Claims. (CI. 204—193.2)



The invention relates to improved methods of and means for heating gaseous plasma and more particularly to an arrangement for obtaining the best or at least an improved radio frequency for plasma heating so> as to provide the maximum rate of heating.



Several research devices have been devised for studying effects in and properties of high temperature plasmas and for production of thermonuclear reactions. In such devices, it is necessary that the plasma be raised to a high temperature. The plasmas generally comprise deuterium or tritium or mixtures of the two.



In one type of plasma heating, the magnetic field is caused to pulsate at a radio frequency and produce, by induction, an electric field in the plasma transverse to the magnetic field. When, for example, the magnetic field is caused to pulsate at a frequency close to the ion cyclotron frequency, the heating method is called "ion cyclotron resonance heating." A description of this method of heating is presented by T. H. Stix and R. W. Palladino in the Proceedings of the Second United Nations Conference on the Peaceful Uses of Atomic Energy, September 1 to 13, volume 31.



In bringing a controlled fusion plasma up to thermonuclear temperatures, the choice of radio frequency for heating is an important factor. The radio frequency should be selected so as to come close to and keep in step with some natural resonance of the plasma. However, these resonances are not fixed frequencies. The cyclotron resonance frequency referred to above depends on the resultant magnetic field which, in turn, depends on the direct current in the plasma, the applied magnetic field, and the prior history of the plasma configuration and temperature.



It is an object of the invention therefore to provide an improved method and means for controlling the heating of gaseous plasmas.



Another object is to provide improved method and means for obtaining frequency control of the radio frequency heating of a gaseous plasma.



A still further object is to provide an improved method and means for automatically controlling the frequency of an induction heater for gaseous plasma so as to maximize the rate of heating.



Briefly, the above objects of the invention are accomplished in accordance with typical embodiments of the invention by a servo-loop system in which a small cyclical frequency deviation is used to "feel" or sense the direction of plasma temperature with frequency. The system, in effect, indicates whether the plasma temperature is going up or down when the heating frequency is changed. The sensing signal is compared in a phase comparator with a component of a temperature-sensitive signal from the plasma. A control signal derived from the phase comparator is used to set the center frequency of the radio frequency energy employed to heat the gaseous plasma.



A more detailed description of the invention will now be given with the assistance of the accompanying drawing in which:



FIGURE 1 is a partially schematic sectional view of one example of a gas plasma device of the type with which the present invention is intended for use;



FIGURE 2 is a schematic perspective view illustrating two adjacent sets of adjacent electrode structures shown



in FIGURE 1 and a radio frequency circuit for feeding radio frequency energy of appropriate frequency and phase to the electrode structure; FIGURE 3 is a block diagram of one embodiment of



5 a servo-loop system to be used according to the invention with a gas plasma device of the type shown in FIGURES 1 and 2; and



FIGURES 4a and 4b are curves useful in describing the operation of the servo-loop system shown in FIGURE 3.



10 In the drawing, similar elements are identified by similar reference characters.



In the gas plasma device shown in FIGURE 1 for illustrative purposes only, the resonance box is patterned after the type employed in a typical stellarator, such as de



15 scribed in the Stix et al. publication, cited above. The elements of the box include, for example, a non-magnetic cylindrical housing 11 slightly over 21 inches in length. Surrounding the housing 11 'are a plurality of magnetic field producing windings 13. Within the housing 11



20 there is mounted a ceramic tube 15, 21 inches long and 4 inches in diameter, which defines a plasma reaction zone. The windings 13 are designed to produce a uniform confining field over a length of about 18 inches. Additional windings 14 are provided at each end of the



25 ceramic tube 15 to produce mirror fields of a 3-2 mirror ratio at each end of the ceramic tube 15. In a stellarator, the resonance box of FIG. 1 is coupled into an endless toroid or race track (not shown), plasma being injected into and withdrawn from the resonance box via 4 inch



30 diameter tubular sections 16 connected to either end of the resonance box. As shown on page 284 of the above mentioned article by Stix et al., an additional coil is provided to which radio frequency is applied to produce a pulsating magnetic field which causes heating of the



35 plasma.



