Examination of the Stark Effect of Hγ in a Plasma Arc

Master of Science in Physics - Thesis

Quick Introduction to Atomic Physics

Atomic physics is the discipline of physics concerned with phenomena related to electron configurations around atomic nuclei or inside molecules, which can be considered stable with respect to the effects of interest. Quantum physics provides an accurate model to describe these interactions. When dealing with complex particle arrangements and interactions, however, e.g. as found in stars or plasmas , statistical approaches are introduced in addition.

Bohr atomic model Bohr atomic model For the purpose of a brief introduction, it is feasible to use the simpler and planetary system-like Bohr atomic model , as illustrated on the right. It envisions a central, fixed nucleus (in the case of hydrogen a single positively charged proton p+ as references by Z = 1) with one or multiple negatively charged electrons e- circling on fixed orbitals (marked n) specific to the environment or atomic state. Higher orbitals represent higher energetic states than lower orbitals. Whenever an electron transitions from an orbital with higher energy to one with lower energy, a light particle or photon is emitted by the electron. And the energy of the photon (which in the visible spectrum determines its color) equals the energy difference between the two orbital energies involved.

Note, that the photon energy depends on its frequency (or light color, if in the visible spectrum) or wavelength as described by the
Planck-Einstein relation: E = hν (energy = Planck constant ∙ frequency)
and ν = c / λ (frequency = constant speed of light in vaccum over wavelength).
Inversely, an electron can absorb photons of specific energies only, if the photon energy equals the amount needed to transition an electron into one of the higher energetic orbitals (but not somewhere in between orbitals).

The orbitals or energetic levels determine what energetic states electrons can assume and therefore are a characteristic of a specific atom. The energetic levels themselves are determined by the nucleus and may be disturbed by external influences like the presence of other charged or neutral particles. When the atom is disturbed, its energetic levels are also disturbed resulting in slightly different photons to be emitted or absorbed by present electrons. This causes spectral lines as shown below in Figure 6 to be widened and/or shifted and sometimes split into multiples lines.

Thus, by looking at a spectrum, a great deal of information can be gathered about the state that the electron and consequently the atom was in from which the photons originated. This is the basis for emission spectroscopy, essentially looking closely at all energy or color components of an object's electro-magnetic emmissions.


Emission spectroscopy is one of the standard diagnostic tools for examining optical media. It provides information about the observed object without directly disturbing it and is the only available method if the object cannot be directly influenced, as is the case when examining star atmospheres.

In such environments, high pressure effects predominantly from charged particles become relevant among the influencing broadening mechanisms on spectral lines: natural broadening; Doppler broadening; pressure broadening: Stark (electric), Zeeman (magnetic), homogeneous particle (from the same neutral particles) and van-der-Waals (from other neutral particles) broadening.

To investigate these effects, hydrogen with the simplest of atomic structures is a good starting point as its spectrum has been well researched. Hydrogen's Balmer series poses an excellent candidate for observation since its spectral lines can be observed in the visible spectrum as opposed to e.g. the Lyman ultraviolet or Paschen infrared series.

Several experimental studies are available but recent new theoretical approaches regarding the Stark effect, i.e. the effect of electrical fields on spectral lines as relevant in star atmospheric spectroscopy, have revealed discrepencies with previous experiments. In general, spectral lines broaden, shift and may split into multiple component lines. As the broadening and shift of sprectal lines are not completely explained in theory, a more precise look at Balmer Hγ was warranted.

This thesis was part of a DFG, German Research Foundation research project in cooperation with the University of Rostock.

Plasma Arc

For this experiment, a wall-stabilized H. Maecker design cascade plasma arc as shown in Figure 1 was used. Figure 1: High pressure plasma arc Figure 1: High pressure plasma arc This design has been refined at Kiel University since the 1930's and is capable of delivering stable plasma arc burn times of up to 30 h at up to 9 bar pressure.

Figure 2: Maecker design wall-stabilized high pressure plasma arc schematics Figure 2: Maecker design wall-stabilized high pressure plasma arc schematics Figure 2 shows a cut-away schematic view of the design revealing the internal gas flow and the 64 mm long 13-plate cascade core assembly. The end plates each hold four thorium wolfram electrodes positioned at a 45° angle and 7 mm in length and 3 mm anode width and 2 mm cathode width. The effects around these electrodes had been investigated previously in this working group.
Since a pure hydrogen plasma would produce too high temperatures, an inert gas was used as carrier gas. In this case, neon was a good choice because it does not have any spectral lines in the vicinity of Hγ (or Hβ, which was measured concurrently to establish the plasma's electron density). A neon 4.0 and 10% hydrogen 5.6 mixture was injected at 2 cascade plates while being flooded with neon 4.0 from both cascade ends to contain the hotter hydrogen.

