  Recently-proposed tokamak concepts use magnetic fields up to 12 T, far higher
than in conventional devices, to reduce size and cost. Theoretical and
computational study of trends in plasma behavior with increasing field strength
is critical to such proposed devices. This paper considers trends in Alfv\'en
eigenmode (AE) stability. Energetic particles, including alphas from D-T
fusion, can destabilize AEs, possibly causing loss of alpha heat and damage to
the device. AEs are sensitive to device magnetic field via the field dependence
of resonances, alpha particle beta, and alpha orbit width. We describe the
origin and effect of these dependences analytically and by using
recently-developed numerical techniques (Rodrigues et al. 2015 Nucl. Fusion 55
083003). The work suggests high-field machines where fusion-born alphas are
sub-Alfv\'enic or nearly sub-Alfv\'enic may partially cut off AE resonances,
reducing growth rates of AEs and the energy of alphas interacting with them.
High-field burning plasma regimes have non-negligible alpha particle beta and
AE drive, but faster slowing down time, provided by high electron density, and
higher field strength reduces this drive relative to low-field machines with
similar power densities. The toroidal mode number of the most unstable modes
will tend to be higher in high magnetic field devices. The work suggests that
high magnetic field devices have unique, and potentially advantageous, AE
instability properties at both low and high densities.
