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The stability of current-driven external-kink modes is investigated in a tokamak plasma surrounded by an external shell of finite electrical conductivity. According to conventional theory, the ideal mode can be stabilized by placing the shell sufficiently close to the plasma, but the non-rotating 'resistive shell mode', which grows as the characteristic L / R time of the shell, always persists. It is demonstrated, using both analytic and numerical techniques, that a combination of strong edgedoi:10.1088/0029-5515/36/1/i02 fatcat:bykli7digbaobkdkrlcioauwby