The direct implicit method with a second-order implicit integration scheme is formulated for and applied to the electron parallel nonlinearity in global electrostatic gyrokinetic particle-in-cell simulations of toroidal fusion plasmas. The method shows improved numerical accuracy and stability properties compared to the direct implicit method with a first-order integration scheme. The conservation of total energy and toroidal angular momentum are analyzed by both techniques and the results are presented.
- fusion plasma physics
- gyrokinetic particle simulation
- kinetic electrons