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Abstract
Generally, it is difficult for the common backward wave oscillator (BWO) to produce powerful THz radiation when the operating frequency increases to a high level such as over 1 THz due to the very small structural dimensions. The concept of generating powerful THz radiation from the interaction between high-order mode THz wave and multiple sheet electron beams is a promising solution to address the issue. For the high-order mode operation, a novel orthogonal grating waveguide is proposed, which is relatively ease of fabrication compared with the overmoded structure based on the double staggered grating waveguide. A high-order mode BWO based on the orthogonal grating waveguide and multiple sheet electron beams is studied by simulations. Particle-in-cell simulations show that the BWO can provide over 1.08 W power in the frequency range of 1.18-1.30 THz. Such a methodology opens up a new way to extend the BWO’s operating frequency to a higher level and provides a potential solution for developing compact powerful THz radiation sources with wide tunable bandwidth.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) technology has become a very important research hotspot in the past decades because of its promising applications including security imaging, plasma diagnostic, high resolution radar, biomedical science, and high-data-rate communications [1,2]. Driven by these applications, the development of powerful THz radiation sources has been promoted. Compared with the optical techniques for the generation of THz radiation, the electron beam driving radiation sources have some advantages such as high radiation power, high electronic efficiency, and room temperature operation. Great efforts have been made to develop this kind of THz radiation source, including the backward-wave oscillators (BWOs) [3–6], extended interaction klystrons/oscillators [7–9], gyrotrons [10,11], travelling wave tubes (TWTs) [12,13], radiation sources based on the Smith-Purcell effect [14–17], and some other electron beam driving THz sources [18–20]. Among them, the BWO is one of the most important radiation sources in the low terahertz band due to its high radiation power, wide tunable bandwidth and compact configuration. However, the development of the BWO will be hindered when the operating frequency increases to a higher level such as over 1 THz. Due to the reduced structural dimensions, the fabrication and assembly of the BWO will face greater challenges, the power capacity will be limited and the required beam current density will be higher. To address the issue, adopting the high-order mode instead of the fundamental mode for the beam wave interaction could be a promising solution. For the same operating frequency, the geometrical dimensions of the interaction circuit operating at the high-order mode will be larger. The enlarged structure contributes to reduce the requirement in the accuracy of the fabrication and lower the beam current density. In addition, it is beneficial to increase the power capacity due to the smaller power loss per unit area and the increased heat dissipation area [21].
In fact, the idea of generating powerful THz radiation from the interaction between the multiple electron beams and the high-order mode has ever been studied [6,21–24]. A 140 GHz overmoded folded-waveguide driven by two pencil electron beams was used to amplify the THz-wave operating at the TE20 mode [21]. The radiation power can be further improved if adopting sheet electron beams rather than pencil electron beams due to the enlarged area of the beam cross section [12-13,25]. The interaction between an overmoded double staggered grating waveguide loaded with dielectric absorbers and multiple sheet electron beams in a TWT was studied and the operating mode is TM31 mode [22]. However, the introduced dielectric absorbers will increase the structural complexity and the difficulties in the assembly due to the limited space. To alleviate the difficulties in the engineering implementation, we have ever introduced mental ridges instead of the dielectric absorbers in the double staggered grating waveguide [6]. However, it is still not easy for the fabrication due to the additional introduced structure. In addition, the overmoded structure in [6,22] is both based on thedouble staggered grating waveguide as shown in Fig. 1(a), which is sensitive to the deviation of the shift distance L between the upper and lower grating waveguide. Hence, it is a great challenge to the assembly as the structure is generally split into two parts in the fabrication: an upper grating waveguide and a lower grating waveguide [12].
Fig. 1 Schematic of (a) a double staggered grating waveguide [6, 12, 22], (b) a single grating waveguide [4, 26], (c) an orthogonal grating waveguide, and (d) simulation model of an orthogonal grating waveguide cell.
