## 1 Introduction  
With the increase in the use of electrical equipment, there is a possibility that high-power DC distribution systems will be needed, such as the 270 V DC power-supply system developed by More/All Electric Aircraft. If electrical power can be transmitted at a high voltage, resulting in low current and low conduction losses, the cable weight can be reduced. An investigation [1] showed that the \(\pm\)270 V DC power distribution system architecture is the most reliable configuration that can sustain an operation, even under severe supply transients [2]. The 270 V DC electrical power is used primarily in military vehicles and military aircrafts. It is advantageous in terms of the ease of paralleling DC electrical bus bars and integration with loads such as actuators. To satisfy the growing demand for high-capacity short-circuit protection, several methods that interrupt direct currents have been extended [3; 4; 5; 6]. Forced current zero (FCZ) is a common method used to interrupt the DC current. This method for DC interruption forces the current to zero by injecting a high-frequency current of the opposite polarity [7]. In the FCZ method, an oscillating current is generated by the resonance of a precharged capacitor and an inductor, and by superimposing this oscillating current over the current in the main circuit, a current zero is produced. Thus, the burning arc in the vacuum interrupter (VI) [8] can be extinguished by the FCZ. Then, the breaker in the main circuit can successfully interrupt the DC current [9; 10]. A successful interruption is significantly influenced by the transient characteristics of the current-commutation process, such as the rates of the current and voltage at zero-crossing (\(\,|\,di/dt\,|\) and \(\,|\,dv/dt\,|\)). To reduce the size and cost of the forced-commutation branch, a high frequency is usually selected for the commutation branch. However, this condition is unfavorable for the recovery of dielectric strength, as well as for the thermal interruption capability of the VI after current zero [11]. Thus, an optimal design for the forced-commutation branch is important. It is known that the transient characteristics are influenced by the commutating capacitor, commutating inductor, precharged voltage, etc. As these parameters may demonstrate coupling effects, the apparent relationships among the transient characteristics and the parameters of the forced-commutation branch are mostly worthy of investigation, during the design. Since VIs have excellent insulating and arc-quenching capabilities, the vacuum circuit breaker is often used as the main circuit breaker for DC interruption. Substantial research has been carried out on the axial magnetic field (AMF) contacts, based on FCZ. It is suggested that, when the current falls to zero very rapidly during DC interruption, the vacuum arc characteristics mainly depend on the characteristics before the instant of the countercurrent injection. However, the AMF has an inhibiting effect on the initial expansion stage. The vacuum arc is constricted by the magnetic field, while the arc columns in the butt electrodes expand much faster [12]. The AMF VI can maintain the diffusion of ions and electrons to the entire electrode; however, it is harmful for deionization [13]. The structure of the vacuum circuit breaker contact has been of paramount importance for vacuum arc modes and successful current interruptions. Two different versions of transverse magnetic field (TMF) contacts are being used--spiral-type and cup-shaped contacts. [PERSON] patented the spiral design in the USA in the late 1950s [14], and the cup-shaped design was patented by Lake and Reece in the early 1960s [15]. Several previous papers [16; 17; 18; 19; 20; 21; 22; 23] have dealt with the investigation of the behavioral patterns of vacuum arcs on TMF and butt contacts at line frequencies (50 Hz).