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Dislocations are topological defects known to be crucial in the onset ofplasticity and in many properties of crystals. Classical Elasticity still failsto fully explain their dynamics under extreme conditions of high straingradients and small scales, which can nowadays be scrutinized. In suchconditions, corrections to the Volterra dislocation fields and to thePeach-Koehler force, for example, become relevant. One way to go beyond theVolterra solution is to consider other terms in the total Laurent seriessolution. This is the so called core field. One of its consequences is topredict a driving force on the dislocation due to background strain/stressgradients, which has also been suggested by other core energy calculations.Here we confirm its existence by presenting a direct observation of straingradients driving edge dislocations in 2D atomistic simulations. We show that,in systems with scale invariance, the results for such core force can be usedto obtain the total core energy, allowing a standard value for this energy tobe compared with other classical methods of obtaining it. The force measured inour system differs from the prediction obtained by a direct core fieldanalysis. Moreover, we found that higher order gradients of strains can alsoact as relevant forces.

Driving forces on dislocations due to strain gradients and higher order gradients