Based on the single grating waveguide as shown in Fig. 1(b), a novel orthogonal grating waveguide as shown in Fig. 1(c) is proposed for the high-order mode operation. The lower part of the orthogonal grating waveguide (the longitudinal grating waveguide) is the same as that of the single grating waveguide, where the vanes of the grating are uniformly arranged along the z-axis. The upper part of the proposed waveguide (the transverse grating waveguide) is placed over the longitudinal grating waveguide, where the vanes of the grating are uniformly arranged along the x-axis. The gratings from the lower and upper part are orthogonal to each other. Each component of the orthogonal grating waveguide can be made by an oxygen-free copper in the fabrication. The beam-wave interaction at each beam tunnel is separated by the gratings of the transverse grating waveguide. Neither dielectric absorbers nor metal ridges are introduced in the new structure. In addition, the proposed waveguide can lower the requirement of the accuracy in the assembly as it eliminates the need for the accurate shift between the upper and lower waveguide. In the fabrication, it can be divided into two parts: a transverse grating waveguide and a longitudinal grating waveguide. Each of them can be separately fabricated by the micro-machining technique, such as the UV-LIGA (ultraviolet lithography, electroplating and molding) technique or the Nano-CNC (computer numerically controlled) machining technology. The above two techniques have ever been used to fabricate a 220 GHz folded waveguide slow wave structure [12] and a 220 GHz double staggered vane grating circuit [13], respectively. The study of its dispersive characteristics, transmission properties, and the interaction performance will be presented.
2. Orthogonal grating waveguide
The simulation model of an orthogonal grating waveguide cell is shown in Fig. 1(d). The initial structural parameters can be decided as the following principle. The synchronous condition for the beam wave interaction is that the velocity of the electron beam ve should be a little larger than the phase velocity of the electromagnetic wave vp. For deciding the initial structural parameters, we assume that ve is equal to vp. Then the equation for calculating pl can be achieved.
where c is the velocity of light. When the phase difference per period ψ is 1.67π (300°), the operating frequency f = 1.2 THz, and the operating voltage U = 23 kV, pl of 60.6 um can be achieved according to Eqs. (1-2). The vane thickness (pl-dl) of 30.3 μm is half the period. The vane height hl and the waveguide width w have an effect on the tunable frequency range and the coupling impedance of the waveguide cell, which represents the beam wave interaction intensity and is related to the interaction efficiency. Their initial value is set as 60.5 μm and 1000 μm, respectively. The period of the transverse grating waveguide pt is initially set as 200 µm, which is one fifth of w. The initial beam tunnel’s width dt of 133.3 μm is two third of pt. The height of the beam tunnel ht has an effect on the coupling impedance and is initially set as 33.3 μm. The reason for setting ht as one fourth of dt is to match the length and width ratio of the beam (4:1). The orthogonal grating waveguide cell is further optimized using the CST (Computer Simulation Technology) eigen-mode solver [27]. In the simulation, the electrical conductivity of the simulation model’s background material is set as σCu/3 (σCu = 5.8 × 107 S/m) to take the copper loss into account [28]. The optimized parameters of the novel waveguide cell are: w = 950 µm, dt = 130 µm, ht = 30 µm, pt = 190 µm, dl = 30 µm, hl = 60 µm, and pl = 60 µm.As shown in Fig. 2, the operating mode (TM51-like mode) has five different electric field distributions but almost has the same dispersive property as shown in Fig. 3. Therefore, they can be regarded as five degenerated modes. 2π, 1/4π, 2/4π, 3/4π and π in Fig. 2 means that the number of changes in the direction of the Ez field along the x-axis is 0, 1, 2, 3, and 4, respectively. As shown in Fig. 2, the TM51-like mode has a longitudinal component of the electric field, which is necessary for the axial beam-wave energy exchange.
Fig. 2 Vector electric field distribution of the TM51-like modes across the xz plane of the orthogonal grating waveguide cell (a) TM51-like 2π mode, (b) TM51-like 1/4π mode, (c) TM51-like 2/4π mode, (d) TM51-like 3/4π mode, (e) TM51-like π mode.
