Part 7: Footnotes

Figures 7.0.01 and 7.0.02: Energy spectrum of solar wind electrons and the SWEPAM instrument

Figure 7.0.03: The patent cover page

Test Results and Analysis [from the Phase I SBIR Final Report]

We were immediately impressed with the results of the tests of the SCM. It is not unusual to spend weeks troubleshooting and modifying a newly designed electron spectrometer before getting meaningful data from it. We got useful data from the prototype SCM on the first attempt. The large field-of-view of the SCM compared to other electron energy analyzers we have used is partly responsible for the ease at which we could gather spectra. We found that the electronics of the SCM prototype were very well integrated and performed flawlessly. The PC-based user interface was effortless to use.

Background noise due to electrons scattered from metallic surfaces within the SCM analyzer and other surfaces within the vacuum chamber was not present in any of the spectra we collected. We believe the lack of background noise is due to the excellent metallic-ejected-secondary-electron suppressing qualities of the SCM sensor head design (as described in Section IV-A). Our use of a very well collimated, exceptionally monochromatic electron source (a monochomator with the same performance described in Goembel and Doering, 1995) also contributed to the excellent quality of the spectra collected by the SCM.

Three spectra from the SCM appear in this report. The first two contain far more information than the last. The first two spectra are "secondary electron spectra" of helium. The electron monochromator produced a beam of 48 eV electrons that struck the helium atoms in the collision center. The 48 eV electrons could either strike the helium and lose no energy (an "elastic collision") or could lose energy in the collision (an "inelastic collision"). The SCM detected electrons that had struck the helium and lost energy and those that were ejected in the ionization process. Electrons that are ejected from an atom or molecule in the ionization process are called "secondary" electrons and those that are not the product of ionization are called "scattered primaries."

Figure 7.0.04: SCM Electron Impact Spectrum of Helium

The spectrum shown above is from the SCM set to count electrons in 0.1 eV steps from 0-30 eV. The peaks that appear at energies greater than 23 eV are evidence of the discrete energy levels of atomic helium. The electrons produced in the impact of 48 eV electrons with the helium are allowed to have only certain energies when producing electrically excited helium atoms. The final state of the electrically excited helium atom produced is labeled above each of the peaks in the spectrum. The tallest peak in the spectrum (at about 27 eV) is the first in the Rydberg series which converges to a continuum to the left of the peaks at ~23.4 eV: 48 eV minus the ionization potential of helium (I.P.He = 24.58 eV). The table, below, gives the final state of the He produced, and the energy lost by the 48 eV electron in the inelastic collision with the gas.

The ionization of helium to certain final electronic states produces the peaks in the spectra.

To the left of 23.4 eV can be seen the electrons produced by ionization of the He atoms

He +e0 ? He+ + e0' + es

where e0 is the incident or "primary" electron, es is the knocked-out or "secondary " electron, and e0' is the scattered primary electron that has lost energy ionizing the Helium.

This distribution is a featureless continuum since there are two outgoing electrons from each ionization event. Conservation of energy requires that

E0 = E0' + Es + IPHe

where the Es are the energies of the various electrons and IPHe is the first ionization potential of He, 24.58 eV. In other words, only the sum of E0' + Es is fixed. For individual ionization events, the two outgoing electrons can share the available energy in any proportion.

The characteristic "U" shape of the distribution which is clearly visible in the figure between 1 eV and 23 eV is a consequence of the fact that the most probable energy sharing between the two outgoing electrons is one in which one electron has almost all the available energy and the other has almost none. Electrons from these events are found at the two ends of the distribution. The least probable event is one in which the two electrons leave with equal energy. These events are at the center of the distribution near the 12eV minimum.

