B342 Stability limits

The spheromak is generally considered a low-beta configuration. However, experimental values of beta in excess of 20% have been obtained above the Mercier limit (i.e., the beta limit for flute-like interchange modes [Jarboe, 1994]). The most important unstable modes are briefly summarized below:

— Tilt mode. The dipole moment of a spheromak in a vertical field is anti-parallel to the magnetic field. Hence, in a uniform magnetic field the spheromak will tend to flip its axis to make the dipole moment parallel to the vertical field. The mode can be stabilized in a mirror field, but then the shift mode becomes unstable. If equilibrium is provided by the flux conserver, instead of a vertical field, the axisymmetric solution is stable for oblate flux conservers (i.e., for a cylindrical flux conserver, if the length of the cylinder is lower than 1.67 times the radius).

— Current-driven modes. Current-driven modes may become unstable when the J / B radial profile (J is the current density component parallel to the equilibrium field) departs from a constant that corresponds to the minimum energy state predicted by theory: J = AB from Equation (B.37). Internal current-driven modes have been observed in good agreement with theoretical predictions.

— Pressure-driven modes. The spheromak has unfavorable flux surface averaged curvature everywhere. Ideal interchange instability can arise if the Mercier criterion is violated.

It should be noted that many spheromaks have been modified by inserting a central conductor, making this configuration evolve towards a (ultra) low-aspect-ratio tokamak. Such a modification is especially beneficial to stabilize the tilt mode (which is opposed by the presence of a central conductor). Whether such a modified topology can still be of interest for space propulsion is a matter that should be further investigated.

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