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[Abridged] We present an 8.5-hour simultaneous radio, X-ray, UV, and opticalobservation of the L dwarf binary 2MASSW J0746+20. We detect strong radioemission, dominated by short-duration periodic pulses at 4.86 GHz withP=124.32+/-0.11 min. The stability of the pulse profiles and arrival timesdemonstrates that they are due to the rotational modulation of a B~1.7 kGmagnetic field. A quiescent non-variable component is also detected, likely dueto emission from a uniform large-scale field. The H-alpha emission exhibitsidentical periodicity, but unlike the radio pulses it varies sinusoidally andis offset by exactly 1/4 of a phase. The sinusoidal variations requirechromospheric emission from a large-scale field structure, with the radiopulses likely emanating from the magnetic poles. While both light curves can beexplained by a rotating mis-aligned magnetic field, the 1/4 phase lag rules outa symmetric dipole topology since it would result in a phase lag of 1/2(poloidal field) or zero (toroidal field). We therefore conclude that either(i) the field is dominated by a quadrupole configuration, which can naturallyexplain the 1/4 phase lag; or (ii) the H-alpha and/or radio emission regionsare not trivially aligned with the field. Regardless of the field topology, weuse the measured period along with the known rotation velocity (vsini=27 km/s),and the binary orbital inclination (i=142 deg), to derive a radius for theprimary star of 0.078+/-0.010 R_sun. This is the first measurement of theradius of an L dwarf, and along with a mass of 0.085+/-0.010 M_sun it providesa constraint on the mass-radius relation below 0.1 M_sun. We find that theradius is about 30% smaller than expected from theoretical models, even for anage of a few Gyr.

Periodic Radio and H-alpha Emission from the L Dwarf Binary 2MASSW J0746425+200032: Exploring the Magnetic Field Topology and Radius of an L Dwarf