Influence of surface emission processes on a fast-pulsed dielectric barrier discharge in air at atmospheric pressure

To compare with experimental results, first we have carried out simulations with the same initial condition as in previous works (Pechereau et al 2012, Pechereau and Bourdon 2014): a low uniform preionization of electrons and positive ions in both air gaps (above and below the dielectric layer) with a density of ${{10}^{4}}~\text{c}{{\text{m}}^{-3}}$. For these conditions, the discharge ignites at the point electrode at ${{\tau}_{\text{igni}}}=0.9$ ns. We define the time of ignition ${{\tau}_{\text{igni}}}$ as the time when the electric field on the symmetry axis, which is the Laplacian electric field initially, starts to be disturbed by the electric field induced by the space charge created close to the point electrode. Figure 3 shows the distributions of the electron density and absolute values of the electric field at t  =  2.6, 4.9 and 6.5 ns. As already observed in Pechereau et al (2014) for the same geometry but without a dielectric plane obstacle on the discharge path, the discharge first develops as a spherical discharge and then propagates axially towards the cathode plane. As shown in figure 3, this first positive discharge impacts the dielectric layer at ${{\tau}_{\text{impact}}}=2.6$ ns. We define the time of impact ${{\tau}_{\text{impact}}}$ as the time just before the sudden increase of the electric field in the head of the discharge on the symmetry axis, due to the creation of the sheath close to the dielectric surface. Then the discharge starts to spread on the upper surface of the dielectric layer. At the same time, we observe that the amplitude of the electric field in the second air gap below the dielectric plane increases. At ${{\tau}_{\text{rei}}}=4.9$ ns, a second positive discharge is ignited close to the bottom surface of the dielectric plane. Figures 4(a) and (b) show the time evolutions of the radial profiles of surface charges on both faces of the dielectric layer for the same condition as figure 3 and for t  =  2 ns upto ${{\tau}_{\text{rei}}}=4.9$ ns. As the first positive discharge spreads on the surface of the dielectric plane, its upper surface is charged positively by positive ions and its bottom surface is charged negatively mostly by electrons and negative ions. It is interesting to note that due to the fast pulsed high voltage applied to the sharp point electrode, the radius of the discharge impacting the dielectric surface is larger than in conditions studied in Pechereau et al (2012) and Pechereau and Bourdon (2014). As a consequence, we observe a faster surface charging. However, as in Pechereau et al (2012) and Pechereau and Bourdon (2014), we have checked that the amount of surface charges is too low at ${{\tau}_{\text{rei}}}=4.9$ ns to increase significantly the electric field in the second air gap and then to explain the discharge reignition. Then the increase of the electric field in the second air gap is mostly due to the potential redistribution in the interelectrode gap after the positive streamer propagation in the first air gap (i.e. most of the voltage difference is applied between the upper dielectric surface and the cathode). In the second air gap, as the first discharge spreads on the upper dielectric surface for $t>{{\tau}_{\text{impact}}}=2.6$ ns, we observe an almost homogeneous electric field that is $\geqslant$50 kV · $\text{c}{{\text{m}}^{-1}}$, i.e. higher than the breakdown field of air at atmospheric pressure. As a consequence, the charged species density increases rapidly due to ionization processes in the second air gap for $t>{{\tau}_{\text{impact}}}=2.6$ ns and at ${{\tau}_{\text{rei}}}=4.9$ ns a second positive discharge ignites on the symmetry axis close to the bottom surface of the dielectrics. This discharge propagates and impacts the cathode at $\tau _{\text{connec}}^{\text{plane}}=6.5$ ns. The time of impact on the cathode surface $\tau _{\text{connec}}^{\text{plane}}$ is defined as the time just before the rapid decrease of the electric field in the head of the discharge and the formation of a conducting channel between the surface of the cathode and the lower surface of the dielectrics. The numerical results obtained in figures 3 and 4 show that in the studied experimental geometry, the reignition process (${{\tau}_{\text{rei}}}-{{\tau}_{\text{impact}}}=2.3$ ns) and the dynamics of the reignited discharge ($\tau _{\text{connec}}^{\text{plane}}-{{\tau}_{\text{rei}}}=1.6$ ns) are very fast. In the simulations, the delay between the time of ignition of the first discharge at the point anode and the impact on the cathode of the reignited discharge is of $\Delta t_{\text{delay}}^{\text{num}}=\tau _{\text{connec}}^{\text{plane}}-{{\tau}_{\text{igni}}}=5.6$ ns and is much less than the delays measured experimentally $\Delta t_{\text{delay}}^{\text{exp}}\in \left[18,22\right]$ ns. In the following sections, we discuss and analyze physical processes that could allow longer reignition delays to be obtained in the simulations.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In the simulations presented in the previous section, it is assumed that the initial level of seed charges in air is ${{10}^{4}}~\text{c}{{\text{m}}^{-3}}$. For the air gap above the dielectric layer, based on the good agreement obtained in Pechereau et al (2014) for the same geometry but without a dielectric plane obstacle on the discharge path, we consider that this low value of ${{10}^{4}}~\text{c}{{\text{m}}^{-3}}$ allows the discharge ignition to be modelled accurately at the point. As shown in figure 3, after the first discharge impact on the upper dielectric surface, rapidly, around the symmetry axis in the second air gap, a region where the electric field is uniform and higher than the breakdown field is formed and expands radially. Then, even with a low preionization density of ${{10}^{4}}~\text{c}{{\text{m}}^{-3}}$ in the second gap, a fast reignition process is observed. So first, we have questioned the value of ${{10}^{4}}~\text{c}{{\text{m}}^{-3}}$ for seed charges below the dielectric plane for our conditions.

