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As a simple example from the physics of magnetically confined plasmas, consider an axisymmetric system with circular, concentric magnetic flux surfaces of radius (a crude approximation to the magnetic field geometry in an early tokamak but topologically equivalent to any toroidal magnetic confinement system with nested flux surfaces) and denote the toroidal angle by and the poloidal angle by .
In electromagnetism, a toroidal moment is an independent term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distributions can be expanded into a complete set of electric and magnetic multipole coefficients.
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.
A toroid using a square. A torus is a type of toroid. A useful device that can produce a magnetic field is a toroid , which we can describe as a solenoid bent into the shape of a doughnut. [1] In mathematics, a toroid is a surface of revolution with a hole in the middle.
Toroidal machines can be axially symmetric, like the tokamak and the reversed field pinch (RFP), or asymmetric, like the stellarator.The additional degree of freedom gained by giving up toroidal symmetry might ultimately be usable to produce better confinement, but the cost is complexity in the engineering, the theory, and the experimental diagnostics.
Magnetic fields in a tokamak Tokamak magnetic field and current. Shown is the toroidal field and the coils (blue) that produce it, the plasma current (red) and the poloidal field created by it, and the resulting twisted field when these are overlaid.
A model of a spheromak forming inside a chamber (far right) A spheromak is an arrangement of plasma formed into a toroidal shape similar to a smoke ring. [1] The spheromak contains large internal electric currents and their associated magnetic fields arranged so the magnetohydrodynamic forces within the spheromak are nearly balanced, resulting in long-lived (microsecond) confinement times ...
This toroidal field can run along the same or opposite direction as the spinning plasma. [22] In the spheromak the strength of the toroidal magnetic field is similar to that of the poloidal field. By contrast, the FRC has little to no toroidal field component and is confined solely by a poloidal field. The lack of a toroidal field means that ...