Theoretical calculation of the Stark shifts of the spectral lines of atomic helium 

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Energy measurements

The current that flows through the operating circuit of the plasma jet when the plasma is on consists of a capacitive component and a conductive component as given by Itot = Icap +Icon [40]. The capacitive current Icap, also known as displacement current, is the current that arises from the circuit of the plasma operating equipment, which acts as a capacitor. The conductive current Icon is the current that flows through the plasma, which is a conductor, and therefore we will call this the plasma current from now on. If all settings are kept constant, the capacitive current is the same at plasma On as at plasma Off, when the voltage is still applied but the flow is turned off. Furthermore, it is the only current that flows when the plasma is off. The plasma current, in which we are interested, is thus given by Iplasma = Itot􀀀Icap : (2.1).
Using the setup shown in figure 2.3, the current at the anode of the plasma jet is measured with a Rogowski coil (Pearson Current Monitor 6585) and read out on the oscilloscope (LeCroy waveRunner 6100A 1GHz). Itot is measured as the total current when the plasma is on and Icap as the total current when the plasma is off. Similar as in section 2.1, the voltage that is applied to the anode of the jet is measured with the same high voltage probe (LeCroy PHV4-3432) and read out on the oscilloscope. The voltage in the circuit at plasma On is equal at plasma Off, thus Vplasma =Vtot =Vcap holds. The energy that is dissipated in the plasma can then be calculated as Eplasma = Z T 0 Pplasma dt = Z T 0 Vtot Iplasma dt.

ICCD imaging

The discharge in the plasma jet is not a continuous event, but rather a series of fast consecutive events, because of the pulsed applied voltage. At every applied voltage pulse, a discharge event takes place, which is called a guided ionization wave, ionization front or plasma bullet. To investigate these ionization waves and determine their velocity, ICCD imaging is used. An ICCD camera consists of a CCD (Charge Coupled Device, the chip) with an intensifier in front that uses a photocathode, a micro-channel plate (MCP) and a phosphor screen to enhance the light of the incoming photons. The gate of the intensifier can be controlled, and both these characteristics make an ICCD camera very suitable for imaging the fast ionization waves that have low light emission.
The setup that is used for the ICCD imaging is shown in figure 2.5. The ICCD camera (Stanford Computer Optics 4Picos S20Q) with objective (TAMRON 70-300 mm, f/4-5.6 DI LD Macro) is placed such that the full trajectory of the ionization wave from below the grounded electrode of the jet until the end of the plasma plume is visible on the chip. The camera is triggered by the output of the waveform generator.
On a computer, the software 4Spec is used to control the camera. In this software, there are different settings to adjust when taking images:
the delay: the time between which the camera receives the trigger and opens the gate.
the exposure time: the time that the gate stays open, during which charge can accumulate on the chip.
the gain: the voltage set on the MCP to accelerate electrons, thus enhancing the incoming light.
the number of frames: the number of times the gate is opened to accumulate charge on the chip before it is read out.

Stark polarization spectroscopy

To determine the electric field in the front of the ionization wave, a Stark polarization spectroscopy setup was built, in which the jet is placed. This setup is shown schematically in figure 2.7. As will be shown in section 3.2, the electric field can be determined from the peakto- peak wavelength difference between the allowed and the forbidden component of a certain helium line. To get this wavelength difference, a high resolution spectrum needs to be obtained of the desired helium line, emitted by the plasma.
The light emission from the plasma is focused with two identical plano-convex lenses (Thorlabs LA1050, f = 10 cm) onto the slit of a 1 m spectrometer (Jobin-Yvon HR1000, equipped with a 1200 l/mm grating, blazed at 0:4􀀀1:1 μm). Before entering the spectrometer, the light passes a linear polarizer (Thorlabs) to make sure only linearly polarized light remains, in order to measure the axial electric field, as explained in section 3.5. At the exit of the spectrometer, an ICCD camera (Stanford Computer Optics 4QuickE S20) is mounted to capture the spectral images. The camera is controlled on a computer by the software 4Spec and it is triggered by the output of the waveform generator. The same settings as for the 4Picos ICCD camera in section 2.3 are adjusted when taking images, but now also the integration time is available. The integration time is the time during which exposures (time between the gate opening and closing) are accumulated on the chip within one frame. In general, the delay is set between 180􀀀600 ns, the exposure time to 10 ns, the gain to the maximum value of 1000 V, the number of frames to 20 and the integration time to 2􀀀20 s (depending on the intensity of the light), but in particular cases these values may be slightly altered.

