We present the results of a search for short and intermediate-duration gravitational-wave signals from four magnetar bursts in Advanced LIGO's second observing run. We find no evidence of a signal and set upper bounds on the root sum squared of the total dimensionless strain (hrss) from incoming intermediate-duration gravitational waves ranging from 1.1 x 10-22 at 150 Hz to 4.4 x 10-22 at 1550 Hz at 50% detection efficiency. From the known distance to the magnetar SGR 1806-20 (8.7 kpc) we can place upper bounds on the isotropic gravitational wave energy of 3.4 x 1044erg at 150 Hz assuming optimal orientation. This represents an improvement of about a factor of 10 in strain sensitivity from the previous search for such signals, conducted during initial LIGO's sixth science run. The short duration search yielded upper limits of 2.1 x 1044erg for short white noise bursts, and 2.3 x 1047erg long ringdowns at 1500 Hz, both at 50% detection efficiency.
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