Commun. Comput. Phys., 10 (2011), pp. 899-911. Gyrokinetic Simulation of Magnetic Compressional Modes in General Geometry Peter Porazik 1, Zhihong Lin 1*1 Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA. Received 24 November 2010; Accepted (in revised version) 28 January 2011 Available online 13 June 2011 doi:10.4208/cicp.241110.280111a Abstract A method for gyrokinetic simulation of low frequency (lower than the cyclotron frequency) magnetic compressional modes in general geometry is presented. The gyrokinetic-Maxwell system of equations is expressed fully in terms of the compressional component of the magnetic perturbation, $\delta B_\|$, with finite Larmor radius effects. This introduces a "gyro-surface" averaging of $\delta B_\|$ in the gyrocenter equations of motion, and similarly in the perpendicular Ampere's law, which takes the form of the perpendicular force balance equation. The resulting system can be numerically implemented by representing the gyro-surface averaging by a discrete sum in the configuration space. For the typical wavelength of interest (on the order of the gyroradius), the gyro-surface averaging can be reduced to averaging along an effective gyro-orbit. The phase space integration in the force balance equation can be approximated by summing over carefully chosen samples in the magnetic moment coordinate, allowing for an efficient numerical implementation. Notice: Undefined variable: ams in /var/www/html/issue/abstract/readabs.php on line 163 PACS: 02.60.-x, 02.70.-c, 52.65.Tt Key words: Finite Larmor radius effects, gyrokinetic simulation, compressional modes, gyro-surface average. *Corresponding author. Email: pporazik@uci.edu (P. Porazik), zhihongl@uci.edu (Z. Lin)