# Detailed Investigation of the Electric Discharge Plasma between Copper Electrodes Immersed into Water

^{1}

^{2}

^{*}

## Abstract

**:**

_{α}and H

_{β}hydrogen lines, and Cu I 515.3 nm line, exposed to the Stark mechanism of spectral lines’ broadening. Estimations of the electrodes’ erosion rate and bubbles’ size depending on the electrical input parameters of the circuit are presented. Experimental results of this work may be valuable for the advancement of modeling and the theoretical understanding of the pulse electric discharges in water.

## 1. Introduction

_{2}, and H

_{2}O

_{2}from the electric breakdown in water [7,8]. Moreover, shock waves produced by high-energy plasma discharges inside liquids are used for various applications, including underwater explosions [9], rock fragmentation [10], and lithotripsy [8]. A great deal of work has been done by Locke et al. [11], who presented the review of the current status of research on the application of high-voltage electrical discharges for promoting chemical reactions in the aqueous phase, with particular emphasis on applications to water cleaning. Another important application of the underwater electric discharges, which has attracted significant attention, is the nanomaterial synthesis by plasma-liquid interactions, including plasma-over-liquid and plasma-in-liquid configurations [12].

## 2. Experimental Method

#### 2.1. Experimental Setup

_{0}is 430 V for a 1000 µF capacity and a maximal current of 4 kA.

_{α}and Cu I lines with central wavelength set on λ = 616.2 and 515.0 nm, correspondingly) and 1800 lines/mm grating (for H

_{β}line with central wavelength set on λ = 486.1 nm). The spectral resolution of the system is 0.056 nm for the 300 lines/mm grating and 0.0078 nm for 1800 lines/mm grating. The exposure time of the EMCCD camera is 200 μs. It is triggered as the value of current rises above 120 A, which occurs ~10 µs after the pulse start. In turn, the EMCCD camera trigs the high-speed camera with negligible delay (of <1 µs) as the acquisition occurs, therefore one acquisition corresponds to one pulse.

#### 2.2. Optical Emission Spectroscopy (OES)

#### 2.2.1. Registered Spectra

#### 2.2.2. Broadening of Spectral Lines

_{e}), with applications not only in laboratory plasmas but also in astrophysical ones. This broadening is due to the collisions of the emitter with the charged particles in the surroundings of the emitter, according to the Stark effect. Stark broadening of the Balmer lines is the most popular approach to the determination of Ne since the broadening of the hydrogen lines, resulting from the linear Stark effect, is the strongest. These lines are, thus, those most sensitive to electron density variations. For the purposes of completeness and comparison, the electron density was also determined from the profile of Cu I 515.3 nm line, which is exposed to the quadratic Stark effect. In addition to Stark broadening, ideally, one should consider other broadening mechanisms, namely instrumental broadening, natural broadening, Doppler broadening, pressure broadening (resonance broadening, Van der Waals broadening), which have been reviewed in detail in [19,20]. More information about the broadening phenomena (physical phenomena, mathematical expressions of FWHMs, convolution procedure, etc.) are presented in Appendix A.

#### 2.2.3. Line Broadening Values in Our Configuration

_{N}values showed to be of ~10

^{−5}nm and is negligible in comparison to the impact of other broadening mechanisms. Values of w

_{R}and w

_{VdW}are of the order of magnitude of ~10

^{−3}nm and doesn’t vary significantly with the values of gas temperature T

_{g}, and as well can be excluded out of calculations of the electron density. Therefore, profiles of the registered lines are fitted with a Voigt function, whereas the Gaussian part is presented by convolution of the instrumental and Doppler broadening, giving the values of 0.02–0.04 nm, and the Lorentzian part of the profile is considered to be only the Stark FWHM.

## 3. Results

#### 3.1. Electron Density

#### 3.2. High-Speed Imaging

#### 3.3. Erosion of Electrodes

## 4. Discussion and Conclusions

- For all the four current regimes studied in this work (I = 450 A, I = 660 A, I = 800 A and I = 1000 A), duration of the pulse in average shows to be 320–346 μs with the rise time of a current up to its maximum value of 90–100 μs (see Table 1). While raise time of a current up to its maximum value is the shortest for the current regime I = 450 A, the maximum bubble’s size is reached the fastest for the case of the current regime of I = 800 A, for which the current raise time is the longest. The only pattern that can be distinguished (see Figure 7 and Figure 9) is that the bubble reaches it maximum size not at the same time when the current value is on peak, but before that, maintaining its size more or less constant while current value equals to its maximum value for the given current regime. In order to be able to make any conclusions, more experiments must be performed, which will give the more reliable statistical data.
- The erosion does not change much for the different current regimes. Table 2 shows that for current of 800 A, which is approximately two times greater than the first current regime, increase of the eroded mass per pulse is ~20%. Erosion of anode shows to be greater than that of cathode (in our experiments anode is the moving electrode). This is consistent with the results obtained by other authors studying the submerged pulsed arc discharges [22], and may have one of the possible explanations that the energy dissipated in the anode is larger than in the cathode. As expected, the size of craters produced on the electrodes during arcing (Figure 10) increases with the measured erosion. The larger craters were formed on the anode where the erosion was larger.
- Calculation of the electron density shows (Figure 5) disagreement the values of Ne calculated using the Cu I 515.3 nm, H
_{α}and H_{β}lines. While Ne determined from the widths of Cu I 515.3 and H_{α}line are of the same order of magnitude for all the studied current regimes, values of Ne obtained from the width of H_{β}line are by two orders of magnitude lower for cases of I = 660 and 800 A, and by one order of magnitude lower for the case of I = 1000 A.

