Bourdier A, Gond S
Commissariat a l'Energie Atomique, Direction Ile de France, Departement de Physique Theorique et Appliquee, Boiinsertion markte Postale 12, 91680 Bruyeres-le-Chainsertion marktel, France.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Sep;62(3 Pt B):4189-206. doi: 10.1103/physreve.62.4189.
The relativistic motion of a charged particle in a transverse circularly or almost circularly polarized homogeneous electromagnetic wave is studied using the Hamiltonian formalism. First, the case of a circularly and almost circularly polarized traveling wave propagating in a nonmagnetized space is studied. In the case of an almost circularly polarized wave, it is shown that the charged particle has an average velocity along the propagation direction of the wave. The same result is derived considering a cold electron plasma. The case of a traveling wave propagating along a constant homogeneous magnetic field is then considered. Using canonical transformations, it is shown that the equations of motion can be derived from an autonomous Hamiltonian which has two degrees of freedom and a first integral. As a consequence, the system is completely integrable. An equation is found for the particle energy when it is initially resonant. This equation is solved exactly, and the asymptotic solution is obtained. The expression for the energy allows a solution for the system in terms of quadratures, and in consequence the asymptotic solution for all the variables. The case of an almost circularly polarized wave propagating along a constant homogeneous magnetic field is also studied. Finally, a magnetic field gradient is considered, and new acceleration mechanisms are found.
利用哈密顿形式体系研究了带电粒子在横向圆偏振或近圆偏振均匀电磁波中的相对论运动。首先，研究了在非磁化空间中传播的圆偏振和近圆偏振行波的情况。在近圆偏振波的情况下，表明带电粒子沿波的传播方向具有平均速度。考虑冷电子等离子体也能得出相同结果。接着考虑沿恒定均匀磁场传播的行波情况。通过正则变换表明，运动方程可从具有两个自由度和一个第一积分的自治哈密顿量导出。因此，该系统是完全可积的。找到了粒子初始共振时的能量方程。精确求解该方程并得到渐近解。能量表达式使得可以通过积分求解该系统，进而得到所有变量的渐近解。还研究了沿恒定均匀磁场传播的近圆偏振波的情况。最后，考虑磁场梯度并发现了新的加速机制。
