An analytical formulation of the nodal forces induced by a dislocation segment on a surface element is presented. The determination of such nodal forces is a critical step when associating dislocation dynamics simulations with continuum approaches to simulate the plastic behaviour of finite domains. The nodal force calculation starts from the infinite-domain stress field of a dislocation and involves a triple integration over the dislocation ensemble and over the surface element at the domain boundary. In the case of arbitrary oriented straight segments of dislocations and a linear rectangular surface element, the solution is derived by means of a sequence of integrations by parts that present specific recurrence relations. The use of the non-singular expression for the infinite-domain stress field ensures that the traction field is finite everywhere even at the dislocation core. A specific solution is provided for virtual semi-infinite segments that can be used to enforce global mechanical equilibrium in the infinite domain. The proposed model for nodal forces is fully analytical, exact and very efficient computationally. A discussion on how to adapt the proposed methodology to more complex shape functions and surface element geometry is presented at the end of the paper. © 2014 IOP Publishing Ltd.

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G_{target} of 1.5. This is the first laboratory demonstration of exceeding "scientific breakeven" (or G_{target}>1) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the Lawson criterion for fusion ignition as reported in a previous NIF implosion [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129, 075001 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.075001]. This achievement is the culmination of more than five decades of research and gives proof that laboratory fusion, based on fundamental physics principles, is possible. This Letter reports on the target, laser, design, and experimental advancements that led to this result.