CN114664617A - Axial cascade relativistic magnetron based on ring rod coupling structure frequency locking and phase locking - Google Patents

Axial cascade relativistic magnetron based on ring rod coupling structure frequency locking and phase locking Download PDF

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CN114664617A
CN114664617A CN202210185797.1A CN202210185797A CN114664617A CN 114664617 A CN114664617 A CN 114664617A CN 202210185797 A CN202210185797 A CN 202210185797A CN 114664617 A CN114664617 A CN 114664617A
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anode
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CN114664617B (en
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周豪
李天明
何朝雄
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University of Electronic Science and Technology of China
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J23/00Details of transit-time tubes of the types covered by group H01J25/00
    • H01J23/36Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy
    • H01J23/40Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy to or from the interaction circuit
    • H01J23/44Rod-type coupling devices
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J23/00Details of transit-time tubes of the types covered by group H01J25/00
    • H01J23/16Circuit elements, having distributed capacitance and inductance, structurally associated with the tube and interacting with the discharge
    • H01J23/18Resonators
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J23/00Details of transit-time tubes of the types covered by group H01J25/00
    • H01J23/36Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy
    • H01J23/40Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy to or from the interaction circuit
    • H01J23/46Loop coupling devices
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J25/00Transit-time tubes, e.g. klystrons, travelling-wave tubes, magnetrons
    • H01J25/50Magnetrons, i.e. tubes with a magnet system producing an H-field crossing the E-field
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J2223/00Details of transit-time tubes of the types covered by group H01J2225/00
    • H01J2223/16Circuit elements, having distributed capacitance and inductance, structurally associated with the tube and interacting with the discharge
    • H01J2223/18Resonators
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J2223/00Details of transit-time tubes of the types covered by group H01J2225/00
    • H01J2223/36Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy
    • H01J2223/40Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy to or from the interaction circuit
    • H01J2223/44Rod-type coupling devices
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J2223/00Details of transit-time tubes of the types covered by group H01J2225/00
    • H01J2223/36Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy
    • H01J2223/40Coupling devices having distributed capacitance and inductance, structurally associated with the tube, for introducing or removing wave energy to or from the interaction circuit
    • H01J2223/46Loop coupling devices
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01JELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J2225/00Transit-time tubes, e.g. Klystrons, travelling-wave tubes, magnetrons
    • H01J2225/50Magnetrons, i.e. tubes with a magnet system producing an H-field crossing the E-field
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E30/00Energy generation of nuclear origin
    • Y02E30/10Nuclear fusion reactors

Abstract

The invention discloses an axial cascade relativistic magnetron based on a frequency locking phase locking of a ring-rod coupling structure, and belongs to the technical field of microwaves. The high-frequency coupling device comprises a plurality of high-frequency systems, wherein two adjacent high-frequency systems are axially cascaded through a coupling section, and the coupling section comprises a cylindrical shell, a cathode connecting rod, a plurality of coupling rods which are the same in size and are uniformly distributed along the circumference, and two coupling rings. The invention adjusts the electromagnetic coupling strength between high-frequency electromagnetic fields in adjacent high-frequency structures by loading the ring-rod coupling structure between the adjacent high-frequency structures, overcomes the interference of a strong current effect associated electromagnetic field of a relativistic magnetron, and realizes the frequency locking and phase locking of the cascaded relativistic magnetron.

