High-voltage transformers can be built with coaxial transmission lines. This paper describes a transformer design that uses the coaxial screen as primary winding and the inner conductor as secondary. An advantage of transmission line transformers is that the insulation problem is solved and the construction can be kept simple; the coupling between the primary and secondary coils is high even though the transformer uses an air core. The air core brings another advantage: the capacity to store large quantities of magnetic energy. The combination of a high coupling factor and large energy storage capacity makes this transformer ideal for charging high-voltage capacitors fast. The winding type for the transformer is alternating Archimedean spirals. Here, we present a magnetic field analysis of the transformer's primary, secondary, and mutual inductance using a finite-element solver. We compare the measured magnetic flux density versus the calculated value. The step-up winding ratio of the transformer influences the coupling factor marginally if the construction has an even number of spiral layers for each set of windings. However, the result from the finite-element solver predicts a drop in coupling factor if the step-up transformer construction has an odd number of spiral layers. The copper conductors used in the transformer resemble isotropic copper pipes.