# Exact energy conservation laws for full and truncated nonlinear gyrokinetic equations

## Related Articles

- The physics of the second-order gyrokinetic magnetohydrodynamic Hamiltonian: Î¼ conservation, Galilean invariance, and ponderomotive potential. Krommes, J. A. // Physics of Plasmas;Dec2013, Vol. 20 Issue 12, p124501
Some physical interpretations are given of the well-known second-order gyrokinetic Hamiltonian in the magnetohydrodynamic limit. Its relations to the conservation of the true (Galilean-invariant) magnetic moment and fluid nonlinearities are described. Subtleties about its derivation as a...

- Compact form for the relativistic ponderomotive Hamiltonian. Cary, John R.; Newberger, Barry S. // Physics of Fluids (00319171);Jan85, Vol. 28 Issue 1, p423
The infinite series of functions present in the ponderomotive Hamiltonian are explicitly summed using Newbergerâ€™s sum rule. The result is a compact and easily evaluated expression for the ponderomotive Hamiltonian. Application of the K-Ï‡ theorem yields the linear susceptibility of...

- Guiding center Hamiltonian theory of free-electron lasers. Grebogi, Celso; Uhm, Han S. // Physics of Fluids (00319171);Jun85, Vol. 28 Issue 6, p1984
The relativistic guiding center ponderomotive Hamiltonian for free-electron lasers is derived. The ponderomotive Hamiltonian together with the Poisson structure gives the full dynamical description of the slow electron motion. The derivation takes into account arbitrary signal wave polarization...

- On the Lie-Poisson structure of the nonlinearized discrete eigenvalue problem. Wu, Yongtang; Yongfang Wu; Du, Dianlou; Dianlou Du // Journal of Mathematical Physics;Aug2000, Vol. 41 Issue 8
A 3x3 discrete eigenvalue problem and corresponding discrete soliton equations are proposed. Under a constraint between the potentials and eigenfunctions, the 3x3 discrete eigenvalue problem is nonlinearized into an integrable Poisson map with a Lie-Poisson structure. Further, a reduction of the...

- The Conditions of Existence of First Integrals and Hamiltonian Structures of Lotkaâ€“Volterra and Volterra Systems. Dubovik, V. M.; Galperin, A. G.; Richvitsky, V. S.; Slepnyov, S. K. // Physics of Atomic Nuclei;Apr2000, Vol. 63 Issue 4, p629
A study of a certain subset of Volterra equations has revealed that some statements about time-independent constants of motion, Hamiltonian functions, and Poisson structure matrices appearing in the LotkaVolterra equations, either regarded as proven or of the sort that could be proven, are not...

- On separability of bi-Hamiltonian chain with degenerated Poisson structures. Blaszak, Maciej // Journal of Mathematical Physics;Jun98, Vol. 39 Issue 6, p3213
Proves the separability of bi-Hamiltonian finite-dimensional chains with two degenerated Poisson tensors. Presence of a quasi-bi-Hamiltonian representation in the generalized Henon-Heiles systems; Condition of the quasi-bi-Hamiltonian vector field; Construction of canonical transformation to...

- Pressure surface distortion by applied ion cyclotron waves and magnetic field asymmetries. Myra, J. R.; D’Ippolito, D. A. // Physics of Fluids (00319171);Jan88, Vol. 31 Issue 1, p149
In magnetic confinement devices the pressure surfaces must obey the parallel current constraint. In a tandem mirror, nonquadrupole magnetic field components or ion cyclotron range of frequencies (ICRF) ponderomotive effects enter the parallel current equation in a nontrivial way. The extra terms...

- Ponderomotive force on solitary structures created during radiation pressure acceleration of thin foils. Tripathi, Vipin K.; Sharma, Anamika // Physics of Plasmas;May2013, Vol. 20 Issue 5, p053104
We estimate the ponderomotive force on an expanded inhomogeneous electron density profile, created in the later phase of laser irradiated diamond like ultrathin foil. When ions are uniformly distributed along the plasma slab and electron density obeys the Poisson's equation with space charge...

- Ponderomotive force in a collisional warm two-fluid plasma. Lee, Nam C. // Physics of Plasmas;Aug2001, Vol. 8 Issue 8
An expression for the ponderomotive force of high frequency electromagnetic waves in a warm two-fluid collisional plasma in an ambient magnetic field is obtained by a microscopic method. In addition to the previously known results of collisionless plasmas, the expression contains a term that...