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A relativistic magnetron using all cavity extraction and semi-transparent cathode has the virtues of compactness, high output power and high efficiency. The three-dimensional particle-in-cell simulations show that 1.15 GW output microwave with an efficiency about 50% can be obtained at S-band with pure TE11 mode of the fan waveguide. However, due to the fact that the output structure is composed of three detached fan waveguides, mode conversion structure in the output region is required for the convenience of practical applications. Therefore, two mode conversion structures are studied for the output mode conversion. The first structure is to widen gradually or abruptly the fan waveguide in the azimuthal direction from a given position (starting point) along the microwave transport direction. And then the three fan waveguides are connected into one coaxial waveguide. The effects of the position of the starting point on the beam-wave interaction and microwave extraction are numerically studied. For the convenience of description, we define L as the axial distance between the center of the output coupling hole and starting point. Simulation results show that for the abrupt and gradual variation case, when the length of L changes in a relatively wide region, the output power is larger than 1.0 GW in TEM mode at S-band. It is about 90% of the conventional fan waveguide with 1.15 GW. For the gradual variation case, the optimal value of L equals 10.0 cm, and the corresponding output power is beyond 1.0 GW. For the abrupt variation case, the optimal value of L equals 13.75 cm, the corresponding output power is about 1.15 GW. But in the abrupt variation case, the output power is a little more sensitive to the value of L. The second structure is to convert the fan waveguide into a rectangular waveguide. Ａcompound waveguide composed of a section of fan waveguide and a section of rectangular waveguide is designed for studying its feasibility. In the compound waveguide, the wide edges of the cross section of the rectangular waveguide are tangent to the inner and outer arc of the fan cross section respectively. And the narrow edges cross the end points of the outer arc. Simulation results show that in the compound waveguide the microwave with TE11 mode of the fan waveguide input at the inlet can be changed into the TE10 mode of the rectangular waveguide at the outlet with almost no power loss. In all, the output microwave power larger than 1.0 GW could be obtained after using the two proposed mode conversion structures. In practical applications, one could choose the relevant mode conversion structure according to the requirement.

Relativistic magnetron is a kind of compact cross-field high power microwave source. It has the virtues of wide frequency tunability and ability to operate with relative lower external magnetic field. To improve the compactness and reduce the size and weight of the relativistic magnetron further, a novel relativistic magnetron using all-cavity output and semi-transparent cathode is investigated theoretically and numerically. By using the all-cavity output structure, the radial dimension is reduced markedly (from 10.5 cm to 6.6 cm) and the axial dimension is also shortened considerably (from larger than 40 cm to less than 30 cm). Since the radiation fields in the interaction cavity are coupled through the coupling hole to the output fan waveguide, the cutoff frequencies of the fundamental mode and three higher order modes in the fan waveguide with different outer radii are calculated. The calculation results show that the mode separation is wide enough for the single mode operation on the fundamental mode. And by using the semi-transparent cathode, the high output efficiency can be obtained and the output characteristics are insensitive to the depth and width of each cathode slot. To verify the characteristic of the proposed magnetron, numerical simulations are carried out by using the three-dimensional particle-in-cell code. After careful optimization, simulations show that with a beam voltage of 395 kV and beam current of 5.6 kA, 1.15 GW output microwave with an efficiency of about 50% can be obtained at S-band with purer mode. The corresponding applied magnetic field is 4.75 kGs (1 Gs=1-4 T). In a relatively large range, both radiation power and the optimal magnetic field increase with the beam voltage. But the output efficiency keeps almost unchanged. The effects of the depth, width and length of the coupling hole, width of the fan waveguide and the distance from the beginning position of the fan waveguide to the coupling hole center Lsc on the output characteristics are also analyzed. Simulation results show that when the dimension of the coupling hole is small, the output power is low. But there is no mode competition and the device works on the up mode. With the increase of the coupling hole, the output power increases accordingly. When the coupling hole is large enough, the mode competition between the up mode and /3 mode becomes so serious that the mode cannot win any more. At the same time, the output power decreases markedly. There also exist optimal values of both the fan width and the beginning position of the fan waveguide (Lsc) for maximal output power.

In this paper, an electromagnetic-field FDTD method coupled with plasma fluid model is put forward to investigate the different physical phenomena of high power microwave (HPM) flashover and breakdown on inner and outer surface of output-window. Based on the above theoretical models, a one-dimensional (1D) electromagnetic field and plasma interaction code is programmed by authors. By using the code, the HPM flashover and breakdown on inner and outer surface of output-window are simulated. The numerical results could be concluded as follows. For flashover and breakdown on outer surface, output microwave pulse is shortened without cut-off; there is a standing-wave distribution of electric field RMS (Root-Mean-Square) value before the window with fixed-positions of wave nodes and antinodes; there is a ultra-high-density (～1021 m-3) and ultra-thin (～mm) plasma shell with slow diffusion, microwave could penetrate the plasma-shell partly; the shortening of output microwave is caused by plasma absorption mostly. The output pulse of microwave could be lengthened by reducing the initial density or depth of plasmas; the other way is to shorten incident microwave pulse or reduce the value of incident microwave power. For flashover and breakdown on inner surface, there is also a standing-wave distribution of electric field RMS value before the window but the positions of wave nodes and antinodes vary with time; the plasma region moves toward the microwave source; with strong-outgassing, output microwave pulse is shortened without cut-off, there are “thread-like” ultra-high-density (～ 1021 m-3) and ultra-thin (～mm) plasma regions with slow diffusion, the distance between two “thread-like” regions is about a quarter of microwave wavelength, the shortening of output microwave is caused by plasma absorption mostly; with weak-outgassing and low electric field value, the output pulse of microwave is lengthened but cut-off finally, there are “belt-like” high-density (～ 1018 m-3) and thin (mm-cm) plasma regions with fast diffusion, the distance between two “belt-like” region is about a quarter of microwave wavelength, the shortening of output microwave is caused by plasma absorption mostly; with weak-outgassing and high electric field value, output pulse of microwave is cut-off quickly, “block-like” diffuse ultra-high-density (～1021 m-3) and deep (～ cm) plasma regions are formed with very fast diffusion, and the shortening of output microwave is caused by plasma reflection mostly.

