Few academic applications exist for viewing the sun in Hydrogen Beta, as this lower wavelength light represents a lower energy level. The view through Hydrogen Beta, however provides an interesting and contrasted view vs. Hydrogen Alpha.
The Hydrogen Beta line is narrower than the Hydrogen Alpha line. The H-alpha line is 0.8Å wide, whereas the H-beta is approximately 0.5Å wide. Therefore, in order to extinct unwanted continuum of the surrounding solar spectrum, a narrower equivalent bandpass would be required.