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Studies have shown that emission of gravitational wave drives an instabilityin the $r$-modes of young rapidly rotating neutron stars carrying away most ofthe angular momentum through gravitational wave emission in the first year orso after their formation. Magnetic field plays a crucial role in the evolutionof these $r$-modes and hence the evolution of the neutron star itself. Anattempt is made here to investigate the role of magnetic field in the evolutionof $r$-mode instability and detectibility of gravitational waves emitted by anewly born, hot and rapidly and differentially rotating neutron star. It isfound that magnetic field tend to suppress the $r$-mode amplitude. The {\itsignal-to-noise ratio} analysis shows that gravitational waves emitted from the$r$-mode instability from neutron stars with magnetic fields upto the order of$10^{14}$ gauss may be detectable by the Advanced LIGO at 20 Mpc.

Gravitational Waves from the $r$-mode instability of neutron stars: effect of magnetic field