4.4 Input parameters
4.5.3 Measured and simulated spectra
Graphs containing (parts of) simulated and measured spectra are shown in figures 4.13, 4.14, as well as in appendix E, in figures E.2 to E.5. The spectral lines included in the model are indicated by their wavelengths above the spectra. Simulation parameters are shown in the box at the top-left corner of the page and measurement parameters in the legends. The initially estimated value for the quenching rate kQ= 3.3 · 105s−1is used. It is important to note that the measured intensities (using the ´echelle spectrometer) are absolute; giving additional information, as compared to the line ratios.
Line broadening in the simulated spectra is due to the apparatus profile of the ´echelle spec-trometer, which is approximated by a pseudo-Voigt profile with wV= λ0/18, 000 and wG= 4wL, where λ0 is the transition wavelength.
Line escape factors ΘL are used, calculated using optical path length lp as indicated in each legend and (Lorentz) line widths according to equation (4.16). Figures 4.13, 4.14 also include the simulation results obtained when ΘL = 1 is used for all transitions. Optical thickness is important for most transitions for t . 100 ms.
In the initial phase, e.g. at t = 75 ms, r = 0 in figure 4.13 or at t = 55 ms, r = 0 (figure E.2) or r = 3 (figure E.3), the signal-to-noise ratios are high and the agreement of measurement and simulation is generally very good, i.e. within 50 % for nearly all lines. In some cases (e.g. for the line at 430.3 nm at t = 55 ms), a deviation of line width due to optical thickness (only line-integrated escape factors are included) or Stark broadening can be seen, and as a consequence the simulated line is too high.
At later times, measurement and simulation are less consistent and only the stronger lines can be matched unambiguously to those in the measured spectra. Finally, the electron densities, tem-peratures and ground state densities obtained from compared spectra are summarized in table 4.2.
4.6. Discussion and conclusions CHAPTER 4 A CRM for calcium
measurement simulation
t r [cm] n1 [m−3] ne [m−3] Te [K] lp[cm]
55 0 1.5 · 1021 5.0 · 1021 4500 5 55 3 1.5 · 1021 4.0 · 1021 3600 5 75 0 1.1 · 1021 2.0 · 1021 3900 8
95 0 5 · 1020 2.5 · 1020 3100 10
155 0 5 · 1020 1.6 · 1020 2500 12 145 3 5 · 1020 1.0 · 1020 2400 11
Table 4.2: Simulation parame-ters used for the simulated spec-tra, shown in figures 4.13, 4.14, and E.2–E.5.
4.6 Discussion and conclusions
The results obtained for ne and Te agree well with those previously obtained in section 3.4.2.
Particularly the electron temperatures at r = 0 for t . 75 ms are consistent with those determined from the Cu I lines and LTE assumption in figure 3.20. Also the electron temperature of 3600 K at r = 3 cm and t = 55 ms is the same as in figure 3.21.
As opposed to the Cu I LTE line-ratios in figure 3.21, the simulated Ca I spectra indicate a further decrease of Te for t > 75 ms, down to about 2500 K at t = 155 ms, in the autonomous phase. This confirms that the values obtained from the Cu I lines are indeed incorrect at later times. Is must be noted however, that the values in table 4.2 for t = 95 ms, 145 ms and 155 ms have a considerable error margins, i.e. about 50 % for the densities and 500 K for the temperatures is estimated.
The estimated electron densities obtained from the line ratios in figure 4.10 are higher initially and decrease faster than those in table 4.2. It is important to note however, that different sets of measurement data are used: as mentioned, the data in figure 4.10 uses 0.4 g/l CaCl2, whereas the comparison of measured and simulated spectra is done using 0.2 g/l HCl in tap water. The reason that a different data set is used for comparing the spectra, is that a lower light amplification (MCP voltage) was used for the experiments with added CaCl2, to prevent overexposure of the strong calcium resonance lines. As a consequence, many of the weaker lines can not be resolved well.
Overall, the values of ne obtained from the simulated spectra in the initial phase are consistent within an order of magnitude with those measured from Stark broadening, in figure 3.23. A note-worthy result of both the line-ratios in figure 4.10 and of the spectrum simulations in figures 4.14 and E.5, is that ne & 1020 at t ≈ 150 ms, so in the autonomous phase.
