magnetic confinement fusion Magnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, along with i ...

, quasisymmetry (sometimes hyphenated as quasi-symmetry) is a type of

continuous symmetry In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some Symmetry in mathematics, symmetries as Motion (physics), motions, as opposed to discrete symmetry, e.g. reflection symmetry, which is invariant u ...

in the magnetic field strength of a

stellarator A stellarator is a plasma device that relies primarily on external magnets to confine a plasma. Scientists researching magnetic confinement fusion aim to use stellarator devices as a vessel for nuclear fusion reactions. The name refers to the ...

. Quasisymmetry is desired, as

Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in ...

implies that there exists a conserved quantity in such cases. This conserved quantity ensures that particles stick to the

flux surface In magnetic confinement fusion, a flux surface is a surface on which magnetic field lines lie. Since the magnetic field is divergence-free (and magnetic nulls are undesirable), the Poincare-Hopf theorem implies that such a surface must be either ...

, resulting in better confinement and

neoclassical transport Neoclassical transport, also known as neoclassical diffusion and often associated with banana orbits, is a type of diffusion seen in fusion power reactors that have an overall toroidal layout (like a donut). It is a modification of classical diffu ...

. It is currently unknown if it is mathematically possible to construct a quasi-symmetric magnetic field which upholds

magnetohydrodynamic Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, ...

force balance, which is required for stability. There are stellarator designs which are very close to being quasisymmetric, and it is possible to find solutions by generalizing the magnetohydrodynamic force balance equation.{{Cite journal , last1=Rodríguez , first1=E. , last2=Bhattacharjee , first2=A. , date=January 2021 , title=Solving the problem of overdetermination of quasisymmetric equilibrium solutions by near-axis expansions. I. Generalized force balance , url=http://aip.scitation.org/doi/10.1063/5.0027574 , journal=Physics of Plasmas , language=en , volume=28 , issue=1 , pages=012508 , doi=10.1063/5.0027574 , arxiv=2008.04715 , bibcode=2021PhPl...28a2508R , s2cid=221095564 , issn=1070-664X Quasisymmetric systems are a

subset In mathematics, Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are ...

of omnigenous systems. The

Helically Symmetric eXperiment The Helically Symmetric Experiment (HSX, stylized as Helically Symmetric eXperiment), is an experimental plasma confinement device at the University of Wisconsin–Madison, with design principles that are intended to be incorporated into a fusion ...

and the

National Compact Stellarator Experiment The National Compact Stellarator Experiment, NCSX in short, was a magnetic fusion energy experiment based on the stellarator design being constructed at the Princeton Plasma Physics Laboratory (PPPL). NCSX was one of a number of new stellarator d ...

are designed to be quasisymmetric.

References

Magnetic confinement fusion