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The toroidal solenoid was an early 1946 design for a fusion power device designed by George Paget Thomson and Moses Blackman of Imperial College London.It proposed to confine a deuterium fuel plasma to a toroidal (donut-shaped) chamber using magnets, and then heating it to fusion temperatures using radio frequency energy in the fashion of a microwave oven.
This equation is valid for a solenoid in free space, which means the permeability of the magnetic path is the same as permeability of free space, μ 0. If the solenoid is immersed in a material with relative permeability μ r, then the field is increased by that amount: =.
The solenoid can be useful for positioning, stopping mid-stroke, or for low velocity actuation; especially in a closed loop control system. A uni-directional solenoid would actuate against an opposing force or a dual solenoid system would be self cycling. The proportional concept is more fully described in SAE publication 860759 (1986).
The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the ...
Because the toroid is a closed-loop core, it will have a higher magnetic field and thus higher inductance and Q factor than an inductor of the same mass with a straight core (solenoid coils). This is because most of the magnetic field is contained within the core.
Let be the solenoid constructed this way, then the topology of the solenoid is just the subset topology induced by the Euclidean topology on . Since the parametrization is bijective, we can pullback the topology on S {\displaystyle S} to R {\displaystyle \mathbb {R} } , which makes R {\displaystyle \mathbb {R} } itself the solenoid.