Related papers: On the Child-Langmuir Law in One, Two, and Three D…
We consider the steady state limiting current that can be carried by an infinite periodic array of thin electron sheets spaced by period p in a planar diode of gap voltage V and gap separation d. Our primary assumptions are (1) electron…
In the so-called Child-Langmuir law, established since 1911, an electron beam is formed linking two electrodes, which are assumed to be two parallel plates of area $A$, separated to a finite distance $D.$ When $% D\ll \sqrt{A},$…
We simulate numerically the classical charge dynamics in a microscopic, planar, vacuum diode with a finite emitter area and a finite number of electrons in the gap. We assume electrons are emitted under space-charge limited conditions with…
The Child-Langmuir law is investigated numerically using a fully electromagnetic particle-in-cell code for a closed axially symmetric diode. It is found that the average current transmitted to the anode increases with the injected current…
We analyze the motion of charged particles in a vacuum tube diode using a new set of variables. We obtain the space charge limited current for a charged particle moving non-relativistically in one dimension for the case of zero and non zero…
The maximum current that can be transported across a vacuum diode is limited by forces arising due to space charge. In a planar diode configuration, the space charge limited (SCL) current density from a planar emitting patch is given by the…
This paper describes a new solution formulation for fully nonlinear and unsteady planar flow of an electron beam in a diode. Using characteristic variables - i.e., variables that follow particle paths - the solution is expressed through an…
An approximate analytic solution is constructed for the 2-d space charge limited emission by a cathode surrounded by non emitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic…
The current associated with field emission is greatly dependent on the electric field at the emitting electrode. This field is a combination of the electric field in vacuum and the space charge created by the current. The latter becomes…
We present a microscopic derivation of the space charge limited current for the motion of non-relativistic charged particles inside a parallel vacuum tube diode taking into account the radiation reaction force. We study the space charged…
The space-charge limited current (SCLC) in a vacuum diode is given by the Child-Langmuir law (CLL), whose electric potential $\varphi(x) = (\it{x/D})^{4/3}$, where x is the spatial coordinate across the gap and D is the gap separation…
Using a combination of Eulerian and Lagrangian variables we obtain some exact results and good approximation schemes for the time evolution of the electron flow from a no-current state to a final stationary current state in a planar…
The Child-Langmuir law relates the voltage applied across a planar diode to the saturation value J_CL of current density that can be transmitted through it in case the injection velocity of electrons into the diode is zero. The…
Numerical solutions to the 1D steady-state Vlasov-Poisson system are used to develop a straightforward empirical formula for the electric current density transmitted through a vacuum diode (voltage gap) as a function of gap distance, gap…
An approximate analytic theory is developed and implemented numerically for calculating the space charge limited current and electric field of a thin cylindrical beam or current sheet between two wide parallel electrodes. The flow is…
Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be…
It is shown using dimensional analysis that the maximum current density J_{QCL} transported on application of a voltage V_g across a gap of size D follows the relation J_{QCL} ~ \hbar^{3 - 2\alpha} V_g^\alpha /D^{5 - 2\alpha}. The classical…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…
In this paper we analyze the motion of charged particles in a vacuum tube diode by solving linear differential equations. Our analysis is based on expressing the volume charge density as a function of the current density and coordinates…
First, this chapter introduces the expressions for the electric and magnetic space-charge internal fields and forces induced by high-intensity beams. Then, the root-mean-square equation with space charge is derived and discussed. In the…