As the experiments are single shot, there are at least a few minutes between each applied voltage pulse. In Pancheshnyi (2005), it is pointed out that different key physical and chemical processes occur in an air post-discharge after the end of a voltage pulse:

• First at 300 K, electrons quickly attach to ${{\text{O}}_{2}}$:
  $$\begin{eqnarray}&&{{\text{e}}^{-}}~+~{{O}_{2}}+~{{O}_{2}}~\to ~O_{2}^{-}+~{{O}_{2}}.\end{eqnarray} \tag{ 2 }$$
  The exponential decay time of this process at atmospheric pressure is $\Delta {{\text{t}}_{1}}=20$ ns after the end of the discharge.
• Then, for times that are greater than $\Delta {{\text{t}}_{1}}$, the ion–ion dissociative recombination of $\text{O}_{2}^{-}$ and ${{\text{O}}^{+}}_{4}$ occurs:
  $$\begin{eqnarray}&&\text{O}_{2}^{-}+~{{\text{O}}^{+}}_{4}~\to ~{{\text{O}}_{2}}~+~{{\text{O}}_{2}}~+~{{\text{O}}_{2}},\end{eqnarray} \tag{ 3 }$$
  $$\begin{eqnarray}&&\text{O}_{2}^{-}+\text{O}_{4}^{+}+\text{M}\to ~{{\text{O}}_{2}}~+~{{\text{O}}_{2}}+{{\text{O}}_{2}}+\text{M},\\ &&~\text{with} ~\text{M}=~{{\text{N}}_{2}},{{\text{O}}_{2}},\end{eqnarray} \tag{ 4 }$$
  with a characteristic time $\Delta {{\text{t}}_{2}}~=~10-100$ ns for the conditions studied in this work.
• Finally, on longer timescales, ion diffusion losses at the reactor surfaces and the cathode have to be considered.

Then, according to Pancheshnyi (2005), after a few seconds of post-discharge, the density of positive and negative ions is $\sim {{n}_{\text{n},\text{p}}}={{10}^{4}}~\text{c}{{\text{m}}^{-3}}$ and, for a longer time between two consecutive applied voltage pulses, the diffusion of ions to the reactor surfaces will decrease the level of seed charges to lower values.

First, it is interesting to point out that in the previous section, we have used ${{10}^{4}}~\text{c}{{\text{m}}^{-3}}$ as the initial condition for densities of electrons and positive ions, that is to say we have assumed an instantaneous detachment of electrons from negative ions as soon as an electric field is applied. To check the influence of this hypothesis, we have carried out a simulation with an initial density of seed charges of ${{\text{n}}_{\text{n},\text{p}}}={{10}^{4}}~\text{c}{{\text{m}}^{-3}}$ (and no electrons) in the second air gap and we have used as in Tholin and Bourdon (2013b) the detachment rate given by Mnatsakanyan and Naidis (1991). As the electric field becomes rapidly higher than $E~\geqslant 50~\text{kV}~\centerdot ~\text{c}{{\text{m}}^{-1}}$ in the second gap, only a short delay is induced by detachment and we finally obtain $\Delta t_{\text{delay}}^{\text{exp}}\in \left[6,7\right]$ ns, which is still much less than experimental values.

