A part of a flux surface (yellow), and the magnetic axis (black). The magnetic flux passing through the red and blue surface is called the poloidal and toroidal flux, respectively. There is furthermore a rational magnetic field line (green) on 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 a torus, or a knot. In the tokamak and the stellarator flux surfaces have toroidal shapes, whereas the more exotic knotatron[1] has a knotted flux surface. Flux surfaces are typically characterized by the poloidal magnetic flux or the toroidal magnetic flux. The poloidal flux is the magnetic flux passing through a ribbon going from the magnetic axis (the centre of the device) to the flux surface, and the toroidal flux is the magnetic flux passing through a circle which encloses the magnetic axis. The total flux passing through flux surface itself is zero, as magnetic field lines are everywhere tangent to the surface.
Flux surfaces can either be rational or irrational, depending on the behavior of magnetic field lines on the flux surface. Rational surfaces have magnetic field lines are which are periodic; the magnetic field line closes back on itself. Conversely irrational surfaces have magnetic field lines which do not close back on themselves, and a magnetic field line traces out the entire flux surface (the magnetic field line comes arbitrarily close to each point on the flux surface). Rational magnetic surfaces are very sensitive to perturbations and can degenerate into magnetic islands.[2][3] Flux surfaces are not guaranteed to exist; the magnetic field line can fill a volume chaotically.[4] The theory of magnetic field lines in toroidal systems is closely related to the theory of 2-dimensional Hamiltonian systems.[5]
^Hudson, S. R.; Startsev, E.; Feibush, E. (January 2014). "A new class of magnetic confinement device in the shape of a knot". Physics of Plasmas. 21 (1): 010705. Bibcode:2014PhPl...21a0705H. doi:10.1063/1.4863844. ISSN 1070-664X.
^Hegna, Chris C.; Bhattacharjee, A. (February 1989). "Magnetic island formation in three-dimensional plasma equilibria". Physics of Fluids B: Plasma Physics. 1 (2): 392–397. Bibcode:1989PhFlB...1..392H. doi:10.1063/1.859152. ISSN 0899-8221.
^Smolyakov, A. I.; Hirose, A.; Lazzaro, E.; Re, G. B.; Callen, J. D. (May 1995). "Rotating nonlinear magnetic islands in a tokamak plasma". Physics of Plasmas. 2 (5): 1581–1598. Bibcode:1995PhPl....2.1581S. doi:10.1063/1.871308. ISSN 1070-664X.
^Sugimoto, H; Kurasawa, T; Ashida, H (March 1, 1994). "Stochastic diffusion of magnetic field lines". Plasma Physics and Controlled Fusion. 36 (3): 383–402. Bibcode:1994PPCF...36..383S. doi:10.1088/0741-3335/36/3/002. ISSN 0741-3335. S2CID 250897544.
^Morrison, P. J. (June 2000). "Magnetic field lines, Hamiltonian dynamics, and nontwist systems". Physics of Plasmas. 7 (6): 2279–2289. Bibcode:2000PhPl....7.2279M. doi:10.1063/1.874062. ISSN 1070-664X.
In magnetic confinement fusion, a fluxsurface is a surface on which magnetic field lines lie. Since the magnetic field is divergence-free (and magnetic...
electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted...
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied...
the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small. Heat flux is often...
In electromagnetism, electric flux is the measure of the electric field through a given surface, although an electric field in itself cannot flow. The...
component contributes to the flux. Based on this reasoning, to find the flux, we need to take the dot product of v with the unit surface normal n to S at each...
radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power...
In radiometry, irradiance is the radiant flux received by a surface per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The...
the flux leaving the volume through these two surfaces will be zero, so the flux leaving through S 2 {\displaystyle S_{2}} will be equal to the flux entering...
explosively pumped flux compression generator (EPFCG) is a device used to generate a high-power electromagnetic pulse by compressing magnetic flux using high...
Energy flux is the rate of transfer of energy through a surface. The quantity is defined in two different ways, depending on the context: Total rate of...
is only quadratic. Axial flux motors have a larger magnetic surface and overall surface area (for cooling) than radial flux motors for a given volume...
A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field...
Radiative flux, also known as radiative flux density or radiation flux (or sometimes power flux density), is the amount of power radiated through a given...
is, the component of mass flux passing through the surface (i.e. normal to it) is jm cos θ. While the component of mass flux passing tangential to the...
Ostrogradsky's theorem, is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed...
in which case the flux linkage is simply the flux passing through the loop. The flux Φ {\displaystyle \Phi } through the surface delimited by a coil...
critical heat flux (CHF) is the heat flux at which boiling ceases to be an effective form of transferring heat from a solid surface to a liquid. Boiling...
A heat flux sensor is a transducer that generates an electrical signal proportional to the total heat rate applied to the surface of the sensor. The measured...
{i} }}},} where Φer is the radiant flux reflected by that surface and Φei is the radiant flux received by that surface. The spectral hemispherical reflectance...
particles, which can circulate freely around the fluxsurface, are automatically confined to stay on a fluxsurface. For trapped particles, omnigeneity relates...
{i} }}},} where Φet is the radiant flux transmitted by that surface; Φei is the radiant flux received by that surface. Spectral hemispherical transmittance...
law. Volumetric flux is not to be confused with volumetric flow rate, which is the volume of fluid that passes through a given surface per unit of time...
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