**1. Introduction**

Various studies on vacuum interrupters (VIs) have been performed in recent decades. VI has been considered as an excellent interrupting technology, which is able to interrupt high-frequency currents [1–3]. The e ffect of the magnetic field on the arc in VI has been investigated both experimentally and analytically for axial and transverse magnetic fields because of the vital role of the magnetic field in VI design. This research gives an approach to VI designers to improve the structure of VI contacts and materials. The interpretation of the plasma behavior under magnetic fields is limited to the selected physical model. Earlier investigations [4,5] applied a constant temperature model. Other researchers [6] used a magneto-hydro-dynamic model, which is a single fluid model. In [7,8], researchers considered the movement of a constricted arc column, which is imposed by Lorentz force and move freely according to fluid dynamic equations.

Extensive experimental investigations were performed in [9,10], where the e ffect of the magnetic field on the cathode spot displacement was reported. Interesting experimental observations were reported in [11] in which an increment in arc voltage by using an external magnetic field was studied.

In the case of DC current breaking, there are several technologies, which are currently used. The passive inductive-capacitive oscillator circuit and active current injection are the applicable technologies now. As described in [12,13], there is a basic trend to find and present new technologies to make an artificial current zero-crossing and optimize the structure of existing DC circuit breakers in terms of technical complexity, weight, and cost.

This paper introduces a novel idea for making a zero-crossing in DC arc currents by using an ultrafast transverse magnetic field (UFTMF). This idea is based on the transient disturbances in plasma caused by imposed external UFTMF to a low-pressure plasma chamber such as a VI during arcing. The main disturbance is an immediate response of electrons to the change of plasma medium characteristics and lagged movement of heavy charged particles.

Simulation of the phenomenon needs a two-fluid plasma model, which ensures di fferent fluxes and temperatures of electrons and ions. By this analysis, expected disturbances in copper vapor plasma have been investigated and the results have been presented. In this paper, a similar plasma model has been employed to simulate the copper vapor plasma, which is the medium of commercial VIs, and a parallel capacitor with specific characteristic considered as an external circuit of VI. It is observed that a fast increment in arc voltage caused by external UFTMF leads to a successful commutation of arc current from VI to the parallel capacitor. This resulted in a zero-crossing in the arc current, which can be considered as a successful current interruption in VI because of the high-frequency interruption capability of VI technology.

In the next sections, the physical model and simulation results for copper vapor plasma in VI have been presented, and the idea that shows how an ultrafast transverse magnetic field can make a zero-crossing in the arc current has been discussed.

### **2. Physical Model and Geometry Simulation**

Two disks with a radius of 5.5 mm were considered as contacts of the interrupter. The maximum contact separation distance was assumed to be 12 mm as what is implemented in commercial VIs. A DC voltage source with an amplitude of 1000 V supplied the current of 50 A through a 20 Ohm resistance, which is placed in series with the interrupter.

The employed physical model was as described in [14]. The continuity equation of electrons, mass conservation equations of heavy species were considered as well as the heat transfer and Maxwell equations [15–19]. These equations are as follows:

$$\begin{array}{c} \frac{\partial u\_{\text{electron}}}{\partial t} + \nabla \cdot \overrightarrow{\Gamma}\_{\text{electron}} = \text{RR} \quad \text{electron} \quad - \left( \overrightarrow{\boldsymbol{\mu}} \cdot \nabla \right) n\_{\text{electron}} \\\\ \overrightarrow{\Gamma}\_{\text{electron}} = - (\overrightarrow{\boldsymbol{\mu}}\_{\text{electron}} \cdot \overrightarrow{E}) n\_{\text{electron}} - \overrightarrow{D}\_{\text{electron}} \cdot \overrightarrow{\nabla} n\_{\text{electron}} \\\\ \frac{\partial u\_{\text{energy}}}{\partial t} + \nabla \cdot \overrightarrow{\Gamma}\_{\text{e.c.} \text{nr} \text{cy}} + \overrightarrow{E} \cdot \overrightarrow{\Gamma}\_{\text{e.c.} \text{nr} \text{cy}} = \text{RR}\_{\text{e.c.} \text{nr} \text{cy}} - (\overrightarrow{\boldsymbol{\mu}} \cdot \nabla) n\_{\text{e.c.} \text{nr} \text{cy}} \\\\ \end{array} \tag{1}$$

