# Tracking Temporal Development of Optical Thickness of Hydrogen Alpha Spectral Radiation in a Laser-Induced Plasma

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## Abstract

**:**

## 1. Introduction

## 2. Theory

## 3. Experimental Details

## 4. Results and Discussion

#### 4.1. Temporal Self-Absorption Behavior

#### 4.2. Self-Absorption Impact on Line Shapes

^{®}scripting environment [43]. The Fadeeva function was numerically calculated using the Algorithm 916 method of Zaghloul et al. [44]. Line shape fitting was carried using a Trust Region nonlinear curve fitting routine [45,46] in which the fit parameters were the line width, amplitude, and shift as well as two terms used characterize a linear offset to model any continuum components in the spectra signals.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Alterations of a Lorentzian line profile under the influence of self-absorption for increasing optical density. The undistorted line width is 1 [a.u.].

**Figure 3.**Temporal development of the H${}_{\alpha}$ line in the first 100 ns following plasma initiation. (

**a**) Measured spectra and (

**b**) spectra measured with its duplication.

**Figure 4.**Temporal development of the H${}_{\alpha}$ line between 150 ns and 2150 ns following plasma initiation. (

**a**) Measured spectra and (

**b**) spectra measured with its duplication.

**Figure 5.**Ratios of the doubled H${}_{\alpha}$ spectra to the non-doubled emissions through the plasma decay from 30 ns to 2150 ns. Each image has the wavelength and ratio ranges.

**Figure 6.**Relationship between optical depth, $\tau $, and the ratio of a spectral line with its duplication compared to the line without duplication.

**Figure 7.**Results of correcting the H${}_{\alpha}$ spectrum using the methods of Equations (8) and (9) and also directly calculating the optical depth with assumed losses in conjunction with Equation (7) for (

**a**) 100 ns and (

**b**) 400 ns time delays in the plasma decay.

**Table 1.**Line widths of the H${}_{\alpha}$ line prior to and after self-absorption correction using all the stated methods. The 30 ns time delay is excluded form the table because the H${}_{\alpha}$ has not yet emerged from the continuum at this point.

Time [ns] | Uncorrected $\Delta \mathit{\lambda}$ [nm] | Kcorr $\Delta \mathit{\lambda}$ [nm] | No Loss $\Delta \mathit{\lambda}$ [nm] | 10% Loss $\Delta \mathit{\lambda}$ [nm] | 20% $\Delta \mathit{\lambda}$ [nm] |
---|---|---|---|---|---|

40 | 8.42 ± 0.34 | 7.33 ± 0.43 | 6.80 ± 0.34 | 6.77 ± 0.34 | 6.74 ± 0.34 |

50 | 9.80 ± 0.28 | 9.01 ± 0.28 | 8.89 ± 0.25 | 8.88 ± 0.25 | 8.86 ± 0.25 |

60 | 9.24 ± 0.23 | 8.32 ± 0.23 | 8.20 ± 0.23 | 8.19 ± 0.23 | 8.17 ± 0.23 |

70 | 8.98 ± 0.26 | 8.12 ± 0.21 | 8.03 ± 0.21 | 8.01 ± 0.22 | 7.99 ± 0.21 |

80 | 8.57 ± 0.24 | 7.63 ± 0.19 | 7.64 ± 0.20 | 7.61 ± 0.20 | 7.60 ± 0.20 |

90 | 8.11 ± 0.21 | 7.34 ± 0.19 | 7.31 ± 0.19 | 7.30 ± 0.19 | 7.29 ± 0.19 |

100 | 7.80 ± 0.20 | 6.93 ± 0.18 | 6.93 ± 0.18 | 6.92 ± 0.18 | 6.90 ± 0.18 |

150 | 6.30 ± 0.17 | 5.46 ± 0.16 | 5.51 ± 0.16 | 5.49 ± 0.16 | 5.47 ± 0.16 |

400 | 3.72 ± 0.15 | 3.17 ± 0.15 | 3.28 ± 0.15 | 3.28 ± 0.15 | 3.27 ± 0.15 |

650 | 2.53 ± 0.15 | 2.19 ± 0.15 | 2.27 ± 0.15 | 2.26 ± 0.15 | 2.25 ± 0.15 |

900 | 1.88 ± 0.15 | 1.58 ± 0.15 | 1.66 ± 0.15 | 1.66 ± 0.15 | 1.65 ± 0.15 |

1150 | 1.51 ± 0.15 | 1.36 ± 0.15 | 1.40 ± 0.15 | 1.40 ± 0.15 | 1.40 ± 0.15 |

1650 | 1.10 ± 0.15 | 1.02 ± 0.15 | 1.04 ± 0.15 | 1.04 ± 0.15 | 1.04 ± 0.15 |

2150 | 0.90 ± 0.15 | 0.57 ± 0.15 | 0.87 ± 0.15 | 0.87 ± 0.15 | 0.87 ± 0.15 |

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**MDPI and ACS Style**

Surmick, D.M.; Parigger, C.G. Tracking Temporal Development of Optical Thickness of Hydrogen Alpha Spectral Radiation in a Laser-Induced Plasma. *Atoms* **2019**, *7*, 101.
https://doi.org/10.3390/atoms7040101

**AMA Style**

Surmick DM, Parigger CG. Tracking Temporal Development of Optical Thickness of Hydrogen Alpha Spectral Radiation in a Laser-Induced Plasma. *Atoms*. 2019; 7(4):101.
https://doi.org/10.3390/atoms7040101

**Chicago/Turabian Style**

Surmick, David M., and Christian G. Parigger. 2019. "Tracking Temporal Development of Optical Thickness of Hydrogen Alpha Spectral Radiation in a Laser-Induced Plasma" *Atoms* 7, no. 4: 101.
https://doi.org/10.3390/atoms7040101