Nitrogen plasma: what did the analyzer detect?

Kovac’s experiment

Kovac’s December 1994 report describes earlier apparatus with a perforated glass partition and a later tube containing two stainless-steel needle electrodes with no constriction. He estimated helium-4 and lithium-5 at 3.75% and 2.50%, respectively, relative to the parent gas. The report also describes a comparison with feed gas and a sample processed twice. [1]

These percentages depend on the species assignments and the analyzer’s response to each species. A nominal mass channel alone cannot establish elemental identity.

From force to a helix

The Lorentz-force law gives a nonrelativistic charged particle’s motion. In SI units: [2]

Here m is particle mass, q its signed charge, v velocity, E electric field, and B magnetic flux density. With E = 0, the magnetic force is perpendicular to velocity: it changes direction without changing kinetic energy. An initial velocity parallel to the field remains constant; the perpendicular component rotates.

K denotes kinetic energy in joules. Convert electronvolts to joules before substituting an energy into this expression. For pitch angle α measured from the field direction, the velocity components are v_⊥ = v sin α and v_∥ = v cos α.

Here ω_c is angular gyrofrequency, r_L is orbit radius, and ℓ is axial advance per revolution. The charge sign determines rotation direction. Circular motion across the field combines with uniform motion along it to form a helix.

For the model's initial 100 eV electron, 5 mT field, and 50° pitch angle, these equations give a radius of about 5.17 mm and an axial advance of 27.2 mm per revolution. Doubling the field halves both lengths. Raising energy fourfold doubles them at fixed angle. Increasing the angle widens the orbit while reducing axial advance.

The model describes one particle in a uniform magnetic field. A discharge also involves collisions, electric sheaths, ionization, boundaries, and collective fields. Calculating its chemistry or any proposed nuclear reaction requires more than the single-particle orbit shown here.

Reading the mass spectrum

A quadrupole residual-gas analyzer ionizes sampled gas and measures current in mass-to-charge channels. Ionization can fragment molecules or produce multiple charge states. One species can therefore contribute to several channels, while several species can contribute to one channel. Peak heights also depend on the analyzer’s sensitivity to each species. [3]

In a calibrated linear operating regime, channel currents can be modeled as:

I_j is measured current in channel j, and p_i is species i’s partial pressure. Each coefficient A_ji combines fragmentation and instrument sensitivity. The terms b_j and ε_j add background and measurement error to the standard mixture-spectrum relation. [3]

Partial pressures can then be estimated by nonnegative weighted least squares:

Bold symbols collect currents or partial pressures into vectors; W weights the residuals by measurement uncertainty. The fit restricts partial pressures to nonnegative values. If a species is missing from A, its signal can be assigned to other candidates. Species with similar response patterns may also remain indistinguishable despite a small fitting error.

The lithium-5 assignment

Evaluated nuclear data describe ⁵Li as an unbound resonance that decays into a proton and an alpha particle. This decay rules out its accumulation as a stable constituent of the collected gas. [4] A mass-to-charge signal near five therefore needs another explanation unless measurements can connect it to the production and decay of ⁵Li.

The missing measurements

The unresolved assignments call for the original spectra and analyzer settings, species calibrations, feed-gas spectra, and procedural blanks. Repeated measurements could establish whether the low-mass signals follow processing or arise from background, carryover, or sampling. Independent identification and a material balance would then address whether a confirmed product was generated in the discharge.