Secondly, if we consider that there are several minutes between consecutive voltage pulses, according to Pancheshnyi (2005), the level of seed charges in the second small air gap, closed by lateral reactor walls, is ${{n}_{\text{n},\text{p}}}~\leqslant ~{{10}^{4}}~\text{c}{{\text{m}}^{-3}}$. As a limit case, we have considered that there are no seed charges in the volume of the second air gap. As the electric field in the second air gap is directed towards the cathode plane, we have assumed that the only source of electrons in the second air gap is the metallic cathode surface. In the following section we propose to carry out a detailed analysis of the processes that could explain an electron emission from the cathode surface.

In the literature, two emission processes are put forward:

• The thermionic emission processThe current density ${{J}_{\text{R}-\text{S}}}$ ($\text{A}\centerdot \text{c}{{\text{m}}^{-2}}$) at the cathode surface is calculated with the Richardson–Schottky equation (Murphy and Good 1956):
  $$\begin{eqnarray}&&{{J}_{\text{R}-\text{S}}}~=~{{A}_{1}}\exp \left(-\frac{\phi -{{F}^{1/2}}}{kT}\right)~\text{with}~F\propto \beta {{E}_{\text{cath}}},\end{eqnarray} \tag{ 5 }$$
  where ${{A}_{1}}=0.5{{\pi}^{-2}}{{(kT)}^{2}}\left(\pi d/\sin (\pi d)\right)$ and $d={{F}^{3/4}}/(\pi kT)$ where ϕ is the work function in eV representing the energy required for an electron at the energy Fermi level to be released outside of the metallic cathode and β is the amplification factor of the electric field at the cathode surface E_cath (that represents microscopic roughness at the cathode surface). The thermionic effect represents the emission of electrons from a metallic cathode surface induced by the temperature of the cathode surface (here T  =  300 K). The presence of an exterior electric field at the cathode surface lowers the surface barrier and increases the emission current.
• The field emission processThe current density ${{J}_{\text{F}-\text{N}}}$ ($\text{A}\centerdot \text{c}{{\text{m}}^{-2}}$) at the cathode surface is calculated with the Fowler–Nordheim equation (Murphy and Good 1956):
  $$\begin{eqnarray}&&{{J}_{\text{F}-\text{N}}}~=~{{A}_{2}}\exp \left(-\frac{{{B}_{2}}{{\phi}^{3/2}}}{F}\right)~\text{with}~F\propto \beta {{E}_{\text{cath}}},\end{eqnarray} \tag{ 6 }$$
  where
  $$\begin{eqnarray}&&{{A}_{2}}=\frac{{{F}^{2}}}{16{{\pi}^{2}}\phi {{t}^{2}}}\frac{\pi ckT}{\sin (\pi ckT)},\quad {{B}_{2}}=\frac{4\sqrt{2}v}{3},\quad c=2\sqrt{2}{{F}^{-1}}{{\phi}^{1/2}}t,\end{eqnarray}$$
  where v and t, functions of $\left({{F}^{1/2}}/\phi \right)$, are tabulated in Burgess et al (1953). For field emission, the electrons tunnel easily through the field deformed surface barrier. It is interesting to note that the field emission process coupled with the positive-ion bombardment at the cathode was used in negative streamer simulations to demonstrate the role of the field-effect emission in both the ignition and development of negative coronas in Reess and Paillol (1997) and Paillol et al (2002).

