(Color online) WKB wave vector solutions for the following set of parameters, S = 2, Q = 4, λ = 10, and μ = 1.
(Color online) Diagram of various regions in complex y plane for the choices of various linear independent solutions as per Ref. 31. Dashed line corresponds to the integration path.
(Color online) Lowest mode number sweep down RSAE structures obtained using the shooting technique. Shown are the first (dashed), third (points), and fifth (solid line) RSAEs.
(Color online) Down sweep RSAE damping rate as a function of the collisonality parameter δ (in our case).
(Color online) Both real and imaginary parts of the RSAE solution corresponding to the “third” solution shown in Fig. 3. Its mode frequency in the normalized units is .
(Color online) RSAE eigenfrequency obtained from the analytical dispersion (dashed line), Eq. (31), and from numerical shooting technique simulations (solid lines). The differences between the eigenfrequencies and the continuum frequencies are shown on the left figure and the absolute value of RSAE eigenfrequencies are shown on the right figure. For the comparison, the TAE frequency in the normalized units is .
(Color online) Down sweep RSAE eigenfrequency (Eq. (31), q min = 2.02, (a)) and sweep bottom mode eigenfrequency (q min = 2, (b)) are compared with numerical simulations of the growth rates. Only the difference between the eigenfrequency and the continuum frequency at q min is shown. RSAE eigenfrequencies as computed with NOVA are shown as circles. A number of similar solutions were found with NOVA near the frequency range indicated with the vertical bars around the circles. The safety factor is q min = 2.02.
(Color online) Sweep bottom RSAE mode dominant harmonic radial structures computed using the shooting numerical scheme and using NOVA ideal MHD code, as indicated. (a),(b), and (c) correspond to three values w = 0.5, 0.9, 1,7, respectively, and q min = 2. The shooting scheme RSAE structures have both real and imaginary parts as indicated.
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