We report the discovery of two systems of cyclotron emisson lines in p
hase-resolved low-resolution spectra of the recently discovered AM Her
culis binary RXJ 1938.6-4612. The fieldstrengths inferred are B-1 simi
lar or equal to 47 MG and B-2 similar or equal to 70-80 MG, which migh
t be indicative of a non-dipolar field structure. The latter value is
the highest found so far for white dwarfs in cataclysmic variables. We
present a spectroscopic ephemeris of sufficient accuracy to connect o
ur optical and ROSAT All Sky Survey X-ray observations separated by a
few years. Using this, the X-ray bright accretion spot which is visibl
e for less than 40% of the binary cycle may be identified with the low
-field accretion region. The high-field spot dominates the optical lig
htcurve. We find slight evidence for a quadratic term in the ephemeris
, P = (-3.4+/-2.1) x 10(-9). Low-state spectra reveal M-star features,
Zeeman absorption troughs from the white dwarf and cyclotron emission
lines originating in the high-field region. Photospheric Zeeman model
s using a slightly decentered dipole along the axis, z(off) similar or
equal to 0.1 R(wd), B-pole similar or equal to 60 MG, fit some absorp
tion features in the blue spectral range and confirm the results of hi
gh-state cyclotron spectroscopy. The implied distance to RXJ 1938.6-46
12 is similar to 150-190 pc.