Fig. 3 Beam line, light line and dispersion curves of the proposed orthogonal grating waveguide cell (TM51-like mode) and the traditional single grating waveguide cell (TM11-like mode).
The beam line and light line in Fig. 3 are achieved by Eq. (2)-(3).
As shown in Fig. 3, the orthogonal grating waveguide cell has a wide tunable frequency range from 1.18 THz to 1.3 THz, corresponding to a voltage range of 18-30 kV. A single grating waveguide with the same structural dimensions was also simulated, which operates at the low-order mode (TM11-like mode). As shown in Fig. 3, the operating frequency of the novel waveguide cell is higher at each phase point. For example, the operating frequency has increased from 0.43 THz to 1.21 THz when ψ is 1.78π (~320°). If the single grating waveguide would like to operate at the same frequency such as 1.21 THz, its structural dimensions need reduce to about one third, for example the grating period needs reduce from 60 µm to 20µm. Simulation results show that when w becomes larger, the tunable frequency range of the proposed waveguide will overall shift down, and the operating frequency of the BWO will become smaller. In addition, the tunable frequency range will enlarge as the cutoff frequency at the lower frequency end will reduce when w become larger. Also, with the increase of w, the coupling impedance will reduce as the electric filed will be more scattered.As shown in Fig. 4, the interaction circuit is composed by 150 orthogonal grating waveguide cells and two rectangular waveguides. It has a compact configuration with a 3D dimension of 0.95 mm × 0.04 mm × 10 mm. As shown in Fig. 5(a), the TM51-like mode will be excited in the orthogonal grating waveguide when a TE50 mode is input from port 1 of the interaction circuit. The transmission curve of the interaction circuit is shown in Fig. 5(b). It looks like a band-pass filter and has a passband of ~0.12 THz (1.18-1.3 THz).
Fig. 5 (a) Electric field distribution across the xz plane and (b) transmission curve when exciting TE50 mode.
3. Beam wave interaction simulation and discussion
To verify the proposed idea and study the performance of the BWO operating at the high-order mode, particle-in-cell (PIC) beam-wave interaction was carried out by CST Particle Studio [27]. As shown in Fig. 6(a), five sheet electron beams with identical parameters were injected from port 1 to perform the beam wave interaction in the orthogonal grating waveguide. The parameters for each sheet electron beam are as follows: the beam voltage of 23 kV, the beam current of 6 mA (375 A/cm2), and the beam size of 80 µm × 20 µm. The sheet electron beam with a current density of 375 A/cm2 can be obtained by a sheet electron gun based on a nanocomposite scandate tungsten cathode [12] or an impregnated scandate dispenser cathode [29]. The electron beam was focused by an axial magnetic field Bz of 1 T.
Fig. 6 (a) Electron energy distribution and (b) vector electric field distribution across the xz plane of the structure.
As shown in Fig. 6(a), each sheet electron beam has an obvious electron bunching, which implies an effective beam wave interaction. As shown in Fig. 6(b), the TM51-like π mode is excited in the interaction circuit and its electric filed distribution is in good agreement with the one achieved in the cold cavity analysis as shown in Fig. 5(a). Also, its electric field distribution along the x-axis matches with the electron bunching distribution ( + - + - + ). The TM51-like π mode will be converted into the TE□50 mode in the rectangular waveguide 1. The TE□50 mode can be converted into the fundamental mode (TE□10 mode) by the use of a TE□50 - TE□10 mode converter. A similar structure related to such a mode convertor can be found in [30].