$$\begin{array}{lcl} \stackrel{\text{5}}{\longrightarrow} & \stackrel{\text{5}}{\text{m}} & \stackrel{\text{e}}{\text{m}} & \stackrel{\text{g}}{\text{m}} & \stackrel{\text{g}}{\text{m}} & \stackrel{\text{g}}{\text{m}} & \stackrel{\text{g}}{\text{m}} & \stackrel{\text{g}}{\text{m}} \\ \stackrel{\text{5}}{\longrightarrow} & \stackrel{\text{5}}{\text{m}} & \stackrel{\text{5}}{\text{m}} & \stackrel{\text{5}}{\text{m}} & \stackrel{\text{5}}{\text{m}} & \stackrel{\text{5}}{\text{m}} & \stackrel{\text{5}}{\text{m}} \\ \stackrel{\text{5}}{\longrightarrow} & \stackrel{\text{5}}{\text{m}}\_{\text{e,m}\text{r},\text{gy}} & \stackrel{\text{5}}{\text{W}}\_{\text{e,c,m}\text{r},\text{gy}} & & & & \\ \end{array} \tag{2}$$

$$\begin{aligned} \rho\_{\text{bs}} \frac{\partial M\_f}{\partial t} &= \\ \rho\_{\text{bs}} \frac{\partial M\_f}{\partial t} &= \mathbf{F} \cdot (\rho\_{\text{bs}} M\_f D\_a^m \overrightarrow{\nabla} \ln(M\_f) + D\_a^T \overrightarrow{\nabla} \ln(T) + \rho\_{\text{bs}} M\_f z\_{\text{ion}} \mu\_{\text{ion}} \overrightarrow{E}) \end{aligned} \tag{3}$$

$$
\rho\_{\rm hs} \mathcal{C}\_P \frac{\partial T}{\partial t} + \rho\_{\rm hs} \mathcal{C}\_P \stackrel{\rightarrow}{u'} \stackrel{\rightarrow}{\nabla} T = \nabla \cdot (k \stackrel{\rightarrow}{\nabla} T) + Q\_s \tag{4}
$$

$$
\nabla \cdot \overrightarrow{E} = \frac{e(zn\_{\text{ion}} - n\_{\text{el}}c\_{\text{el}}n\_{\text{ion}})}{\varepsilon\_0} \tag{5}
$$

$$
\stackrel{\rightarrow}{j\_{\text{total}}} = \mathcal{e} \left( z n\_{\text{in}} \stackrel{\rightarrow}{v\_{\text{in}}} - n\_{\text{electron}} \stackrel{\rightarrow}{v\_{\text{electron}}} \right) \tag{6}
$$

The continuity equation of electrons was described as Equation (1). In this equation *nelectron*, *u*, *Delectron*, *RRelectron*, μ*electron*, and *E* represent the electron number density, convection velocity of fluid, di ffusion coe fficient and reaction rate of electron production, electron mobility, and electric field, respectively.

Energy conservation of electrons was described as Equation (2). In this equation *ne,energy*, *De,energy*, and μ*e,energy* represent the electron energy density, electron energy diffusion coefficient, and electron energy mobility, respectively. The rate of change in electron energy according to inelastic impacts between electrons and heavy species was described by *RRe,energy*.

Mass conservation of the heavy particles was described in Equation (3). In this equation *Mf*, ρ*hs*, *RRhs*, *Dhsm*, *Dhs<sup>T</sup>*, *zion*, *uion*, and *T* are the mass fraction, fluid density, production rate of heavy species, drift diffusion coefficient, thermal diffusion coefficient, ion charge number, ion mobility, and temperature of the heavy species, respectively. The type of heavy particle—neutral atom, excited atom, or ion—was presented by index 'a'.

Heat transfer in a fluid medium was described in Equation (4). In this equation *Cp*, *k*, and *Qs* are the heat capacity, thermal conductance, and heat source, respectively.

Maxwell description for the electric field was presented in Equation (5). In this equation, *nion* and ε0 are the ion number density and vacuum permittivity respectively.

Equation (6) represents the total current density flowing through the arc in which *nion*, *e*, *velectron*, and *vion* are the ion density, electric charge of electron, electron velocity, and ion velocity, respectively.

