The diagram at the right is a schematic of a design for a space habitat that solves some problems that some people have claimed make the idea invalid.
A space habitat in which people will be living for a long term requires radiation shielding. Unfortunately, radiation shielding can actually make the problem of radiation in space worse instead of better, because cosmic rays (very fast moving large atomic nuclei) will produce secondary radiation when they strike thin shielding.
The design shown here makes it completely practical to use leftovers from mining to produce shielding several feet thick which surround the people in the habitat from absolutely all directions.
Many of the ideas in this design are not new with me, of course. The use of nonrotating shielding and a 45-degree relay mirror were part of the well-known Stanford Torus design, and using a parabolic mirror to concentrate sunlight for distribution within a space settlement even predates Gerard O'Neill, as part of a hollowed-out asteroid proposal by Dandridge Cole. The paperback edition of The High Frontier shows a design by an MIT class which strongly resembles this one, as it involves both a 45-degree relay mirror, and a Cassegrain optical system to concentrate sunlight. However, that design is not identical to this one, as the shielding also serves as the ground under the habitat and rotates; another design in the book, the "Crystal Palace" or "Hatbox" design has a rotating cylinder within vacuum inside cylindrical shielding, and that is the basic scheme of the habitat area in this design. In addition to combining elements of those designs, the use of a long, narrow tube of shielding to admit sunlight, facing a slab of shielding on the far side of the mirrors is the major innovation of this design.
It is intended that the vertical axis in the diagram shall be perpendicular to the ecliptic. In this way, the incoming yellow lines, representing sunlight, are reflected by a thin flat reflector which is turned to face the sun. It is not necessary to have the habitat as a whole realigned to face the sun, with the expenditure of consumables.
A Cassegrain optical system concentrates the sunlight, so it can enter the narrow neck of a bottle-shaped shielding structure, within which the rotating cylindrical habitat is located. This too is made of thin aluminized plastic, held in the desired shape by a metal framework. Concentrating the sunlight in this way allows enough to go through to provide light for a long rotating habitat cylinder.
The diagram also shows two blue lines representing cosmic rays. The large flat disk of shielding material at the top of the diagram blocks all radiation approaching the habitat from the direction in which the neck of the bottle-shaped shielding structure points, unless it comes in at an oblique enough angle that it is unable to go all the way down the neck to the habitat. As the blue line entering from the upper right-hand corner of the diagram, which grazes the edge of the disk, and then hits the edge of the neck, illustrates.
The blue line entering from the left-hand side of the diagram hits the underside of the disk, generating secondary radiation which can enter the neck of the cylinder. As the inside of the "bottle" is in vacuum, no glass window, which, with chevron shielding, could block the secondary radiation is present. But because of the length of the neck, the secondary radiation is limited to a narrow cone in the center, which does not reach the cylindrical habitat. However, if it is desired to make the habitat longer without lengthening the neck, some areas could be reached by the secondary radiation. If, at that distance, it is still a problem, a window in the neck of the shielding material would be required.
However, as pictured, while secondary radiation from the inside of the slab won't reach the habitat, secondary radiation from cosmic rays hitting the inside of the neck will still do so. This may not be a serious hazard, but it can be completely eliminated simply by doubling the length of the neck from that shown in the diagram.
The green line on the left-hand side of the cylinder is not to scale, but represents the profile of a layer of reinforced clear plastic which would be used to contain the habitat's air. Since the surface is made up from pieces of toruses, the "skin" of the habitat meets the shape conditions for a pressure vessel, except for the boundaries between different toruses.