A compact L-band relativistic Cherenkov microwave generator

Abstract

The invention relates to a microwave source device in the field of high-power microwave technology, in particular to an L-band compact relativistic Cherenkov microwave generating device, belonging to the field of high-power microwave technology; the device comprises a cathode structure, an external electromagnetic structure and an internal electromagnetic structure, wherein the cathode structure comprises a cathode seat and a cathode; the external electromagnetic structure comprises an anode outer cylinder, an external cut-off neck, an external conductor corrugation, a collector, a collector baffle and a solenoid coil; the internal electromagnetic structure comprises an internal cut-off neck, an internal conductor corrugation, a short-circuit block and a microwave output port; the entire structure is rotationally symmetric about a central axis; the invention adopts a coaxial non-uniform double-corrugated slow-wave structure to strengthen beam-wave coupling through reasonable design of the electromagnetic structure, realizes a high-efficiency beam-wave effect in a relatively short period, adopts a coaxial collector structure to improve the resonance characteristics of the slow-wave structure to reduce the axial size, thereby realizing miniaturization and compactness of the device.

Description

Technical Field

[0001] The invention relates to a microwave source device in the field of high-power microwave technology, in particular to an L-band compact relativistic Cherenkov microwave generating device, belonging to the field of high-power microwave technology. Background Art

[0002] High-power microwave (HPM) is usually defined as electromagnetic waves with a frequency of 300MHz ~ 300GHz and a peak power of more than 100MW. HPM source refers to the device in the HPM system that converts the energy of high-current relativistic electron beams into microwave energy, that is, generates HPM. Thanks to the in-depth research on pulse power technology, relativistic vacuum electronics and plasma physics, HPM source technology has developed rapidly in recent years.

[0003] L-band high-power microwaves have important application prospects in various fields of the national economy due to their advantages such as low free-space transmission loss and strong diffraction ability, and have attracted the attention of scientific researchers. However, the biggest challenge in the research of L-band relativistic high-power microwave generating devices is the difficulty in miniaturization due to the size effect. Therefore, the research on miniaturized, high-power, and high-efficiency low-frequency relativistic microwave generating devices is a research hotspot in the field of high-power microwaves.

[0004] The patent scheme of the invention patent "A compact high-power microwave device with low-guiding magnetic field in L-band (patent number: ZL 201811500555.7)" applied by Zhang Yunjian et al. from the Institute of Applied Electronics, China Academy of Engineering Physics (hereinafter referred to as prior art 1, such as Figure 1 (as shown in the figure) adopts a four-cavity coaxial inner conductor slow-wave structure. The designed L-band device consists of four resonant cavities, namely a microwave reflection cavity, a beam-wave interaction cavity and a microwave double extraction cavity. Under the conditions of a diode voltage of 450kV and a current of 6.0kA, an L-band microwave output with a power of 500MW was obtained, and the conversion efficiency was 18.5%. The length of the beam-wave interaction region of the device is 0.78λ, and the compact design has been well completed, but the following problems still exist: (1) The device output efficiency is 18.5%, and the output power is only hundreds of megawatts. The device's efficiency in extracting electron beam energy is extremely low, which does not meet the practical requirements of compact devices; (2) The device adopts a rectangular slow-wave structure design, which easily forms charge accumulation at the right-angle vertex, leading to RF breakdown, making it difficult to meet high-power output requirements.

[0005] In 2022, Zhang Peng and others from the National University of Defense Technology designed a sub-microsecond compact L-band relativistic Cherenkov oscillator [Research on Sub-Microsecond Compact L-Band Relativistic CherenkovOscillator [J]. IEEE Transactions on Electron Devices, 2022, 69(10): 6352-6357.] (hereinafter referred to as prior art 2, such as Figure 2 As shown). The device introduces a coaxial external corrugated slow-wave structure to improve the power capacity of the slow-wave structure. At the same time, the collector structure is improved to suppress the expansion of the plasma. Under the conditions of diode voltage of 450kV and current of 10kA, a microwave output of 2GW and frequency of 1.5 GHz is obtained, with a power efficiency of 44%. The scheme has a high conversion efficiency, and the size of the device beam action area is 0.75λ, but the device still has the following problems: (1) The single corrugated slow-wave structure design is adopted, and the high-frequency field generated by the slow-wave structure has limited modulation strength on the electron beam, making it difficult to achieve high-efficiency beam coupling; (2) The device adopts a cascade design of reflection cavity-slow-wave structure-extraction cavity, resulting in a long beam action area, which still needs further compact design.