The considered particles in copper vapor plasma were electron, *Cu*, *Cu\**, *Cu*+, and *Cu*++, which are major species in this type of plasma [6]. The reaction rates between electrons and heavy species, which cause ionization and generation of the ions and excited particles, were calculated by using the impact cross-section data. In this way, an effective cross-section of electrons was calculated as a function of the electron energy distribution function. Required data were extracted from [15,20].

The two main parameters for calculation of reaction rates were the collision cross section value of electrons and the Townsend ionization coefficient versus electron energy. The assumption of the Maxwellian distribution function for electron energy was taken into account [15,16]. The considered particles in this analysis and chemical reactions between electrons, ions, and atoms were expressed as Equations (7)–(12).

$$
\varepsilon + \mathbb{C}\mu \Rightarrow \varepsilon + \mathbb{C}\mu \text{ (Elastic reaction)}\tag{7}
$$

$$
\epsilon \,\,\epsilon + \mathbb{C}\Lambda \Rightarrow \epsilon + \mathbb{C}u^\* \left( \text{Excitation} \right) \tag{8}
$$

$$2e + \text{Cu} \Rightarrow 2e + \text{Cu}^+ \text{ (Ionization)}\tag{9}$$

$$
\varepsilon + \mathbb{C}u^+ \Rightarrow 2\varepsilon + \mathbb{C}u^{++} \text{ (Ionization)}\tag{10}
$$

$$
\varepsilon + \mathbb{C}\mathfrak{u}^\* \Rightarrow 2\varepsilon + \mathbb{C}\mathfrak{u}^+ \text{ (Stepwise Lorentzian)}\tag{11}
$$

$$\text{Cu} + \text{Cu}^\* \Rightarrow \text{e} + \text{Cu}^{+} + \text{Cu} \ (\text{Penning} \ \text{Ionization}) \tag{12}$$

### *2.1. Boundary Condition of the Cathode*

According to [6], 70 percent of the cathode surface was considered as an active area for electric current injection. A diffused mode arc was taken into account when a 50 A plasma channel existed between the contact area and the magnetic field of the plasma current was unable to constrict the arc column. In this situation, variations of plasma parameters in an arc medium were considered while the arc–cathode interaction area was assumed to be unchanged.

Two other assumptions to make up the cathode boundary in the equations were secondary electron emission and considering the cathode to be hot enough to emit the electrons with respect to the electric field of the sheath region.

Equations describing the behavior of the cathode in an electron flux issue are as below:

$$\begin{aligned} \stackrel{\rightarrow}{n} \stackrel{\rightarrow}{\cdot} \stackrel{\rightarrow}{\cdot}\_{\text{electron}} &= \frac{1}{2} \upsilon\_{\text{electron},th} \, n\_{\text{electron}} + n\_{\text{electron}} \, (\stackrel{\rightarrow}{\mu}\_{\text{electron}} \cdot \stackrel{\rightarrow}{E}) \cdot \stackrel{\rightarrow}{n} - \\ \left( \gamma\_{\text{ion}} (\stackrel{\rightarrow}{n} \cdot \stackrel{\rightarrow}{\Gamma}\_{\text{ion}}) + \stackrel{\rightarrow}{n} \cdot \stackrel{\rightarrow}{\Gamma}\_{\text{electron},\text{injected}} \right) \end{aligned} \tag{13}$$

$$\begin{aligned} \overrightarrow{n} \cdot \overrightarrow{\Gamma}\_{\varepsilon, \text{norm}, \text{yy}} &= \frac{1}{2} \upsilon\_{\text{electron}, \text{th}} n\_{\varepsilon, \text{nrorg}} + n\_{\varepsilon, \text{nrorg}} (\overrightarrow{\mu}\_{\varepsilon, \text{zerorg}} \cdot \overrightarrow{E}) \cdot \overrightarrow{n} - \\ \left( \gamma\_{\text{ion}} \varepsilon\_{\text{ion}} \left( \overrightarrow{n} \cdot \overrightarrow{\Gamma}\_{\text{ion}} \right) + \varepsilon \stackrel{\leftarrow}{n} \overrightarrow{\Gamma}\_{\text{electron}, \text{injected}} \right) \end{aligned} \tag{14}$$

In Equations (13) and (14), *velectron,th,* γ*ion,* ε*ion,* ε, <sup>Γ</sup>*electron,injected*, and *n* are the electron thermal velocity, secondary electron emission coefficient, mean energy of the ion secondary emitted electrons, mean energy of thermally emitted electrons, total injected electron flux, and normal vector, respectively. The total injected electron flux was determined by the current flowing through the plasma by the external circuit as described later.

