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The polywell is a design for a fusion reactor based on two ideas: heating ions by concentrating (-) charge to accelerate the ions and trapping a diamagnetic plasma inside a cusp field.
This kind of plasma trap is based on the idea that a plasma will create its own magnetic field that rejects the outside field. That is not common behavior for a fusing plasma. A similar trapping concept was tested by the Lockheed-Martin high beta fusion reactor team, which tried to hold a plasma in a similar way.
The Polywell attempts to heat plasma by creating a negative voltage, which attracts positive ions. Like a fusor, as the ions accelerate towards the negative center, their kinetic energy rises. Ions that collide at high enough energies can fuse. But getting this heating approach to work means the Polywell must also concentrate negative charge, which breaks the quasi-neutral assumption.