As illustrated in FIGURES I and 2, the heating means comprises a plurality of electric field generating means mounted within the ceramic tube 15. Each means comprises a plurality of arcuate electrodes 17 and 17' equally



40 spaced around the inner surface of the ceramic tube 15. RF energy is fed to the electrodes by means of leads 19, which may be, for example, conventional coaxial transmission lines, passing through one or more vacuum sealed entry ports 20 in the housing 11.



^g During operation, the confining field windings 13 are energized to produce a strong axial magnetic field of the order of 20,000 to 50,000 gauss. A column of plasma 21 is then injected into the ceramic tube 15 in the direction shown by the arrow 23. This may be accomplished, for



gn example, in the manner set forth in U.S. Patent 2,910,414 to Lyman Spitzer, Jr. Preferably the plasma 21 is as fully ionized as possible. The plasma may comprise, for example, deuterium or tritium ions, or mixtures thereof, and electrons separately orbiting about the magnetic lines



g,- of force in a helical path.



The plasma 21 is confined by the magnetic field in a compact column isolated from the inner surface of the ceramic tube 15 and the electrodes 17. A circuit for feeding RF energy to one set of electrodes 17 is shown



60 in FIGURE 2. For conveniece, electrodes 17 and 17' are respectively numbered 17fl, 176, 17c, 17d, and 17a'; 176', 17c', Ud' in FIGURE 2. One pair of oppositely disposed electrodes 176 and 17d are fed 180° out of phase directly from an RF generator 23. In the same



6g manner, RF energy is applied to the other pair of electrodes 17a and 17c but since they are fed from the generator 23 through a conventional 90° phase shifter 25, each electrode is fed 90° out of phase with respect to the next adjacent electrode. In this manner, a circularly



„„ polarized electric field is established within the ceramic tube 15.



Power requirements for creating the circularly polar



ized fields may range as high as 20 kw. Suitable RF generators are described in "Induction and Dielectric Heating," by J. W. Cable, 1954, Kheinhold Publishing Co., New York, New York. The plasma resonance and, therefore, the frequency of the energy supplied by the 5 generator 23 may shift appreciably in the manner described. The shifter 25 preferably in a 90° phase shift lumped circuit. Lumped circuits with wide-band 90° phase shifts are known. Waveguide or coaxial line ar



nuclear plasma, the neutron output is a sensitive measure of temperature, it may be used as an indicator. As will become evident, any one of a number of indicators providing a sensitive measure of temperature other than the neutron output may be used.



In the arrangement of FIGURE 3, a neutron detector 32 detects the neutron output of the gas plasma 31 and applies a signal to a phase comparator 33 through a suitable filter 37 which passes substantially only the funda



rangements may be used in other applications according 10 mental frequency component of the signal. A low freto the frequency, method of heating, and so on. _ quency signal of frequency fs is applied from a suitable



source 34 to the phase comparator 33 and to a frequency control circuit 35. A direct current control sig



nal derived from the phase comparator 33 is also fed



In FIGURE 2, two sets of electrodes 17 and 17' are shown connected to the RF generator 23 and to the 90° phase shifter 25. The first set of electrodes 17a—VI d are fed with RF energy as described heretofore so that the 15 to the control circuit 35 over a path which includes a potentials on adjacent electrodes are 90° out of phase to low-pass filter 38 for removing alternating current cornestablish a circularly polarized electric field. The next axially adjacent set of electrodes Via'—17rf' are fed in the same manner, however the instantaneous potential on



20



ponents from the control signal. The output of the control circuit 35 is applied to the RF induction heater 30 to determine the frequency of the RF power applied to the gas plasma 31. A third input 36 to the control circuit 35 is provided to permit a rough setting of the servoloop to provide approximately the correct RF heating frequency, whereby the servo-loop can thereafter automatically determine the correct RF operation frequency.



each electrode 17a'—17^' is caused to be 180° out of



phase with the corresponding electrode of the first set



of electrodes 17a—17rf.



