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

14 1 Physics and Applied Physics, University of Massachusetts Lowell, Lowell, MA 01854; david_surmick@uml.edu 2 Physics, University of Tennessee Space Institute, Tullahoma, TN 37388 2; cparigge@utsi.edu * Correspondence: cparigge@tennessee.edu; Tel.: (931) 841-5690 Abstract: In this paper, we consider the temporal development of the optical density of the Hα spectral line in a hydrogen laser induced plasma. This is achieved by using the so-called duplication method in which the spectral line is re-imaged onto itself and the ratio of the spectral line with it duplication is taken to its measurement without the duplication. We asses the temporal development of the self-absorption of the Hα line by tracking the decay of duplication ratio from its ideal value of 2. We show that when 20% loss is considered along the duplication optical path length, the ratio is 1.8 and decays to a value of 1.25 indicating an optically thin plasma grows in optical density to an optical depth of 1.16 by 400 ns in the plasma decay for plasma initiation conditions using Nd:YAG laser radiation at 120 mJ per pulse in a 1.11×105 Pa hydrogen/nitrogen gas mixture environment. We also go on to correct the Hα line profiles for the self-absorption impact using two methods. We show that a method in which the optical depth is directly calculated from the duplication ratio is equivalent to standard methods of self-absorption correction when only relative corrections to spectral emissions are needed.


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The act of tightly focussing a laser beam of sufficient energy creates a dynamic, micro sized Specific to the LIBS field of study, there is a long history of accounting for self-absorption [16][17][18][19][20][21][22][23][24].  In the present work, we detail the optical density of a laser induced plasma through out the 51 plasma decay by monitoring the temporal progression of the hydrogen Balmer series α line (H α ). This 52 is completed through the standard practice of using a doubling mirror to re-image the plasma onto 53 itself and take ratios of the plasma spectroscopic image collected with and without its doubled image. 54 In the following section, we detail the standard method for applying the doubling mirror method and 55 suggest a potential alternative that requires less post processing of the measured spectra. We go on 56 to apply both methods to measurements of the H α line and use the corresponding electron density The radiation transport equation details how light can be absorbed as it passes through a dense 61 medium [11]. Specifically the amount of radiation (L(λ, x)) that leaves a column of absorbing material 62 is detailed as where (λ, x) the emission coefficient, κ(λ, x) is the absorption along dx, and dx is a slab of absorbing 64 material. A solution to the radiation transport equation when spatial homogeneity is assumed is given where S(λ) is the source function, which is taken as the ratio of the emission and absorption coefficients 67 ( (λ)/κ(λ)). L(λ) is the normalized line profile and τ is the optical depth, which is defined as where is the size of the absorption path length. When the source is in local thermodynamic 69 equilibrium the source function takes the form of the Planck function [28]. In order to account 70 for absorption, one can rearrange Equation 2 to isolate the emission coefficient as such that if one can calculate a correction factor, apart from a multiplication of , of the form absorption can be taken into account along a particular line of sight in a relative manner.

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One methods for taking absorption into account is to duplicate the emission source with reflective 74 optics and compare the original emission source to source with its duplication. In the case of laser 75 induced plasma, duplication is typically done using some optical setup using a retro-reflecting mirror 76 [8,22,23]. The retro-reflection is reduced by a factor of e −τ as it passes through the original emission 77 source such that the ratio of the reflection plus the original source to the original emission is which reduces to where G(λ) is a term that accounts for losses along the duplication optical path length. The method the optical losses, G(λ). This method will hereafter be referred to the Kcorr method. In this scheme the 83 correction factor is calculated as where R c (λ) is the ratio of the continuum with and without the emission duplication. Rearranging 7  were nearly identical. Further fine adjustments were made by comparing collected ICCD spectra with 143 and without the duplication such that the ratio was as large as possible, with an ideal ratio limit of 2.   method. Both methods rely on finding the ratio of the spectra collected with and without its duplication. wings of the later time ratios are most impacted. In this case the wings represent a part of the spectrum that is characterized by an also decaying spectral continuum that will largely be the same between 202 spectra collected with and without the duplication. Furthermore, this weakly intense continuum is 203 more susceptible to noise contributions which is further amplified when the ratio is taken. This would 204 also manifest in the early investigated times prior to 150 ns, the H α line has contributions beyond 205 the spectral range of our instrument, making it difficult to asses the contributions of the continuum 206 radiation.

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As a reference, Figure 6 shows the relationship between optical depth and the ratio of the spectral 208 line with and without its duplication and without any losses given by Equation 5. At zero optical 209 depth, the ratio is 2. As the optical depth increases to values greater than 1 (τ = 1 is often cited as being   In terms of characterizing the electron density of the plasma, one typically uses the line width.

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As a result, the behavior of the width before and after the self-absorption corrections is considered.

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These results are displayed in Table 1  the H α line is very broad (∆λ > 9 nm) and subsequently decays to a relatively narrow line (∆λ < 1 nm).

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The uncertainties on the indicated line widths represent contributions from both the minimum spectral continuum is likely to be well characterized within the measurement. Table 1 shows that regardless of the method of correcting the spectrum, the line width is reduced 306 when the self-absorption factor is applied. The reduction in line widths ranges from 9 to 3.5 percent    The spectral line profiles were then corrected using two methods. The first was the standard