2016/10/13 by Gianluca Geloni, Geloni, Gianluca, Vitali Kocharyan +3
Engineering · Physics and Astronomy · #Accelerator Physics (physics.acc-ph) #FOS: Physical sciences #Geophysics and Sensor Technology #Ionosphere and magnetosphere dynamics #Magnetic confinement fusion research
paper · pdf · doi:10.48550/arxiv.1610.04139
openalex publication_date 2016/10/13 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28
In accelerator and plasma physics it is accepted that there is no need to\nsolve the dynamical equations for particles in covariant form, i.e. by using\nthe coordinate-independent proper time to parameterize particle world-lines in\nspace-time: to describe dynamics in the laboratory frame, there is no need to\nuse the laws of relativistic kinematics. It is sufficient to account for the\nrelativistic dependence of particles momenta on the velocity in the second\nNewton's law. Then, the coupling of fields and particles is based on the use of\nresult from particle dynamics treated according to Newton's laws in terms of\nthe relativistic three-momentum and on the use of Maxwell's equations in\nstandard form. Previously, we argued that this is a misconception. Here we\ndescribe in detail how to calculate the coupling between fields and particles\nin a correct way and how to develop a new algorithm for a particle tracking\ncode in agreement with the use of Maxwell's equations in their standard form.\nAdvanced textbooks on classical electrodynamics correctly tell us that\nMaxwell's equations in standard form in the laboratory frame and charged\nparticles are coupled by introducing particles trajectories as projections of\nparticles world-lines onto coordinates of the laboratory frame and then by\nusing the laboratory time to parameterize the trajectory curves. We show a\ndifference between conventional and covariant particle tracking results in the\nlaboratory frame. This essential point has never received attention in the\nphysical community. Only the solution of the dynamical equations in covariant\nform gives the correct coupling between field equations in standard form and\nparticles trajectories in the laboratory frame. Previous theoretical and\nsimulation results in accelerator and plasma physics should be re-examined in\nthe light of the pointed difference between conventional and covariant particle\ntracking.\n