The cathode acted on ions and excited atoms as Equations (15)–(17). According to these equations, the cathode provides electrons to neutralize the positive ions and absorbs the excitation energy of the excited atom

$$
\mathbb{C}u^+ \Rightarrow \mathbb{C}u \tag{15}
$$

$$\mathbb{C}u^{++} \Rightarrow \mathbb{C}u \tag{16}$$

$$\mathbb{C}u^\* \Rightarrow \mathbb{C}u \tag{17}$$

In the heat transfer phenomenon, the cathode surface absorbs the heat flux from plasma and the temperature of the cathode material rises. Indeed, the cathode acts as the outgoing path of the heat flux.

### *2.2. Boundary Condition of the Anode*

The anode acts as a perfect sink for electrons [6]. In comparison with the cathode, the perfect sink is a boundary condition in which the total electron flux on the anode is equal to the sum of the drift and thermal electron fluxes with no sources. In this research, the temperature of the anode will not increase up to the melting point thus the anode will remain inactive during the process and no heavy species are emitted from the anode. Under these conditions, the anode acts as an electron wall, which provides electrons for positive ions hitting the anode, and converts them to neutral atoms. Equations (15)–(17) are valid for the anode too.

The performance of the anode in heat transfer phenomena is the same as the cathode.

### *2.3. Boundary Conditions of Chamber Walls*

The walls of the plasma chamber act for heavy species based on Equations (15)–(17). The effect of the walls on electrons is the same as the anode with the difference that in electrical equations the wall acts as a surface charge accumulator. These effects are described as:

$$\begin{aligned} \frac{\partial \rho\_s}{\partial t} &= \overrightarrow{n} \cdot \overrightarrow{j}\_{\text{electron}} + \overrightarrow{n} \cdot \overrightarrow{j}\_{\text{ion}} \\ \overrightarrow{n} \cdot \overrightarrow{D} &= -\rho\_s \end{aligned} \tag{18}$$

In this equation, ρ*s, jelectron, jion, D,* and *n* are the surface charge density, electron current density, ion current density, electrical displacement, and normal vector, respectively.

### *2.4. Interaction between the External Transverse Magnetic Field and Low-Pressure Plasma*

In the present research, the effect of the magnetic field on the electron movement was considered as a change in the mobility tensor of electrons. The tensor expression of electron mobility was replaced by a scalar one to model the magnetized plasma parameters. Equation (19) represents the mobility tensor.

$$
\boldsymbol{\mu}\_{magnetizad}^{-1} = \begin{bmatrix}
\boldsymbol{\mu}^{-1} & -\boldsymbol{B}\_{\boldsymbol{z}} & \boldsymbol{B}\_{\boldsymbol{y}} \\
\boldsymbol{B}\_{\boldsymbol{z}} & \boldsymbol{\mu}^{-1} & -\boldsymbol{B}\_{\boldsymbol{x}} \\
\end{bmatrix} = \begin{bmatrix}
\boldsymbol{\mu}\_{\rm xx} & \boldsymbol{\mu}\_{\rm xy} & \boldsymbol{\mu}\_{\rm xz} \\
\boldsymbol{\mu}\_{\rm yx} & \boldsymbol{\mu}\_{\rm yy} & \boldsymbol{\mu}\_{\rm yz} \\
\boldsymbol{\mu}\_{\rm zx} & \boldsymbol{\mu}\_{\rm zy} & \boldsymbol{\mu}\_{\rm zz}
\end{bmatrix} \tag{19}
$$

In Equation (19) μ*magnetized*, μ, *Bx*, *By*, *Bz*, μ*xx*, μ*yy*, μ*zz*, μ*xy*, μ*xz*, and μ*yz* are the mobility tensor, mobility of electron in non-magnetized plasma, magnetic flux density along the x, y, and z axes, and elements of the mobility tensor, respectively. In the present research, an external transverse magnetic field was applied to the current path perpendicularly. In 2D modeling, if the plasma was assumed to be placed in the X–Y plane, a desirable external magnetic field should be along the *Z*-axis. This magnetic field pushes the plasma to one side of the chamber depending on the magnetic field direction. Cylindrical coordinates and axial symmetry were used in this paper to reach a convergen<sup>t</sup> solution. By this assumption, moving of plasma to one side of the chamber changes to concentration or dispersion of the plasma.