_{α}line can lead to the following problems:

- It could present a non-negligible self-absorption and it is necessary to evaluate how it affects the line broadening;
- It has a strong broadening by ion dynamics, an effect that can be evaluated by using some computational methods recently developed which allow us to simulate the profiles of the spectral lines [23].

_{α}line width. However, at the same time, values of Ne obtained from H

_{α}line and Cu I 515.3 nm line show good agreement leading to the conclusion that the suggested value of the electron temperature Te = 10,000 K and N

_{e}~10

^{23}m

^{−3}are close to the experimental values of the electron density and electron temperature in our discharge.

_{e}, which has been derived from the Kepple–Griem theory (KG) [25], in case of use of H

_{α}line, overestimates the electron density by about 80% with respect to the Ne obtained from the H

_{β}line. This overestimation is due to the KG theory not taking into account the influence of the ion dynamics on the spectral profiles of the Balmer series lines. Computational methods taking into consideration these ion dynamic effects have been developed, among them the Gigosos–Cardenoso model (GC) [26] permitting the use of a line different from H

_{β}for measuring the electron density, obtaining in this way the same value of density as the one obtained from H

_{β}.

_{α}and H

_{β}lines with the corresponding Ne and Te = 10,000 K for the case of μ = 0.9 (reduced perturber mass corresponding to the hydrogen emitter and any perturbing atom or ion) are showed in Table 3.

_{β}line must be between 3 and 4 times greater than that of H

_{α}, while the experimentally obtained values of FWHM of H

_{β}line are around 2–6 times smaller than that of H

_{α}. (see Table 4), which, to our beliefs, leads to the correspondingly lower values of the estimated N

_{e}.

_{α}line are in the 30–33% agreement with the data given by GC in [23] in terms of N

_{e}/FWHM ratio.

_{α}line in order to double-check the results. Moreover, other techniques for the electron density determination should be used to validate the obtained results, for instance, determination of the electron density from continuum radiation, or, for instance, technique proposed in [27].

## Author Contributions

## Conflicts of Interest

## Appendix A

_{s}, which is used to determine Ne from the comparison with theoretical widths at the same electron temperature (T

_{e}).

- Instrumental broadening;
- Natural broadening;
- Doppler broadening;
- Pressure broadening (resonance broadening, Van der Waals broadening).

_{G}and w

_{L}. The FWHM of a Voigt profile can be represented through the combination of the Gauss and Lorentz components as follows [21]:

_{G}determined as:

#### Appendix A.1. Instrumental Broadening

#### Appendix A.2. Natural Broadening

_{nm}is the wavelength of a spectral line corresponding to transition from an upper state n to the lower state m (in cm), A

_{nu}, A

_{mu}are the transition probabilities of transitions between the states n, m and any ‘allowed’ level u, correspondingly Natural broadening is largest when one of the two levels is dipole-coupled to the ground state. Even in this case, it is usually negligible (of the order of 10

^{−4}nm). However, it may be of some importance for low electron density plasmas generated in low-pressure gas discharges. The values of the Einstein A coefficients for calculations were taken from [28].

#### Appendix A.3. Resonance Broadening

_{a}is the density of ground state particles which are the same species as the emitter, and g

_{i}and g

_{k}are the statistical weights of the upper and lower state; λ

_{R}and f

_{R}are the wavelength and f-value (oscillator strength), respectively, of the resonance transition from level “R”. The level “R” is the upper or lower level of the observed transition, which happens also to be the upper level of a resonance transition to the ground state. Not all transitions involve such a level. The values of f

_{R}, g

_{i}and g

_{k}for calculations were taken from [28].

