## 1 Introduction  
Terahertz radiation sources have gleaned much attention due to the wide range of potential applications of such devices, such as high data rate communications; the identification of concealed weaponry; remote, high-resolution imaging; and biomedical diagnostics [1; 2; 3; 4; 5]. Several existing technologies to generate terahertz waves are currently available, including quantum cascade lasers, solid state electron devices, and optical devices [6; 7; 8; 9]. Unfortunately, they have many intrinsic restrictions such as poor anti-interference performance, deleterious responsiveness to incident radiation, and the need for cryogenic cooling, which is often coupled to challengingly low output power. Vacuum electronic devices (VEDs) have been applied widely to realize terahertz radiation sources due to their high output power and high operation frequency [10; 11]. VEDs include gyrotrons, extended-interaction klystrons (EIKs), traveling wave tubes (TWTs), and backward wave oscillators (BWOs) [12; 13; 14; 15]. In particular, the BWO is an effective solution that is capable of producing relatively high power and stable monochromatic terahertz signals. BWOs can be electronically tuned over a wide frequency range around an arbitrary operating frequency and afford high frequency stability, along with compact designs at relatively inexpensive costs. To date, commercially available modern BWOs employ thermionic cathode electron guns that suffer from the need for large working volumes, high temperature operation, and slow temporal response. Field emission cold cathodes are a leading candidate for the replacement of incumbent thermionic electron sources in terahertz BWOs. Cold cathodes offer low operating temperature, instantaneous response time, facile and inexpensive integration, and the potential for miniaturization. 0.22 THz is an important terahertz frequency of atmospheric window, which is of great value in application. Here, a 0.22 THz BWO based on a cold cathode has been designed. Central to this is the development of field emission cold cathode materials suitable for terahertz BWOs. Carbon nanotubes (CNT)-based field electron emitters have a high emission current density, as well as impressive chemical and temporal stability [16; 17; 18; 19; 20], and are well suited to the miniaturization of terahertz VEDs. Nevertheless, there are still various challenges plaguing CNT cold cathode VEDs. Principally, the emission current density of CNT in a large area is very small. Therefore, it is vital to choose a suitable electron gun architecture that has the ability to simultaneously generate a high beam emission current and high emission current density. Several existing types of CNT-based field emission structures have been developed during the last two decades, including Spindt-type, magnetic injection type and separating gridded type [21; 22; 23; 24]. Spindt-type CNT field emission structures have many difficulties and insurmountable processing challenges, such as regular short circuits between the cathode and grid, high grid losses, and poor emission spatial uniformity. A truncated-cone CNT cold cathode electron gun, based on magnetic injection, has proven a need for superconducting magnetic fields in order to confine or control the electron beam [21; 22]. Conversely, the separating grid-type CNT field emission structure can be easily achieved in experiments and can operate at lower magnetic field at the gauss level. Such an operation would make the separating gridded structure widely appealing to a variety of small-scale vacuum microelectronic devices. However, it has been reported that a conventional, single-separating, gridded electron gun with the planar annular CNT cold cathode suffers from low emission current, high gate losses, and grid deformation [23], the latter of which stems from the small effective emission area, electrostatic shielding effect, and drop in electric field beneath the grid center.