Attosecond bursts of coherent synchrotronlike radiation are found when driving ultrathin relativistic electron disks in a quasi-one-dimensional regime of wakefield acceleration, in which the laser waist is larger than the wake wavelength. The disks of overcritical density shrink radially due to focusing wakefields, thus providing the transverse currents for the emission of an intense, radially polarized, half-cycle pulse of about 100 attoseconds in duration. The electromagnetic pulse first focuses to a peak intensity (7×10(20)W/cm(2)) 10 times larger than the driving pulse and then emerges as a conical beam. Basic dynamics of the radiative process are derived analytically and in agreement with particle-in-cell simulations. By making use of gas targets instead of solids to form the ultrathin disks, this method allows for high repetition rates required for applications.