is simply an velocity, so where is the out-of-plane electric field, is the characteristic inflow velocity, and is the characteristic upstream magnetic field strength. By neglecting displacement current, the low-frequency Ampere's law, , gives the relation where is the current sheet half-thickness. This relation uses that the magnetic field reverses over a distance of . By matching the ideal electric field outside of the layer with the resistive electric field inside the layer (using Ohm's law), we find that where is the magnetic diffusivity. When the inflow density is comparable to the outflow density, conservation of mass yields the relationship where is the half-length of the current sheet and is the outflow velocity. The left and right hand sides of the above relation represent the mass flux into the layer and out of the layer, respectively. Equating the upstream magnetic pressure with the downstream dynamic pressure gives where is the mass density of the plasma. Solving for the outflow velocity then gives where is the Alfvén velocity. With the above relations, the dimensionless reconnection rate can then be written in two forms, the first in terms of using the result earlier derived from Ohm's law, the second in terms of from the conservation of mass as Since the dimensionless Lundquist number is given by the two different expressions of are multiplied by each other and then square-rooted, giving a simple relation between the reconnection rate and the Lundquist number Sweet–Parker reconnection allows for reconnection rates much faster than global diffusion, but is not able to explain the fast reconnection rates observed in solar flares, the Earth's magnetosphere, and laboratory plasmas. Additionally, Sweet–Parker reconnection neglects three-dimensional effects, collisionless physics, time-dependent effects, viscosity, compressibility, and downstream pressure. Numerical simulations of two-dimensional magnetic reconnection typically show agreement with this model. Results from the Magnetic Reconnection Experiment (MRX) of collisional reconnection show agreement with a generalized Sweet–Parker model which incorporates compressibility, downstream pressure and anomalous resistivity. Fast reconnection: Petschek model The fundamental reason that Petshek reconnection is faster than Parker-Sweet is that it broadens the outflow region and thereby removes some of the limitation caused by the build up in plasma pressure. The inflow velocity, and thus the reconnection rate, can only be very small if the outflow region is narrow. In 1964, Harry Petschek proposed a mechanism where the inflow and outflow regions are separated by stationary slow mode shocks that stand in