TY - JOUR

T1 - The ideal MHD stability of line-tied coronal loops: A truncated Fourier series approach

AU - de Bruyne, P.

AU - Velli, M.

AU - Hood, A. W.

PY - 1990/5/1

Y1 - 1990/5/1

N2 - The stability behaviour of a line-tied cylindrically symmetric coronal
loop is investigated using a general method presented by Velli, Einaudi
and Hood. The plasma perturbation in the linearised equation of motion
is expanded in a truncated Fourier series in the poloidal and axial
directions, and the resulting system of ordinary differential equations
for the radial displacement is solved as an eigenvalue problem. The
eigenvalue, be it the critical loop length or the growth rate, is found
to converge rapidly with the order of the truncation (approximately as
N-2, where N is the number of terms in the Fourier series).
Results for the non-force-free uniform-twist field of Gold and Hoyle are
presented and compared with a previous study based on the energy
principle. The instability threshold for the m = 1 kink mode and the m =
∞ balloning mode are found to be of the same order of magnitude
when substantial pressure gradients are present. Preliminary results for
higher-m modes indicate that they yield instability thresholds
comparable to the ballooning threshold for smaller gradients too.

AB - The stability behaviour of a line-tied cylindrically symmetric coronal
loop is investigated using a general method presented by Velli, Einaudi
and Hood. The plasma perturbation in the linearised equation of motion
is expanded in a truncated Fourier series in the poloidal and axial
directions, and the resulting system of ordinary differential equations
for the radial displacement is solved as an eigenvalue problem. The
eigenvalue, be it the critical loop length or the growth rate, is found
to converge rapidly with the order of the truncation (approximately as
N-2, where N is the number of terms in the Fourier series).
Results for the non-force-free uniform-twist field of Gold and Hoyle are
presented and compared with a previous study based on the energy
principle. The instability threshold for the m = 1 kink mode and the m =
∞ balloning mode are found to be of the same order of magnitude
when substantial pressure gradients are present. Preliminary results for
higher-m modes indicate that they yield instability thresholds
comparable to the ballooning threshold for smaller gradients too.

U2 - 10.1016/0010-4655(90)90155-T

DO - 10.1016/0010-4655(90)90155-T

M3 - Article

VL - 59

SP - 55

EP - 59

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 1

ER -