The kilo-tesla-class converging magnetic field effects on the core heating properties and the energy and duration of relativistic electron beam (REB) required for ignition in fast ignition laser fusion has been evaluated by parametric 2D hybrid simulations where a uniformly compressed DT core with ρ = 300 g/cm3 is heated by REB with TREB = 3 MeV, IREB = 0.69 × 1020 W/cm2 and θREB = 40° under sufficiently strong magnetic field (Bext = 3 kT at the REB injection position). The kilo-tesla-class converging magnetic field can intensify REB and then enhances the core heating power drastically. As the results, the fusion ignition can be initiated by the REB with EREB ≧ 50 kJ and τREB = 10 ~ 30 ps. With increasing mirror ratio RM, the negative effect of converging field, i.e., mirror reflection, becomes significant, which enhances the REB energy required for ignition (EREB,ig = 49 kJ for RM = 3 → EREB,ig =77 kJ for RM = 20).
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