Thomson and rotational Raman scattering setup

For the measurements on Thomson and rotational Raman scattering, the jet is placed in the laser setup of [30]. The Thomson and rotational Raman scattering setup has been described in detail in [30, 43, 44]. Here, the most important details are summarized. A schematic overview of the jet in this setup is shown in figure 2.10. A Nd:YAG laser (Spectra Physics, Quanta-Ray, Lab-190-100) is used with a frequency doubled wavelength of 532 nm, operating at 100 Hz with 140 mJ per pulse. Each laser pulse has a width of 100 μm at the focal point and a duration of 10 ns. The laser scattered light is captured at 90 to the laser path and the vertical axis of the jet, after which it is focused into a glass fiber. The Rayleigh stray light is removed by a volume Bragg grating (OptiGrate, BragGrate, BNF-532-OD4-12.5M) with a FWHM of 7 cm􀀀1 [43] as Notch filter. The remaining Thomson and Raman scattered light is focused onto the 100 μm wide slit of the spectrometer (Jobin-Yvon, HR 640) that has a 1200 l/mm grating (Horiba, 530 24 Holographic Grating, blazed at 500 nm). Then, the spectrum is captured by a self-assembled ICCD camera (Allied vision BigEye G-132B Cool, with KATOD, EPM102G-04-22 F intensifier; ICCD 1 in figure 2.10) integrating every exposure of 70 ns over 2.5 to 50 minutes, depending on the intensity of the signal. This spectrum has a wavenumber range of 510 cm􀀀1 and a resolution of 0.398 cm􀀀1 [30]. The jet is placed on a mount with translation stages in the x-, y- and z-direction so that it can move precisely in all directions. To align the center of the jet with the focus of the laser beam, an ICCD camera (Andor iStar DH734 18mm; ICCD 2 in figure 2.10) is used from the side of the jet as well as a CCD camera (Hama Webcam HD 00053950; not shown in figure 2.10) next to the top of the jet. The laser clock is used as trigger signal for the other equipment in the setup: the pulse generator of the jet, ICCD camera 1 and ICCD camera 2.

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Center of jet determination

To perform temperature measurements along the center of the jet, equally to the rotational Raman measurements, the temperature probe needs to be positioned precisely in the center of the jet. The center of the jet is determined by taking a cross section along the xy-plane of the jet when the plasma is on at z = 0:9 mm, which is close to the nozzle, with a range of 8 mm in the x-direction and 6 mm in the y-direction at a step size of 0.2 mm. The result of this measurement is shown in figure 2.13, where the colors represent the temperature. When the plasma is on, it will heat the gas, which is visible in figure 2.13 as the circle-like shape of higher temperature.
Finding the center of this shape then corresponds to finding the center of the jet. In order to do so, cross sections in figure 2.13 are taken around the expected position of the center, thus at y-positions 1.4, 1.6 and 1.8 mm and at x-positions 4.6, 4.8 and 5.0 mm. Then, the mean of the temperature in both the x- and the y-positions is taken and the results are shown as the two curves in figure 2.14. Taking the middle positions of the plateau of both curves then yields the position of the center of the jet at x = 4:6 mm and y = 1:55 mm.