As shown in Fig. 7(a), most of the electrons have a kinetic energy lower than the initial energy of 23 keV at the end of the interaction circuit, which means that the electron energy has been given out to the THz-wave. As shown in Fig. 7(b), an output voltage signal with a sinusoidal form was observed at port 1. The amplitude of the signal will gradually raise and then become stable after 2.5 ns. The corresponding frequency spectrum can be achieved through Fourier transform, which is shown in Fig. 7(c). The frequency spectrum is pure and has an obvious peak at 1.24 THz. The envelope curve of the radiation power dependent on the interaction time can be obtained from the output voltage signal. As shown in Fig. 7(d), the radiation power of both the TM51-like 2π mode and the TM51-like 2/4π mode will firstly raise to a certain of level but then reduce to a very small value. It is demonstrated that all of the other degenerated modes will be suppressed by the TM51-like π mode after 2.5 ns. The peak radiation power of the BWO can be up to 1.7 W. From the simulations, we find that the frequency spectrum of the five degenerated modes almost all peak at 1.24 THz, which is in good agreement with the dispersive curves as shown in Fig. 3. PIC simulations demonstrate that a small deviation of the voltage of each individual electron beam has a small effect on the tube performance. For example, if the tolerance of the voltage difference for each electron beam is controlled at ± 0.2 kV, the radiation power will decrease by ~0.03 W (1.7%) and the oscillation frequency will almost stay unchanged.
Fig. 7 PIC simulation results when the voltage and current are 23 kV and 30 mA, respectively. (a) Electron energy along the z-axis, (b) time-correlated output voltage observed at port 1, (c) the corresponding frequency spectrum, (d) and the envelope curve of the radiation power calculated from the output voltage.
The performance of the radiation source dependent on the beam voltage and current was studied. As analyzed in section 2, the orthogonal grating waveguide has a wide tunable voltage range. As shown in Fig. 8(a), the operating frequency will vary from 1.18 THz to 1.30 THz when the beam voltage sweeps from 18 kV to 30 kV. The radiation power predicts over 1.08 W in the frequency range and can be up to 2.06 W at 1.29 THz. Figure 8(b) shows the radiation power and the electronic efficiency dependent on the total beam current. It is demonstrated that the beam wave interaction will enter into the over-saturated state when the total beam current is 35 mA (the current per beam is 7 mA). The BWO can still produce 0.15 W output power when the total beam current reduces to 15 mA (187.5 A/cm2) and the maximum efficiency is up to 0.25% at 30 mA.
Further PIC simulations were conducted to make the model closer to the actual situation, leading to increasingly realistic predictions. To estimate the effect from the copper loss on the tube performance, the PIC simulations using different background materials with varied electrical conductivity (EC) were performed. As shown in Fig. 9(a), simulations demonstrate that the radiation power and the efficiency will reduce with a decrease of the electrical conductivity, corresponding to an increase of copper loss. The BWO can generate 0.48 W power when the electrical conductivity is set as 0.58 × 107 S/m (σCu/10). To estimate the effect from the electron interception on the tube performance, the PIC simulations with different Bz were also conducted. As shown in Fig. 9(b), the radiation power and beam propagation rate almost remain unchanged when Bz is more than 0.6 T. When Bz reduces to 0.4 T, the beam propagation rate and radiation power will reduce to 93.3% and 0.50 W, respectively. Simulations show that the BWO still can provide a radiation with hundreds of milliwatts at the frequency of over 1 THz when considering a more actual situation.
Fig. 9 Interaction performance dependent on (a) the EC of the background material and (b) the focusing magnetic field Bz.
4. Conclusion
To extend the operating frequency of the terahertz backward wave radiation, an orthogonal grating waveguide operating at a high-order mode is proposed to interact with multiple sheet electron beams. Compared with the overmoded structure based on the double staggered grating waveguide, the proposed waveguide is relatively ease of fabrication and assembling. Particle-in-cell simulations predict that the BWO has a stable THz radiation with pure frequency spectrum and can produce >1.08 W output power in the frequency range of 1.18-1.30 THz. It can be extended to higher-order mode operation by adding the number of cells of the transverse grating waveguide. Simulation studies show that the BWO based on the novel orthogonal grating waveguide provides a promising solution for compact THz radiation sources with high radiation power and wide tunable bandwidth.
Funding
National Natural Science Foundation of China (NSFC) (61601095); Natural Science Foundation of SZU (2018046)
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