To determine the time required to emit one electron from the cathode surface in our conditions, we have integrated in time the flux of electrons emitted at the cathode surface by thermionic and field emission processes. In these calculations, we have considered no seed charges in the second air gap at t  =  0 ns. As the experimental reignition delay in section 3 is $18~\text{ns}\leqslant \Delta t_{\text{delay}}^{\text{exp}}\leqslant 22~\text{ns}$, we have carried out simulations during a total simulation time of ${{t}_{\text{simu}}}=24$ ns, i.e. until the end of the voltage plateau. We have varied the value of the work function $\phi \in \left[3,4\right]$ eV which corresponds to the usual values for metallic electrodes. In Reess and Paillol (1997), a value of $\beta =120$ for the amplification factor was used, albeit it was for a point metallic cathode. Nevertheless in Little and Whitney (1963), it was found that even on a polished flat metallic cathode, small point like structures of 2 μm in height were experimentally found and a value of $\beta =100$ was defined as an acceptable amplification factor. In Le Delliou (2014), a segmented cathode is used, and so it is difficult to estimate the value of β. Therefore, in this work, we have varied the amplification factor $\beta \in \left[100,220\right]$. In the simulations, we have assumed that the chosen values of ϕ and β are constant on the entire cathode surface.

In table 1, the time ${{\tau}_{\text{e}}}$ to emit an electron from the cathode surface is given for different values of $\phi \in \left[3,4\right]$ eV and $\beta \in \left[100,220\right]$. For a fixed value of the work function $\phi =3$ eV, we note that when the value of β decreases from 220 to 140, ${{\tau}_{\text{e}}}$ increases from 3.1 ns to 6.4 ns. When the value of β becomes less than 120, the time required to emit an electron increases significantly and becomes larger than ${{\tau}_{\text{e}}}>24$ ns. We note that the transition between ${{\tau}_{\text{e}}}<7$ ns and ${{\tau}_{\text{e}}}>24$ ns occurs for higher values of β as ϕ increases from 3 to 4 eV. For a fixed value of $\beta =220$, we see that when the value of the work function increases from 3 eV to 4 eV, ${{\tau}_{\text{e}}}$ increases from 3.1 ns to 6.2 ns. As β decreases and is between 200 and 140, we observe a transition between conditions with ${{\tau}_{\text{e}}}<7$ ns and with ${{\tau}_{\text{e}}}>24$ ns. We note that the transition occurs at lower values of ϕ as β decreases. For $\beta \leqslant 120$, we have ${{\tau}_{\text{e}}}>24$ ns for all values of $\phi \in \left[3,4\right]$ eV.

In table 2, the number of electrons N_e accumulated at the cathode surface at ${{t}_{\text{simu}}}=24$ ns is given for the same conditions as in table 1. For a fixed value of the work function $\phi =4$ eV, we see that when the amplification factor decreases from $\beta =200$ to 100, N_e decreases from $2.1\times {{10}^{-1}}$ to $4.9\times {{10}^{-21}}$. For $\phi =4$ eV, by just increasing the value of β from 200 to 220, an electron is emitted at ${{\tau}_{\text{e}}}=6.2$ ns. Finally, the results presented in tables 1 and 2 show that the time ${{\tau}_{\text{e}}}$ to emit an electron at the cathode surface is strongly dependent on the values of β and ϕ. To be close to the experimental reignition delay $\Delta t_{\text{delay}}^{\text{exp}}~\in \left[18,22\right]$ ns, the emission of an electron has to occur at ${{\tau}_{\text{e}}}<{{t}_{\text{simu}}}=24$ ns. In table 1, the only conditions to emit an electron from the cathode surface with ${{\tau}_{\text{e}}}<24$ ns, give an emission time ${{\tau}_{\text{e}}}\in \left[3.1,6.9\right]$ ns.

Table 2. Influence of the value of the work function ϕ and the amplification factor β on the number of electrons N_e accumulated at the cathode surface at ${{t}_{\text{simu}}}=24$ ns for the same conditions as in table 1.

