This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON PLASMA SCIENCE 1 Design Methodology and Beam–Wave Interaction Study of a Second-Harmonic D -Band Gyroklystron Ampliﬁer M. V. Swati, Madan Singh Chauhan, and Pradip Kumar Jain, Senior Member, IEEE Abstract— The design methodology of a gyroklystron ampliﬁer has been discussed and subsequently used for the design and opti- mization of a second-harmonic D-band four-cavity gyroklystron ampliﬁer. The multimode beam–wave interaction behavior of the device operating in the TE 02 mode has been analyzed using the time-dependent multimode analysis and also simulated using a commercial 3-D particle-in-cell code “CST Particle Studio.” The effect of various parameters, such as driver frequency, driver power, beam voltage, and beam current, has been studied to understand its sensitivity on the device performance. The simu- lation results predict that the designed second-harmonic gyrokly- stron ampliﬁer produces a stable RF output power of ∼1 kW (assuming 0% velocity spread) at 140 GHz center frequency, with ∼2.5% electronic efﬁciency, ∼30 dB gain, and ∼1 GHz bandwidth for a 40-kV, 1-A electron beam. Index Terms— Beam–wave interaction, gyroklystron ampliﬁer, millimeter-wave, particle-in-cell (PIC) simulation, second-harmonic operation, time-dependent multimode analysis. I. I NTRODUCTION T HE development of gyroklystron ampliﬁers has received a considerable attention due to their potential as the millimeter-and submillimeter-wave high-power ampliﬁer for the applications in the ﬁeld of spectroscopy, communications, and radars [1]. The phase bunching phenomenon due to the CRM instability in the cavities as well as the ballistic phase bunching in the drift tubes are the main reasons that make possible the higher power operation of the gyroklystron ampliﬁer with a high efﬁciency and an appreciable gain. The gyroklystron ampliﬁers can also be operated at the higher cyclotron harmonics requiring reduced dc magnetic ﬁeld at the millimeter-wave frequencies. However, device efﬁciency decreases with the increase of harmonic number; hence, oper- ation at the second harmonic is of primary importance [2]. Sometimes second-harmonic modes are difﬁcult to excite due to the mode competition from the fundamental harmonic modes and other nearby competing modes. Hence, the study of the multimode interaction mechanism becomes essential for the harmonic operation of the device. Several simulation and modeling techniques have been reported to describe the beam–wave interaction mechanism Manuscript received June 16, 2016; revised September 4, 2016; accepted September 13, 2016. The authors are with the Department of Electronics Engineering, IIT (BHU), Varanasi 221005, India. Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/TPS.2016.2611140 and facilitate the design of the gyroklystron devices. Different simulation codes, such as MAGY, CHICPIC, and ARGUS, which are based on different numerical techniques, are successfully employed over the years to get insight of the electromagnetic (EM) behavior of these devices and can also be used for the validation and design optimization of such devices but are not commercially available [3]–[5]. A commercial particle-in-cell (PIC) simulation code MAGIC has been successfully reconﬁgured to study the gyroklystron ampliﬁers [6], [7]. Another PIC simulation code, CST particle studio, is based on the ﬁnite integration method [8] with the provision to exhibit the temporal signal growth in the main mode along with the other possible competing modes simultaneously. The second-harmonic gyroklystron ampliﬁers that can generate peak power in kilowatts at D-band is not yet reported to the best of our knowledge as per the literature review. This paper presents the conceptual design of a 140-GHz, 1-kW second-harmonic four-cavity gyroklystron ampliﬁer with gain ∼30 dB, which can be used in spectrometers for electron paramagnetic resonance experiments. Furthermore, the multimode behavior of the device is studied with the com- mercially available 3-D PIC code “CST Particle Studio” and is also validated with the time-dependent multimode analysis. The temporal growth of the RF output power corresponding to the possible competing modes in the RF cavity is also presented. In this paper, Section II describes the conceptual design methodology used for the design of a gyroklystron ampli- ﬁer. The basic theory needed to carry out the multimode nonlinear analysis of the gyroklystron ampliﬁer is described in Section III. Section IV gives the brief description of the PIC simulation code and the modeling of the RF interaction structure. PIC simulation has been carried out to understand the beam–wave interaction phenomenon in terms of RF output power growth and the bunching phenomenon. The results are also discussed. The sensitivity of the RF output power and efﬁciency to the various device parameters have been studied in Section V and also validated with the devel- oped time-dependent multimode code. The major ﬁndings are summarized. The conclusions are drawn in Section VI. II. DESIGN APPROACH The design of the gyroklystron ampliﬁer is more rigorous at higher frequencies and for higher cyclotron harmonics 0093-3813 © 2016 IEEE. 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