  Deterministic models for radiation transport describe the density of
radiation particles moving through a background material. In radiation therapy
applications, the phase space of this density is composed of energy, spatial
position and direction of flight. The resulting six-dimensional phase space
prohibits fine numerical discretizations, which are essential for the
construction of accurate and reliable treatment plans. In this work, we tackle
the high dimensional phase space through a dynamical low-rank approximation of
the particle density. Dynamical low-rank approximation (DLRA) evolves the
solution on a low-rank manifold in time. Interpreting the energy variable as a
pseudo-time lets us employ the DLRA framework to represent the solution of the
radiation transport equation on a low-rank manifold for every energy. Stiff
scattering terms are treated through an efficient implicit energy
discretization and a rank adaptive integrator is chosen to dynamically adapt
the rank in energy. To facilitate the use of boundary conditions and reduce the
overall rank, the radiation transport equation is split into collided and
uncollided particles through a collision source method. Uncollided particles
are described by a directed quadrature set guaranteeing low computational
costs, whereas collided particles are represented by a low-rank solution. It
can be shown that the presented method is L$^2$-stable under a time step
restriction which does not depend on stiff scattering terms. Moreover, the
implicit treatment of scattering does not require numerical inversions of
matrices. Numerical results for radiation therapy configurations as well as the
line source benchmark underline the efficiency of the proposed method.
