  Radio U-bursts and J-bursts are signatures of electron beams propagating
along magnetic loops confined to the corona. The more commonly observed type
III radio bursts are signatures of electron beams propagating along magnetic
loops that extend into interplanetary space. Given the prevalence of solar
magnetic flux to be closed in the corona, it is an outstanding question why
type III bursts are more frequently observed than U-bursts or J-bursts. We use
LOFAR imaging spectroscopy between 30-80 MHz of low-frequency U-bursts and
J-bursts, for the first time, to understand why electron beams travelling along
coronal loops produce radio emission less often. The different radio source
positions were used to model the spatial structure of the guiding magnetic flux
tube and then deduce the energy range of the exciting electron beams without
the assumption of a standard density model. The radio sources infer a magnetic
loop 1 solar radius in altitude, with the highest frequency sources starting
around 0.6 solar radii. Electron velocities were found between 0.13 c and 0.24
c, with the front of the electron beam travelling faster than the back of the
electron beam. The velocities correspond to energy ranges within the beam from
0.7-11 keV to 0.7-43 keV. The density along the loop is higher than typical
coronal density models and the density gradient is smaller. We found that a
more restrictive range of accelerated beam and background plasma parameters can
result in U-bursts or J-bursts, causing type III bursts to be more frequently
observed. The large instability distances required before Langmuir waves are
produced by some electron beams, and the small magnitude of the background
density gradients make closed loops less facilitating for radio emission than
loops that extend into interplanetary space.
