The Levitated Dipole Experiment (LDX) is used to study high-temperature plasma confined by the magnetic field produced by a high-current superconducting ring. Multiple-frequency electron cyclotron resonance heating (ECRH) heats and sustains plasma discharges for long, quasi-steady periods, and conditions of high plasma beta are reached by adjusting the rate of neutral fueling. When the superconducting ring is levitated by attraction to a coil located above the vacuum chamber, cross-field transport becomes the main loss channel for plasma particles and energy. We find operation with a levitated dipole always leads to centrally peaked density profiles, even when the plasma ionization source occurs near the plasma edge. In recent experiments, we also observe the normalized gradient, or shape, of the density profile to be 'stationary' while the ECRH heating power and gas fueling rates are strongly modulated. Theoretically, stationary profiles result in an energy confinement time (of the thermal plasma) that greatly exceeds the particle confinement time. This condition, along with high-beta plasma stability, is a necessary condition for utilizing advanced fuels in a fusion power source.