The improvements in multi-mirror confinement due to an asymmetrically applied ion cyclotron resonance field (ICRF) are determined. The resonance field is used to selectively reflect ions that travel away from the centre of the device, thus creating a net ion drift towards the centre. The ICRF effects in heating and scattering the ions and modifying the loss cone geometry are determined in detail. A onedimensional, non-ignited (finite Q = fusion power/recirculating power) model of a multiple-mirror system is used to investigate confinement. Various scaling laws are numerically derived and compared to those of a symmetric system without ICRF. Radial diffusion due to classical collisions and ICRF effects is calculated. A 21-cell machine with a peak field of 280 kG and Q = 5 is reduced from 845 m to 580 m in length with the addition of the asymmetric ICRF. The total fusion power generated by the system is reduced from 8 to 6.3 GW.