  We present a design for producing precisely adjustable and alternating
single-axis magnetic fields based on nested Halbach dipole pairs consisting of
permanent magnets only. Our design allows for three dimensional optical and
mechanical access to a region with strong adjustable dipolar fields, is
compatible with systems operating under vacuum, and does not effectively
dissipate heat under normal operational conditions. We present a theoretical
analysis of the properties and capabilities of our design, and construct a
proof-of-concept prototype. Using our prototype, we demonstrate fields of up to
several kilogauss with field homogeneities of better than 5%, which are
harmonically modulated at frequencies of $\sim$1Hz with a power consumption of
approximately 1W. Moreover, we discuss how our design can be modified to
generate adjustable quadrupolar magnetic fields with gradients as large as
9.5T/m in a region of optical and mechanical access. Our design is scalable and
can be constructed to be suitable for table-top experiments, as in the case of
polarimetric and magnetometric setups that require strong alternating magnetic
fields, but also for large scale applications such as generators.