[0006] In summary, L-band relativistic high-power microwave generating devices have achieved a conversion efficiency of 40%, but the beam-wave interaction zone length of the existing technical solutions is above 0.75λ. Therefore, it is urgent to study an L-band relativistic high-power microwave generating device that can take into account both high efficiency and high compactness. Summary of the invention

[0007] The technical problem to be solved by the present invention is: the present invention provides an L-band compact relativistic Cherenkov microwave generating device, which overcomes the problems of large device size and insufficient compact structure of conventional L-band relativistic high-power microwave generating devices, and through reasonable design of electromagnetic structure, adopts a coaxial non-uniform double-corrugated slow-wave structure to strengthen beam-wave coupling, realizes high-efficiency beam-wave action in a shorter period, and adopts a coaxial collector structure to improve the resonant characteristics of the slow-wave structure to reduce the axial size, thereby realizing miniaturization and compactness of the device.

[0008] The technical solution of the present invention is:

[0009] An L-band compact relativistic Cherenkov microwave generating device comprises a cathode structure, an external electromagnetic structure and an internal electromagnetic structure. The cathode structure comprises a cathode seat 301 and a cathode 302; the external electromagnetic structure comprises an anode outer cylinder 303, an external cut-off neck 304, an external conductor corrugation 306, a collector 307, a collector baffle 311 and a solenoid coil 312; the internal electromagnetic structure comprises an internal cut-off neck 305, an internal conductor corrugation 308, a short-circuit block 309 and a microwave output port 310; and the entire structure is rotationally symmetric about a central axis.

[0010] The cathode 302 is a thin-walled cylinder, which is sleeved on the right end of the cathode seat 301, with a wall thickness of 0.1mm, a radius equal to the radius R1 of the electron beam, and a length of L1. The left side of the anode outer cylinder 303 is a cylindrical cylinder with an inner radius of R2, and the inner surface on the right side has irregular corrugations, forming a high-frequency structure; the inner cutoff neck 305 is disc-shaped, with a radius of R3 and a length of L2; the outer cutoff neck 304 is annular, and a slope is formed on its left side, which gradually changes from the radius R2 to the radius R4. The slope is used to increase the radial confinement electric field of the electrons at the cathode and improve the quality of the electron beam, satisfying R2>R4>R1>R3, and the length is L3. The values ​​of L2 and L3 are 0.01-0.1 times the working wavelength.

[0011] The outer conductor corrugation 306 is composed of two trapezoidal cavities. The outer radius of the first trapezoidal cavity is R7, the length of the upper base is L5, and the length of the short hypotenuse projection is L 15 , the length of the long hypotenuse projection is L 18 , satisfying L 18 >L 15 >L5; the outer radius of the second trapezoidal cavity is R 10 , satisfying R 10 >R7, the length of the upper base is L9, satisfying L9>L5, and the length of the short hypotenuse projection is L 22 , the length of the long hypotenuse projection is L 20 , satisfying L9>L 20 >L 22 The first trapezoidal cavity and the second trapezoidal cavity are connected by a ring with an inner radius of R9 and a length of L8, where L8 is 5mm-15mm; the collector 307 is a circular ring cavity with a parallelogram cross section and an outer radius of R 16 , the inner radius is R 13 , the length of the upper base is L 12 The projection lengths of the two hypotenuses are L 11 and L 24 , L 11 and L 12 According to the comprehensive design of electron beam bombardment position and magnetic field configuration, L 11 The value is 0.1-0.2 times of the working wavelength λ, L 12The value is 0.1-0.2 times of the working wavelength λ; the inner radius between the outer conductor corrugation 306 and the collecting electrode 307 is R 12 , length L 10 The ring connection, L 10 The value is 5mm-15mm; the short-circuit block 309 is a circular ring with a rectangular cross section and an outer radius of R 14 , the inner radius is R 15 , length L 13 , L 13 The value is 15mm-20mm. This structure can enhance the resonance characteristics of the device and achieve the function of frequency selection. The collector baffle 311 is an outer radius of R 13 , inner radius is R 14 The ring is used to prevent the plasma generated by electrons bombarding the collector from spreading to other parts of the device.