The arrangement shown in FIGURES 1 and 2 makes



use of the fact that, while electrons cannot be moved



radially in this arrangement, they can be moved in an 25 An example of a suitable control circuit is a reactance



axial direction. The sets of electrodes 17 and 17' pro- tube circuit coupled to the RF induction heating genera



duce two radial fields out of phase with respect to each



other and transverse to the axis of the column of plasma.



When the uppermost electrode 17a' of the second set



of electrodes 17' is positive, an excess of electrons is 30



created in the plasma adjacent to this electrode 17a'.



These electrons are attracted by the positive space charge



created near the uppermost electrode 17a of the first set



of electrodes 17. Upon reaching the positive space



charge region of the plasma the electrons neutralize that 35 ample, by manual bias voltage control means so that the



charge and permit the externally applied electric field to control signal applied to the heater 30 from the control



circuit 35 results in a setting of the radio frequency at approximately the correct frequency, i.e. at the peak rate of heating as shown in the curve of FIGURE 4a. Alternatively, the tuning of the RF induction heating oscillator 30 may be manually adjusted. The signal of low-frequency /s supplied to the control circuit 35 from the low frequency source 34 causes the radio frequency



tor 30, the reactance being responsive to voltages from the low frequency source 34, the output of the phase comparator 33, and if desired, the manual bias control 36.



As an example of the operation of the system, it will be assumed that the plasma 31 has the heating characteristics of the curve shown in FIGURE 4a. The input 36 to the frequency control circuit 35 is adjusted, for ex



penetrate the plasma and transfer energy to the ions therein.



In each of the transverse electric fields, ions are moved radially to the negative portion of the fields leaving an excess of electrons in the positive portion of each field. These electrons "feel" the positive space charge created by the ions in the adjacent field and are axially attracted thereto. The axial movement of electrons results in neu



40



applied to the plasma 31 to be altered up and down rap



tralization of the positive space charge and permits pene- 45 idly enough to leave the mean plasma temperature rising tration of the externally applied fields into the plasma to at an unaltered rate, depending on the average rate of promote heating of the ions therein. The frequency of the RF energy applied to the elec



trodes 17 and 17' will depend on what type of ions in the



gaseous plasma are to be heated and upon the intensity of the magnetic confining field. For example, when deuterium ions are to be heated and the confining field has an intensity of 20,000 gauss, the cyclotron resonance frequency is 15 me. Hence, RF energy at about the same frequency will be applied to the electrodes. If the field intensity is 50,000 gauss, a frequency of about 37.5 me. will be employed. The frequency with respect to tritium at 20,000 gauss will be about 10 me. and at 50,000 gauss will be about 25 me.



plasma heating.



As the center frequency of the radio frequency energy differs from the resonance of the plasma 31, a corre



50



spending change in temperature, and consequently the neutron output, occurs. This change is reflected in the signal output of detector 32. At a condition of plasma resonance, only the fundamental component of the signal from detector 32 passes through zero. The signal from 55 detector 32 is all second harmonic. In the absence of an input to the comparator 33 from filter 37, no output occurs from the comparator 33. Below the frequency of resonance, one phase of the fundamental component in the signal from detector 32 occurs. Above resonance,



In the operation of a device of the type shown in FIG- 60 the opposite phase of the fundamental component occurs. URES 1 and 2, the frequency of the radio frequency These two signal conditions are comparable in amplitude, energy used to heat the plasma should be close to the The phase comparator 33 is responsive to one phase of



the fundamental component to produce a positive control signal for application to the control circuit 35. The opvaries according to various factors as indicated above. 65 posite phase of the fundamental component results in the In order to maximize the rate of heating, the radio fre- production by the comparator 33 of a negative control quency must be controlled during the time of heating so signal. A typical control signal output from comparator



33 is shown in FIGURE 4b. The conventional phase comparator 33 functions to



selected natural resonance of the plasma ions. In practice, this natural resonance is not a fixed frequency but



as to keep in step with the particular resonance being used, for example, the cyclotron resonance.



