Abstract
In this paper， an efficient resonant circuit based on integrated interaction units is proposed to improve the beam-wave interaction for increasing the peak power of a Ka-band klystron to 200 kW. The integrated-unit circuit is designed with connecting two or several single-beam-wave interaction units across the cross section （each of which is typically used in a conventional single-beam klystron） based on the cascaded field structure in the rectangular gap waveguide with specific fusion boundary conditions. For the input cavity， two interaction units have been efficiently integrated to obtain the optimal absorption efficiency with the constant input power at ~35 GHz， through optimizing both the beam-loading parameters and cavity parameters. The output cavity has been 1） designed with two output ports for balancing the effect of the power extraction on the integrated circuit， and 2） optimized to deliver 200-kW peak power through injecting two pre-modulated beams. The overall interaction circuit of a Ka-band klystron is accordingly designed to produce the peak power of 202.9-kW with the efficiency of 40.2% and the maximum gain of 47 dB using particle-in-cell （PIC） simulations， when the two beams with the voltage of 45 kV and every current of 5.6 A are used to drive the klystron.
Klystrons， are widely used microwave amplifiers based on the vacuum electronic technology
For single-beam klystrons， Communications & Power Industries （CPI） have produced Ka-band extended interaction klystrons with the 1-kW continuous wave （CW） or the 3.5-kW pulsed power
To increase the power to over 100 kW and higher level， however， the single-beam-wave interaction used in conventional single-beam klystrons is difficult to generate such high power because the beam power is limited by the small beam current density at low voltage （lower than 50 kV）. Accordingly， the efficient beam power transferred to millimeter waves is insufficient with a single interaction circuit in single-beam klystrons. To explain clearly the basic idea in this paper， we regard the single interaction circuit as a typical model of one beam-wave interaction unit.
For the high power and high efficiency specifications， the efficient combination of several beam-wave interaction units is fundamental to the design of a klystron or EIK， since it can be used not only for matching with distributed electron beams， but also for forming an improved interaction mechanism through promoting and achieving each other between the units. Every interaction unit follows a typical single-beam-wave interaction supporting conventional klystrons.
There have been several schemes suggested to integrate two or more interaction units， such as 1） the double-beam circuits
In fact， the development of Ka-band klystrons toward over 100 kW needs not only integrate efficient interaction units， but also efficient power extractions for improving the power capacity and the circuit efficiency. This paper provides a new method of integrating two interaction units for producing two times the current level （100 kW）. The integrated two units are supported by the in-phase electric field and on this basis， we propose a Ka-band klystron with two output ports for generating 200-kW peak power. The evolution from an interaction unit to the new circuit integrating two units is analyzed from the physical mechanism. The basic designs of the input cavity and output cavity with two output ports are shown to support the proposed Ka-band klystron amplifier. Finally， the beam-wave interaction capability of the amplifier is simulated to demonstrate the effectiveness of the amplifier operation.
A beam-wave interaction unit is defined as a single-gap resonant cavity usually used in single-beam klystrons. Here， its basic structure is a rectangular gap with its narrow side being placed along the z-direction.
Fig. 1 （a） The conventional interaction unit with the Ez field across the λg0/2 length， （b） two such units connected along the x-direction to form an integrated-two-unit circuit， （c） the integrated-three-unit circuit formed by connecting three such units along the x-direction， and （d） the proposed integrated-two-unit circuit with specific coupling cavities for power extraction
图1 （a）具有λg0/2长度分布的Ez场的传统互作用单元电路，（b）沿x轴方向级联的两个该单元电路形成的一个两单元集成互作用电路，（c）由沿x轴方向级联的三个该单元电路形成的三单元集成互作用电路，和（d）用于功率提取的具有特定耦合腔的两单元集成电路
Two or three such units can be directly arranged along the x-direction， as shown in Figs.
It should be noted from the case shown in
However， this case still faces the same points as 2） and 3）. With the motivation for eliminating these two points， we consider designing two identical coupling cavities to locate on both sides of the middle unit along the y-direction， and choosing to place no electron beam in the middle unit. Then the output structure of power extraction can be designed upon one of the coupling cavities or upon both， as shown in
Fig. 2 The schematic drawing of the integrated-two-unit circuit with two output ports located on both sides of the two symmetrical coupling cavities
图2 两个输出端口位于两个对称耦合腔两侧的两单元集成电路的示意图
According to the basic idea above， the directly connected three-unit cavity shown in
The structural symmetry of the integrated units determines that the two units have the same Ez field distribution. Then the beam loading in the two units of the integrated cavity would exert the same effect on the electromagnetic characteristics of the cavity. For a beam-loaded cavity， the beam parameters， and the cavity parameters should be selected and optimized in both directions to obtain the optimal modulation and absorption of the input power at a given frequency. This depends on the matching between the beam perveance and the field distribution across the gap of the unit. It is consequently important to select the gap width of every unit for determining the shape factor of the Ez field， which makes the ge value larger than 0 or close to 0 within the designed beam perveance.