The plasma chamber was assumed to carry the current of 50 A in the di ffused mode. Copper vapor plasma with the pressure of 10 mbar was assumed between contacts [14].

The space between the contacts was exposed to a transverse magnetic field. First, the simulation results in the case of a small magnetic field (e.g., 20 mT) were presented. Then, the impact of stronger magnetic fields (e.g., 1 T) on the arc voltage behavior was discussed. Finally, the contribution of the arc voltage fluctuation to a successful current commutation was investigated.

### **3. Simulation Results and the Proposed System**

A finite element (FEM) simulation was performed to study the e ffect of UFTMF on the arc voltage and other plasma characteristics. The described geometry of contacts and plasma medium was implemented for calculations in a 2D geometry with the assumption of axial symmetry. This symmetry completely expressed the plasma characteristics in the absence of a transverse magnetic field. There may be doubt about how a transverse magnetic field in axial symmetry, ϕ-direction, will be physically realized. The axial symmetry was employed just to reach a convergen<sup>t</sup> numerical simulation for ultrafast transients in plasma parameters. The transformation from cylindrical (r, ϕ, and z) coordinates to Cartesian (*x, y,* and *z*) coordinates is straightforward. A magnetic field in the ϕ-direction acts on the plasma in the RZ plane in the same way as a magnetic field in the z-direction does in the XY plane.

In this simulation, a homogeneous background distribution of electrons, copper ions, and neutral copper atoms was assumed as the initial condition of the plasma. By considering boundary conditions for the anode and the cathode, the voltage was applied to the arc chamber and after 1 ms plasma reached the steady state with an electric current of 50 A. Then, an external UFTMF was applied to the arc chamber with a value of 20 mT and a rise-time of 500 nSec. The disturbances in electron distribution and the energy level of electrons and the electron temperature in plasma have been illustrated in Figure 1 at di fferent time steps. As depicted in Figure 1, electrons were trapped behind the magnetized region because of an abrupt change in the mobility tensor of electrons. The peak value of electron density changed from 8.59 × 10<sup>19</sup> to 1.25 × 10<sup>20</sup> m<sup>−</sup><sup>3</sup> within 500 μSec.

A net space charge appeared near the magnetized region, and so there would be a strong electric field compared to what existed in the neutral plasma medium. This electric field caused electrons to gain more energy. That is why there were high-temperature electrons as depicted in Figure 1e–h. Indeed, there was an increment in the electron temperature from 1.38 to 2.29 eV. These high-temperature electrons caused high reaction rates and high power dissipation in the plasma medium. Figure 1i–l shows the variations of power dissipation in plasma.

Electron flux and related streamlines have been illustrated in Figure 2. The trajectory of electrons was broken when electrons entered the magnetized region. If the magnetic field region contains contacts, what may happen in reality is a high electric field region that forms from the cathode to the anode. This instantaneous disturbance in the electron flux and consequently electron density and net space charge was responsible for the instantaneous extreme value of the electric field in the plasma medium and the increment in arc voltage.

**Figure 1.** Distribution of electron, electron temperature, and power dissipation in plasma at different time steps: (**<sup>a</sup>**,**e**,**i**) initial moment, (**b**,**f**,**j**) 1 μSec, (**<sup>c</sup>**,**g**,**k**) 1.5 μSec and (**d**,**h**,**l**) 500 μSec after application of 20 mT ultrafast transverse magnetic field (UFTMF).

**Figure 2.** Distribution of the electron flux at different time steps: (**a**) initial moment, (**b**) 1 μSec and (**c**) 500 μSec after application of 20 mT UFTMF.

Figure 3a shows the electric potential distribution across the central axis of the plasma chamber at different time steps 0, 1 μSec, 1.5 μSec, 30 μSec, and 500 μSec after application of UFTMF. As it can be seen in Figure 3a, there was a dramatic increment in arc voltage in a short time duration. Actually, arc voltage jumped from 5.9 to 10.1 V within 1 μSec. This instantaneous increment in arc voltage caused a transient voltage change with a rate of rise of 4.2 MV/sec. In this situation, a strong electric field region appeared near the magnetized region. The difference between the density of the electrons and ions, which was caused by the applied UFTMF, was responsible for this extreme electric field in the plasma medium. This region was about 3 mm from the cathode where there was an approximately zero electric field in the plasma medium before application of UFTMF. This strong electric field was the main reason for high-temperature electrons, high reaction rates, and the high power dissipation mentioned before.