Figure 3: Plasma arc plates Figure 3: Plasma arc plates The plasma arc plate types used are shown in Figure 3. Each plate is 4 mm thick and has a 4 mm drill hole at its center for the plasma. The plates were electrically isolated from each other by Pertinax rings. The plate on the left has 4 inner cooling water connectors and 4 gas connectors, which allow to inject or extract gas from the arc through small holes in the plates. The middle plate with its small holes allows for pressure differences caused by the gas flow within the arc to equalize. The plate on the right with only a center arc hole was used to extend the cascade to reach a total length of 64 mm. All of the cascade plates, the end plates as well as the electrodes themselves were cooled with water.

Experiment & Data Analysis

Figure 4 shows the experiment setup. The plasma arc power supply was able to produce a maximum of 200 A at 600 V. During the experiment electric currents were varied between 20 A and 80 A while pressure ranged between 1 and 7 bar. Figure 4: Experiment setup Figure 4: Experiment setup Due to neon's relatively high ionization energy of 21.56 eV, argon 4.8 with a lower ionization energy of 15.76 eV was used to ignite an initial plasma. This was sometimes achievable only by introducing another 1200 V charge on one of the inner cascade plates. Once ignited, the argon was swapped out for neon as carrier gas.

The plasma light was used to measure Balmer Hγ in a 1 m Monochromator and concurrently Balmer Hβ in a 30 cm Monochromator to establish the electron density of the plasma via its full width at half maximum.
Figure 5: Data process & analysis software on SUN SPARCstation 10 Figure 5: Data process & analysis software on SUN SPARCstation 10 A folding mirror allowed to overlay the plasma light with light from a low pressure gas discharge lamp, which emitted unshifted Balmer lines allowing to determine the wavelengths in a dataset. For each measurement, two Hγ datasets, one overlaid with the low pressure gas-discharge (Geissler tube) light and one without, as well as one Hβ dataset were produced for later analysis.
In order to correct for the experiment induced wavelength dependent error, the spectrum of a Wolfram (Tungsten) filament lamp with a well-known emission spectrum was measured by flipping a mirror, which routed the Wolfram light into the light path previously taken by the plasma light.

A SUN SPARCstation 10 was used to program the data processing & analysis software. A screenshot of the STAR analysis software written in C (using the vogle graphical library initially) is shown in Figure 5.


Figure 6 shows an overview of the hydrogen Balmer series from Hγ to the series convergence limit at electron densities of 2.4 and 11.2∙1016/cm3. Figure 6: Hydrogen Balmer series at different electron densities Figure 6: Hydrogen Balmer series at electron densities at 2.4 (blue) and 11.2∙1016/cm3 (red) The spectral lines are becoming broader and move closer together towards the convergence limit until they cannot be distinguished from each other.

Figure 7: Balmer-γ at different electron densities Figure 7: Balmer Hγ at electron densities between 0.4 and 12.5∙1016/cm3 The Stark effect causes Hγ to broaden and shift with increasing electron density as shown in Figure 7.

Balmer Hγ Broadening and Shift

Figures 8 shows the Hγ FWHM broadening (full width at half maximum) over electron density with previous experimental datapoints marked by triangles and rectangles. Figure 8: Balmer-γ broadening (full width at half maximum) over electron density Figure 8: Balmer Hγ broadening (full width at half maximum) over electron density with previous experimental datapoints marked by triangles and rectangles The fitted blue line clearly shows the proportionality with the electron density to the power of ⅔ as expected for the linear Stark effect: FWHM ∝ Ne.

Figures 9 provides a plot of the Hγ shift, defined here as the wavelength at maximum intensity, which was relatively easily determined due to the well defined Hγ peak and little overlap with the far end of Hδ. The shift was determined by comparison with an unshifted Hγ line from the low pressure gas discharge Geissler tube, which allowed for much greater precision than other methods like interpolation towards zero electron density Ne.

Figure 9: Balmer-γ shift over electron density Figure 9: Balmer Hγ shift over electron density The fitted line has a slope of 7.4 nm per 1017/cm3. Previous experimental results of 7 nm (1995) and 6.8 nm (1981) were within the error margin, albeit based on measuring the ELC shift, which is more prone to influence from adjacent spectral lines. The analysis could have been further improved by using sufficiently accurate theoretical line profiles, which at the time of publishing were not available yet.

Further external links

University of Kiel

Plasma Lab