One embodiment of a servo-loop system employed ac- 70 provide a direct current control signal according to the



cording to the invention to effect this frequency control is shown in FIGURE 3. A radio frequency (RF) induction heater 30 supplies RF power to heat a gas plasma 31. The heater 30 and plasma 31 may be as shown in



phase difference between a first and a second alternating current signal applied thereto. It is important that the connection for the control signal from the comparator 33 to the control circuit 35 be completed with attention



FIGURES 1 and 2, for example. Since, in a thermo- 75 being given to the correct polarity. Should the control



5



3,052,614



signal be applied to the control circuit 35 in the incorrect polarity, the frequency of the energy supplied by heater 30 will be driven too high or too low instead of being placed at the desired center.



The output of the phase comparator 33 is zero, when the fundamental component of the detector 32 output is zero at the correct center frequency. When the radio frequency is too low, the output of the comparator 33 is of one polarity, causing the control signal from the control circuit 35 to effect a rise in the RF heating frequency. When the radio frequency is too high, the output of the comparator 33 is of the opposite polarity, and the frequency is lowered by the control signal from the control circuit 35.



By the above operation, the radio frequency supplied by heater 30 will, as the plasma heats up, track in frequency to cause substantially maximum heating, no matter what causes the change in plasma resonance. The servoloop controls the mean radio frequency so as to hold it substantially at that frequency which produces the greatest increase in neutron output at all times. If needed, additional amplification may be provided in the servo-loop.



In describing the invention, a single heating stage has been assumed. Actually, a plurality of heating stages may be provided, as indicated by the dotted lines in FIGURE 1. The plurality of heating stages may all be operated at the same frequency or at different frequencies, /i, /2, and /3, with a separate RF generator and delay structure for each heating stage. Thus, if a plasma made up of a mixture of deuterium and tritium is to be heated, one heating stage can be operated at the deuterium resonane frequency and another at the tritium resonance frequency, thereby providing for maximized heating of all the ions in the plasma. Each radio frequency is controlled by a servo-loop system of the invention during the time of heating so that it keeps in step with the corresponding resonance of the plasma.



The principles of the invention are applicable to gas plasma devices not necessarily concerned with controlled fusion. For example, it is possible to obtain atomic nitrogen from molecular nitrogen in an RF gas discharge. When atomic nitrogen is frozen into a solid at very low temperature, it remains in the atomic state for long periods of time, until it is allowed to warm up. Thereafter, it releases a great deal of energy (10 e.v. per atom) and is useful fuel for rockets, and so on. Frozen atomic nitrogen can be obtained by a gas plasma heated by radio frequency, followed by a cold trap to freeze out the dissociated nitrogen.



To use the radio frequency heating to best advantage, it is desirable to alter the radio frequency as the plasma conditions change. By substituting an indicator of the •atomic nitrogen content for the neutron detector 32 of FIGURE 3, this can be done by the servo-loop system of the present invention. A mass-spectrograph can be connected to the gas discharge vessel and set up to indicate atomic nitrogen. The spectrograph can be made to provide an electrical output at frequency fs, indicating by its phase and amplitude whether the radio frequency for beating should be raised or lowered. The servo-loop operates in the manner described in connection with the embodiment of FIGURE 3.



The invention is useful in every instance where an electrical signal output can be obtained which indicates the quantity of the desired result. Dissociation of gas is one example, and new molecular combinations is a further example. Some molecules do not combine at low temperatures (i.e. silicon carbide) and can be caused to combine at high plasma temperatures. A mass-spectrograph can be used as the indicator of the desired compound formation.



