Higher Harmonics in Multipactor Induced Plasma Ionization Breakdown near a Dielectric Surface

In this Letter, the novel physics of higher harmonic (HH) generation of the normal electric field near a dielectric surface is reported in multipactor induced plasma ionization breakdown, as determined by kinetic particle-in-cell simulations. The observed HH frequency is around ten times the fundamental rf driving frequency, but lower than the electron plasma frequency. A theory is constructed which indicates that stream plasma interaction-induced instability is the mechanism of HH generation in the collisional regime. The HH frequency and its corresponding growth rate of the HH oscillation amplitude from the theory are in good agreement with kinetic particle-in-cell simulations.

Figure 1

Schematic of the system for multipactor induced ionization breakdown in fully kinetic particle-in-cell simulations. The small close-up plot qualitatively shows the secondary electron yield (SEY), $\delta$, as a function of electron impact energy for normal incidence.

Figure 2

Spatiotemporal plots of the (a) normal electric field $E_x$, (b) the normalized rf electric field (red dashed line), $E_y/E_{\mathrm{rf}0}$, and normal electric field, $E_x/E_{\mathrm{rf}0}$ at $x=12\mu \mathrm{m}$, (c) the spatial plots of electron and ion density at $t/T=7$, 8.

Figure 3

The spatiotemporal plots of the (a) electron density from ionization impact and (b) secondary electron density from the surface emission; (c) the velocity distribution functions at $x=12\mu \mathrm{m}$ of the ionization and secondary electrons normalized to each species density.

Figure 4

(a) Theoretical dispersion relationship solution, real and imaginary part of $\omega$, $\mathrm{Re}(\omega )$ (black line) and $\mathrm{Im}(\omega )$ (red line), versus $k$, and the blue dashed line indicates the maximum $\mathrm{Im}(\omega )$. (b) The time varying frequency spectrum (color bar from simulation) of the normal electric field $E_x$ over time range of 7.0–8.6 rf periods. The color bar gives the relative strength of the magnitude of the Fourier transform of the normal electric field. The time window is 64% of the rf period, with a 78% overlap between successive windows. The white rectangle line shows the theoretical calculation oscillation frequency. (c) The amplitude of the fast oscillation as a function of time in simulation (black dashed line), its linear fitting (black line), and theory (red line).