Investigation of Transient and Steady-State Behavior of Current Components in Spatial Harmonic Magnetron by Drift Orbital Resonance Theory

The drift orbital resonance theory has the potential to analyze and estimate the electron dynamics in a magnetron. Hence it has been utilized to examine the behavior of the rotating electron cloud in a spatial harmonic magnetron (SHM). Alteration of the theory variables, namely the orbital velocities, coefficients of radial expansion, gyrating circle radius, accelerating factor, etc., affects the electron trajectory forming numerous epicycloid, hypocycloid, and circular patterns. These variables are dependent on some of the physical and electrical input parameters, namely the structural geometry, the applied voltage, the applied magnetic field, etc. They thus can be used to alter and predict the rotating electron's trajectories, which in turn control the device performance as well as help to understand and visualize the response of the rotating electron cloud in the designed SHM. The manuscript also presents the analysis of the nature of the steady-state and transient response of the current components of the designed SHM (operating at 136 GHz) obtained from CST simulations and provide reasonable explanation using drift orbital resonance theory.

I. Introduction

Spatial harmonic magnetrons (SHMs) have been extensively researched and thus have emerged as compact, efficient, and high-power radio frequency sources in millimeter (mm), sub-mm and near terahertz (THz) frequency regime. Also, SHM operation provides numerous advantages over conventional magnetrons such as reduced magnetic field requirements, greater mode separation, longer lifetime, and increased cavity dimensions at higher frequency [1], [2]. There have been numerous efforts of design and development of SHMs in its various aspects like SHMs theoretical modeling [1], [3], [4], studies on aspects of mode interaction [5], [6], circuit efficiency analysis [7], and 3-D particle in cell simulations and optimization [8]–[15] for various high-frequency applications [16]–[19]. Even with all of these research works, there is still scope for better understanding and modeling of the electron dynamics occurring in SHMs. The present manuscript aims to study these electron dynamics in SHM by drift orbital resonance (DOR) theory. It comprises the results obtained using DOR theory, which have the potential to elucidate the steady-state and transient behavior of the current components of a designed SHM. The design parameters of the SHM model have been obtained by using the spatial harmonic amplitude study and the admittance matching field theory method [20]. The major geometrical parameters are shown in Fig. 1 and summarized in Table I. With these design parameters, a model of SHM with novel secondary electron emission cold cathode [21] was made in CST particle studio (CST-PS), and numerous simulations were conducted [22]. The present work, which is an extension of [22], throws light on the grounded physics of the electron dynamics in the designed SHM. The manuscript has been sectioned such that Section II details the peculiarities of DOR theory and highlights various results obtained from it. The obtained results and the inferences from the DOR theory and the CST simulation results of the designed SHM were collated and have been discussed in Section III, followed by conclusion in Section IV. The results comparison enables the designer to visualize the effect of various design parameters and the input electrical parameters on the electron trajectories and thus predict their resultant phenomena such as back-bombardment, cathode–anode grazing, electron cloud trajectory pattern, emission current trend, and collision current trends.TABLE I Structural Design Parameters of SHM

Design Parameters	Value
Anode Radius ()	1.30 mm
Cathode Radius ()	0.70 mm
Vane Thickness ()	0.13 mm
Vane Depth ()	0.35 mm
Cavity opening angle ()	7.07°
Mean radius ()	1.00 mm
New mean radius ()	1.15 mm

Fig. 1.

Schematic of modeled SHM with design parameters.