4.5 Derivatives

Since the coordinate system is defined we can derive the expressions for the derivatives in (??)

where Y = . The derivatives of the index of refraction are computed using (??) and (??) using N = kc∕ω and

(51)

. The equilibrium properties are by definition function of only such that

(52)

and since β_Ts is independent of ω

(53)

Since we consider a constant axisymmetric equilibrium

The the temperature and density are flux coordinates such that

(56)

and we are left with calculating numerically

(57)

Explicit expressions for these derivatives are found in Appendix 1.2.