Here， the perveance of a single electron beam driving one unit is limited by the constant beam power of ~500 kW with the efficiency of 40 % and the peak microwave power of 200 kW in consideration. The marks 1， 2， 3， 4， 5， 6， 7， 8 represent the beam voltages of 30 kV， 33 kV， 36 kV， 39 kV， 42 kV， 45 kV， 48 kV， 51 kV， with the currents of 8.4 A， 7.64 A， 7 A， 6.46 A， 6 A， 5.6 A， 5.25 A， and 4.94 A， respectively. Through dozens of optimizations in simulations， the gap width is chosen as 0.9 mm， which makes ge larger than 0 within the full range of the perveance， as shown in
Fig. 3 The effect of the beam perveance on ge and Qa
图3 电子束导流系数对电子电导ge和Qa的影响
Fig. 4 （a） The Ez field along the axis of tunnel 1 and 2， and （b） the three-dimensional （3-D） model of the input cavity with the 3-D distribution of the Ez field
图4 （a）沿电子束通道1和2轴线分布的Ez场和（b）具有Ez场的三维分布的输入腔三维（3-D）模型
More importantly， the Ka-band input cavity needs sufficient beam loading to lower its quality factor （Q）. For an ideal input cavity， the input RF power should be consumed by the electrons and the ohmic loss， which can be characterized by the beam loaded quality factor （Qb）， and the ohmic quality factor （Q0）. The total ideal loss of the input cavity is represented by the total quality factor （Qa）， which can be obtained by
| , | （1） |
where Qb1 and Qb2 is the beam-1 loaded quality factor and the beam-2 loaded quality factor， respectively. According to the calculation method reported in Ref. ［
Accordingly， the two beams with the voltage of 45 kV， and every beam current of 5.6 A are used to load the input cavity. The external quality factor （Qe）， is optimized to obtain the optimal matching between the beams and the input cavity
Fig. 5 （a） The effect of
图5 （a）M2R/Q对电子束电压的影响，和（b）在电压45 kV、每个束电流5.6 A的两电子束加载条件下吸收效率η对输入腔输入信号频率的影响
It should be noted that the power level of 200 kW requires the output cavity and the output waveguide with a high power capacity. So the output cavity is designed with two output ports for sharing the extracted power and accordingly enhancing the power capacity. To balance the effect of two output ports on the field uniformity of the output cavity， we design the output cavity as the model shown in
At Ka-band， a conventional klystron cavity is typically characterized by a high ohmic quality factor （Q0） and the power extraction from the cavity is closely related to Qe from the perspective of the cavity circuit. When the stored energy is constant， the integrated-unit cavity distributes the stored energy into three components along the x direction. The ohmic loss is therefore distributed across the enlarged cross section and Q0 is increased as compared with Q0 of a conventional single-unit cavity. This allows to design a lower Qe for efficiently extracting the power from the two ports.