Description

Axial cascade relativistic magnetron based on ring rod coupling structure frequency locking and phase locking
Technical Field
The invention belongs to the technical field of microwaves, and particularly relates to an axial cascade relativistic magnetron based on a frequency locking phase locking of a ring-rod coupling structure.
Background
From the perspective of practical high-power microwave systems, the development of high-power microwave systems mainly focuses on the following aspects: (1) the system is miniaturized and compacted, and the power consumption ratio is improved; (2) high repetition frequency operation; (3) the frequency can be tuned; (4) outputting in multiple frequencies; (5) and (4) synthesizing the output of the phase-locked array and the power. Since its birth, the relativistic magnetron has been receiving attention due to its compactness and high efficiency. In order to meet the development and application requirements of future high-power microwave sources, a relativistic magnetron with the characteristics of high output power, high conversion efficiency, suitability for long-pulse and high-repetition-frequency operation, frequency-locking phase-locking multiport output and the like becomes an important research target of people.
Classified according to the topology, there are 3 types of relativistic magnetron phase-locking methods proposed at present, which are allelic phase-locking, injection phase-locking, and cascade phase-locking, respectively. In 1989, the relativistic magnetron of allelic phase locking was proposed by the company James N.Benford, U.S. Physics International, and the output ports of 2A 6 relativistic magnetrons placed in parallel were connected by rectangular waveguides to realize locking, and the other ports were used for microwave output, and the output power of about 3GW was obtained under the condition that the two magnetrons work together. In 1991, Todd A.Treado et al, Varian Associates, Inc. in the United states, proposed a relativistic magnetron with injection phase locking, and it was experimentally determined that the relativistic magnetron can generate 52MW output power under the condition of phase locking by injecting power to one port of the relativistic magnetron with an S-band 3MW coaxial magnetron. In 1992, General Dynamics group Keith g.kato et al, usa proposed a relativistic magnetron with cascade phase locking, where anodes of 4 eight-cavity magnetrons were arranged at equal intervals in the axial direction, and corresponding cathodes in the respective tubes were connected into one body, and it was intended to obtain output power with a total of more than 1GW at 16 output ports. In 2015, Andrey d.andreev, Raytheon, usa proposed a slot-type conventional magnetron that implemented cascade locking using an axial spacer strip to connect the anode blocks of adjacent magnetrons.
When a plurality of relativistic magnetrons are arranged in a cascade manner, a strong current which is several times of the working current of a single magnetron flows through a cathode rod close to one end of an accelerator, an angular induction magnetic field with amplitude which is similar to that of an axially applied magnetic field is caused in an injection-wave interaction region, and further, the axial drift of electrons, the jump of a working mode, the frequency shift effect and the pulse shortening effect are caused, so that the frequency locking and phase locking of the cascade relativistic magnetron fails.
The coupling mode of the currently proposed cascaded phase-locking scheme is single, the cascaded phase-locking relativistic magnetron realizes high-frequency electromagnetic field interaction mainly by drawing the distance between adjacent magnetrons, and the cascaded phase-locking conventional power magnetron realizes electric coupling by conducting anode blocks in the adjacent magnetrons by using an axial mode isolation belt, and the two schemes still have more limitations in practical application.
The structural characteristics of the resonance system can be changed by shortening the distance between the adjacent anode blocks, so that the coupling impedance of each intrinsic mode of the magnetron is changed, the working area of the expected working mode of the magnetron is easily narrowed, a certain electronic tuning range is lost, higher requirements on the regulation and control precision of an external anode voltage and an external axial magnetic field are provided, and the practicability of the magnetron is reduced. Meanwhile, the axial distance between adjacent magnetron extraction channels is too small, so that the structural design difficulty is improved, and the layout flexibility is reduced.
The design scheme of the axial diaphragm band has good operation effect in the cascade conventional power magnetron, but the ideal working state is difficult to achieve in the cascade relativistic magnetron. The strong current flowing through the cathode of the cascade relativistic magnetron causes a strong angular induced magnetic field in the injection-wave interaction region between the cathode and the anode, and the strong angular induced magnetic field and the radial electric field between the cathode and the anode jointly push electrons to do axial drift motion, so that the electron density distribution in each interaction region of the cascade magnetron is unbalanced, and further the output power difference of each tube is overlarge. The strong angular electric field has a higher harmonic mode which is easy to excite and has a larger difference with the working frequency point of the fundamental mode. Phase locking is difficult to achieve with only conventional diaphragm band structures.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the axial cascade relativistic magnetron based on the frequency locking and phase locking of the ring-rod coupling structure on the basis of the axial cascade relativistic magnetron.
