# Charged Particle Oscillations in Transient Plasmas Generated by Nanosecond Laser Ablation on Mg Target

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

^{−5}Torr residual pressure. The radiation from a Quantel Brilliant, Nd-YAG nanosecond laser (355 nm-3rd harmonic, pulse width = 5 ns, 10 Hz repetition frequency, variable fluences) was focused by a f = 30 cm lens onto a magnesium target (the spot diameter at the impact point was approximately 0.3 mm) placed in the vacuum chamber. The magnesium target rotated during the experiments and was electrically grounded from the vacuum chamber. Before each measurement, a surface-cleaning procedure was implemented in order to remove the oxide layer present at the surface of the target.

## 3. Langmuir Probe Measurements

^{3}plasma volume at 2 cm with respect to the target surface. By recording the saturation charge currents, we are assuring the collection of global ionic and electronic charge ejected as a result of the ablation process coupled with the ionization and neutralization process occurring during expansion of the laser-produced plasmas. We can distinguish different features for both saturation currents. The electronic current has a longer lifetime induced by the increased collision rate and the higher diffusion rate of the electrons as opposed to the ions. For the same applied voltage, the ionic Mg species have a lifetime of 3 μs while the electrons present almost twice as much, approximately 6 μs. There is, however, a recurring oscillating feature that can be found on all collected signals regardless of the applied voltage. The choice to represent here only the temporal trace for the saturation currents is supported by their higher amplitude and a better highlight of the smaller features, like the oscillatory part of the signal, noticeable below 1 μs. In the inset of Figure 2a,b we can see a zoomed in view of the oscillatory regime. We observe that for higher fluences, the first oscillatory maximum is reached at a shorter expansion time, with no significant increase in the amplitude of the current. The results indicate an increase in the kinetic energy of the ejected particle as induced by the increase in laser fluence, while the overall ejected charge remains quasi-constant. The oscillatory behavior has been previously reported for a wide range of materials, in classical or more complex ablation geometries [12,21,22,23].

^{2}. The observed oscillations are damped after approximately 1 μs. This can also be seen from the oscillation frequency evolution with the measurement distance where we notice a decrease of about 25% for both measured frequencies. Admittedly, the laser fluence values are much higher than those used in the pulsed-laser deposition or material processing applications, where we can find reports of fluences below 5 J/cm

^{2}[1,2,3,4,5,6], depending on the irradiation conditions and the nature of the thin film envisioned in each report. However, the results become relevant for the fundamental new generation of high-power laser–matter interactions.

_{e}, V

_{p}, n

_{i}) is determined by evaluating all the recorded I–V characteristics, in the hypothesis that in the moments of time selected for analysis, the plasma has properties imposed by LP theory. This hypothesis cannot always be verified, as the implementation of the technique induces some limitations. In the incipient part of the evolution (<1 μs) and in the proximity of the target (few mm), the probe-collecting surface is significantly larger than the measured plasma volume; therefore, LP theory is no longer valid, as the measurement electrode must not impact the plasma around it. In these special space−time coordinates, data reveals the presence of a complex oscillatory regime of the ionic and electronic temporal traces, which are also part of our reported results in this paper [11].

_{e}= 1 eV and V

_{p}= 9.3 V for the measurements performed at 1.5 cm and a laser fluence of approximately 114 J/cm

^{2}, while the lowest are found for 28 J/cm

^{2}with the values decreasing with almost one order of magnitude: T

_{e}= 0.1 eV and V

_{p}= 2 V. For a fixed distance, the time-resolved analysis reveals important changes in both shapes of the I−V characteristics. These changes are induced by the decrease in all the plasma parameters as indicators of the laser-produced plasma expansion, particle density, and particle energy losses, showcased in the inset of Figure 5b where the temporal evolutions of T

_{e}and V

_{p}are presented.

