2024.07.12

[日時]　2024年 7月 23日(火) 13:30〜15:00

[場所]　核融合科学研究所 研究II期棟5階509セミナー室 ＋ オンライン併用

（接続情報は別途メールにて、参加申込・招待された方へお知らせします）

[講師]　Alain Brizard (Saint Michael’s College)

[講演題目]　Metriplectic structures for reduced Vlasov-Maxwell-Landau equations

[講演概要]
Structure-preserving algorithms have gained increased attention recently because of the possibility of explicitly satisfying important conservation laws while implementing numerical simulations of complex magnetized plasmas. An important structure found in plasma physics is a metriplectic structure, which combines a dissipationless (Hamiltonian) time evolution, generated by a Hamiltonian functional H and an antisymmetric Hamiltonian bracket [ , ], and a dissipative (collisional) time evolution, generated by an entropy functional S and a symmetric dissipative bracket ( , ). Hence, the time evolution of a generic functional F is expressed in metriplectic form as ∂F/∂t = [F, H] + (F, S). We note here that the entropy functional S is a Casimir functional of the Hamiltonian bracket, i.e., [S, G] = 0 for any functional G, which immediately leads to an H-theorem: ∂S/∂t = (S, S) ≥ 0. The metriplectic conservation laws involve functionals P that satisfy [P, H] = 0, which follows from the Noether theorem, and (P, G) = 0 for any functional G, which serve as constraints on the dissipative bracket.

In the first part of this talk, I will review the metriplectic structure of the Vlasov-Maxwell-Landau equations, in which the Hamiltonian bracket was discovered by Morrison (1980,1982) and the dissipative bracket is constructed from the Landau form of the Fokker-Planck collision operator (Kaufman, 1984; Morrison, 1984, 1986). In the second part, I will present new results on the metriplectic structure of the guiding-center Vlasov-Maxwell-Landau equations. The metriplectic structure of the gyrokinetic Vlasov-Maxwell-Landau equations will also be briefly discussed.

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