The technical scheme adopted by the invention is as follows:
an axial cascade relativistic magnetron based on frequency locking and phase locking of a ring-rod coupling structure comprises a plurality of high-frequency systems;
the high-frequency systems respectively comprise a cathode, an anode and a plurality of coupling gaps;
the anode comprises a cylindrical anode shell and a plurality of fan-shaped anode blades which are uniformly distributed in the anode shell along the circumference, and the fan-shaped anode blades of each high-frequency system are the same in number; a sector cavity between two adjacent sector anode vanes is a resonant cavity;
the cathode comprises a cathode electron emission structure; the cathode electron emission structure is arranged at the central position of the inner cavity of the anode shell and is coaxial with the anode shell;
the coupling gap is arranged on the anode shell and used for radially coupling and outputting energy in the resonant cavity;
the method is characterized in that two adjacent high-frequency systems are axially cascaded through a coupling section; the coupling section comprises a cylindrical shell, a cathode connecting rod, a plurality of coupling rods which are the same in size and are uniformly distributed along the circumference, and two coupling rings;
the cylindrical shell makes the inner walls of the anode shells of two adjacent high-frequency systems linearly transition;
the cathode connecting rod is of a cylindrical structure, and two ends of the cathode connecting rod are respectively connected with and support cathode electron emission structures of two adjacent high-frequency systems;
the coupling rod is of a cylindrical structure, and two ends of the coupling rod are respectively connected with the end surfaces of the fan-shaped anode blades of two adjacent high-frequency systems;
the coupling ring is of a circular ring structure and is coaxial with the coupling section; the coupling rings are communicated with the coupling rods.
Furthermore, the high-frequency systems are all in the same cavity structure or all in different cavity structures.
Furthermore, the distance from the center of the cross section of the coupling ring to the axis of the coupling section is greater than the inner radius of the fan-shaped anode blade and less than the outer radius of the resonant cavity.
Further, the distance between the coupling ring and the nearest anode blade is 0.5-2 times of the axial length of the anode blade; the axial length of the coupling section is 0.5-2 times of the working wavelength.
Further, the diameter of the coupling rod is 1-20 mm; the diameter of the cross section of the coupling ring is 1-20 mm.
Further, the number of the fan-shaped anode vanes is 2N, the number of the coupling rods is N, and N is usually 3-9.
Further, a rectangular waveguide is arranged outside the coupling gap to serve as an energy output structure.
The working principle of the cascade relativistic magnetron of the invention is as follows: high-frequency electromagnetic fields are transmitted into adjacent high-frequency structures from one high-frequency structure through the ring-rod coupling structure, and electromagnetic resonance frequency synchronization and high-frequency electromagnetic field phase locking in the two pipes are achieved. In the loop-rod coupling phase-locking relativistic magnetron structure, a coupling loop, a coupling rod and an anode blade form an electromagnetic oscillation loop, an axial magnetic field in a high-frequency electromagnetic field is on a closed curved surface surrounded by the coupling loop, the change of magnetic flux enables the coupling loop to generate loop electromotive force, induced electromotive force is transmitted to the coupling loop close to an adjacent magnetron along the axial direction through the coupling rod, finally, high-frequency electromagnetic resonance with the frequency and the phase related to the original magnetron is excited in the interaction area of the adjacent magnetron, a loop-rod coupling structure is adjusted, the potential synchronization relation of the resonant cavities of the adjacent high-frequency systems and the magnetic flux distribution rule in the transition region between the adjacent high-frequency systems can be changed, therefore, the electromagnetic coupling strength between high-frequency electromagnetic fields in adjacent high-frequency structures is adjusted, the interference of a relativistic magnetron strong current effect accompanying electromagnetic fields is overcome, and the frequency locking and phase locking of the cascaded relativistic magnetron are realized.
The invention has the beneficial effects that:
(1) the loop-rod coupling structure provides enough coupling strength for adjacent high-frequency structures, overcomes the interference of non-uniform electromagnetic fields accompanied by the strong current effect of the relativistic magnetron on the phase locking process, and realizes the cascade frequency locking and phase locking output of the relativistic magnetron.
(2) Due to the arrangement of the coupling section structure, the anode blades of the adjacent high-frequency structures in the cascade magnetron have larger intervals, so that a reasonable geometric structure is provided for the working mode, the mode purity can be improved, and the mode competition can be avoided.
(3) The coupling section structure reserves a large enough anode end space on the premise of ensuring enough coupling degree between the tubes, and solves the problems of pulse shortening, frequency drift, efficiency reduction and the like caused by the growth of plasmas generated by explosive emission in an interaction region.
