Model order reduction approach to the one-dimensional collisionless closure problem

The problem of the fluid closure for the collisionless linear Vlasov system is investigated using a perspective from control theory and model order reduction. The balanced truncation method is applied to the 1D-1V Vlasov system. The first few reduction singular values are well-separated, indicating potentially low-dimensional dynamics. To avoid large-dimensional numerical work, a reduced model is formulated using rational interpolation, generalizing the seminal work from Hammett and Perkins. The resulting models are found to outperform the state-of-the-art models for thermal phase velocities. Thanks to the versatility of this formulation, an application to toroidal gyrokinetic dynamics is discussed.