Since from Maxwell's equations (specifically Gauss's law for magnetism) magnetic fields are divergenceless, magnetic flux tubes have this property, so flux tubes are mainly used as an aid in visualizing magnetic fields. However flux tubes can also be useful for visualizing other vector fields in regions of zero divergence, such as electric fields in regions where there are no charges and gravitational fields in regions where there is no mass. In particle physics, the hadron particles that make up all matter, such as neutrons and protons, are composed of more basic particles called quarks, which are bound together by thin flux tubes of strong nuclear force field. The flux tube model is important in explaining the so-called color confinement mechanism, why quarks are never seen separately in particle experiments. In 1861, James Clerk Maxwell gave rise to the concept of a flux tube inspired by Michael Faraday's work in electrical and magnetic behavior in his paper titled "On Physical Lines of Force". Maxwell described flux tubes as:"If upon any surface which cuts the lines of fluid motion we draw a closed curve, and if from every point of this curve we draw lines of motion, these lines of motion will generate a tubular surface which we may call a "tube of fluid motion."" The flux tube's strength, formula_2, is defined to be the magnetic flux through a surface formula_11 intersecting the tube, equal to the surface integral of the magnetic field formula_12 over formula_11 Since the magnetic field is solenoidal, as defined in Maxwell's equations (specifically Gauss' law for magnetism): formula_15. the strength is constant at any surface along a flux tube. Under the condition that the cross-sectional area, formula_16, of the flux tube is small enough that the magnetic field is approximately constant, formula_2 can be approximated as formula_18. Therefore if the cross sectional area of the tube decreases along the tube from formula_19 to formula_20, then the magnetic field strength must increase proportionally from formula_21 to formula_22 in order to satisfy the condition of constant flux F. From the condition of perfect conductivity in ideal Ohm's Law, (formula_24), in ideal magnetohydrodynamics, the change in magnetic flux, formula_25, is zero in a flux tube, known as Alfvén's Theorem of flux conservation. With flux conservation, the topology of the flux tube does not change. This effect arises when there is a high Magnetic Reynolds number, Rm » 1, where induction dominates and diffusion is neglected, allowing for the magnetic field to follow the flow of the plasma resulting in "frozen-in" flux.formula_26where formula_27The rate of change of the magnetic flux is given by:formula_28  In ideal magnetohydrodynamics, if a cylindrical flux tube of length L0 is compressed while the length of tube stays the same, the magnetic field and the density of the tube increase with the same proportionality.