  The existence and ballooning-stability of low aspect ratio stellarator
equilibria is predicted for CNT with the aid of 3D numerical tools. In addition
to having a low aspect ratio, CNT is characterized by a low magnetic field and
small plasma volume. Also, highly overdense plasmas were recently heated in CNT
by means of microwaves. These characteristics suggest that CNT might attain
relatively high values of plasma $\beta$ and thus be of use in the experimental
study of stellarator stability to high-$\beta$ instabilities such as ballooning
modes. As a first step in that direction, here the ballooning stability limit
is found numerically. Depending on the particular magnetic configuration we
expect volume-averaged $\beta$ limits in the range 0.9-3.0%, and possibly
higher, and observe indications of a second region of ballooning stability. As
the aspect ratio is reduced, stability is found to increase in some
configurations and decrease in others. Energy-balance estimates using
stellarator scaling laws indicate that the lower $\beta$ limit may be
attainable with overdense heating at powers of of 40 to 100 kW. The present
study serves the additional purpose of testing VMEC and other stellarator codes
at high values of $\beta$ and at low aspect ratios. For this reason, the study
was carried out both for free boundary, for maximum fidelity to experiment, as
well as with a fixed boundary, as a numerical test.
