Constrained resonance in magnetic self-organization

In a linear driven problem with integral constraints, resonant phenomena can still persist but occur away from the fundamental frequencies of the unconstrained linear system. The frequency and the mode structure of the constrained resonances are found to be the intrinsic properties of the undriven and unconstrained linear systems. This is shown with a Taylor-relaxed magnetized plasma in a torus that conserves the net toroidal flux. The constrained resonance leads to a number of modifications to the standard paradigm of Taylor relaxation in a toroidal plasma.