Caption: Figure 4: Top: the stationary transmission clock time [t.sup.T.sub.c] (k) (blue) and the

wave number distribution [rho](k) = [[absolute value of (S(k))].sup.2] (orange, dashed, and arbitrary scale), for [V.sub.0] = 7, a = 1, b = 5, and [k.sub.0] [approximately equal to] 2.175932), with the initial state given by (18).

When the incident wave is of

wave number Ai, we have derived the energy balance relation as

For the threshold Alfveen Mach number of 4.062 we obtained one instability window and instability starts at the critical dimensionless

wave number of 1.944, or equivalently at [[lambda].sup.m=4.sub.cr] [congruent to] 8.0 Mm.

in which [k.sub.b] = [omega]/[[beta].sub.b] represents the shear

wave number of the shear wall.

where [mathematical expression not reproducible] are spectral current density amplitudes of electric and magnetic sources, respectively; [k.sub.[rho]] = [square root of ([k.sup.2.sub.0] - [k.sup.2.sub.z])] is the radial

wave number; b is the source radial distance.

The corresponding frequency for these dimensionless

wave numbers is [omega] = 154.83 rad/s.

Based on the dispersion relation, it is possible to determine the travelling

wave number under certain frequencies.

Averaged curves from 32 repeated scans were obtained between

wave numbers of 4,000 and 400 [cm.sup.-1].

We will use the discrete approximation with evenly spaced [[omega].sub.k] with spacing [[DELTA].sun.[omega]] and corresponding

wave numbers [[kappa].sub.k] given by the dispersion relation.

where k = [omega]/c = 4[square root of [zeta][[omega].sup.2]/[xi] is the

wave number.

The

wave number and radius update function determine how fast algorithm approaches to solution.

Comparing this with spectrum of pure FeNi [14], we can see that there is no peak in

wave number 2400 [cm.sup.-1] in pure FeNi, because there is no bond between Fe and Ni atoms in this condition and no optical mode excitation is expected.