Gyrotron is a kind of vacuum electronic device, of which the operation is based on the stimulated cyclotron radiation of electrons oscillating in a strong magnetic field. In a gyrotron, electrons that are emitted by the cathode, are accelerated in a strong electric field. While the electron beam travels through the intense magnetic field, the electrons start to gyrate at a specific frequency given by the strength of the magnetic field. In the beam–wave interaction circuit, located at the position with the highest magnetic field strength, the electromagnetic radiation is strongly excited. The output radiation leaves the gyrotron through a window and the spent electron beam is then dissipated in the collector. In general, the cyclotron interaction condition is
, where ω is the frequency of the electromagnetic wave, kz is the axial wave number of the operating mode, vz is the axial velocity of the electron passing through the cavity, s is the harmonic number,
is the rest-mass (me) electron cyclotron frequency, and γ is the relativistic factor of the electron. As the above principle of stimulated cyclotron radiation, the electrons energy can be transferred to the fast-wave in the interaction circuit. Thus, it can be operated at high-order mode in the cavity, the dimensions of the interaction structure can be much larger compared to the wavelength of the radiation, which provides capability to generate extremely high-power radiation.
Due to its excellent power output in the millimeter-wave and sub-millimeter wavebands, gyrotron has caused extensive and in-depth research by experts and scholars all over the world [
1]. Lots of researches are focused on high-power, high-voltage gyrotrons used in ITER (International Thermonuclear Experimental Reactor), EAST(Experimental Advanced Superconducting Tokamak), etc. [
2]. Currently, low-voltage gyrotron with hundreds of watts to several kilowatts output power has been arousing the interest of many scientists, because they are preferable from the engineering and reliability point of view [
3,
4]. For low-voltage gyrotrons, the problem of efficiency must be solved due to the weak relativistic factor. A prodigious amount of work has been done to improve the efficiency of gyrotron, like installing depressed collectors [
5], changing the interaction structure [
6], and using double electron-beam [
7,
8]. In this paper, we proposed a way to improve the beam–wave interaction by increasing the pitch factor. The interaction process of the gyrotron is mainly between the transverse electron cyclotron velocity and the perpendicular electric field, so increasing the velocity ratio can directly improve the interaction efficiency and thus becomes a key method to improve the efficiency of the low-voltage gyrotron. The efficiency of interaction is limited by the
where
is the transverse energy,
is the total beam energy,
. Electron efficiency
was shown in
Figure 1, when the velocity ratio reaches 3 the electron efficiency comes to 90% which is remarkable during the beam–wave interaction [
9]. This scheme adopts a triode type magnetron injection gun with thermionic cathodes within the velocity spread under 10% [
8]. The final ratio of transverse to longitudinal velocity in the interaction region is typically between α = 1 and α = 2 for gyrotrons [
10]. The most frequent velocity ratio used in the MIG is 1.5 and it rarely exceeds 2, so the feasibility of ultra-high velocity ratio (MIG) is particularly valuable in compact gyrotron. In 2007, MIT has achieved a 3.5 kV gyrotron with a MIG, velocity ratio ranges from 2 and 5 with an operating current 10 mA [
11]. The present development status of low-voltage (less than 10 kV) gyrotron improves the efficiency by increasing the pitch factor within low velocity spread, which are shown in
Table 1. However, the operating current is often extremely low around 100 mA, with an output power of 10 W.
The required properties of the electron beam are basically determined by the chosen operating mode, frequency, and output power [
3,
17]. Parameters of this specific low-voltage gyrotron are shown in
Table 2. According to the theory of space charge effects, the operating current is restricted. At the same time, considering the power requirements, beam voltage and current should reach a certain level. Restrictions of velocity ratio are investigated including the electrostatic field, limiting current, and velocity spread. Both theoretical analysis and particle-in-cell (PIC) simulation are adopted to investigate the feasibility of ultra-high velocity ratio MIG and give a specific design of MIG. The purpose of the present paper is to analyze the possibilities of ultra-high pitch-factor (α) for MIG operating at low-voltage with operating current about 500 mA. This paper is organized as follows. In
Section 2, fundamental effects electrostatic and magnetostatic field on the α are analyzed theoretically, space charge effects in low-voltage operation are demonstrated, and velocity spread relevant to pitch factor is studied. In
Section 3, a numerical simulation is implemented to obtain a specific MIG with ultra-high α and appropriate velocity spread. Variation of α and perpendicular velocity spread ratio with operating current and modulating voltage are studied. Conclusions and plans are discussed in
Section 4.