There is often an advantage gained in the radio fre



quency heating of only the desired gas particles by best choice of frequency. For example, the cyclotron resonance of silicon and carbon can be used with separate controlled RF heaters to selectively heat them for molecu



5 lar combination, without at the same time excessively heating the silicon carbide molecule. Any dissociation of this molecule results in a loss of some of the desired output material. A system for accomplishing such doublefrequency heating would require only a separate servo



10 loop system as shown in FIGURE 3 for each radio frequency heater. What is claimed is:



1. In a device for heating a gaseous plasma within a substantially cylindrical container, the combination of



15 means for producing a substantially constant magnetic field directed along the axis of said container for confining said plasma,



means for heating said plasma with radio frequency energy including first and second groups of electrodes

Tables of frequency allocations and other extracts from : Manual of regulations and procedures for federal radio frequency management (SuDoc C 60.8:R 11/2000/TABLES)

20 positioned on said cylinder and spaced along the



longitudinal axis of the container, each group including a plurality of electrodes positioned about the circumference of said container and equally spaced at a predetermined angle with respect to each other



25 from said axis,



energy supplying means including a radio frequency source and phase shift means connected to both said first and second groups of electrodes and to all of said electrodes within each group for supplying to



30 each of the electrodes in any one group radio fre

International telecommunications and international law: The regulation of the radio spectrum

quency energy of different phase in proportion to their predetermined displacement angle within the group and in which the phase supplied to any electrode of one group is displaced 180° from the phase

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35 supplied to a similarly positioned electrode of the
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other group whereby two rotating radio frequency electric fields are produced along the longitudinal axis and transverse thereto which are phase displaced 180° with respect to each other,



40 means for supplying a first signal to said energy supplying means to cause said radio frequency to be altered up and down rapidly enough to leave the mean temperature of said plasma rising at an unaltered rate depending upon the average rate of heating, means coupled to said plasma and responsive to the neutron output of said plasma for producing a second signal indicative of the difference between the frequency of said radio frequency energy and a selected resonance frequency of said plasma, a comparator responsive to said first and second signals for producing a control signal, and means to apply said control signal to said energy supplying means to maintain the frequency of said energy substantially at said resonance frequency.



2. A combination as in claim 1 further including third and fourth groups of heating electrodes positioned on said cylinder along the axis of tube and displaced from said first and second groups, and means for connecting said third and fourth groups of electrodes to said radio frequency source in the same manner as the first and second groups were connected to thereby provide additional heating.
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Rundfunkubertragung: Rechtsfragen der Nutzung terrestrischer Rundfunkfrequenzen (Schriften zu Kommunikationsfragen) (German Edition)

Property System Approach to the Electromagnetic Spectrum: A Legal Economic Engineering (Cato paper)

Mexican radio station warned to keep its frequency to itself. (XEK-AM): An article from: San Diego Business Journal

  Changing frequencies: the merger of Maui's two largest broadcasters proves the Valley Isle's $3.5 million radio industry is getting a lot tougher.: An article from: Hawaii Business

SCA: A new medium / by Lorne A. Parker

Manual of regulations and procedures for federal radio frequency management (SuDoc C 60.8:R 11/2000)

Radio frequency spectrum : communication from the President of the United States transmitting notification that the government frequency assignments in ... Act of 1993 (SuDoc Y 1.1/7:105-43)

The IFRB handbook on radio regulatory procedures

NILECJ standard for personal FM transceivers: A voluntary national standard promulgated by the National Institute of Law Enforcement and Criminal Justice (Law enforcement standards program NILECJ-STD)

Coming, a law of communications conference (Working paper)

Federal Communications Commission unlicensed NII devices in the 5 GHz frequency range (SuDoc GA 1.13:OGC-97-19)

Final acts of the Regional Administrative Radio Conference to Establish a Plan for the Broadcasting Service in the Band 1605-1705 kHz in Region 2, Rio de Janeiro, 1988

Partial Revision (1985), Radio Regulations relating to broadcasting-satellite service in region 2 : report (to accompany Treaty doc. 102-28) (SuDoc Y 1.1/6:102-42)

Frequency spectrum deregulation alternatives to current FCC allocation, assignment and standards setting practices

FCC auction : location and monitoring service auction : economic area licenses, frequency blocks A-C : bidder information package (SuDoc CC 1.2:AU 2/3)

