Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $phi$ and $psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $phi (X)= [M_2^*psi (Y)M_1]^{-w^*}$ and $psi (Y)=[M_2phi (X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.

Nonlinear frequency coupling in dual radio-frequency driven atmospheric pressure plasmas

Plasma ionization, and associated mode transitions, in dual radio-frequency driven atmospheric pressure plasmas are governed through nonlinear frequency coupling in the dynamics of the plasma boundary sheath. Ionization in low-power mode is determined by the nonlinear coupling of electron heating and the momentary local plasma density. Ionization in high-power mode is driven by electron avalanches during phases of transient high electric fields within the boundary sheath. The transition between these distinctly different modes is controlled by the total voltage of both frequency components.

The influence of the relative phase between the driving voltages on electron heating in asymmetric dual frequency capacitive discharges

The influence of the relative phase between the driving voltages on electron heating in asymmetric phase-locked dual frequency capacitively coupled radio frequency plasmas operated at 2 and 14 MHz is investigated. The basis of the analysis is a nonlinear global model with the option to implement a relative phase between the two driving voltages. In recent publications it has been reported that nonlinear electron resonance heating can drastically enhance the power dissipation to electrons at moments of sheath collapse due to the self-excitation of nonlinear plasma series resonance (PSR) oscillations of the radio frequency current. This work shows that depending on the relative phase of the driving voltages, the total number and exact moments of sheath collapse can be influenced. In the case of two consecutive sheath collapses a substantial increase in dissipated power compared with the known increase due to a single PSR excitation event per period is observed. Phase resolved optical emission spectroscopy (PROES) provides access to the excitation dynamics in front of the driven electrode. Via PROES the propagation of beam-like energetic electrons immediately after the sheath collapse is observed. In this work we demonstrate that there is a close relation between moments of sheath collapse, and thus excitation of the PSR, and beam-like electron propagation. A comparison of simulation results to experiments in a single and dual frequency discharge shows good agreement. In particular the observed influence of the relative phase on the dynamics of a dual frequency discharge is described by means of the presented model. Additionally, the analysis demonstrates that the observed gain in dissipation is not accompanied by an increase in the electrode’s dc-bias voltage which directly addresses the issue of separate control of ion flux and ion energy in dual frequency capacitively coupled radio frequency plasmas.