FPIC Study of the n$=$1 Toroidal Mode in FRC Plasmas

The near term goal of TAE's experiments is to sustain through the of use of neutral beam heating and edge biasing an advanced beam-driven FRC for many milliseconds, i.e., well beyond the growth times of common instabilities. Here we apply FPIC, a quasineutral hybrid code with fully kinetic ions, to study the growth rate of the n$=$1 mode and related kinetic effects versus different equilibrium parameters in configurations of interest for upcoming TAE's experiments. In particular we address how the n$=$1 growth rate scales versus S*/E and E. The mode strength is computed taking into account a full 3D mode decomposition of the FRC separating the physically distinct contributions, namely tilt, radial shift and interchange modes and we study the role of each one of them.