  Magnetic energy around compact objects often dominates over plasma rest mass,
and its dissipation can power the object luminosity. We describe a dissipation
mechanism which works faster than magnetic reconnection. The mechanism involves
two strong Alfv\'en waves with anti-aligned magnetic fields $\boldsymbol{B}_1$
and $\boldsymbol{B}_2$ that propagate in opposite directions along background
magnetic field $\boldsymbol{B}_0$ and collide. The collision forms a thin
current sheet perpendicular to $\boldsymbol{B}_0$, which absorbs the incoming
waves. The current sheet is sustained by electric field $\boldsymbol{E}$
breaking the magnetohydrodynamic condition $E<B$ and accelerating particles to
high energies. We demonstrate this mechanism with kinetic plasma simulations
using a simple setup of two symmetric plane waves with amplitude
$A=B_1/B_0=B_2/B_0$ propagating in a uniform $\boldsymbol{B}_0$. The mechanism
is activated when $A>1/2$. It dissipates a large fraction of the wave energy,
$f=(2A-1)/A^2$, reaching $100\%$ when $A=1$. The plane geometry allows one to
see the dissipation process in a one-dimensional simulation. We also perform
two-dimensional simulations, enabling spontaneous breaking of the plane
symmetry by the tearing instability of the current sheet. At moderate $A$ of
main interest the tearing instability is suppressed. Dissipation transitions to
normal, slower, magnetic reconnection at $A\gg 1$. The fast dissipation
described in this paper may occur in various objects with perturbed magnetic
fields, including magnetars, jets from accreting black holes, and pulsar wind
nebulae.
