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)