Agreement for the medium frequency broadcasting service in region 2 : report (to accompany Treaty doc. 100-7) (SuDoc Y 1.1/6:102-38)

Handbook, federal radio use, Boulder support

Emerging Telecommunications Technologies Act of 1991 : report (to accompany H.R. 531) (SuDoc Y 1.1/8:102-113)

Spectrum deregulation and market forces

Emerging telecommunication technologies : hearings before the Subcommittee on Telecommunications and Finance of the Committee on Energy and Commerce, House ... and March 12, 1991 (SuDoc Y 4.En 2/3:102-2)

Spectrum reallocation report response to Title III of the Balanced Budget Act of 1997 (SuDoc C 60.9:98-36)
A comparison of alternative spectrum regulatory approaches

The wireless craze, the unlimited bandwidth myth, the spectrum auction faux pas, and the punchline to Ronald Coase's 'big joke': An essay on airwave allocation policy (Working paper)

Emerging telecommunications technologies : hearing before the Subcommittee on Telecommunications and Finance of the Committee on Energy and Commerce, House ... spectrum (SuDoc Y 4.En 2/3:102-94)

Regional agreement on broadcasting service expansion in the Western Hemisphere : report (to accompany Treaty doc. 102-10) (SuDoc Y 1.1/6:102-39)

Troisieme edition de l'Annexe 1 a l'Accord regional (Geneve, 1975): Contenant, le plan d'assignations de frequence pour les stations de radiodiffusion ... (en dB), janvier 1987 (French Edition)

Seconde edition de l'Annexe 1 a l'Accord regional (Geneve, 1975): Contenant, le plan d'assignations de frequence pour les stations de radiodiffusion a ... gain de l'antenne (en dB), novembre 1981

Regional agreement on broadcasting service expansion in the Western Hemisphere : message from the President of the United States transmitting the Regional ... on June 8, 1988 (SuDoc Y 1.1/4:102-10)

An investigation of economic factors in FCC spectrum management

Communications airwaves: The private sector option (Backgrounder / The Heritage Foundation)

ICR mass spectroscopy

   Half Collision Resonance Phenomena in Molecules (AIP Conference Proceedings)
Radio Frequency Power in Plasmas: Charleston, SC 1991 (AIP Conference Proceedings)


Radio Frequency Power in Plasmas: 14th Topical Conference, Oxnard, California, 7-9 May 2001 (AIP Conference Proceedings)

Nuclear Science & Medical Imaging Including Nuclear Power Systems, 2000: Symposium


Radio Frequency Power Plasmas: 16th Topical Conference on Radio Frequency Power in Plasmas (AIP Conference Proceedings / Plasma Physics)


Nuclear Magnetic Phenomena: International Conference Proceedings, 1977
Model study of wave resonance in the cooling water intake structure, Tarapur Power Plant (Technical report)


Seminar on 238U Resonance Capture: Jointly sponsored by the Electric Power Research Institute and U.S.Energy Research and Development Administration (BNL-NCS-50451)

Medical Physics: Sixth Mexican Symposium on Medical Physics (AIP Conference Proceedings)
2000 IEEE Nuclear Science Symposium Conference Record: October 15-20, 2000





        inherent in all swept frequency excitation techniques is the fact that the excitation of different resonances does not occur simultaneously, but only at the time the resonant frequency is present in the excitation signal. 40 Additionally, the instrumentation required to produce chirp excitation for ICR mass spectroscopy is very sophisticated and expensive.