#### Appendix A.4. Van der Waals Broadening

_{a}. This is a short-range C

_{6}/r

_{6}interaction. The full-width at half-maximum of the Lorentzian profile w

_{VdW}can be written as [19]:

_{0}units) of the upper and lower level, and μ is the atom-perturber reduced mass in a.m.u. In the Coulomb approximation the values of $\overline{{R}_{U}^{2}}$ and $\overline{{R}_{L}^{2}}$ in (7) may be calculated from

_{H}is the ionization potential of hydrogen (109,737.32 cm

^{−1}). Here ${E}_{IP}$ is the ionization potential of the studied element and E

_{j}is the energy of the upper or lower level of the transition.

_{EXC}is the energy of the first excited level of the perturber.

_{VdW}. In our case, we consider that discharge occurs at atmospheric pressure (or higher) in air with 1–2% of the hydrogen, similar to [30]. Therefore, value of $\overline{\alpha}$ presents a sum of atomic polarizabilities of air components (O, N, O

_{2}, N

_{2}, NO), and it was not taken from [29], but was calculated using Equation (A8). Mean atom-perturber reduced mass μ is taken to be equal to one (reduced perturber mass corresponding to the hydrogen emitter and any perturbing atom or ion).

#### Appendix A.5. Doppler Broadening

_{g}the line profile due to the presence of Doppler effects can be well described by a Gaussian profile with a FWHM (nm):

^{−1}) and T

_{g}the gas temperature in K, and m

_{a}–the mass of the emitter (a.m.u.).

#### Appendix A.6. Stark Broadening

_{S}is the FWHM of a Lorentzian contribution to the overall line profile and the parameter C(N

_{e},T

_{e}) depends (only weakly) on N

_{e}and T

_{e}, which can normally be treated as being constant. The constant C for H Balmer lines is available in the literature [35]. Usually, the first choice for the electron density determination is H

_{β}line (with an error of 5%) [35] because of its large intensity and sufficiently large line broadening, which can be measured precisely using spectrometer of moderate resolution. The possibility of self-absorption in this case is relatively small. The second best choice among the Balmer series is the H

_{ϒ}line. The H

_{α}line is suitable in the cases where the electron density is not too high (N

_{e}~10

^{17}cm

^{−3}), because at higher electron densities this strong line is quite susceptible to self-absorption, which severely distorts the line profile.

_{e}= 10

^{16}cm

^{−3}, and α is the ion broadening parameter. These parameters can be found easily from the literature [35]. Since the second term after opening the brackets in Equation (A13) is normally small, so the expression reduces to

_{β}line and H

_{ϒ}line data were in good agreement with each other, while the electron density estimated from the H

_{α}line is not purely Stark broadened. The additional broadening might be due to the onset of self-absorption.

_{β}, H

_{α}lines from the following equations presented in [26], which takes into account the ion dynamic effects:

_{e}= 10

^{17}cm

^{−3}and T

_{e}= 10,000 K. These values were assumed as parameters for the estimations presented in this work.

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**Figure 2.**Typical spectra obtained throughout the experiments (cross-section of the arc halfway between the electrodes); exposure time of the EMCCD τ = 200 μs: (

**a**) spectrum of Cu I lines registered for I = 450 A, central wavelength λ = 515.0 nm, grating 300 lines/mm; (

**b**) H

_{α}line registered for I = 450 A, central wavelength λ = 616.5 nm, grating 300 lines/mm; (

**c**) H

_{β}line registered for I = 660 A, central wavelength λ = 486.1 nm (Hβ line wasn’t registered for the current regime of 450 A due to its low intensity), grating 1800 lines/mm.

**Figure 3.**Spatially resolved spectrum images of the selected lines; exposure time of the EMCCD τ = 200 μs: (

**a**) spectrum of Cu I lines registered for I = 400 A; (

**b**) H

_{α}line registered for I = 400 A; (

**c**) H

_{β}line registered for I = 660 A.

**Figure 4.**Line profiles and Voigt fit of the registered lines for current regime I = 1000 A, radial position r = 0 mm (discharge axis): (

**a**) Cu I 515.3 nm line; (

**b**) H

_{α}line; (

**c**) H

_{β}line.

**Figure 5.**Radial profiles of the electron density calculated using broadening of the selected registered lines for different experimental current regimes: (

**a**) I = 450 A, Ne calculated using Cu I 515.3 nm line and H

_{α}line; (H

_{β}line was not registered for this regime); (

**b**) I = 660 A, Ne calculated using Cu I 515.3 nm, H

_{α}and H

_{β}lines; (

**c**) I = 800 A, Ne calculated using Cu I 515.3 nm, H

_{α}and H

_{β}lines; (

**d**) I = 1000 A, Ne calculated using Cu I 515.3 nm, H

_{α}and H

_{β}lines.