[0012] The inner conductor corrugation 308 is composed of two trapezoidal cavities. The inner radius of the first trapezoidal cavity is R5, the length of the upper base is L4, and the length of the short hypotenuse projection is L 14 , the length of the long hypotenuse projection is L 16 , satisfying L 16 >L4>L 14 ; The inner radius of the second trapezoidal cavity is R8, satisfying R5>R8, the length of the upper base is L7, satisfying L4>L7, and the length of the short hypotenuse projection is L 17 , the length of the long hypotenuse projection is L 19 , satisfying L 19 >L 17 >L7; the first trapezoidal cavity and the second trapezoidal cavity are connected by a disk with a radius of R6 and a length of L6, where L6 is 5mm-15mm; the right side of the second trapezoidal cavity is connected to a disk with a radius of R 11 , length L 21 The disk, L 21 The value is 30mm-35mm; the microwave output port 310 is an outer radius of R 14 , the inner radius is R 17 , length L 25 The annular cavity, L 25 The value is 0.5-1 times of the working wavelength; the left side of the microwave output port 310 forms a 11 Gradient to radius R 17 The length of the projection of the inclined plane is L. 23 , L 23 The value is 2mm-6mm; a radius of R is set at the center of the microwave output port. 17 , length L 25The cylindrical structure is connected to the inclined surface and forms a coaxial output structure with the anode outer cylinder 303; the right end of the microwave output port 310 is connected to the antenna;

[0013] The solenoid coil 312 is a wound solenoid magnetic field. By changing the magnitude of the current passing through the solenoid magnetic field, the intensity of the magnetic field generated by the solenoid is changed, thereby achieving transmission guidance of the electron beam.

[0014] The working process of the present invention is as follows: The pulse voltage generated by the pulse power driving source acts on the cathode 302 through the cathode seat 301. The right end face of the cathode 302 generates a strong current relativistic electron beam based on the explosive emission, which is transmitted to the high-frequency structure under the guidance of the solenoid magnetic field 312. The electron beam passes through the cutoff neck (outer cutoff neck 304, inner cutoff neck 305), the slow wave structure (outer conductor corrugation 306, inner conductor corrugation 308), and finally bombards the collector 307. The coaxial double-corrugated slow-wave structure has a higher coupling impedance than the coaxial single-corrugated slow-wave structure. In the process of beam-wave interaction, the electron beam transfers more energy to the radio frequency field, thereby oscillating and generating microwaves. The generated microwaves are finally radiated outward through the microwave output port 310.

[0015] The present invention can achieve the following technical effects: in particle simulation, under the conditions of diode voltage 426kV, current 6.5kA, and guide magnetic field 1.28 T, the microwave power is outputted at 1.12GW, and the power conversion efficiency is 40%.

[0016] Compared with the prior art, the present invention can achieve the following technical effects:

[0017] 1. The present invention adopts a specially designed slow-wave structure, the main functions of which are as follows:

[0018] (a) Double-corrugated coaxial structure: The double-corrugated coaxial structure is conducive to the formation of a strong body wave field, increasing the electron beam clustering speed, improving the electron beam clustering depth, strengthening beam-wave coupling, achieving high-efficiency beam-wave action in a shorter period, and realizing high-power and high-efficiency output of compact devices.

[0019] (b) Single-segment type: The slow-wave structure period of the L-band device is relatively long (>7cm). If a segmented slow-wave structure is used, the slow-wave action area will be relatively long, which requires the axially uniform magnetic field to be distributed in a relatively long area, which will inevitably increase the volume of the magnetic excitation coil and bring difficulties to the confinement and transmission of the electron beam. The present invention adopts a single-segment double-period slow-wave structure, and the axial length of the beam action area is 13.5cm, which is 0.56 times the wavelength of the radiated microwave. Under the premise of ensuring the efficiency of the device, the axial length of the device is effectively shortened.

[0020] (c) Trapezoidal structure: Compared with the rectangular structure, the trapezoidal structure can better modulate the electron beam passing through the center of the cavity. In addition, the distance between the conductor tips on both sides of the cavity is increased, which can weaken the local field strength at the conductor tip and reduce the risk of strong field breakdown, which is beneficial to improving the power capacity of the device.