The two output ports produce two Qes for the output cavity， which can be defined by the external quality factor 1 （Qe1）， and the external quality factor 2 （Qe2） from port 1 and port 2. The time domain simulation is conducted to obtain the group delay τg varying with frequency， as shown in
Fig. 6 （a） The group delay τg from two output ports， and （b） the absolute amplitude of the normalized Ez field along the axis of the y-direction of the output cavity
图6 （a）两个输出端口的群时延τg，和（b）沿输出腔y方向轴线分布的归一化Ez场的幅值绝对值
To examine the capability of extracting power from the two ports， the output cavity is driven by two pre-modulated electron beams equivalently generated by the Gaussian model
Fig. 7 （a） The shape of a bunch current by the Gaussian model， and （b） the effect of the ratio of the critical parameter σ to Δt， on the output power extracted from the output cavity and the electronic efficiency
图7 （a）高斯模型得到的群聚电流分布形状，和（b）关键参数σ与Δt的比值对输出腔提取的输出功率和电子效率的影响
When σ/Δt is 68%， the output cavity can deliver the total peak power of 200 kW， corresponding to the electronic efficiency of ~40%. Every port produces 100 kW. The corresponding shapes of bunch currents of the two pre-modulated beams are the same， as shown in
Fig. 8 （a） The waveform of the bunch currents corresponding to the output power of 200 kW （Beam 1 and 2 represent specifically the pre-modulated beam 1 and beam 2）， and （b） the output signal obtained from port 1 and 2
图8 （a）对应200 kW输出功率的群聚电流波形（束1和2具体地表示预调制电子束1和电子束2），和（b）从端口1和端口2得到的输出信号
Fig. 9 FFT of the bunch currents in the gap centers beam 1 and beam 2 located （I0 is the DC current of the beams and I1 is the current of the fundamental harmonics of the two bunches）
图9 电子束1和电子束2所在间隙中心位置的群聚电流的快速傅里叶变换（I0是电子束直流电流，I1是两个群聚块的基波电流）
According to the design method above， the overall interaction circuit of the klystron has been designed and simulated to demonstrate the effectiveness of the application of the integrated-unit circuits in the Ka-band klystron. The overall circuit consists of the input cavity， buncher cavity 1， buncher cavity 2， and the output cavity， as shown in
Fig. 10 The overall interaction circuit of the designed klystron with the Ez field
图10 具有Ez场分布的所设计速调管的整体互作用电路
| Structural parameters | Input cavity | Output cavity |
|---|---|---|
| Gap width （size along z direction） | 0.9 mm | 0.7 mm |
| Height of the coupling cavity（size along y direction） | 1.4 mm | 1.4 mm |
| Length of the coupling cavity （size along x direction） | 4.7 mm | 4.7 mm |
| Width of the coupling cavity （size along z direction） | 1.7 mm | 1.5 mm |
The PIC simulations
Fig. 11 The effect of the input power on the output power and the gain of the klystron
图11 输入功率对速调管输出功率和增益的影响
Fig. 12 The effect of the frequency of the input signal on the output power and the electronic efficiency of the klystron
图12 输入信号频率对速调管输出功率和电子效率的影响
When the frequency and power of the input signal are 34.96 GHz and 5 W respectively， the average output power obtained from every port is 100 kW and the output frequency is 34.96 GHz， as shown in
Fig. 13 （a） The output power versus time， （b） the FFT amplitude of the input signal， and output signals from port 2 and port 3 （Output signal 1 and 2 are extracted from port 2 and port 3）
图13 （a）输出功率随时间变化图，（b）输入信号和端口2、3的输出信号的快速傅里叶变换幅值（从端口2和端口3提取得到输出信号1和2）
Fig. 14 The beam trajectories
图14 电子束轨迹图
Fig. 15 The phase space of the electrons
图15 电子的相空间图
It should be noted that the frequency tuning of buncher cavity 1 and 2 is very important to achieve the efficient operation and bandwidth for the klystron in practice. The efficient integration of the two interaction units largely depends on the energy and distribution pattern of the Ez field across the λg1/2 of the cross section. The coupling cavities distributed on both sides of the λg1/2 section offer the opportunity for mechanical tuning. One of the two ends along the y-direction of the buncher cavities can be replaced by a piston， which is designed to adjust the height of the coupling cavity. Accordingly， the frequency of the buncher cavities can be tuned to compensate the frequency shift caused by fabrication errors.
Fig. 16 The effect of the height of the coupling cavity on the frequency and Q0 value of the buncher cavity
图16 耦合腔高度对群聚腔频率和Q0的影响
In this paper， an integrated-unit resonant circuit is proposed to support the efficient beam-wave interaction of a Ka-band klystron for producing 200-kW peak power in the design level and simulation domain， which is a breakthrough power level for Ka-band klystrons nowadays. Two or several typical single beam-wave interaction units， each of which is usually used in conventional klystrons， are integrated to form a new resonant circuit based on the distributed field distribution across the cascaded cross section. Two units have been focused on the design of the input cavity and output cavity with two output ports. The input signal with constant power at ~35 GHz can be absorbed by the input cavity with an absorption efficiency of almost 100%. The output cavity has shown its great potential in producing 200-kW peak power. Finally， the overall interaction circuit of a Ka-band klystron has been designed and simulated to show an effective interaction capability for producing 202.9-kW peak power with the electronic efficiency of 40.2% and the maximum gain of 47 dB.
This paper has focused on the basic designs of the interaction circuit of the Ka-band klystron. The basic integrated-unit circuit has been demonstrated to be efficient for supporting such a klystron with high peak power from the simulation domain. To increase the gain and power capacity， the extended interaction technology may be used in future.
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