辛几何算法在计算非磁化等离子体中波传播轨迹时的应用

为了在数值计算中保持哈密顿系统的辛几何结构不变，利用辛几何算法得到了在线性哈密顿系统中射线追踪方程的一般辛差分格式。通过具体算例，利用辛几何算法计算了波在非磁化等离子体中的传播轨迹，并且与传统Runge-Kutta-Fehlberg算法所得结果进行了比较。利用辛几何算法所得传播轨迹与解析解一致，其色散函数值的误差随时间线性增长，能在长时间内保持色散函数值在一个很小的误差范围内。利用传统的Runge-Kutta-Fehlberg算法所得传播轨迹与解析解不一致，其误差随时间做大幅振荡增加。计算结果表明辛几何算法在保持传播轨迹和色散函数值方面具有独特的优势。

Application of symplectic geometric algorithm in calculating propagation trajectory of wave in unmagnetized plasma

In order to preserve the symplectic geometric structure of Hamiltonian system, symplectic geometric algorithm is used to solve ray tracing equations. Symplectic geometric algorithm assures that conversion between two steps is symplectic. Symplectic geometric algorithm and Runge-Kutta-Fehlberg method are used to solve ray tracing equations respectively. The accuracy of both methods is fourth order. The results calculated by a simplistic geometric algorithm are in accordance with the analytic solution. In symplectic geometric algorithm, the error of dispersion function value increases with time linearly. The dispersion function value is within high accuracy. The results calculated by Runge-Kutta-Fehlberg method are different with the analytical solution. The calculation results show that the symplectic geometric algorithm has irreplaceable advantages in maintaining propagation trajectory and dispersion function value. Next symplectic geometric algorithm will be applied in magnetized plasma and nonlinear Hamiltonian systems.