A variational approach to charged-particle transport

Details A variational approach to charged-particle transport A variational approach to charged-particle transport

Nov 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974apj...193..711l&link_type=abstract

Astrophysical Journal, vol. 193, Nov. 1, 1974, pt. 1, p. 711-719.

Astronomy and Astrophysics

Astrophysics

1

Calculus Of Variations, Charged Particles, Eigenvalues, Electromagnetic Interactions, Liouville Equations, Transport Theory, Extremum Values, Magnetohydrodynamic Flow, Time Dependence, Variational Principles

Scientific paper

The equations describing the transport of charged particles in turbulent electromagnetic fields are investigated from a variational point of view. We demonstrate that (1) the transport equation (which is normally not self-adjoint) follows from an extremal variation of a Lagrangian; (2) the equations adjoint to the transport equation also follow from an extremal variation of the same Lagrangian; (3) the Lagrangian approach automatically gives a variational principle for computing the eigenvalues of the transport equation subject to the boundary conditions at hand; and (4) the quasi-linear approximation follows by neglecting a single term in a Lagrangian for the self-adjoint Liouville's equation, and neglect of this term turns the self-adjoint equation into a non-self-adjoint equation.

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