In Figure 3b, potential distribution along the arc axis in the diffuse mode arc with the current of 15 kA has been depicted [6], which is rarely mentioned in the literature. As illustrated in Figure 3b from the perspective of the potential distribution, the arc consists of four major regions: cathode spots, cathode jet mixing, the plasma bulk, and the anode sheath [6]. The considered model for the diffuse mode vacuum arc in the present paper had mathematically modeled only three regions: cathode jet mixing, plasma bulk, and anode sheath because the focus was on what happened in plasma due to UFTMF and mechanisms of forming and extinguishing of cathode spots was not considered. Another issue in this paper is the level of the arc current. A voltage drop along the plasma bulk region was proportional to the arc current. Thus, a voltage drop of 8 V for the arc current of 15 kA in Figure 3b will disappear in Figure 3a. By this description and comparing Figure 3a,b, it can be seen that if the voltage drop across the cathode spot region and plasma bulk was neglected from Figure 3b, there would be a trend similar to what has been presented in Figure 3a at "Time = 0" and this similarity validates the physical model, which was used in this paper.

Observation of such a high rate of rise in arc voltage, 4.2 MV/sec, illustrates the idea that a higher value UFTMF will give a sufficient rate of rise in arc voltage to commutate the arc current to a parallel capacitor. Another simulation with 1 T UFTMF was performed to investigate this idea, and the results were as expected.

At the first step, no parallel capacitor was assumed in the circuit, and an UFTMF of 1 T was applied to the arc. An increment of 20 times in the arc voltage appeared, as shown in Figure 4.

(**b**) 

**Figure 3.** (**a**) Distribution of the electric potential across the symmetry axis of the plasma chamber at time steps: 0 μSec, 1 μSec, 1.5 μSec, 30 μSec, and 500 μSec after application of 20 mT UFTMF. (**b**) Distribution of the electric potential from the cathode to the anode according to the 15 kA arc imposed by the axial magnetic field [6].

**Figure 4.** Distribution of the electric potential across the symmetry axis of the plasma chamber at time steps: 0 and 1 μSec after application of 1 T UFTMF.

Figure 4 shows that the arc voltage increased from 5.9 to 117 V by the application of an UFTMF of 1 T within just 1 μSec. A value of the parallel capacitor as illustrated in Figure 5 was calculated by performing numerous simulations with a focus on the commutation of the arc current. Various values of the parallel capacitor were chosen and simulated simultaneously with a plasma analysis in a range of a few pF to several μF. An appropriate value for successful commutation was calculated as 200 nF.

**Figure 5.** The external circuit of the plasma chamber, which is equipped by a parallel capacitor.

As it is mentioned before, arc current commutation from the plasma chamber to the parallel capacitor will be considered as an interruption of the arc current if the interrupter is capable of a high-frequency current interruption. Waveforms of currents flowing through the arc and the parallel capacitor were calculated and depicted in Figure 6.

**Figure 6.** Waveforms of the plasma chamber and parallel capacitor current after application of an UFTMF of 1 T. Successful commutation is achieved with the 200 nF parallel capacitor.

As it can be seen in Figure 6, a successful current commutation was achieved by placement of a 200 nF capacitor in parallel to the plasma chamber, where a zero-crossing in the arc current was observed. In the commutation process, the impedance of the parallel capacitor was much lower than the source side because of the high-frequency content of the arc voltage. The capacitor will charge up to a higher voltage than the initial arc voltage because of the direction of the electric current. By the charging process, the arc voltage will be restrained by the capacitor and a high arc voltage of 100 V as expressed in Figure 3 will not appear. Actually, the voltage of the capacitor scales up from 5.9 to 13.7 V. In addition, the effect of a stray inductance of the main circuit between the interrupter and parallel capacitor was considered for three values of 0, 10, and 100 nH. As depicted in Figure 6, by increment in stray inductance, a zero crossing time will occur with more delay and a zero crossing may be lost with large values of stray inductance. A design with a minimum value of stray inductance in this commutation system will be one of the key points.

The mentioned performance of this circuit under strong UFTMF expresses that successful interruption of the DC current will be accessible by this method while the transient recovery voltage across the interrupter will be limited by the parallel capacitor. There are, however, some technological issues, which have been discussed in the following.