In contrast to the Ca I resonance line measurements of section 3.4.2, the results of the collisional radiative model do not indicate that the ground state density decreases faster than expected from the plasmoids expansion. Rather, the densities in the order of 1020 m−3 are needed to achieve the measured intensities at reasonable values for ne and reproduce the measured relative line intensities (insofar these could be measured). It is likely that the calcium density at t = 145 ms in table 3.2 is incorrect, due to wrongfully assuming an LTE population of the resonance state in that section.
CHAPTER 4 A CRM for calcium 4.6. Discussion and conclusions
427 428 429 430 431 432
λ [nm]
0 5.0•1021 1.0•1022 1.5•1022
Iλ [ph m-3 s-1 nm-1] 428.301 nm 428.936 nm 429.899 nm 430.253 nm 430.774 nm 431.865 nm
Electron temperature: Te=3900 K Electron density: ne=2E+021 m-3 Ground state density: n1=1.1E+021 m-3 Ca+ ion fraction: xCa+=1
Quenching: kQ=3.3E+005 s-1 Optical path length: lp=8 cm
t=75ms, r=0cm, 0.2 g/l HCl simulation
simulation, ΘL=1
t=75ms, r=0cm, 0.2 g/l HCl simulation
simulation, ΘL=1
(a) (a)
558.0 558.5 559.0 559.5 560.0 560.5 561.0
λ [nm]
0 5.0•1021 1.0•1022 1.5•1022
Iλ [ph m-3 s-1 nm-1] 558.197 nm 558.876 nm 559.012 nm 559.447 nm 559.849 nm 560.129 nm 560.285 nm
(b) (b)
644 646 648 650
λ [nm]
0 5.0•1021 1.0•1022 1.5•1022 2.0•1022
Iλ [ph m-3 s-1 nm-1] 643.907 nm 644.981 nm 645.560 nm 646.257 nm 647.166 nm 649.378 nm 649.965 nm 650.885 nm
(d) (d)
Figure 4.13: Measured and simulated calcium emission spectrum. The measured spectrum was recorded at r = 0 and t=75 ms (top view). The simulation parameters are shown in the top left corner. The measured and simulated spectrum fit very well (also for transitions not shown here).
4.6. Discussion and conclusions CHAPTER 4 A CRM for calcium
427 428 429 430 431 432
λ [nm]
0 2•1019 4•1019 6•1019 8•1019 1•1020
Iλ [ph m-3 s-1 nm-1] 428.301 nm 428.936 nm 429.899 nm 430.253 nm 430.774 nm 431.865 nm
Electron temperature: Te=2400 K Electron density: ne=1E+020 m-3 Ground state density: n1=5E+020 m-3 Ca+ ion fraction: xCa+=1
Quenching: kQ=3.3E+005 s-1 Optical path length: lp=11 cm
t=145ms, r=3cm, 0.2 g/l HCl simulation
simulation, ΘL=1
t=145ms, r=3cm, 0.2 g/l HCl simulation
simulation, ΘL=1
(a) (a)
558.0 558.5 559.0 559.5 560.0 560.5 561.0
λ [nm]
0 5.0•1019 1.0•1020 1.5•1020 2.0•1020
Iλ [ph m-3 s-1 nm-1] 558.197 nm 558.876 nm 559.012 nm 559.447 nm 559.849 nm 560.129 nm 560.285 nm
(b) (b)
610 612 614 616 618
λ [nm]
0 2•1020 4•1020 6•1020
Iλ [ph m-3 s-1 nm-1] 610.272 nm 612.222 nm 615.602 nm 616.129 nm 616.217 nm 616.376 nm 616.644 nm 616.906 nm 616.956 nm
(c) (c)
Figure 4.14: Measured and simulated calcium emission spectrum. The measured spectrum was recorded away from the electrode at r = 3 and t=145 ms (top view). Also shown is the simulation result when an optically thin plasma is assumed (blue dots). Optical thickness does not play a role here.
Chapter 5
Molecules
This chapter consists of three smaller parts, each dealing with molecular processes in a different way. The first part studies the dissociation of water, using the theory of chemical equilibrium and relates this to thermodynamic properties of the plasmoid via a simple model. The second section describes spectroscopic measurements on molecular bands and makes comparison with other experiments in literature. Also the vibrational distribution of OH is estimated from simula-tions. The part section deals with the measurements of the rotational temperature (and rotational distribution) of the OH band with its head at 306.4 nm.
5.1 Chemical composition and thermodynamics
The model presented here consists of two parts. The first part calculates the chemical composition of (partly dissociated) water as a function of temperature. The second part uses the outcomes of the first part, as well as some of the calorimetry results, in a simple model that calculates the enthalpy and some other thermodynamic properties of the plasmoid.