  The effect of a magnetic field on the characteristics of capacitively coupled
radio frequency discharges is investigated and found to be substantial. A
one-dimensional particle-in-cell simulation shows that geometrically symmetric
discharges can be asymmetrized by applying a spatially inhomogeneous magnetic
field. This effect is similar to the recently discovered electrical asymmetry
effect. Both effects act independently, they can work in the same direction or
compensate each other. Also the ion energy distribution functions at the
electrodes are strongly affected by the magnetic field, although only
indirectly. The field influences not the dynamics of the sheath itself but
rather its operating conditions, i.e., the ion flux through it and voltage drop
across it. To support this interpretation, the particle-in-cell results are
compared with the outcome of the recently proposed ensemble-in-spacetime
algorithm. Although that scheme resolves only the sheath and neglects
magnetization, it is able to reproduce the ion energy distribution functions
with very good accuracy, regardless of whether the discharge is magnetized or
not.