The particle-in-cell (PIC) simulation method is used to get the reliable ionization parameters of high power microwave flashover and breakdown on dielectric surface for fluid modeling. Firstly, the PIC method is presented briefly, including dynamic equations, secondary emission and Monte-Carlo collision (MCC) between electron and gas atom. Secondary, the fluid global model (GM) is introduced including continuity and energy conservation functions. Finally, by using a 1D3V PIC-MCC code programmed by the authors, the ionization parameters are calculated under different microwave electric-field values, microwave frequencies, gas types and pressures for fluid modeling, including ionization frequency, breakdown delay time, average electron energy, electron energy distribution function (EEDF). The numerical results could be concluded as follows. Average electron energy is unrelated to EEDF type. At middle and low gas pressures, electron energy satisfies Maxwell distribution, and ionization parameters are unrelated to EEDF type. At middle and high gas pressures, ionization parameter is related to EEDF type, and the relevant coefficient X of EEDF tends to be of high older. Different gases have different EEDF types, and the relevant coefficient X of EEDF should be corrected by PIC simulation. The value of X is also related to microwave electric-field value and frequency, and its value increases with the increase of microwave electric-field value and the decrease of microwave frequency. In a fixed range (microwave electric-field value below 7 MV/m, and microwave frequency below 40 GHz), at middle and low gas pressures, the average electron energy increases with the increase of electric-field value and the decrease of microwave frequency rapidly, and the ionization frequency increases and then decreases with the increase of microwave electric-field value and frequency respectively; at high gas pressure, the average electron energy increases with the increase of electric-field value slowly, the ionization frequency increases with the increase of electric-field value, and the average electron energy and ionization frequency are unrelated to microwave frequency.

For investigating the mechanism of high power microwave flashover and breakdown on dielectric surface with outgassing, firstly, the theoretical modeling is put forward, including dynamic equations, particle-in-cell (PIC) method, secondary emission, Monte-Carlo collision (MCC) method and outgassing model. Secondly, based on the theoretical modeling, the 1D3V PIC-MCC code is programmed by authors. By using this code, the flashover and breakdown on dielectric surface with weak and strong outgassing course under different gas moving velocities are studied numerically. The numerical results are concluded in the following. The flashover and breakdown on dielectric surface are caused by continuous increase of deposited power. For weak outgassing, multipacting is dominant. As outgassing coefficient increases, multipacting is promoted by ionization collision. The typical phenomena are the increases of space-charge field, average energy of surface-collision electrons and the number of surface-collision electrons. Here, the surface-collision electrons are caused by multipacting mostly. With the increase of gas molecule velocity, ionization course is suppressed by gas pressure decreasing near to the dielectric surface. For strong outgassing, ionization collision is dominant. As outgassing coefficient increases, the number of ions increases exponentially with ionization frequency increasing, multipacting is suppressed by ionization collision. The typical phenomena are the negative value of space-charge field on dielectric surface, the decrease of average energy of surface-collision electrons, and the exponential increase of surface-collision electrons caused by ionization collision near to dielectric surface. Here, the surface-collision electrons are caused by ionization mostly. With the increase of gas molecule velocity, the depth of gas is enlarged, thereby promoting the ionization collision.

By using a P3D3V PIC code programmed by the authors, the multipactor discharge effects on dielectric inner and outer surface under high-power microwave with TE10 mode in the BJ32 rectangular waveguide are numerically studied. The electron spatial distribution, distribution of electric field in the normal direction of the dielectric surface, and electron density spatial distribution are presented. Numerical results could be concluded as follows. For inner surface, the multipacting first occurs in the area with large electric-field of microwave; for the outer surface, multipacting first occurs in the area with small electric-field of microwave. The above phenomena could be explained as follows. Poynting direction of microwave is the same as the outer surface normal direction and opposite to the inner surface normal direction. So the drift in the area with large electric-field of microwave causes electrons easy to move back to inner surface, and so electrons are easy to leave from outer surface. Compared with 1D3V model, in P3D3V model, we have for inner surface multipactor discharge with long oscillator forming time, small secondary electron number, high average electron energy, low incident power of microwave, and low level deposited power; for outer surface, we have multipactor discharge with short oscillator forming time, small secondary electron number, low average electron energy, low incident power of microwave, and low level deposited power. The deposited power is about 1%–2% of incident microwave power both in 1D3V and P3D3V models; while the ratio between deposited power and incident power of microwave has nothing to do with microwave parameters and inner or outer surface.