Ideal MHD limits to beta and bootstrap fraction are computed for pressure profiles
similar to those of JET discharges with both internal and H mode transport barriers.
Several non-monotonic current profiles are tested, and the pressure profile is constrained
so that no negative current drive is required in steady state. Calculations are made both
with and without an ideally conducting wall. The main result is that, for such peaked
pressure profiles, the limits to beta and bootstrap fraction improve at low internal
inductance, in particular when wall stabilization is taken into account. The highest
limits to beta, and often also to normalized beta, occur for the maximum plasma
current. There is also a weak dependence on qmin, for which three favourable
regions have been identified. A highly advantageous region is found at qmin ≃ 1.6,
where the limits to β* are 7.0% with, and 4.8% without, wall stabilization.
The corresponding limits are 68 and 50%, respectively, for the bootstrap fraction and 4.0 and 2.9 for the
normalized beta. These equilibria have low internal inductance, li = 0.62. For higher
inductance, an optimum occurs when qmin ≃ 1.2, where the limit to β* is 5.3%
with a wall and 4.7% without. The corresponding bootstrap fractions are about 46 and 38%, respectively.
A third type of equilibrium that is interesting for steady state operation
has qmin ≃ 2.1 and low inductance. Here the β* limits are lower, 4.9 and 3.4%,
but the bootstrap fractions are higher, 77 and 60%.