β	ϕ
	3 (eV)	3.5 (eV)	3.8 (eV)	4 (eV)
220	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}>1$
200	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}~=~2.1\times {{10}^{-1}}$
180	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}~=~5.1\times {{10}^{-2}}$	${{N}_{\text{e}}}~=~6.8\times {{10}^{-4}}$
160	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}~=~8.6\times {{10}^{-2}}$	${{N}_{\text{e}}}~=~7.3\times {{10}^{-5}}$	${{N}_{\text{e}}}~=~6.0\times {{10}^{-7}}$
140	${{N}_{\text{e}}}>1$	${{N}_{\text{e}}}~=~5.2\times {{10}^{-5}}$	${{N}_{\text{e}}}~=~1.8\times {{10}^{-8}}$	${{N}_{\text{e}}}~=~7.7\times {{10}^{-11}}$
120	${{N}_{\text{e}}}~=~7.6\times {{10}^{-3}}$	${{N}_{\text{e}}}~=~3.4\times {{10}^{-9}}$	${{N}_{\text{e}}}~=~3.4\times {{10}^{-13}}$	${{N}_{\text{e}}}~=~6.5\times {{10}^{-16}}$
100	${{N}_{\text{e}}}~=~2.4\times {{10}^{-7}}$	${{N}_{\text{e}}}~=~1.4\times {{10}^{-14}}$	${{N}_{\text{e}}}~=~2.5\times {{10}^{-18}}$	${{N}_{\text{e}}}~=~4.9\times {{10}^{-21}}$

Note: The notation i.e. ${{N}_{\text{e}}}>1$ stands for a case when an electron is emitted at the cathode for $t<{{t}_{\text{simu}}}=24$ ns.

In the following sections, we propose to simulate what happens in the second air gap, after the emission of an electron at the cathode at ${{\tau}_{\text{e}}}=6.9$ ns. We have chosen the highest value of ${{\tau}_{\text{e}}}$ in expecting to be closer to the experimental reignition delay $\Delta t_{\text{delay}}^{\text{exp}}$ at the end. First, at $t={{\tau}_{\text{e}}}=6.9$ ns, based on the results obtained in section 4.1, in the second air gap, around the symmetry axis, the electric field is uniform and slightly higher than $50~\text{kV}\centerdot \text{c}{{\text{m}}^{-1}}$. Secondly, in section 4.4, we use a Monte Carlo model to follow the dynamics of formation of an avalanche starting from a single electron in a volume with a high and uniform electric field. Finally, in section 4.5, results from the Monte Carlo simulations are used as initial conditions of the fluid model presented in section 2 to simulate the discharge reignition dynamics in the second air gap.

The Monte Carlo model developed in this work simulates trajectories and creation of electrons in 3D space under the influence of constant applied electric field of magnitude $E=53~\text{kV}\centerdot \text{c}{{\text{m}}^{-1}}$. Background gas is composed of 80% of N₂ and 20% of O₂ with total number density of ${{N}_{0}}=2.688\times$${{10}^{19}}~$ cm⁻³. The model is closely based on Moss et al (2006), except that individual electrons are followed, i.e. no remapping in phase space nor in physical space is considered. The set of cross sections used is from the MAGBOLTZ code (Biagi 1999, 2005) and the same set has recently been used in Chanrion et al (2016). The scattering angle after collisions is obtained based on the knowledge of the ratio of momentum transfer and total cross section for individual collision following the scheme of Okhrimovskyy et al (2002). Kinematics of collisions follows (Bird 1994). Energy of a secondary electron created with an ionization collision is determined according to the model of Opal et al (1971). For details of the Monte Carlo model for electron transport in air see Moss et al (2006) and Chanrion and Neubert (2008).

The initial velocity of seed electrons at ${{t}_{0}}={{\tau}_{\text{e}}}$, the time of the electron emission from the cathode, is sampled from Maxwellian velocity distribution with an electron temperature of 0.5 eV. Note that the initial velocity of the seed electron has no effect on the avalanche development. A set of 100 avalanches has been simulated in order to obtain smooth distribution of the electron density in space. Any effect of the space charge on the electric field has been neglected, it is a reasonable simplification considering only early stages of an electron avalanche with low electron density. Moreover, no photoionization is considered for this model. Figure 5 shows the resulting electron density deduced from the Monte Carlo model at times t₀  +  1.0 ns, t₀  +  2.0 ns, and t₀  +  3.0 ns. The electron density has been determined assuming axial symmetry in r-z space, where $r=\sqrt{{{x}^{2}}+{{y}^{2}}}$ is the radial distance from the axis, using 2D histogram with bin size of $4\,\mu \text{m}\times 4\,\mu$m. The electron density has been normalized in such a way that it corresponds to an average density distribution created from a single seed electron. Density profiles have been fitted at selected times by 2D Gaussian function:

