  In recent years, arrays of atomic ions in a linear RF trap have proven to be
a particularly successful platform for quantum simulation. However, a wide
range of quantum models and phenomena have, so far, remained beyond the reach
of such simulators. In this work we introduce a technique that can
substantially extend this reach using an external field gradient along the ion
chain and a global, uniform driving field. The technique can be used to
generate both static and time-varying synthetic gauge fields in a linear chain
of trapped ions, and enables continuous simulation of a variety of coupling
geometries and topologies, including periodic boundary conditions and high
dimensional Hamiltonians. We describe the technique, derive the corresponding
effective Hamiltonian, propose a number of variations, and discuss the
possibility of scaling to quantum-advantage sized simulators. Additionally, we
suggest several possible implementations and briefly examine two: the
Aharonov-Bohm ring and the frustrated triangular ladder.
