Maximum Plasma Pressure for Stability in Magnetic Fields with Finite Minima

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Abstract
The maximum plasma pressure is discussed for stable containment in magnetic fields that possess a nonzero minimum in field strength, (minimum‐B fields or magnetic wells). The basic limitations are ones on the pressure gradient and are calculated exactly for a special class of equilibria and more generally by an expansion procedure based on a shallow‐well approximation. Transcribed into estimates of the critical pressure itself, these results indicate a maximum pressure equal to the depth of the magnetic well. If B1 is the field strength at the largest closed |B| contour and B2 the field strength at the lowest point of the well, then p⊥max ≃ ½(B12 − B22).