At the most fundamental level, the dynamics of each plasma species is governed by the *kinetic equation* [18]:

Equation (2.1) describes plasma dynamics in a six-dimensional space (three spatial dimensions, and
three velocity-space dimensions); as such, it is extremely difficult equation to solve. For dynamics that takes place on timescales
that are long compared to the inverse ion gyro-frequency, which certainly applies to tearing mode dynamics in tokamak plasmas, the equation can be simplified by averaging
over the gyro-motions of charged particles [7,9,25]. The resulting *gyro-kinetic equation* is
only five-dimensional (three spatial dimensions, and
two velocity-space dimensions). The electron and ion gyro-kinetic equations have been used extensively to numerically model plasma turbulence in tokamaks [23,39,50].
It turns out that this is possible because turbulent eddies are localized on toroidal magnetic flux-surfaces in flux-tubes that run parallel to the magnetic field and whose
radial extents are, at most, a few ion gyro-radii. Moreover, the eddies attain a quasi-steady-state in a matter of a few milliseconds.
Hence, despite the high dimensionalities of the gyro-kinetic equations, it is practical to solve them in calculations that only simulate a small fraction of the plasma volume over a time interval of a few milliseconds. Now,
tearing modes are *global* plasma instabilities that evolve on timescales that are hundreds, if not thousands, of milliseconds. Unfortunately, it is simply not practical to simulate the whole plasma over a time interval of a few hundred to a few thousand milliseconds using the gyro-kinetic equations. Hence, a different approach is needed to describe tearing mode dynamics. In fact, the only
practical option is to employ fluid theory.