标题： 带电粒子在史瓦西背景下的四极磁场中的混沌行为 显示英文标题

标题： Chaos of charged particles in quadrupole magnetic fields under Schwarzschild backgrounds

摘要： 在Schwarzschild背景下的外部测试电磁场的四维矢量势是通过偶极子和四极子磁场的组合来描述的。这种组合是无源麦克斯韦方程组的内部解。这种外部测试磁场导致黑洞周围的带电粒子的动力学变得不可积分，并主要负责带电粒子的混沌动力学。除了外部磁场外，混沌的发生还需要一些其他条件。通过显式辛积分器和快速李雅普诺夫指标，磁场所对混沌的影响被清晰地展示出来。与偶极子磁场相比，四极子磁场的引入更容易引起混沌。这一结果是因为四极子磁场产生的洛伦兹力大于偶极子磁场产生的洛伦兹力。此外，洛伦兹力作为吸引力，有助于在不可积分的情况下引发混沌。 显示英文摘要

摘要： A four-vector potential of an external test electromagnetic field in a Schwarzschild background is described in terms of a combination of dipole and quadrupole magnetic fields. This combination is an interior solution of the source-free Maxwell equations. Such external test magnetic fields cause the dynamics of charged particles around the black hole to be nonintegrable, and are mainly responsible for chaotic dynamics of charged particles. In addition to the external magnetic fields, some circumstances should be required for the onset of chaos. The effect of the magnetic fields on chaos is shown clearly through an explicit symplectic integrator and a fast Lyapunov indicator. The inclusion of the quadrupole magnetic fields easily induces chaos, compared with that of the dipole magnetic fields. This result is because the Lorentz forces from the quadrupole magnetic fields are larger than those from the dipole magnetic fields. In addition, the Lorentz forces act as attractive forces, which are helpful to bring the occurrence of chaos in the nonintegrable case.