(4) The loop-rod coupling structure has better coupling and phase-locking performance than the axial mode-separating band structure in the relativistic magnetron.
(5) The axial distance of the magnetron brought by the coupling section structure is large enough, so that the problem that the distance between the output structures of adjacent tubes is too small is solved, the flexibility of structural design is improved, and the practicability of the cascade phase-locked relativistic magnetron is facilitated.
Drawings
FIG. 1 is a schematic diagram of the overall structure of a loop-rod coupled cascade relativistic magnetron according to an embodiment;
FIG. 2 is a longitudinal cross-sectional view of a split large cavity of an embodiment of a loop-rod coupled cascade relativistic magnetron;
FIG. 3 is a longitudinal cross-sectional view of a split small cavity of an embodiment of a loop-rod coupled cascade relativistic magnetron;
FIG. 4 is a transverse cross-sectional view of a magnetron of an embodiment of a loop-rod coupled cascade relativistic magnetron;
FIG. 5 is a dimension drawing of an embodiment of a loop-rod coupled cascade relativistic magnetron;
FIG. 6 is a drawing showing a cross-sectional dimension of a high-frequency system of the loop-rod coupled cascade relativistic magnetron of the embodiment;
FIG. 7 is a graph of output signal power for a loop-rod coupled cascaded relativistic magnetron;
FIG. 8 is a graph of the output signal spectrum of a loop-rod coupled cascaded relativistic magnetron.
Description of the reference numerals: 11. the cathode electron emission structure 12, a cathode connecting rod 21, an anode blade 22, an anode shell 31, a coupling rod 32, a coupling ring 33, a cylindrical shell 41, a rectangular waveguide 42, a coupling gap 51, a large resonant cavity 52 and a small resonant cavity.
Detailed Description
The present invention will be further described with reference to specific embodiments for better illustrating the objects, advantages and technical idea of the present invention. It should be noted that the specific examples given below serve only to explain the present invention in detail, and do not limit the present invention.
Fig. 1 to 5 are schematic diagrams of a loop-rod coupled cascade relativistic magnetron structure according to this embodiment, in which the cascade relativistic magnetron includes two high-frequency systems with the same size, and the two high-frequency systems are axially cascaded through a coupling segment.
The high-frequency structure in this embodiment is an asahi-sun type resonator structure having 8 resonant cavities, and includes a cathode, an anode, and a coupling slit. The anode comprises a cylindrical anode shell and 8 fan-shaped anode blades which are uniformly distributed in the anode shell along the circumference, and a fan-shaped cavity between every two adjacent fan-shaped anode blades is a resonant cavity. The inner radius of the anode shell is 36 mm; axial length h of anode vanea68mm, anode vane opening angle
Figure BDA0003523348270000051
Is 25deg, inner radius RaIs 16 mm; small resonant cavity opening angle
Figure BDA0003523348270000052
And large resonant cavity opening angle
Figure BDA0003523348270000053
Are all 20deg, small resonant cavity radius Rv1Is 28mm, and has a large resonant cavity radius Rv2Is 36 mm; axial dimension h of end spaceeIs 30 mm.
The cathode comprises a cylindrical cathode electron emission structure arranged in the anode shell and coaxial with the anode shell, and the radius R of the cathodecIs 7mm and has an axial length hcIs 52 mm.
The coupling slits are 4 rectangular slits arranged on the anode shell, the size of the wide side and the narrow side w of each rectangular slit is 72x8mm, a rectangular waveguide is arranged outside each rectangular slit, and the size of the wide side a and the narrow side b of each rectangular slit is 72x34mm, so that the coupling slits are used for radially coupling and outputting energy in the resonant cavity.
The coupling section comprises a cylindrical shell with the inner radius of 36mm, a cathode connecting rod, 4 coupling rods with the same size and evenly distributed along the circumference and 2 coupling rings.
The cathode connecting rod is of a cylindrical structure with the radius of 5mm, and two ends of the cathode connecting rod are respectively connected with and support cathode electron emission structures of two adjacent high-frequency systems.
The coupling rod has a diameter DstripIs 2mm and has an axial length daIs a 105mm cylinder structure, two ends of the cylinder structure are respectively connected with the end surfaces of the fan-shaped anode blades of two adjacent high-frequency systems, and the distance R between the central axis of the coupling rod and the central axis of the high-frequency systemsstripIs 23 mm.
The coupling ring is in a circular ring structure communicated with the coupling rods, and the diameter D of the cross section of the coupling ringring2mm, the distance R from the center of the cross section of the coupling ring to the axis of the coupling sectionring23mm, the distance d between the two coupling ringsringIs 51 mm.
The coupling rings are perpendicularly intersected with each coupling rod and realize conductive connection.
A loop-rod coupled cascade relativistic magnetron with the working frequency of 2.89GHz is simulated and realized according to the embodiment. 6-7, under the conditions that the working voltage is 450kV and the axial guiding magnetic field is 0.37T, the adjacent cascaded magnetrons realize phase locking at the moment of 15 ns.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention.