[0021] 2. The present invention adopts a coaxial collector, the main functions of which are as follows:

[0022] (a) After interacting with the microwave field, the electron beam still has high energy. The collector absorbs this energy and reduces the speed of the electron beam, thereby reducing the damage of the electron beam to the device.

[0023] (b) The introduction of a coaxial collector can enhance the resonant characteristics of the operating mode, which is beneficial for reducing the number of periodic slow-wave structures and shortening the axial size of the device.

[0024] (c) The collector baffle can effectively isolate the microwave output area and the electron beam collection area, thereby preventing the large amount of plasma generated by the electron beam bombarding the collector from quickly spreading to the microwave output waveguide, ensuring that the device outputs microwaves normally and stably. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 A schematic diagram of the structure of an L-band low-guided magnetic field compact high-power microwave device disclosed in the prior art 1 in the background introduction;

[0026] Figure 2 A schematic diagram of the structure of a sub-microsecond compact L-band relativistic Cherenkov oscillator disclosed in prior art 2 in the background introduction;

[0027] Figure 3 An AA cross-sectional view of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention;

[0028] Figure 4 A-A cross-sectional stereoscopic schematic diagram of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention;

[0029] Figure 5 A graph showing the variation of microwave output power over time of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention;

[0030] Figure 6 An output microwave spectrum diagram of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention;

[0031] Figure 7A graph showing the variation of the efficiency of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention with the strength of an applied magnetic field;

[0032] Figure 8 A graph showing the variation of efficiency of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention with diode voltage;

[0033] Fig. 9 A comparison diagram of the S21 variation with frequency of the output waveguide when there is a collector and there is no collector in a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention;

[0034] Fig.10 A dispersion curve (corresponding to the L band) of a slow-wave structure of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention;

[0035] Fig.11 A comparison diagram of the Q values ​​of the internal and external output waveguides of a preferred embodiment of an L-band compact relativistic Cherenkov microwave generating device provided by the present invention. DETAILED DESCRIPTION

[0036] The present invention consists of a cathode seat 301, a cathode 302, an anode outer cylinder 303, an outer cut-off neck 304, an inner cut-off neck 305, an outer conductor corrugation 306, a collector 307, an inner conductor corrugation 308, a short-circuit block 309, a microwave output port 310, a collector baffle 311 and a solenoid magnetic field 312, and the entire structure is rotationally symmetrical about the central axis.

[0037] The cathode seat 301, the anode outer cylinder 303, the outer stop neck 304, and the inner stop neck 305 are usually made of non-magnetic stainless steel, the outer conductor corrugation 306 and the inner conductor corrugation 308 are usually made of non-magnetic stainless steel, oxygen-free copper or titanium, etc. The cathode 302 can be made of high-hardness graphite or heat-resistant glass cloth-epoxy resin copper foil (FR-5) material, and the solenoid magnetic field 312 is wound with enameled copper wire or glass fiber copper wire. The left end of the cathode seat 301 is connected to the inner conductor of the pulse power driving source, and the left end of the anode outer cylinder 303 is connected to the outer conductor of the pulse power driving source.

[0038] This embodiment realizes an L-band compact relativistic Cherenkov microwave generating device with an operating frequency of 1.26 GHz (corresponding to a microwave wavelength λ=23.81 cm) (the corresponding dimensions are designed as follows: R1=34 mm, R2=51 mm, R3=30 mm, R4=42 mm, R5=14 mm, R6=30 mm, R7=66 mm, R8=11 mm, R9=40 mm, R 10 =78mm, R 11 =27mm, R 12=39mm, R 13 =35mm, R 14 =29mm, R 15 =22mm, R 16 =44mm, R 17 =4mm, L1=22mm, L2=7mm, L3=21mm, L4=18mm, L5=18mm, L6=12mm, L7=15mm, L8=9mm, L9=23mm, L 10 =8mm; L 11 =44mm, L 12 =37mm, L 13 =16mm, L 14 =5mm, L 15 =24mm, L 16 =19mm, L 17 =16mm, L 18 =26mm, L 19 =20mm, L 20 =15mm; L 21 =32mm, L 22 =6mm, L 23 =5mm, L 24 =51mm, L 25 =120mm).

