An efficient solution of the multi-term multi-harmonic electron Boltzmann equation for use in global models

Solving the electron Boltzmann equation is an essential but costly step in simulating low -temperature plasma kinetics. This work addresses the problem by introducing a solution of the general multi -term multi -harmonic Boltzmann equation (MTMH-BE) optimized for electrons in time -dependent non -equilibrium gases and electric fields. This is accomplished by configuring the numerical Jacobian as the product of a time -independent sparse matrix and an array of time -dependent coefficients. As this approach requires a fixed energy grid, the MTMHBE is discretized using a finite volume scheme with support for non -uniform cell size, enabling robust solutions across a wide range of reduced field strengths. The new MTMH-BE solver is tested against a range of benchmarks, demonstrating excellent agreement with existing methods. Performance with time -dependent electron energy is evaluated using LoKI-B's pulsed electric field model, with the new solver demonstrating improved wall time scaling and an improvement in grid convergence of over three orders of magnitude. Alternatively, performance with quasi -stationary electrons in an evolving non -equilibrium gas is tested using a nitrogen cross-section set with up to 58 vibrational states and 3,570 processes. Here, the MTMH-BE solver achieves a wall time reduction of up to 99.6% over MultiBolt for error -controlled simulations in the two -term limit, reducing the average solution time from 1-2 seconds to less than 10 ms. These results indicate that the new MTMH-BE solver can improve accuracy and performance in state -to -state global models without the use of grid refinement, cross-section pruning, and other time -saving procedures.