回旋运动方程

回旋动理学（gyrokinetics）是在磁化等离子体当中，带电粒子的轨迹是一个围绕磁力线的螺旋运动。它可以解耦为一个快速的回旋运动和和一个相对来说比较慢的导心运动。对于等体中的许多问题，只需要考虑后者就已经足够了。不论是传统的回旋平均，还是现在的李坐标变换，由于去除了不必要的回旋相位角这一维数，使得计算得到了简化。

回旋动理学方程的导出

先是弗拉索夫方程和麦克斯韦方程

使用变换坐标和回旋平均的方法，就得到回旋动理学方程

（x, v ) →( R, μ, U)

或者用李群变换。

发展时间线

Rosenbluth & Simon (1965) ― moment equations are simplest in terms of the drift velocity

Rutherford & Frieman (1968); Taylor & Hastie (1968) ― linearized GKs in general geometry

Hinton & Horton (1971) ― gyroviscous cancellation

Catto (1978) ― do transformation to guiding-center variables first!

Littlejohn (197982) ― noncanonical Hamiltonian techniques

Frieman & Chen (1982) ― first nonlinear GKE

Lee (1983) ― modern form of the GK-Poisson system; GK particle simulation

Dubin, Krommes, Oberman, & Lee (1983) ― self-consistent Hamiltonian GKs

Littlejohn (1983) and Cary & Littlejohn (1983) ― Lagrangian methods; Noether’s theorem

Krommes, Lee, & Oberman (1986) ― GK noise

Hahm (1988) ― GKs via the one-form method

Sugama (2000); Brizard (2000) ― variational principle; gyrokinetic field theory

Parra (2008) ― dissertation on GK momentum conservation

Schekochihin et al. (2009) ― astrophysical GKs

Plunk et al. (2010) ― GK entropy cascade

Zhu & Hammett (2010) ― absolute GK statistical equilibria

Scott & Smirnov (2010) ― GK conservation law for toroidal angular momentum

……

计算机模拟程序

Particle-in-cell (PIC):

GTC ― Lin et al. (1998)

GEM ― Chen & Parker (2003)

GTS ― Wang et al. (2006)

ORB5 ― Jolliet et al. (2007)

XGC1 ― Chang et al. (2009)

Continuum (Vlasov):

GS2 ― Dorland et al. (2000) [based on the linear code of

Kotschenreuther et al. (1995); see also the AstroGK code of

Numata et al. (2010)]

GENE ― Jenko et al. (2000)

GYRO ― Candy & Waltz (2003)

GT5D ― Idomura et al. (2008)

Hybrid (semi-Lagrangian):

GYSELA ― Grandgirard et al. (2006)