General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics

TY - JOUR

T1 - General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics

AU - Fan, Peifeng

AU - Qin, Hong

AU - Xiao, Jianyuan

AU - Xiang, Nong

N1 - Publisher Copyright: © 2019 Author(s).

PY - 2019/6/1

Y1 - 2019/6/1

N2 - A general field theory for classical particle-field systems is developed. Compared to the standard classical field theory, the distinguishing feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-Time, whereas each particle's trajectory is defined on the 1D time-Axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-Time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is developed on the 4D space-Time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-Time. Specifically, the nonvanishing Euler derivative in the weak Euler-Lagrange equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.

AB - A general field theory for classical particle-field systems is developed. Compared to the standard classical field theory, the distinguishing feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-Time, whereas each particle's trajectory is defined on the 1D time-Axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-Time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is developed on the 4D space-Time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-Time. Specifically, the nonvanishing Euler derivative in the weak Euler-Lagrange equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.

UR - https://www.scopus.com/pages/publications/85067545863

UR - https://www.scopus.com/pages/publications/85067545863#tab=citedBy

U2 - 10.1063/1.5092131

DO - 10.1063/1.5092131

M3 - Article

SN - 1070-664X

VL - 26

JO - Physics of Plasmas

JF - Physics of Plasmas

IS - 6

M1 - 062115

ER -