## 4. Mathematical Model

#### 4.1. Ablation Plasma as a Fractal Medium

#### 4.2. Scale Covariant Derivative and Geodesics Equations

^{l}is the fractal spatial coordinate, t is the non-fractal time with the role of an affine parameter of the motion curves, ${D}^{lp}$ is the constant tensor associated with the differentiable-non-differentiable transition, ${\lambda}_{+}^{l}$ is the constant vector associated with the forward differentiable-nondifferentiable physical processes, ${\lambda}_{-}^{l}$ is the constant vector associated with the backward differentiable-nondifferentiable physical processes, and D

_{F}the fractal dimension of the movement curve. For the fractal dimension, we can choose any definition, for example, the Kolmogorov-type fractal dimension or Hausdorff−Besikovici-type fractal dimension [42]. However, once chosen and becoming operational, it needs to be constant and arbitrary: D

_{F}< 2 for the correlative physical processes; D

_{F}> 2 for the non-correlative physical processes [31,32,33,34].

#### 4.3. Ablation Plasma Behavior through a Special Tunneling Effect of Fractal Type

_{0}, which means to the right of z

_{0}, and to the left of −z

_{0}, the increase in the effective potential is fast enough so that it can be approximated with two infinite vertical walls at $z\pm l$, with $l\ge {z}_{0}$ (mandatory);

_{0}is placed below half of the local maxima V

_{0}and, at $\left|z\right|=0.5\left|{z}_{0}\right|$, ${V}_{ef}$ is already higher than V

_{0}/2, the same thought process can done in $z\pm d$, with $d<{z}_{0}$ (mandatory), by placing in each of these points a vertical wall of V

_{0}height. Therefore, $V(\infty )$ for $U\equiv V\left(z\right)$ becomes a condition for the spontaneous symmetry breaking, as well as for U’s symmetry.

_{0}) between −d and d leads to the splitting of the fundamental level ${E}_{0}$ into two sublevels, ${E}_{S},\text{}{E}_{A}$, accounting for the two states of fractal type, symmetric and antisymmetric, respectively, in which the system can be found. In the following, the above results will be calibrated to the LPP dynamics given by our experimental data. Therefore:

_{0}, i.e., $\mathsf{\Delta}E<<{E}_{0}$, which implies the fact that q

_{A,S}are very close to

_{A}, while the slower structure is induced by the symmetrical one E

_{S}.

_{A}is the characteristic frequency of the Coulomb oscillation modes and f

_{s}is the characteristic frequency of the thermal oscillation modes. As E

_{A}> E

_{S}, the oscillation frequency of the Coulomb mode will always be higher than that of the thermal oscillation mode, as it was shown experimentally in Figure 3.

_{0}− E

_{0}). In such a context, according to our previous considerations, the theoretical model at a local scale resolution ${\lambda}_{A}{\left(dt\right)}^{\left(\frac{2}{{D}_{F}}\right)-1}$ and ${\lambda}_{s}{\left(dt\right)}^{\left(\frac{2}{{D}_{F}}\right)-1}$ can describe the experimental behavior of the laser-produced plasmas presented in Figure 3.

_{A}is identified as the velocity of the fast structure and v

_{S}is the velocity of the slower one. Particularly, for the ablation plasma dynamics associated with the scale transitions such as correlative-non-correlative processes (the fractal dimension of the movement curves has the value D

_{F}= 2 [31]), Equation (37) becomes

_{e}is the electron temperature, and m is the atomic mass of the ions. $\overline{{v}_{A}}$ is the ion−electron collision frequency at Coulomb-scale resolutions, and $\overline{{v}_{S}}$ is the collision frequency at thermal-scale resolutions, causing Equations (38) with (39) to become

#### 4.4. Mutual Conditionings of the Plasma Structures through Joint Invariant Functions

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Temporal traces of the electronic (

**a**) and ionic (

**b**) current collected 2 cm from the target.

**Figure 4.**Temporal traces of the ionic and electronic currents recorded for a laser fluence of 56 J/cm

^{2}at 2.5 cm from the target.

**Figure 5.**Evolution of the I−V characteristics in time (

**a**) and space (

**b**); plasma potential (

**c**) and electron temperature (

**d**) evolution with distance and laser fluence and an example of the logarithmic representation of the I–V characteristic (

**e**).

**Figure 7.**The effective potential in the case of the tunneling effect of fractal type for a physical system with spontaneous symmetry breaking (where E

_{0}is the fundamental energy level, V

_{0}is the height of the potential barrier, z = 2d is the width of the potential barrier, and z = l − d is the width of the potential well).

