Eur. Phys. J. Appl. Phys. (2015) 71: 20804
https://doi.org/10.1051/epjap/2015140491

On the fundamental relation of laser schlieren deflectometry for temperature measurements in filamentary plasmas^*

¹ Leibniz Institute for Plasma Science and Technology, Felix-Hausdorff-Str. 2, 17489, Greifswald, Germany
² Department of Physical Electronics, Faculty of Science, Masaryk University, Kotláĭská 2, 61137, Brno, Czech Republic

^a e-mail: jschaefer@inp-greifswald.de

Received: 12 December 2014
Revised: 18 February 2015
Accepted: 26 February 2015
Published online: 15 July 2015

Abstract

Recently, laser schlieren deflectometry (LSD) had been successfully employed as a temperature measurement method to reveal the heat convection generated by micro filaments of a self-organized non-thermal atmospheric plasma jet. Based on the theory of the temperature measurements using LSD, in this work, three approaches for an application of the method are introduced: (i) a hyperbolic-like model of refractive index is applied which allows an analytical theory for the evaluation of the deflection angle to be developed, (ii) a Gaussian shape model for the filament temperature is implemented which is analyzed numerically and (iii) an experimental calibration of the laser deflection with a gas mixture of helium and argon is performed. Thus, these approaches demonstrate that a universal relation between the relative maximum temperature of the filament core (T₁/T₀) and a the maximum deflection angle δ₁ of the laser beam can be written as T₁/T₀=(1 − δ₁/δ₀)⁻¹, where δ₀ is a parameter that is defined by the configuration of the experiment and by the assumed model for the shape of the temperature profile.