Table of contents :

Summary 
R´esum´e 
Samenvatting 
1 Introduction 
1.1 Plasma
1.1.1 Dielectric barrier discharges
1.1.2 Plasma jets
1.1.3 Plasma jet applications
1.2 Motivation and research goals
1.3 Structure of the thesis
2 Diagnostics and experimental setups 
2.1 General plasma jet setup
2.2 Energy measurements
2.3 ICCD imaging
2.3.1 Experimental setup
2.3.2 Data analysis
2.4 Stark polarization spectroscopy
2.4.1 Experimental setup
2.4.2 Data analysis
2.5 Thomson and rotational Raman scattering setup
2.5.1 Experimental setup
2.5.2 Data analysis
2.6 Temperature probe
2.6.1 Experimental setup
2.6.2 Center of jet determination
2.6.3 Measurements
2.6.4 Data analysis
2.7 Schlieren imaging
2.7.1 Experimental setup
2.7.2 Measurements
2.8 Potential of a conductive target
2.8.1 Experimental setup
2.8.2 Data analysis
2.9 Summary
3 Theoretical calculation of the Stark shifts of the spectral lines of atomic helium 
3.1 Introduction
3.2 Stark effect
3.3 Derivation of the Stark shifts
3.3.1 Solving the Schr¨odinger equation for hydrogen
3.3.2 Approximations for the helium atom
3.3.3 Applying degenerate perturbation theory for the influence of the electric field
3.3.4 Application to specific helium lines
3.4 Comparison to previous work
3.5 Selecting the axial component of the electric field
3.6 Summary
4 Comparison of discharge propagation parameters in experiments and simulations of a helium jet without target 
4.1 Introduction
4.2 Setup
4.2.1 Experimental setup
4.2.2 Numerical setup
4.3 Results and discussion
4.3.1 Characterization of discharge propagation and peak electric field
4.3.2 Characterization of electron density and temperature
4.3.3 End of discharge propagation
4.4 Conclusions
5 Flow profile and air entrainment in a free helium jet 
5.1 Introduction
5.2 Experimental setup
5.2.1 Rotational Raman scattering
5.2.2 Stark polarization spectroscopy
5.2.3 Schlieren imaging
5.3 Results
5.3.1 Helium flow expanding in air
5.3.2 Influence of plasma on the flow structure
5.3.3 Quantitative schlieren results
5.3.4 Influence of applied voltage pulse
5.4 Discussion
5.4.1 Comparison with literature
5.4.2 Comparison with a sinusoidal (AC) jet
5.4.3 Quantitative schlieren imaging
5.5 Conclusions
6 Gas temperature in a free helium jet 
6.1 Introduction
6.2 Experimental setup
6.2.1 Rotational Raman scattering
6.2.2 Temperature probe
6.2.3 Energy measurements
6.3 Results
6.3.1 Influence of plasma
6.3.2 Comparison of measurement techniques
6.3.3 Influence of the applied voltage pulse
6.3.4 Influence of a target on the gas temperature profile
6.4 Discussion
6.4.1 Gas heating processes
6.4.2 Determination of main heating mechanism
6.4.3 Comparison to AC jet
6.4.4 Increasing temperature in the effluent
6.4.5 Estimation of the electrohydrodynamic force
6.4.6 Main mechanism that induces turbulence in the flow
6.5 Conclusions
7 Interaction of a plasma jet with grounded and floating metallic targets: simulations and experiments 
7.1 Introduction
7.2 Setup
7.2.1 Experimental setup
7.2.2 Numerical setup
7.3 Results and discussion
7.3.1 Characterization of discharge propagation and peak electric field
7.3.2 Jet-target interaction
7.3.3 Discussion on the discrepancy of charging and uncharging the floating metallic target
7.4 Conclusions
8 General conclusions and perspectives 
8.1 Conclusions
8.1.1 Free jet
8.1.2 Jet with a metallic target
8.2 Outlook
Bibliography 
List of Publications
Contributions of the Author
Acknowledgements / Remerciements / Dankwoord
Curriculum Vitae

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