A transition that depends on the equilibrium
A familiar transition in tokamak plasma calculations can disappear when the magnetic equilibrium is recomputed to stay consistent with the plasma's pressure, according to a new arXiv preprint. In the same pressure-consistent comparisons, reported growth rates fell as equilibrium pressure increased, while the critical beta for KBM modes shifted upward. In the paper, beta is the pressure variable used in the scans, and the threshold is the point at which the mode becomes unstable.
The researchers used two computer models: global gyrokinetic EUTERPE and ideal-MHD CAS3D, calculating growth rates and eigenfunctions. The modeled magnetic geometry was a circular tokamak. The central equilibrium test recalculated the field for every temperature and density profile so that plasma pressure remained consistent with the equilibrium and stability calculations, then compared that setup with cases using fixed geometry.
The pressure scans used two different profile prescriptions. In one, density was varied while the temperature profile stayed fixed to reach the desired pressure. In the later approach, temperature and density were scaled equally. The reported transitions therefore come from defined numerical scan conditions rather than from a single, uniform way of changing beta.
When pressure changes the picture
With fixed or vacuum geometry, the usual ITG-to-KBM transition appeared in the calculations. When the equilibrium field was recomputed consistently for each beta, the transition could disappear. The authors also report that increasing equilibrium pressure reduced growth rates and shifted the critical KBM beta upward. Taken together, the result suggests that the apparent boundary between these two instability regimes depends on how the equilibrium is constructed.
That is the study's main caution for model comparisons. A transition seen while the magnetic geometry is held fixed may not survive after the pressure and equilibrium are made self-consistent. The finding is specific to the modeled circular-tokamak calculations and their tested parameter choices; it is not a result from an operating device.
Agreement depends on the regime
The match between gyrokinetic and MHD calculations was not uniform. In the case with a temperature-to-density gradient ratio of 6.67, full MHD and gyrokinetic results did not match. Removing gyro-averaging, a kinetic-treatment option tested by the researchers, produced reasonable agreement, but the gyrokinetic model was already unstable below the MHD threshold of about 1%.
A different profile, with a temperature-to-density gradient ratio of 1, looked more MHD-like. CAS3D became unstable above 0.3 on the plotted mean-beta scale and peaked near 1%, while EUTERPE followed a similar overall trend but had a lower onset. Removing gyro-averaging had no noticeable effect in that case. At a ratio of 0.5, low-beta scans showed two frequency branches, or distinct oscillation rates: the lower one matched the KBM range and disappeared when gyro-averaging was removed. The remaining frequencies for the 0.5 and 1 cases were nearly constant in the stated normalized regime.
The authors grouped the simulations into three frequency regimes: kinetic modes, diamagnetic-stabilization modes and MHD-like instabilities. The 0.5 and 1 profile cases were placed in the MHD-like group. This classification helps explain why a single answer about whether gyrokinetics agrees with MHD would be misleading: the answer changes with the profile and the treatment of kinetic effects.
Checks at higher pressure
Other tests exposed where the models diverged. Above a mean beta of 3.4%, shifted-Maxwellian electron calculations continued to show rising growth rates, while centered-Maxwellian results stayed approximately constant; at lower mean beta, the two were nearly identical. A mass-ratio check compared the reduced ion-to-electron ratio of 200 used in part of the work with the realistic value of 1836. The realistic ratio lowered absolute growth rates but left the qualitative beta dependence unchanged. Omitting the parallel magnetic perturbation did not significantly change growth rates or frequencies in the tested cases.
A calculation with a defined scope
The item is an arXiv preprint, identified as arXiv:2608.28367v1 and dated 28 Aug 2026. It reports numerical comparisons of growth rates and eigenfunctions in a prescribed circular tokamak model, so the result should be read as a finding about those modeled conditions. The work was conducted within EUROfusion and funded by the European Union through the Euratom Research and Training Programme under Grant Agreement No 101052200.
Paper data and sources
Original title: Electromagnetic pressure-gradient-driven instabilities with moderate high mode numbers in tokamak plasmas
Authors: Yann Narbutt, Ksenia Aleynikova, Matthias Borchardt et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text