WKB ESTIMATES FOR THE ONSET OF IDEAL MHD INSTABILITIES IN SOLAR CORONAL LOOPS

A WKB approach, based on the method of Connor, Hastie, and Taylor (197 9), is used to obtain simple estimates of the critical conditions for the onset of ideal MHD instabilities in line-tied solar coronal loops. The method is illustrated for the constant twist, Gold-Hoyle (1960) f ield, and the critical conditions are compared with previous and new n umerical results. For the force-free case, the WKB estimate for the cr itical loop length reduces to 2pim + square-root 2 pi. For the suffici ently non-force-free case the critical length can be expressed in the form l0 + l1/m. The results confirm the findings of De Bruyne and Hood (1992) that for force-free fields the m = 1 mode is die first mode to become unstable but for the sufficiently strong non-force-free case t his reverses with the m --> infinity mode being excited first.