1 - Nuclear Sciences and Applications - IAEA

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MOREAU et al.
FIG. 1. Modulus of the radial component of the electric field near the magnetic axis (m = 1,
n = 550).
3. COUPLED MODE EQUATION AND RANDOM PHASE
APPROXIMATION
Another approach to this small wavelength, full wave problem is to assume that
the number of unknowns is so large that it can be treated statistically [2]. The first
step towards such a statistical processing is to project Eq. (1) on a basis of cylindrical
functions:
f,m,n
For given n, the toroidal effects induce coupling between the
and Eq. (1) becomes
r,m'
mode amplitudes,
arm'(t) (3)
where w(f,m) is the dispersion relation (Fig. 2), and the matrix elements V^V are
proportional to e |m " m| (e = a/R) and rapidly decreasing with \l—t'\. This
coupling is effective only if it is resonant, i.e. if it couples modes (£,m), (