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, δB_{‖}, with finite Larmor radius effects.
This introduces a "gyro-surface" averaging of δB_{‖ }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.