The significance of the fact that the SCM can so clearly detect the Helium secondary electron spectrum cannot be overemphasized. Ionization of Helium by 48 eV electron impact is closely related to photoionziation. In fact, in the limit of zero momentum change in the ionizing collision (an impossible point to achieve in electron impact since even if the incident electron is scattered at 0°, there is still a small momentum change due to the energy lost by the incident electron) electron impact ionization and photoionization are identical processes with identical cross sections. The energy spectrum of the secondary electrons in the figure is therefore closely related to the photelectron energy distributions we will be measuring from the spacecraft. The results from the He measurement show conclusively that the SCM analyzer is free of undesirable effects such as electrons rejected by the analyzer that could show up as noise obscuring the real spectrum or electron optical effects which could make the sensitivity of the analyzer different at different energies.

There is an important correlation between electron impact spectroscopy and photoionization spectroscopy. The secondary electrons produced by electron impact are indistinguishable from the electrons produced by photoionization (in the limit of zero momentum change). Photoionization, of course, is the source of the photoelectrons the SCM will detect in order to monitor spacecraft floating potential. Since there is no practical laboratory source of monochromatic 304Å radiation for our tests of the SCM, the inelastic scattering spectra of helium collected in this Phase I study simulate photoionization spectra of the sort we expect the SCM to collect in order to monitor spacecraft floating potential.

The second helium scattering-spectrum, below, sampled electrons over a ten-eV range in 200 steps (the same scan mode recommended for 0.1 eV accuracy in spacecraft floating potential determination).

Figure 7.0.05: SCM spectrum over a ten-volt range, similar to the mode that will be used in space

The simulated, dashed line, spectrum superimposed over the SCM data (diamonds) matches the data almost exactly. John Doering simulated the spectrum with the computer program "Labview" by first entering a delta function (stick) spectrum with the peaks at the correct energies and magnitudes (oscillator strengths) obtained from a spectroscopic table. The stick spectrum was then convolved with a triangular peak of variable half width (the instrument function for the SCM is a triangular function). The half width was then varied for the best match with the observed spectrum. The close match to the peak positions and the uniform half widths of the peaks tells us that the spectrometer is working properly and gives a much better measurement of the experimental full-width-at-half-maximum (peak width) than could be obtained from one peak alone. The full-width-at-half-maximum (FWHM) from the simulated spectrum was used to calculate the energy resolution of the SCM.

Figure 7.0.06: Spectrum of the primary beam at 20 eV

Finally, we present the spectrum of the primary beam (electrons from the monochromator that have lost no energy in collisions). The monochromator was adjusted to produce 20 eV electrons, and the spectrum (shown above) was also used to determine the energy resolution of the spectrometer. From previous calibrations of the monochromator used in this experiment, we know that the monochromator's contribution to the peak width is 0.10 ± 0.02 eV (FWHM). The figure shows undeniably that the features observed in the previous figures were due to electron collisions with Helium. Without the Helium present, there is effectively zero background at energies below the primary beam energy. This result shows the remarkable ability of the SCM to produce "clean" spectra.

The energy resolution of the prototype spectrometer is 2.0 (±0.1) % ?E/E (FWHM). This is astounding energy resolution for a space-flight charged particle spectrometer. All of the charged particle spectrometers that we know of that have flown recently or are planned for flight have an energy resolution of greater than 5%, often 15% or more. None would be acceptable for determining spacecraft floating potential. The 2.0% energy resolution of the SCM is even better than the 2.5% energy resolution of the PES instrument, to the best of our knowledge the highest energy resolution instrument ever to have flown. The high energy-resolution measured for the SCM, even though an extended, curved slit was used, indicates that our patent-pending curved aperture design does not sacrifice energy resolution.

The collection of meaningful low-energy electron-spectra in space has proven difficult for other experimenters. The tests we have performed in Phase I show that the SCM will excel in the exclusion of instrumental secondaries and excel in the detection of electrons at low energy (down to 1 eV, in fact) - both are abilities necessary to the successful electron-spectroscopic determination of spacecraft floating potential. The tests have demonstrated the extraordinary performance of the patent-pending Goembel Instruments hemispherical analyzer. The very high energy resolution of the SCM combined with its high geometric factor will revolutionize the way charged particle spectra are gathered in space and will assure the timely determination of spacecraft floating potential by the SCM.