[0039] In the particle simulation, under the conditions of diode voltage 426kV, current 6.5kA, and guided magnetic field 1.28T, the device outputs microwave power of 1.12GW and the conversion efficiency is 40%. From the above results, it can be seen that the present invention overcomes the problem that the conventional relativistic high-power microwave generating device is large in size and not compact in structure. Through the specially designed slow-wave structure and coaxial collector, the device efficiency is guaranteed while the size of the device is shortened, which has important reference significance for the design of other high-power microwave output devices.

[0040] See also Figure 5 It can be seen that the output microwave power of the device is 1.12GW and the conversion efficiency is 40%.

[0041] See also Figure 6 , we can know that the frequency of the output microwave of the device is 1.26GHz.

[0042] See also Figure 7 It can be seen that the external magnetic field has an impact on the device efficiency. With the increase of the external magnetic field strength, the device efficiency first increases and then tends to be stable. The optimal value of the external magnetic field strength is 1.28T, and the conversion efficiency reaches the maximum at this time.

[0043] See also Figure 8It can be seen that the diode voltage has an impact on the device efficiency. As the voltage increases, the device efficiency increases first and then decreases. The optimal value of the diode voltage is 426kV, and the conversion efficiency reaches the maximum at this time. In the range of 356kV to 466kV, the device beam conversion efficiency is greater than 35%, indicating that the device has good robustness to voltage changes.

[0044] See also Fig. 9 It can be seen that when the coaxial collector is loaded, the S21 of the output waveguide at the operating frequency of 1.26 GHz increases from 0.86191 to 0.91897, indicating that the coaxial collector can reflect a small part of the microwaves to the slow-wave structure area. The reflected microwaves will further modulate the electron beam, thereby improving the conversion efficiency and reducing the energy loss during microwave transmission.

[0045] See also Fig.10 It can be seen that the slow-wave structure of the device can operate in a mode with a center frequency of 1.26 GHz (belonging to the L band).

[0046] See also Fig.11 It can be seen that the Q value of the inner output waveguide in the working mode is higher, and it is easier to oscillate than the outer output waveguide current.

Claims

1. An L-band compact relativistic Cherenkov microwave generating device, comprising a cathode structure, an external electromagnetic structure and an internal electromagnetic structure, wherein the cathode structure comprises a cathode seat (301) and a cathode (302); the external electromagnetic structure comprises an anode outer cylinder (303), an external cut-off neck (304), a collector (307), a collector baffle (311), and a solenoid coil (312); the internal electromagnetic structure comprises an internal cut-off neck (305), a short-circuit block (309), and a microwave output port (310); the entire structure is rotationally symmetric about a central axis; and is characterized in that: Also includes an outer conductor corrugation (306) and an inner conductor corrugation (308); The outer conductor corrugation (306) is composed of two trapezoidal cavities. The outer radius of the first trapezoidal cavity is R7, the length of the upper base is L5, and the length of the short oblique side projection is L 15 , the length of the long hypotenuse projection is L 18 , satisfying L 18 > L 15 > L5; the outer radius of the second trapezoidal cavity is R 10 , satisfying R 10 >R7, the length of the upper base is L9, satisfying L9>L5, and the length of the short hypotenuse projection is L 22 , the length of the long hypotenuse projection is L 20 , satisfying L9> L 20 > L 22 ; The inner conductor corrugation (308) is composed of two trapezoidal cavities. The inner radius of the first trapezoidal cavity is R5, the length of the upper base is L4, and the length of the short oblique side projection is L 14 , the length of the long hypotenuse projection is L 16 , satisfying L 16 > L4> L 14 ; The inner radius of the second trapezoidal cavity is R8, satisfying R5>R8, the length of the upper base is L7, satisfying L4>L7, and the length of the short hypotenuse projection is L 17 , the length of the long hypotenuse projection is L 19 , satisfying L 19 > L 17 > L7.