Conference Record of the 1992 IEEE Nuclear Science Symposium and Medical Imaging Conference


High power RF plasma heating and wave propagation near the fundamental and harmonics of the ion cyclotron frequency


Another method of simultaneously exciting multiple resonances is the rf burst excitation technique. This 45 technique is commonly used in NMR. However, rf burst excitation has been found to be inadequate for broad range mass spectroscopy. It was theorized in an article entitled "Theory of Fourier Transform Ion Cyclotron Resonance Mass Spectroscopy: Response to 50 Frequency-sweep Excitation" by Alan G. Marshall and D. Christopher Roe, published in /. Chem. Phys. Vol. 73, No. 4,1980, pp. 1581-1590, that simultaneous excitation of a broad mass range (from 15 to 500, corresponding to cyclotron frequencies from 50 kHz to 2 MHz at 55 2 Tesla) with the rf burst method would require an rf burst excitation signal having a duration of about 30 nanoseconds and an amplitude of 13,200 volts. Since it was and still is extremely impractical to create such a signal, this approach was abandoned in favor of the 60 above described frequency sweep chirp excitation.

Transmode sets the industry standard for low-latency transport at 4 nanoseconds.(NEW PRODUCTS): An article from: Fiber Optics Weekly Update


ELECTRODE PHENOMENA IN A HIGH CURRENT 20 NANOSECOND SPARK.


Nanosecond time differences by dynamic storage of flip-flop pulses (AFCRL)
Low power nanosecond pulse and logic circuits using tunnel diodes (NASA technical note)


Nanoseconds, megabytes, and apathy




Handbook for the nanosecond electron accelerator (NSEA) (ANL-6700. Instruments)


Monte Carlo superposition calculations of resonance integrals in a reactor cell (Riso-M-1257)


Cyclotron Resonance in Human Body Cells (Energy Science Report)


A carbon-13 nuclear magnetic resonance study of carbon dioxide and bicarbonate dynamics in suspensions of red blood cells


Nuclear magnetic resonance analysis of flavonoids (University of Texas publication)


Theory of two compartment water-molecule exchange for NMR relaxation in living tissues (Wisconsin medical physics)



Comprehensive research on stability of amorphous silicon and alloy materials and devices: Annual report, 31 May 1995 - 30 May 1996

Comprehensive research on stability and performance of a-Si:H and alloys: Phase I team annual technical report, 31 May 1994 - 30 May 1995

New plasma source of hydrides for epitaxial growth: Final subcontract report, 15 April 1991 - 3 September 1993 

A further advancement in ion cyclotron resonance mass spectroscopy is disclosed in U.S. Pat. No. 4,535,235 entitled "APPARATUS AND METHOD FOR INJECTION OF IONS INTO AN ION CY- 65 CLOTRON RESONANCE CELL," issued to Robert T. Mclver, Jr. on Aug. 13, 1985. The spectrometer disclosed in this patent is more versatile than those
Defense against nerve agents


previously developed because the ionizer for forming ions is outside the magnetic field and separate from the ion cyclotron resonance cell. Placing the ionizer outside of the magnetic field permits a wide variety of methods to be used to form ions from a sample. The ions are transported by a quadrupole mass filter through the fringing fields of the magnet and are injected into an ion cyclotron resonance cell that is disposed in the homogeneous region of the field. Once the ions are in the cell, they are accelerated and mass analyzed using either the methods of Fourier transform ion cyclotron resonance or ion cyclotron resonance power absorption.
Analysis of Subsynchronous Resonance in Power Systems (Power Electronics and Power Systems)


Analysis of Subsynchronous Resonance in Power Systems


Journal of Humanistic Psychology Vol. 47, No. 2 April 2007 (including Profound Sorrow and Buried Potential in Violent Youth, Transformative Power of Play, Archetypal Synchronistic Resonance)


Correlative Imaging: Nuclear Medicine Magnetic Resonance Computed Tomography Ultrasound


Power and Resonance. The International Tesla Society's Journal. October/November/December 1990 (Volume 6, Number 4)
Resonance Phenomena in Electron-Atom Collisions (Springer Series on Atoms and Plasmas, Vol 11)


