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/content/aip/journal/pop/23/9/10.1063/1.4962506
1.
J. E. Marsden and M. West, “ Discrete mechanics and variational integrators,” Acta Numer. 10, 357514, 5 (2001).
http://dx.doi.org/10.1017/S096249290100006X
2.
A. Stern, Y. Tong, M. Desbrun, and J. E. Marsden, “ Geometric computational electrodynamics with variational integrators and discrete differential forms,” in Geometry, Mechanics, and Dynamics, Fields Institute Communications ( Springer, New York, 2015), Vol. 73, pp. 437475.
3.
H. Qin and X. Guan, “ Variational symplectic integrator for long-time simulations of the guiding-center motion of charged particles in general magnetic fields,” Phys. Rev. Lett. 100, 035006 (2008).
http://dx.doi.org/10.1103/PhysRevLett.100.035006
4.
R. Zhang, J. Liu, H. Qin, Y. Wang, Y. He, and Y. Sun, “ Volume-preserving algorithm for secular relativistic dynamics of charged particles,” Phys. Plasmas 22(4), 044501 (2015).
http://dx.doi.org/10.1063/1.4916570
5.
C. L. Ellison, J. M. Finn, H. Qin, and W. M. Tang, “ Development of variational guiding center algorithms for parallel calculations in experimental magnetic equilibria,” Plasma Phys. Controlled Fusion 57(5), 054007 (2015).
http://dx.doi.org/10.1088/0741-3335/57/5/054007
6.
J. Squire, H. Qin, and W. M. Tang, “ Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme,” Phys. Plasmas 19(8), 084501 (2012).
http://dx.doi.org/10.1063/1.4742985
7.
M. Kraus, “ Variational integrators in plasma physics,” Ph.D. thesis, Technische Universität München, 2013.
8.
F. E. Low, “ A Lagrangian formulation of the Boltzmann-Vlasov equation for plasmas,” Proc. R. Soc. London, Ser. A 248(1253), 282287 (1958).
http://dx.doi.org/10.1098/rspa.1958.0244
9.
H. Ye and P. J. Morrison, “ Action principles for the Vlasov equation,” Phys. Fluids B 4(4), 771777 (1992).
http://dx.doi.org/10.1063/1.860231
10.
J. Larsson, “ An action principle for the Vlasov equation and associated Lie perturbation equations. Part 2. The Vlasov–Maxwell system,” J. Plasma Phys. 49, 255270 (1993).
http://dx.doi.org/10.1017/S0022377800016974
11.
T. Flå, “ Action principle and the Hamiltonian formulation for the Maxwell-Vlasov equations on a symplectic leaf,” Phys. Plasmas 1(8), 24092418 (1994).
http://dx.doi.org/10.1063/1.870569
12.
A. J. Brizard, “ New variational principle for the Vlasov-Maxwell equations,” Phys. Rev. Lett. 84, 57685771 (2000).
http://dx.doi.org/10.1103/PhysRevLett.84.5768
13.
L. D. Landau, “ The kinetic equation in the case of Coulomb interaction,” Zh. Eksp. Teor. Fiz. 7, 203209 (1937) (translated from German).
14.
M. N. Rosenbluth, W. M. MacDonald, and D. L. Judd, “ Fokker-Planck equation for an inverse-square force,” Phys. Rev. 107, 16 (1957).
http://dx.doi.org/10.1103/PhysRev.107.1
15.
N. H. Ibragimov, “ Integrating factors, adjoint equations and Lagrangians,” J. Math. Anal. Appl. 318(2), 742757 (2006).
http://dx.doi.org/10.1016/j.jmaa.2005.11.012
16.
N. H. Ibragimov, “ A new conservation theorem,” J. Math. Anal. Appl. 333(1), 311328 (2007), Special issue dedicated to William Ames.
http://dx.doi.org/10.1016/j.jmaa.2006.10.078
17.
M. Kraus and O. Maj, “ Variational integrators for nonvariational partial differential equations,” Phys. D 310, 3771 (2015).
http://dx.doi.org/10.1016/j.physd.2015.08.002
18.
J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems ( Springer Publishing Company, Incorporated, 2010).
19.
W. Coffey, Y. P. Kalmykov, and J. T. Waldron, The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry, and Electrical Engineering ( EBL-Schweitzer, World Scientific, 2004).
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/content/aip/journal/pop/23/9/10.1063/1.4962506
2016-09-14
2016-09-30

Abstract

An action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

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