$$\begin{eqnarray}&&{{n}_{\text{e}}}(r,z)={{n}_{0}}\exp \left(-\frac{{{\left(z-{{z}_{0}}\right)}^{2}}}{2\sigma _{z}^{2}}\right)\exp \left(-\frac{{{r}^{2}}}{2\sigma _{r}^{2}}\right),\end{eqnarray} \tag{ 7 }$$

with n₀, z₀, ${{\sigma}_{z}}$ and ${{\sigma}_{r}}$ being fit parameters. For example, at t₀  +  3.0 ns for figure 5(c), we have found ${{n}_{0}}=1.03\times {{10}^{10}}~\text{c}{{\text{m}}^{-3}}$, ${{z}_{0}}=6.63\times {{10}^{-2}}~\text{cm}$, ${{\sigma}_{r}}=2.77\times {{10}^{-3}}$ cm, and ${{\sigma}_{z}}=3.29\times$${{10}^{-3}}$ cm. We have checked that the evolution of parameters n₀ and z₀ with time shows an excellent agreement with the Townsend avalanche process at the given electric field with an effective Townsend ionisation coefficient of ${{\alpha}_{\text{eff}}}=10465~{{\text{m}}^{-1}}$ and drift velocity of the avalanche center of ${{v}_{\text{drift}}}=221141~\text{m}\centerdot {{\text{s}}^{-1}}$. It is interesting to note that the Townsend avalanche center would reach the bottom surface of the dielectric layer in a time of about t₀  +  18.1 ns.

Zoom In Zoom Out Reset image size

As at t₀  +  3.0 ns, we have a Gaussian cloud with a sufficiently high peak density to be used in a fluid model, in the next section, we use the Gaussian cloud shown in figure 5(c) as the input parameter for the fluid code.

As discussed in section 4.3, we consider that in our studied conditions, an electron is emitted from the cathode surface at $t={{\tau}_{\text{e}}}=6.9$ ns. Then, based on the results of section 4.4, only 3 ns later, a Gaussian cloud is formed and is defined by equation (7) and n₀, z₀, ${{\sigma}_{z}}$ and ${{\sigma}_{r}}$ given in section 4.4 for t₀  +  3.0 ns. In this section, we simulate with the fluid model presented in section 2, the discharge ignition and propagation in the first gap for t  >  0, with no initial seed charges in the second air gap. Then at t  =  10 ns, we use as the initial condition in the second air gap, a Gaussian neutral plasma cloud with the values of n₀, z₀, ${{\sigma}_{z}}$ and ${{\sigma}_{r}}$ derived from the Monte Carlo simulations.

Figure 6 shows the distributions of the electron density and absolute values of the electric field at t  =  10, 13 and 14.8 ns. We observe a rapid increase of the electron density in the second air gap as electrons drift towards the dielectric plane and a double headed discharge ignites in the second air gap. A positive discharge front propagates towards the cathode surface and a negative discharge front propagates towards the bottom surface of the dielectric plane as shown at t  =  13 ns. At $\tau _{\text{connect}}^{\text{plane}}=14.8$ ns, the positive head impacts the cathode and 0.1 ns later the negative head impacts the bottom surface of the dielectric plane. It is important to note that for $10\leqslant t\leqslant 14.8$ ns, the amount of surface charges is very low and has no influence on the reignited discharge dynamics. Finally, for the simulation presented in figure 6, with the emission of an electron at ${{\tau}_{\text{e}}}=6.9$ ns, the duration of the formation and propagation of the reignited discharge in the second air gap is ${{\Delta }_{\text{ele}}}=\tau _{\text{connect}}^{\text{plane}}-{{\tau}_{\text{e}}}=7.9$ ns. The delay between the time of ignition of the first discharge at the point anode and the impact on the cathode of the reignited discharge is of $\Delta t_{\text{delay}}^{\text{num}}=\tau _{\text{connect}}^{\text{plane}}-{{\tau}_{\text{igni}}}=13.9$ ns. This value is rather close to the experimental delay $\Delta t_{\text{delay}}^{\text{exp}}\in \left[18,22\right]$ ns.

Zoom In Zoom Out Reset image size