Transition from Fowler-Nordheim field emission to space charge limited current in both classical and relativistic regimes

The Fowler-Nordheim law gives the current density extracted from a surface under strong fields; space charge limited current density predicts the maximum transmitted current density by considering the space charge effect. This thesis investigates the transition, as the applied field increases, of the transmitted current density from the Fowler-Nordheim law to the space charge limited current density in both classical and relativistic regimes.;Chapter 1 develops the effective field enhancement model to incorporate geometric surface effects at the sub-grid level, as well as to include field enhancement in models with lower spatial dimensionality. The method represents these microscopic effects in the macroscopic model using an effective field enhancement coefficient, betaeff, which is shown to depend on applied field, and surface morphology. We will demonstrate the model by simulating field emission current density with general cathode geometry in both 1D and 2D.;Chapter 2 conducts simulation of the transition in the classical regime and analyzes the response of the emission model to strong electric fields near the transition point in detail. We show that, lower work function and higher effective field enhancement factor can reduce the transition field and cause a faster approach to the space charge limit.;Chapter 3 develops a second-order accurate time-centering injection algorithm, which allows us to extend our simulation to the relativistic regime. The generalized injection algorithm allows particles to be injected into the simulation region with arbitrary energy and direction, in general electric and magnetic fields including those with spatial and temporal gradients. The model allows for injection at arbitrary times (fractional time steps) in order to maintain statistically continuous current injection.;Chapter 4 expands the space charge limited current density theory with monoenergetic injecting electrons to the relativistic regime. We show two types of solution for the SCL and compare them. The SCL of type II, which requires a potential minimum and a finite surface electric field, will be higher than the SCL of type I where the potential increases monotonically and the surface electric field is zero.;Chapter 5 investigates the theory for the transition of transmitted currents, with initial energy and geometric corrections. The theory works well in both classical and relativistic regimes and shows good agreement with our 1D self-consistent PIC simulation. Both initial velocity and geometric effects enhance the SCL-FN current density, making it closer to the space-charge limited current density. Chapter 6 gives suggestions on future work.