Linearized Reduced DriftMHD Equations
Let us now take the tearing mode perturbation into account. In accordance with Equations (5.22)–(5.25), and (5.30)–(5.31), we can write
where
, and is the rotation frequency of the tearing perturbation in the laboratory frame.
Here, denotes a perturbed quantity.
Substituting Equations (5.33)–(5.38) into the reduced driftMHD model, (5.8)–(5.13), and only retaining terms that
are first order in perturbed quantities, we obtain the following set of linear equations:
Here,

(5.43) 
is the hydromagnetic time,

(5.44) 
the
EcrossB frequency,

(5.45) 
the electron diamagnetic
frequency,
the ion diamagnetic
frequency,
the (total) diamagnetic frequency,

(5.48) 
the Lundquist number [note that this is a slightly different definition to that given in Equation (1.84)],

(5.49) 
the
resistive diffusion time [note that this is a slightly different definition to that given in Equation (1.83)],

(5.50) 
the toroidal momentum confinement time,

(5.51) 
the effective parallel energy equilibration time, and

(5.52) 
the effective energy confinement time.
Furthermore,