New Scaling of Child-Langmuir Law in the Quantum Regime

Abstract

This paper presents a consistent quantum mechanical model of Child-Langmuir (CL) law, including electron exchange-correlation interaction, electrode's surface curvature, and finite emitter area. The classical value of the CL law is increased by a larger factor due to the electron tunneling through the space-charge potential, and the electron exchange-correlation interaction becomes important when the applied gap voltage Vg and the gap spacing D are, respectively, on the order of Hartree energy level, and nanometer scale. It is found that the classical scaling of Vg(3/2) and D(-2) is no longer valid in the quantum regime, and a new scaling of Vg(1/2) and D(-4) is established. The smooth transition from the classical regime to the quantum regime is also demonstrated.

Electrostatic Rayleigh-Taylor Mode in Electron-Positron-Ion Quantum Plasma

“…Dense quantum plasmas may also occur in the next generation of laser-based matter compression schemes [5] [6] [7], in which the plasmon frequency is measurably shifted due to quantum effects. Other applications of dense quantum plasmas which are relevant to the collective dynamics of degenerate electrons/positrons include: the electron-hole plasma in quantum wires [8], metallic nanostructures and thin films [9], the dense quantum diode [10], nanophotonics and nanowires [11], nano-plasmonics [12], high-gain quantum free-electron lasers [13], quantum wells and piezomagnetic quantum dots [14].…”

Solitary and double-layer structures in quantum bi-ion plasma

“…Drift instability has been studied by Rosenberg and Merlino [45] in a magnetized plasma comprising of positive ions and negative ions. On the other hand, investigation of the propagation properties of waves in quantum plasmas is of fundamental importance due to their vital role for understanding the collective behaviors in super-dense astrophysical objects [24], in intense laser-solid density plasma experiments [6,33], in ultra-cold plasma [27], in microelectronic devices [34], in nanowires [67], carbon nanotubes [84], and quantum diodes [7]. New pressure laws and new quantum forces are included in a quantum plasma, such that in the presence of these new forces the collective behavior of quantum plasmas affects significantly.…”

Maximal charge injection of a uniform separated electron pulse train in a drift space

“…In past years, the studies of SCLC in a diode and a drift space have been revised extensively to consider various effects such as finite emission area [12][13][14][15][16], short pulse length and relativistic (and quantum) effects [17][18][19][20][21][22][23][24], semianalytical scaling for cylindrical and spherical diodes [25,26].…”