Tokamaks with large pressure gradients (alpha(max)) formed in regions of weak magnetic shear are shown to be susceptible to novel, low-n, global, kinetic, electromagnetic modes with a toroidal mode number n in the range 2 <= n <= 12. For a weakly varying monotonic safety factor profile q with its minimum q(min)> 1 on the magnetic axis and alpha(max) near q(min), new, global kinetic infernal modes with a strong mode rotation omega(r) and a finite growth rate gamma