A recent development in Fourier transform mass spectroscopy is described in an article entitled "Parametric Mode Operation of a Hyperbolic Penning Trap for Fourier Transform Mass Spectrometry" by D. L. Rempel, E. B. Ledford, Jr., S. K. Huang and M. L. Gross, published in Analytical Chemistry, Vol. 59, No. 20, pp. 2527-2532 (1987). Described in this article is a system wherein the static electric and magnetic fields of a hyperbolic Penning trap form a cell having fields which are similar to those in a single region ion

cyclotron resonance cell. However, instead of six flat electrodes, as disclosed in previously discussed U.S. Pat. No. 3,742,212 issued to Robert T. Mclver, Jr., the hyperbolic Penning trap comprises three electrodes, two "end caps" and one "ring" electrode, which are hyperbolas of revolution. Usable cyclotron resonance signals were obtained with this device by applying a near critically damped sinusoidal signal between the end caps and the ring electrode. The signal used for ion excitation has a peak of approximately +80 volts and a positive voltage duration of approximately 1.55 microseconds followed by a negative voltage portion having a peak of approximately —6.4 volts. However, the authors report that the tuning behavior of the Penning trap is unexpectedly sensitive to the trap voltage and the amplitude of the excitation signal. Furthermore, they suggest that this method can excite the z-axial mode sufficiently to cause ions to be ejected from the cell.




Although there are many advantageous features of the Fourier transform ion cyclotron resonance method, a number of problems and limitations remain. One disadvantage is that the computer-controlled frequency synthesizer, which is used to generate the pulsed broadband oscillating electric field, i.e. frequency chirp, is complex and expensive. Typically, it must be capable of scanning a frequency range of several megahertz in a time period of just a few milliseconds. In addition, the synthesizer must be highly stable and reproducible from scan to scan so that repetitive scans can be summed together coherently to improve the signal-to-noise ratio of the measurement.




Another disadvantage of the above described Fourier transform ion cyclotron resonance spectroscopy techniques is that ions of different mass are accelerated at different times as the frequency of the oscillating electric field is scanned. This complicates the Fourier transform analysis because ions of different mass have different initial phase angles for their cyclotron motion. Correcting the phase angle problem is further complicated by phase shifts in the signal amplifiers. The problem is so complex that most Fourier transform ion cyclotron resonance spectrometers present only a magnitude mode spectrum, which is a composite of the real and imaginary components which result from the Fourier transform analysis. This procedure produces a significantly broader line shape and degrades the mass resolu- lyzed. The Fourier analyzer receives the analog time tion of the spectrometer by about a factor of 2, domain signal and transforms the time domain signal Many of the deficiencies found in presently used into a frequency domain signal which contains informaresonance spectrometer systems could be overcome tion about the numerical magnitude, frequency and with a system which simultaneously excites all of the 5 phase of accelerated ions of each different mass-toresonant components. At the same time, the system charge ratio trapped in the analyzer cell, should be approximately equally sensitive to all of the The improved technique of the present invention also resonant components. Such a system should not be facilitates implementation of a method for using addioverly sensitive to other system parameters. It is also tional high voltage pulses, which are precisely delayed desireable that the system be of simple construction, 10 with respect to the initial excitation pulse to accelerate adaptable to a variety of resonance spectrometer con- or decelerate ions by known amounts of energy. For figurations and cost effective. A need thus exists for a example, if a second high voltage pulse is applied to the system which excites all ions in a short time interval, plates of the analyzer cell after a time delay which corless than a microsecond so as to more closely approxi- responds to an odd number of half cycles for ions of a mate the ideal situation of a delta function acceleration IS particular cyclotron frequency, these ions will be selecof the ions. Additionally, the system should provide tively decelerated by the electric field pulse and their more stable peak heights and better isotope ratios when radius of gyration will decrease. In one embodiment, used in Fourier transform mass spectroscopy. The pres- the initial and delayed pulses are created by a signal ent invention overcomes these and other short comings generator and a delay means precisely determines the of the prior art by providing a new and improved 20 time delay of the delayed excitation signal with respect method and apparatus for impulse acceleration of ions to the initial excitation signal.which is more sensitive, provides better resolution, is The invention further comprises a method of perless complex and less expensive than other broadband forming radiofrequency spectroscopy.