A new class of low aspect ratio toroidal hybrid stellarators is found using a more general plasma confinement optimization criterion than quasi-symmetrization. The plasma current profile and shape of the outer magnetic flux surface are used as control variables to achieve near constancy of the longitudinal invariant J* on internal flux surfaces (quasi-omnigeneity), in addition to a number of other desirable physics target properties. We find that a range of compact (small aspect ratio A), high p (ratio of thermal energy to magnetic field energy), low plasma current devices exist which have significantly improved confinement both for thermal as well as energetic (collisionless) particle components. With reasonable increases in magnetic field and geometric size, such devices can also be scaled to confine 3.5 MeV alpha particle orbits.

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Recent progress in the theoretical understanding and design of compact stellarators is described. Hybrid devices, which depart from canonical stellarators by deriving benefits from the bootstrap current which flows at finite beta, comprise a class of low aspect ratio AϽ4 stellarators. They possess external kink stability ͑at moderate beta͒ in the absence of a conducting wall, possible immunity to disruptions through external control of the transform and magnetic shear, and they achieve volume-averaged ballooning beta limits ͑4%-6%͒ similar to those in tokamaks. In addition, bootstrap currents can reduce the effects of magnetic islands ͑self-healing effect͒ and lead to simpler stellarator coils by reducing the required external transform. Powerful physics and coil optimization codes have been developed and integrated to design experiments aimed at exploring compact stellarators. The physics basis for designing the national compact stellarator will be discussed.