Initial accelerations of pulsars caused by external kicks

Using energy conservation we show that if a sudden external force of unknown nature causes a newborn pulsar of mass $M=1.4M_{\odot }$ and radius R=10 km to have the acceleration $a_0$ then we can derive the relation $a_0\simeq k^{-1}vB_0^{-2/3},$where$v$isthevelocityofthepulsar,$B_0$ its initial magnetic field and $k\approx {10}^{-17}$G${}^{-2\mathrm{/}3}$s. This relation predicts that a newborn pulsar with $v=450$ km experienced the acceleration $a_0\simeq {10}^{13}$g when $B_0\simeq {10}^{13}$G. An external force producing such an acceleration seems not to be physically feasible. This pulsar could have experienced the more realistic acceleration $a_0\simeq {10}^9$g if $B_0\simeq {10}^{18}$G. But this huge magnetic field seems to be unrealistic.