# A Simple and Compact Laser Scattering Setup for Characterization of a Pulsed Low-Current Discharge
## 2 Theoretical Considerations  
The incident laser light, an electromagnetic wave, interacts with charged plasma particles. During the short laser pulse, the duration of which is in the range of 6 ns according to the specification of the laser used [35], the bound and free electrons are accelerated due to their small mass and high mobility, compared to other heavier species and follow the electric field of the incident wave. Thus, the electrons start to oscillate with the frequency of the incident radiation. This oscillation causes the electrons to emit electromagnetic radiation like an oscillating electrical dipole. Depending on the energy of the incident radiation, several interaction mechanisms can be distinguished. These can be mainly divided into those in which some energy is transferred to (or gained from) the interacting particle (called inelastic scattering, in which the emitted radiation has a slightly different wavelength than the incident radiation) and those in which the total kinetic energy is conserved (elastic scattering, in which the emitted and incident radiation have the same wavelength). Elastic scattering of electromagnetic waves in the visible range can be divided into Rayleigh (short RyS) and Thomson (ThS) scattering processes. In the RyS process, photons of the incident radiation are scattered by bound electrons in the atoms/molecules, compared to free plasma electrons in the ThS process. From the recorded ThS signal, the electron density and electron temperature can be derived. In the case of inelastic scattering, when energy is transferred between the incident radiation and plasma particles, the process is called Raman scattering. If longer wavelengths than the incident radiation are observed in the recorded signal, then energy is transferred to the interacting plasma particles, and the process is referred to as Stokes Raman scattering. If a shift to shorter wavelengths can be observed, the internal energy of the scattering particles is reduced and the process is referred to as anti-Stokes Raman scattering. Additionally, since Raman scattering occurs on molecular gases, rotational and vibrational lines can be detected in the scattered signal. Thus, when working with molecular gases, attention should be paid to the rotational Raman lines, which occur in the same wavelength range as the Thomson scattered signal and can therefore influence the evaluated results [27]. A comprehensive description of the scattering processes can be found in the works of [PERSON] and [PERSON] [36] as well as [PERSON] [30] and [PERSON] [37]. For more application-oriented descriptions, refer to [26; 27; 38; 39]. Regardless of the scattering mechanism, the mean scattered power \(\overline{dP_{s}}\) over a spectral frequency range \(d\omega\) is a function of the total spectral distribution of the radiation scattered by (free or bound) electrons \(s(\vec{k},\omega)\) within the scattering volume \(V\) and, since the scattering depends on the electric field strength of the incident radiation, \(\overline{dP_{s}}\) is also a function of incident power \(P_{i}\). Furthermore, the spectral distribution function \(s(\vec{k},\omega)\) depends on the scattering geometry, i.e., on the difference \(\vec{k}\) between the wave vector of the incident radiation \(\vec{k}_{i}\) and the wave vector of the scattered radiation \(\vec{k}_{s}\) as well as the difference \(\omega\) between the angular frequencies of the incident (\(\omega_{i}\)) and scattered (\(\omega_{s}\)) radiation. The incident power \(P_{i}\) is distributed across an area \(A\), which defines the scattering volume \(V\), as shown in Figure 1. This volume results also from the observation through solid angle \(\Omega\) since only a part of the scattering signal can be registered from the chosen viewing direction.