14 May 2024
Current or count: why quantifying ionisation isn't as simple as it sounds
First-principles calculations suggest the 'ionisation' measured by x-ray Thomson scattering is not necessarily the same 'ionisation' that appears in simplistic atomic models.
To understand the notoriously complex dense plasmas found in stellar interiors and nuclear-fusion scenarios, we must often construct simplified models that use only the plasma’s most essential properties, such as its density and temperature. One of the most important (and arguably defining) parameters describing a plasma is its ionisation Z, which expresses the typical charge state of its constituent ions. However, despite its ubiquity in plasma modelling, ionisation does not have a well-defined thermodynamic definition; conventional definitions of Z often derive instead from a highly simplified atomic picture that essentially involves counting the number of ‘free’ (conduction) electrons under given thermodynamic conditions. It is far from obvious whether such a definition guarantees an internally consistent, physical plasma model.
A recent experiment at the National Ignition Facility (NIF) used x-ray Thomson scattering (XRTS) to directly measure the ionisation state of hot, dense CH plasmas. The measured ionisation was substantially greater than predicted by models based on the atomic picture. At first glance, this discrepancy appeared to be attributable to the flawed atomic model of ionisation. To investigate this possibility, Thomas (Tom) Gawne and coworkers used first-principles simulations to model a dense CH plasma at the quantum level, and compared several definitions of its ionisation against the XRTS-based experimental measurements at temperatures of up to one million degrees.
The results were surprising. The ionisation state predicted by the first-principles calculations agreed well that derived from the simplified atomic model. This suggested that the ‘electron-counting’ picture of ionisation is not wrong per se, but that XRTS is in fact measuring something different:
“It suggests that the ionisation state observed in XRTS doesn’t just count the number of electrons freed from the atoms.” explains Tom. “Instead, we believe that XRTS measurements are instead observing how mobile the electrons in your plasma are.”
To verify this, Tom calculated the conductivity of the plasma, finding that the notionally ‘bound’ electrons are actually able to travel between nearby ions.
“This shows that XRTS is fundamentally measuring a different quantity to the mean charge state, even though it is this quantity that is used in XRTS models. Instead, our results suggest that the ionisation state measured in XRTS is a measurement of all the mobile electrons: our calculations find that the electrons around the carbon atoms (considered ‘bound’ in the mean charge state) are actually slightly mobile, which means in XRTS they would appear to be slightly free from the atoms.”
The next natural step following on from this project is the development of alternative ionisation definitions for use in XRTS models that incorporate the mobility of all the electrons, including both conduction and the ‘bound’ (valence) electrons conventionally treated as sessile.
Full article: Quantifying ionization in hot dense plasmas by T. Gawne, S. Vinko, and J. S. Wark, Physical Review E 109, L023201 (2024).
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