Solution of Plasma Angular Equations of Motion
In many situations of interest, the perturbed angular velocity profiles,
and
, are
localized in the vicinity of the rational surface [4]. Hence, it is reasonable to express the perturbed angular
equations of motion, (3.161) and (3.165), in the simplified forms
where
,
, and
.
Let us write [3,5]
where
Here, is a Bessel function, and denotes its th zero [1]. Note that
Equations (3.170)–(3.173) automatically satisfy the boundary conditions (3.166) and (3.167).
It is easily demonstrated that [13]
and
Equations (3.139), (3.140), and (3.168)–(3.177) yield
Here,

(3.180) 
is the momentum confinement time,

(3.181) 
is the Alfvén time,

(3.182) 
is the inverse aspectratio of the rational surface, and