Claims (7)

1. An axial cascade relativistic magnetron based on frequency locking and phase locking of a ring-rod coupling structure comprises a plurality of high-frequency systems;
the high-frequency systems respectively comprise a cathode, an anode and a plurality of coupling gaps;
the anode comprises a cylindrical anode shell and a plurality of fan-shaped anode blades which are uniformly distributed in the anode shell along the circumference, and the fan-shaped anode blades of each high-frequency system are the same in number; a sector cavity between two adjacent sector anode vanes is a resonant cavity;
the cathode comprises a cathode electron emission structure; the cathode electron emission structure is arranged at the central position of the inner cavity of the anode shell and is coaxial with the anode shell;
the coupling gap is arranged on the anode shell and used for radially coupling and outputting energy in the resonant cavity;
the method is characterized in that two adjacent high-frequency systems are axially cascaded through a coupling section; the coupling section comprises a cylindrical shell, a cathode connecting rod, a plurality of coupling rods which are the same in size and are uniformly distributed along the circumference, and two coupling rings;
the cylindrical shell makes the inner walls of the anode shells of two adjacent high-frequency systems linearly transition;
the cathode connecting rod is of a cylindrical structure, and two ends of the cathode connecting rod are respectively connected with and support cathode electron emission structures of two adjacent high-frequency systems;
the coupling rod is of a cylindrical structure, and two ends of the coupling rod are respectively connected with the end surfaces of the fan-shaped anode blades of two adjacent high-frequency systems;
the coupling ring is of a circular ring structure and is coaxial with the coupling section; the coupling rings are communicated with the coupling rods.
2. The axial cascade relativistic magnetron of claim 1, wherein the high-frequency systems are all of the same cavity structure or all of different cavity structures.
3. The axial cascade relativistic magnetron of claim 1 or 2, wherein the distance from the center of the cross section of the coupling ring to the axis of the coupling section is greater than the inner radius of the fan-shaped anode blade and less than the outer radius of the resonant cavity.
4. The axial cascade relativistic magnetron of claim 3, wherein the distance from the coupling ring to the nearest anode vane is 0.5-2 times the axial length of the anode vane; the axial length of the coupling section is 0.5-2 times of the working wavelength.
5. The axial cascade relativistic magnetron based on the frequency locking and the phase locking of the ring-rod coupling structure as claimed in claim 4, wherein the diameter of the coupling rod is 1-20 mm; the diameter of the cross section of the coupling ring is 1-20 mm.
6. The axial cascade relativistic magnetron based on the frequency locking and phase locking of the ring-rod coupling structure as claimed in claim 1 or 2, wherein the number of the fan-shaped anode vanes is 2N, and the number of the coupling rods is N, wherein N is 3-9.
7. The axial cascade relativistic magnetron of claim 1 or 2, wherein the rectangular waveguide is arranged outside the coupling gap as an energy output structure.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2546870A (en) * 1941-10-03 1951-03-27 English Electric Valve Co Ltd High-frequency electrical oscillator
FR2918517A1 (en) * 2007-07-03 2009-01-09 Univ La Reunion Microwave emitting device for e.g. solar power satellite, has locking unit locking frequency of each secondary module and with unit connecting circulator input of each secondary module to output of coupler of previous secondary module
US20110254443A1 (en) * 2009-10-20 2011-10-20 Michael Neubauer Phase and frequency locked magnetron
CN105428191A (en) * 2015-12-21 2016-03-23 电子科技大学 Relativistic magnetron for realizing frequency hopping operation by utilizing transparent negative electrode
US20170169982A1 (en) * 2015-12-10 2017-06-15 Raytheon Company Axial strapping of a multi-core (cascaded) magnetron
CN109686636A (en) * 2018-12-06 2019-04-26 电子科技大学 A kind of magnetron structures with modular nature

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2546870A (en) * 1941-10-03 1951-03-27 English Electric Valve Co Ltd High-frequency electrical oscillator
FR2918517A1 (en) * 2007-07-03 2009-01-09 Univ La Reunion Microwave emitting device for e.g. solar power satellite, has locking unit locking frequency of each secondary module and with unit connecting circulator input of each secondary module to output of coupler of previous secondary module
US20110254443A1 (en) * 2009-10-20 2011-10-20 Michael Neubauer Phase and frequency locked magnetron
US20170169982A1 (en) * 2015-12-10 2017-06-15 Raytheon Company Axial strapping of a multi-core (cascaded) magnetron
CN105428191A (en) * 2015-12-21 2016-03-23 电子科技大学 Relativistic magnetron for realizing frequency hopping operation by utilizing transparent negative electrode
CN109686636A (en) * 2018-12-06 2019-04-26 电子科技大学 A kind of magnetron structures with modular nature

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
刘青雨: "某脉冲磁控管电参数与热性能的分析与优化仿真", no. 2 *

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