The energy confinement characteristics of ICRF-heated Tokamak plasmas are studied at high input power density approximately 2 MW m-3 volume averaged, on the JIPP T-IIU device (R=0.91 m, a=0.23 m). High electron and ion temperatures (Te approximately 2.5 keV, Ti approximately 2.0 keV, at each maximum) have been achieved by the operation at a plasma current IP of 280 kA, plasma line-averaged electron density ne of 7*1013 cm-3 and input power of 2 MW, with a suppression of total radiation loss (30-40% of the total input power) by a carbon coating on the vacuum vessel. The fraction of ICRF power absorbed by the plasma, alpha , is determined experimentally from the decay of the stored plasma energy just after the ICRF pulse is terminated. The value of alpha increases slightly with increasing electron density and decreases from 90 to 70% as the ICRF power is increased from 1 to 2 MW m-3 volume averaged. The global energy confinement time tau epsilon , defined by WP/(POH+ alpha Pr.f), decreases by a factor of 2 approximately 3 from that in Ohmic plasmas as the heating power increases up to 2 MW. It is found that the energy confinement time has a strong line-averaged electron density dependence as tau E varies as ne0.6, which is obtained by the use of the measured absorbed power, while the Kaye-Goldston scaling predicts tau E varies as ne0.26.