The damping of compressional Alfven waves is studied for magnetic configurations that harbor a cusp, i.e., a three-dimensional magnetic null. The objective is to determine the quality factor Q, the ratio of the oscillation frequency to the damping rate. By a numerical solution of the resistive MHD equations in the cusp geometry, it is established that the Q is of order ln [S], where S is the Lundquist number. The result constitutes a generalization of recent findings that show that the Q for two-dimensional magnetic null configurations is of order ln-[S], and suggests extremely efficient conversion of Alfvenic wave energy to heat in magnetic wave configurations incorporating null points. Implications for coronal heating and magnetospheric cusps are discussed.
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