**Table 1.**Comparison between the experimental and theoretical values of the ionic oscillating frequency for the first (

**a**) and second (

**b**) plasma structure.

(a) | 1st Structure Experimental Data (MHz) | 1st Structure Simulated Data (MHz) | ||||||

Fluence (J/cm^{2}) | 1 cm | 2 cm | 2.5 cm | 3 cm | 1 cm | 2 cm | 2.5 cm | 3 cm |

28 | 17.5 ± 0.2 | 15 ± 0.8 | 13 ± 0.5 | 7.6 ± 0.6 | 18.5 ± 0.3 | 16.1 ± 0.1 | 13.5 ± 0.2 | 9.4 ± 0.2 |

57 | 19.5 ± 0.3 | 16.8 ± 0.6 | 13.5 ± 0.7 | 8.5 ± 0.7 | 21.7 ± 0.2 | 18.2 ± 0.4 | 14.2 ± 0.6 | 10.6 ± 0.35 |

85 | 21 ± 0.7 | 19 ± 0.4 | 18 ± 0.5 | 16.3 ± 0.1 | 22.4 ± 0.05 | 20.2 ± 0.6 | 17.7 ± 0.5 | 16.3 ± 0.2 |

115 | 22 ± 0.1 | 19.26 ± 0.2 | 18.5 ± 0.3 | 17.3 ± 0.2 | 22.8 ± 0.5 | 20.9 ± 0.3 | 18.4 ± 0.2 | 17.4 ± 0.1 |

(b) | 2nd Structure Experimental Data (MHz) | 2nd Structure Simulated Data (MHz) | ||||||

Fluence (J/cm^{2}) | 1 cm | 2 cm | 2.5 cm | 3 cm | 1 cm | 2 cm | 2.5 cm | 3 cm |

28 | 7.8 ± 0.1 | 6.5 ± 0.3 | 2 ± 0.4 | 1.2 ± 0.6 | 7.4 ± 0.6 | 6.44 ± 0.1 | 2.4 ± 0.3 | 2.2 ± 0.1 |

57 | 8.4 ± 0.2 | 7.2 ± 0.1 | 5.6 ± 0.1 | 4.58 ± 0.2 | 8.68 ± 0.6 | 7.28 ± 0.04 | 5.68 ± 0.05 | 4.35 ± 0.05 |

85 | 9.5 ± 0.4 | 9.3 ± 0.5 | 9 ± 0.3 | 8.2 ± 0.2 | 8.96 ± 0.6 | 9.08 ± 0.1 | 8.78 ± 0.04 | 8.14 ± 0.04 |

115 | 10 ± 0.5 | 9.8 ± 0.5 | 9.3 ± 0.4 | 8.6 ± 0.3 | 9.12 ± 0.6 | 9.36 ± 0.06 | 8.99 ± 0.05 | 8.4 ± 0.2 |

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**MDPI and ACS Style**

Agop, M.; Mihaila, I.; Nedeff, F.; Irimiciuc, S.A.
Charged Particle Oscillations in Transient Plasmas Generated by Nanosecond Laser Ablation on Mg Target. *Symmetry* **2020**, *12*, 292.
https://doi.org/10.3390/sym12020292

**AMA Style**

Agop M, Mihaila I, Nedeff F, Irimiciuc SA.
Charged Particle Oscillations in Transient Plasmas Generated by Nanosecond Laser Ablation on Mg Target. *Symmetry*. 2020; 12(2):292.
https://doi.org/10.3390/sym12020292

**Chicago/Turabian Style**

Agop, Maricel, Ilarion Mihaila, Florin Nedeff, and Stefan Andrei Irimiciuc.
2020. "Charged Particle Oscillations in Transient Plasmas Generated by Nanosecond Laser Ablation on Mg Target" *Symmetry* 12, no. 2: 292.
https://doi.org/10.3390/sym12020292