Spontaneous tearing instability of m=0 modes in the RFP

Standard RFP discharges in the Madison Symmetric Torus (MST) exhibit cyclic sawtooth oscillations associated with core (m=1, n=6,7) and edge (m=0, n=1) resonant tearing modes. It is believed that the core tearing modes are spontaneously unstable while linearly stable m=0 modes are nonlinearly driven by coupling to core resonant modes. This scenario of forced m=0 magnetic reconnection is based on robust linear stability properties demonstrated in the past by various $\Delta ^{\prime }$ calculations. These earlier results have indicated that the m=0 tearing mode is mainly stable. Recent MST experiments have shown[1] that in some regimes with improved plasma confinement the m=0 mode becomes linearly (spontaneously) unstable. This motivated our interest in revisiting the m=0 tearing mode analysis including a broader range of current profiles. We introduced a three-parameter cylindrical model which permits to vary the radial position and the width of the current gradient independently and found a wide class of unstable current profiles. We report on ideal MHD $\Delta ^{\prime }$ analysis as well as the results obtained from a cylindrical resistive eigenvalue code. [1] S.H.Choi et al., submitted to Phys. Rev. Lett.