A stellarator is a device used to confine a hot plasma with magnetic fields in order to sustain a controlled nuclear fusion reaction. The magnetic field necessary to confine the plasma is generated completely by external coils. It was invented by Lyman Spitzer and the first devices were built at the Princeton Plasma Physics Laboratory in 1951. The name was given to this early fusion concept because of the possibility of harnessing the power source of the sun (which is a stellar object).
Some important stellarator experiments are Wendelstein, in Germany, and the Large Helical Device, in Japan. Princeton Plasma Physics Laboratory started building a new stellarator, NCSX, but as of 2008, work was abandoned  due to high costs.
The stellarator solves issues faced by tokamak fusion reactors where the windings of an electromagnet's wiring around a torus are less dense on the outside of the loop than on the inside, which makes it difficult for magnetic tori to contain plasma. The stellarator addresses this issue by using a toroid bent into a figure-eight shape.
In a standard torus plasma particles (ions) on the inner portion of the tube are subjected to a greater magnetic force than those at the outside. Only particles near the middle receive the optimum amount. Since magnetic forces are generally at right angles to motion, non-centered plasma moving around the toroid would be forced up or down until it hit the edges of the tube.
In a stellerator, when a particle orbits the tube, it spends half the time on the inside of the tube and half on the outside. This helps to equalize the forces and the particle is subject to a much smaller drifting force.
The earliest stellarators were figure-eights, consisting of two sides of a torus connected together with crossed straight tubes. To allow the tubes to cross without hitting, the torus sections on either end were rotated slightly. This arrangement was less than perfect, however, as a particle on the inner portion at one end would not end up at the outer portion at the other, but at some other point rotated from the perfect location due to the tilt of the two ends.
Different geometries were tried to address these problems, starting with simple changes to allow the ends to lie flat at different levels and placing symmetrical bends in the arms instead. A later version solved the problem more convincingly by introducing a peanut-shaped tube instead of a figure-eight, the in-bent sides offsetting the out-bend toroidal sections on either end.
The solution was magnetic rather than mechanical. By rotating the magnetic windings themselves as they were wrapped around the chamber, the plasma would be rotated around a simple torus, slowly moving from inside to outside.
Torsatron: A stellarator configuration with continuous helical coils. It can also have the continuous coils replaced by a number of discrete coils producing a similar field.
Heliotron: A stellarator configuration in which a helical coil is used to confine the plasma, together with a pair of PF coils to provide a vertical field. TF coils can also be used to control the magnetic surface characteristics.
Heliac: (Literally) helical axis stellarator; a stellarator in which the magnetic axis (and plasma) follows a helical path to form a toroidal helix rather than a simple ring shape. The twisted plasma induces twist in the magnetic field lines to effect drift cancellation, and typically can provide more twist than the Torsatron or Heliotron, especially near the centre of the plasma (magnetic axis). The original Heliac consists only of circular coils, and the flexible heliac  (H-1NF, TJ-II, TU-Heliac) adds a small helical coil to allow the twist to be varied by a factor of up to 2.
Helias: A stellarator configuration utilizing an optimized modular coil set designed to simultaneously achieve high plasma, low Pfirsch-Schluter currents and good confinement of energetic particles, i.e. alpha particles for reactor scenarios. The Helias (HELIcal Advanced Stellarator) has been proposed to be the most promising stellarator concept for a power plant, with a modular engineering design and optimised plasma, MHD and magnetic field properties. The Wendelstein VII-X device is based on a five field-period Helias configuration.
Comparison to tokamaks
The tokamak provides the required twist to the magnetic field lines not by manipulating the field with external currents, but by driving a current through the plasma itself. The field lines around the plasma current combine with the toroidal field to produce helical field lines, which wrap around the torus in both directions.
Although they also have a toroidal magnetic field topology, stellarators are distinct from tokamaks in that they are not azimuthally symmetric. They have instead a discrete rotational symmetry, often fivefold, like a regular pentagon.
It is generally argued that the development of stellarators is less advanced than tokamaks although the intrinsic stability they provide has been sufficient to pursue an active development of this concept. Stellarators, unlike tokamaks, do not require a toroidal current, so that the expense and complexity of current drive and/or the loss of availability and periodic stresses of pulsed operation can be avoided. In addition, there is no risk of current disruptions.
On the downside, the three-dimensional nature of the field, the plasma, and the vessel make it much more difficult to do either theoretical or experimental diagnostics with stellarators. On the other hand, it might be possible to use the additional degrees of freedom to optimize a stellarator in ways that are not possible with tokamaks. It is much harder to design a divertor (the section of the wall that receives the exhaust power from the plasma) in a stellarator, the out-of-plane magnetic coils (common in many modern stellarators and possibly all future ones) are much harder to manufacture than the simple, planar coils which suffice for a tokamak, and the utilization of the magnetic field volume and strength is generally poorer than in tokamaks.
The goal of magnetic confinement devices is to transport energy slowly across a magnetic field. Toroidal devices are relatively successful because the magnetic properties seen by the particles are averaged as they travel around the torus. The strength of the field seen by a particle, however, generally varies, so that some particles will be trapped by the mirror effect. These particles will not be able to average the magnetic properties so effectively, which will result in increased energy transport. In most stellarators, these changes in field strength are greater than in tokamaks, which is a major reason that transport in stellarators tends to be higher than in tokamaks.
University of Wisconsin electrical engineering Professor David Anderson and research assistant John Canik recently proved that the Helically Symmetric eXperiment (HSX) can overcome this major barrier in plasma research. The HSX is the first stellarator to use a quasi-symmetric magnetic field. The team designed and built the HSX with the prediction that quasisymmetry would reduce transport. As the team's latest research shows, that's exactly what it does. "This is the first demonstration that quasisymmetry works, and you can actually measure the reduction in transport that you get," says Canik.  
1. ^ Harris, J. H.; J. L. Cantrell, T. C. Hender, B. A. Carreras, and R. N. Morris (1985). "A flexible heliac configuration". Nuc. Fusion 25: 623.
* Stellarator News from ORNL