2. The L-band compact relativistic Cherenkov microwave generating device according to claim 1, characterized in that: The cathode (302) is a thin-walled cylinder, which is sleeved on the right end of the cathode seat (301), has a wall thickness of 0.1 mm, a radius equal to the radius R1 of the electron beam, and a length of L1; the left side of the anode outer cylinder (303) is a cylindrical cylinder with an inner radius R2, and the inner surface of the right side has irregular corrugations, forming a high-frequency structure; the inner cutoff neck (305) is disc-shaped, with a radius R3 and a length L2; the outer cutoff neck (304) is annular, and a slope is formed on its left side, which gradually changes from the radius R2 to the radius R4, and the slope is used to increase the radial confinement electric field of the electrons at the cathode, improve the quality of the electron beam, and meet R2>R4>R1>R3, and the length is L3, and the values ​​of L2 and L3 are 0.01-0.1 times of the working wavelength.

3. The L-band compact relativistic Cherenkov microwave generating device according to claim 1, characterized in that: The first trapezoidal cavity and the second trapezoidal cavity are connected by a ring with an inner radius of R9 and a length of L8, where L8 is 5 mm to 15 mm; the collector (307) is a circular ring cavity with a parallelogram cross section and an outer radius of R 16 , the inner radius is R 13 , the length of the upper base is L 12 The projection lengths of the two hypotenuses are L 11 and L 24 , L 11 and L 12 According to the comprehensive design of electron beam bombardment position and magnetic field configuration, L 11 The value is 0.1-0.2 times of the working wavelength λ, L 12 The value is 0.1-0.2 times of the working wavelength λ; the inner radius R between the outer conductor corrugation (306) and the collecting electrode (307) 12 , length L 10 The ring connection, L 10 The value is 5mm-15mm; the short-circuit block (309) is a circular ring with a rectangular cross section and an outer radius of R 14 , the inner radius is R 15 , length L 13 , L 13 The value is 15mm-20mm. This structure is used to enhance the resonance characteristics of the device and achieve the function of frequency selection. The collector baffle (311) is an outer radius of R 13 , inner radius is R 14 The ring is used to prevent the plasma generated by electrons bombarding the collector from spreading to other parts of the device.

4. The L-band compact relativistic Cherenkov microwave generating device according to claim 1, characterized in that: The first trapezoidal cavity and the second trapezoidal cavity are connected by a disk with a radius of R6 and a length of L6, where L6 is 5mm-15mm; the right side of the second trapezoidal cavity is connected to a disk with a radius of R 11 , length L 21 The disk, L 21 The value is 30mm-35mm; the microwave output port (310) is an outer radius of R 14 , the inner radius is R 17 , length L 25 The annular cavity, L 25 The value is 0.5-1 times of the working wavelength; a microwave output port (310) is formed on the left side with a radius R 11 Gradient to radius R 17 The length of the projection of the inclined plane is L. 23 , L 23 The value is 2mm-6mm; a radius of R is set at the center of the microwave output port. 17 , length L 25 The cylindrical structure is connected to the inclined surface and forms a coaxial output structure with the anode outer cylinder (303); the right end of the microwave output port (310) is connected to the antenna.

5. The L-band compact relativistic Cherenkov microwave generating device according to claim 1, characterized in that: The solenoid coil (312) is a wound solenoid magnetic field. By changing the magnitude of the current passing through the solenoid magnetic field, the intensity of the magnetic field generated by the solenoid is changed, thereby achieving transmission guidance of the electron beam.

6. The L-band compact relativistic Cherenkov microwave generating device according to any one of claims 1 to 5, characterized in that: The operating frequency is 1.26 GHz, corresponding to the microwave wavelength λ = 23.81 cm, and the L-band compact relativistic Cherenkov microwave generator has the following dimensions: R1 = 34 mm, R2 = 51 mm, R3 = 30 mm, R4 = 42 mm, R5 = 14 mm, R6 = 30 mm, R7 = 66 mm, R8 = 11 mm, R9 = 40 mm, R 10 =78mm, R 11 =27mm, R 12 =39mm, R 13 =35mm, R 14 =29mm, R 15 =22mm, R 16 =44mm, R 17 =4mm, L1=22mm, L2=7mm, L3=21mm, L4=18mm, L5=18mm, L6=12mm, L7=15mm, L8=9mm, L9=23mm, L 10 =8mm; L 11 =44mm, L 12 =37mm, L 13 =16mm, L 14 =5mm, L 15 =24mm, L 16 =19mm, L 17 =16mm, L 18 =26mm, L 19 =20mm, L 20 =15mm; L 21 =32mm, L 22 =6mm, L 23 =5mm, L 24 =51mm, L 25 =120mm.

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