**Figure 6.**High-speed image recording of the discharge for different current regimes: (

**a**) I = 450 A, time interval between presented frames–60 μs, image resolution–128 × 96 px, frame rate–100,000 fps; (

**b**) I = 660 A, time interval between presented frames–60 μs; image resolution–128 × 96 px, frame rate–100,000 fps; (

**c**) I = 800 A, time interval between presented frames–65 μs; image resolution–128 × 128 px, frame rate–75,000 fps; (

**d**) I = 1000 A, time interval between presented frames–65 μs; image resolution–128 × 128 px, frame rate–75,000 fps.

**Figure 7.**High-speed imaging of the discharge and bubble size development up to the maximal size for different current regimes: (

**a**) I = 450 A, time interval between presented frames–60 μs, image resolution–128 × 96 px, frame rate–100,000 fps; (

**b**) I = 660 A, time interval between presented frames–60 μs; image resolution–128 × 96 px, frame rate–100,000 fps; (

**c**) I = 800 A, time interval between presented frames–65 μs; image resolution–128 × 128 px, frame rate–75,000 fps; (

**d**) I = 1000 A, time interval between presented frames–65 μs; image resolution–128 × 128 px, frame rate–75,000 fps.

**Figure 9.**Evolution of the bubble’s size depending on a discharge current (its evolution in time within one pulse) for different values of maximal current: (

**a**) for maximal current of 450 A; (

**b**) for maximal current of 660 A; (

**c**) for maximal current of 800 A; (

**d**) for maximal current of 1000 A.

**Figure 10.**Photographs of the cathode (

**left**) and anode (

**right**) after the series of 15 experiments for I = 450 A. Diameter of both electrodes is 6 mm.

**Table 1.**Electric parameters of the experimental setup corresponding to different current regimes (per pulse).

I_{disch}, A ^{1} | U_{c}, V ^{2} | P, kW | τ_{raise}, μs ^{3} | τ_{disch}, μs ^{4} | τ_{total}, μs |
---|---|---|---|---|---|

450 | 120 | 54 | 90 | 230 | 320 |

660 | 150 | 100 | 95 | 240 | 335 |

800 | 180 | 146 | 100 | 240 | 340 |

1000 | 220 | 217 | 96 | 240 | 336 |

^{1}I

_{disch}corresponds to the peak value of the current;

^{2}U

_{c}corresponds to the load capacitor voltage;

^{3}τ

_{raise}corresponds to the duration of the current raise up to its maximum value;

^{4}τ

_{disch}corresponds to the duration of the current decrease.

Current (I, A) | Number of Consecutive Pulses | Erosion of Anode, g | Erosion of Cathode, g | Total Erosion, g | Erosion Per Pulse (g/Pulse) |
---|---|---|---|---|---|

450 | 15 | 0.0038 | 0.0005 | 0.0043 | 0.00028 |

800 | 15 | 0.004 | 0.0012 | 0.0052 | 0.00034 |

logN_{e} (m^{−3}) | FWHM (nm) for H_{α} | FWHM (nm) for H_{β} |
---|---|---|

20.00 | 0.0142 | 0.0424 |

20.33 | 0.0244 | 0.0741 |

20.67 | 0.0404 | 0.129 |

21.00 | 0.064 | 0.217 |

21.33 | 0.102 | 0.361 |

21.67 | 0.16 | 0.601 |

22.00 | 0.25 | 0.999 |

22.33 | 0.393 | 1.67 |

22.67 | 0.621 | 2.80 |

23.00 | 1.01 | 4.70 |

23.33 | 1.68 | 7.77 |

23.67 | 2.84 | 1.27 |

24.00 | 4.86 | 2.05 |

24.33 | 8.31 | 3.25 |

Line | FWHM (nm) at I = 660 A | FWHM (nm) at I = 800 A | FWHM (nm) at I = 1000 A | Average log N_{e} (m^{−3}) |
---|---|---|---|---|

H_{α} | 1.13 | 2.60 | 2.40 | 23.36 |

H_{β} | 0.40 | 0.39 | 0.57 | 21.51 |

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**MDPI and ACS Style**

Venger, R.; Tmenova, T.; Valensi, F.; Veklich, A.; Cressault, Y.; Boretskij, V. Detailed Investigation of the Electric Discharge Plasma between Copper Electrodes Immersed into Water. *Atoms* **2017**, *5*, 40.
https://doi.org/10.3390/atoms5040040

**AMA Style**

Venger R, Tmenova T, Valensi F, Veklich A, Cressault Y, Boretskij V. Detailed Investigation of the Electric Discharge Plasma between Copper Electrodes Immersed into Water. *Atoms*. 2017; 5(4):40.
https://doi.org/10.3390/atoms5040040

**Chicago/Turabian Style**

Venger, Roman, Tetiana Tmenova, Flavien Valensi, Anatoly Veklich, Yann Cressault, and Viacheslav Boretskij. 2017. "Detailed Investigation of the Electric Discharge Plasma between Copper Electrodes Immersed into Water" *Atoms* 5, no. 4: 40.
https://doi.org/10.3390/atoms5040040