Beyond linear polarization in gyrokinetic theory

The concept of linear gyrocenter polarization in gyrokinetic theory is generalized to include contributions from guiding-center polarization as well as nonlinear (quadratic) gyrocenter polarization. The former polarization is obtained from Hamiltonian guiding-center theory in which higher-order corrections due to magnetic-field nonuniformity are retained [1]. The latter polarization can be derived either variationally from the cubic gyrocenter Hamiltonian [2] or directly by push-forward construction [3]. \\[4pt] [1] A.J. Brizard and N. Tronko, submitted for publication (2012).\\[0pt] [2] A. Mishchenko and A.J. Brizard, Phys. Plasmas \underline{18}, 022305 (2011).\\[0pt] [3] A.J. Brizard, Comm. Nonlin. Sci. Num. Sim. \underline {13}, 24 (2008).