Physicists Find a Way to Model Ion Parameters in Plasma in Seconds

Tokamak reactor

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Researchers from HSE University and the Moscow Institute of Physics and Technology (MIPT) have developed a set of simple analytical methods for calculating the properties of heavy ions in helium under the influence of a strong electric field. The new approach speeds up calculations of ion mobility and ion–molecule reaction rates by thousands of times while maintaining sufficient accuracy for plasma jet modelling. The findings have been published in the journal Physica Scripta.

Plasma is a gas composed of charged particles, including electrons, negative ions, and positive ions. This composition makes plasma quasi-neutral overall. It conducts electricity efficiently and exhibits much more complex behaviour than an ordinary gas.

Plasma can be found in fluorescent lamps, welding arcs, and advanced tokamaks—devices used for controlled nuclear fusion. Atmospheric plasma jets are employed to disinfect wounds and work surfaces, as well as to improve the properties of agricultural seeds.

To achieve the desired composition, and therefore the required effect of a plasma jet, researchers first calculate its parameters using computer simulations. These simulations rely on field-dependent characteristics of charged particles, including their mobility and the reaction rate constants that determine ion–molecule interactions.

These characteristics are traditionally calculated using the Monte Carlo method. Although highly accurate, it is computationally demanding: determining the mobility and reaction rate constants of a single ion for just one electric field strength can take several hours, or even several days in particularly complex cases.

Alexander Ponomarev, Associate Professor at the HSE Faculty of Physics, and Nickolay Aleksandrov, Professor at MIPT, derived simple analytical formulas that make it possible to determine ion mobilities and reaction rate constants in a matter of seconds. By modifying and combining classical approaches, they developed several computational methods. The simplest method works at high reduced electric fields (above 60 Td), while a more refined version remains accurate across the entire range of electric field strengths, including low fields. The researchers also developed methods for calculating reaction rates, enabling rapid estimates of how quickly negative ions dissociate and lose electrons—a process that is crucial for modelling plasma composition.

The authors validated the results produced by the new methods against data obtained using the Monte Carlo method. The study focused on negatively charged oxygen, tetraoxygen, and nitric oxide ions, which play an important role in atmospheric plasma. At high electric field strengths, the simplest method calculates ion mobility with an error of up to 10%, while the refined method achieves an error of just 2–7%, depending on the ion type. The researchers also confirmed that the refined method remains applicable at extremely high reduced electric field strengths of up to 250 Td.

The reaction rate constants for plasma ions calculated using the new methods differ from those obtained with the Monte Carlo method by no more than a factor of two.

The reaction rate constants of charged particles can vary by two to three orders of magnitude as the electric field changes. Given this wide range of variation, the researchers argue that the substantial reduction in computation time—from hours to seconds—more than justifies the loss in accuracy.

Alexander Ponomarev

‘Our methods reduce the determination of ion characteristics to calculations that can almost be performed on a calculator. Such a major advance in plasma modelling should significantly accelerate large-scale projects with humanitarian goals. Faster calculations bring us closer to highly effective plasma-based medicine, where plasma is used to treat living tissues, and to improving crop yields and resilience through the timely treatment of seeds with plasma jets. I sincerely hope that our research will contribute to combating disease and, to some extent, help address global hunger,’ concluded the study's lead author, Alexander Ponomarev, Associate Professor at the HSE Faculty of Physics.