Zbigniew Peradzyński

Wall material effects in stationary plasma thrusters. II. Near-wall and in-wall conductivity

Simulations and experimental characterizations of a stationary plasma thruster are compared for four different wall materials to investigate near-wall conductivity (dielectric materials) and in-wall conductivity (conducting materials) in such a discharge. Using a one-dimensional transient fluid model that takes into account a possible electron temperature anisotropy, it is shown that electron-wall backscattering plays a crucial role by maintaining a relatively high electron temperature along the magnetic field lines which in turn drives large electron currents toward the walls. The large differences in discharge current observed experimentally for the dielectric materials are qualitatively recovered, confirming that near-wall conductivity results from the combined effects of secondary electron emission and electron backscattering. A clear correlation is found between the appearance of space charge saturation at the walls and a jump of the discharge current observed in experiments when varying the discharg...

Transit-time instability in Hall thrusters

Longitudinal waves characterized by a phase velocity of the order of the velocity of ions have been recurrently observed in Hall thruster experiments and simulations. The origin of this so-called ion transit-time instability is investigated with a simple one-dimensional fluid model of a Hall thruster discharge in which cold ions are accelerated between two electrodes within a quasineutral plasma. A short-wave asymptotics applied to linearized equations shows that plasma perturbations in such a device consist of quasineutral ion acoustic waves superimposed on a background standing wave generated by discharge current oscillations. Under adequate circumstances and, in particular, at high ionization levels, acoustic waves are amplified as they propagate, inducing strong perturbation of the ion density and velocity. Responding to the subsequent perturbation of the column resistivity, the discharge current generates a standing wave, the reflection of which sustains the generation of acoustic waves at the inlet ...

Spectral analysis of Hall-effect thruster plasma oscillations based on the empirical mode decomposition

Hall-effect thruster plasma oscillations recorded by means of probes located at the channel exit are analyzed using the empirical mode decomposition (EMD) method. This self-adaptive technique permits to decompose a nonstationary signal into a set of intrinsic modes, and acts as a very efficient filter allowing to separate contributions of different underlying physical mechanisms. Applying the Hilbert transform to the whole set of modes allows to identify peculiar events and to assign them a range of instantaneous frequency and power. In addition to 25kHz breathing-type oscillations which are unambiguously identified, the EMD approach confirms the existence of oscillations with instantaneous frequencies in the range of 100–500kHz typical for ion transit-time oscillations. Modeling of high-frequency modes (ν∼10MHz) resulting from EMD of measured wave forms supports the idea that high-frequency plasma oscillations originate from electron-density perturbations propagating azimuthally with the electron drift v...

Ionization oscillations in Hall accelerators

The underlying mechanism of low-frequency oscillations in Hall accelerators is investigated theoretically. It is shown that relaxation oscillations arise from a competition between avalanche ionization and the advective transport of the working gas. The model derived recovers the slow progression and fast recession of the ionization front. Analytical approximations of the shape of current pulses and of the oscillation frequency are provided for the case of large amplitude oscillations.

Calcium waves with fast buffers and mechanical effects

In the paper we consider the existence of calcium travelling waves for systems with fast buffers. We prove the convergence of the travelling waves to an asymptotic limit as the kinetic coefficients characterizing the interaction between calcium and buffers tend to infinity. To be more precise, we prove the convergence of the speeds as well as the calcium component concentration profile to the profile of the travelling wave of the reduced equation. Additionally, we take into account the effect of coupling between the mechanical and chemical processes and show the existence as well the monotonicity of the profiles of concentrations. This property guarantees their positivity.

IS NEAR-WALL CONDUCTIVITY A MISNOMER?

The near-wall conductivity theory outlined by Morozov in 1968 constitutes one of the most prominent outcome of the early investigations of Hall thrusters, which describes the cross-eld electron diffusion mechanism induced by electron-wall collisions. The present work generalizes the near-wall conductivity theory to the case of a non-zero sheath potential at the walls. The general solution is found to differ qualitatively from the no-sheath solution of the classical theory, and puts into question the hypothesis that the so-called near-wall currents are conned to the close vicinity of the walls.

Calcium waves with mechano-chemical couplings

As follows from experiments, waves of calcium concentration in biological tissues can be easily excited by a local mechanical stimulation. Therefore the complete theory of calcium waves should also take into account coupling between mechanical and chemical processes. In this paper we consider the existence of travelling waves for buffered systems, as in [22], completed, however, by an equation for mechanical equilibrium and respective mechanochemical coupling terms. Thus the considered, coupled system consists of reaction-diffusion equations (for the calcium and buffers concentrations) and equations for the balance of mechanical forces.

The Role of The Electron Energy Balance in Plasma Thruster Instabilities

Using the fluid equations of Hall thruster plasma we analyze the influence of the electron energy balance on the stability of ion sound modes. For frequencies lower than ωc = 107 s−1 the gains and losses in the source term are approximately equal, thus the temperature can be in principle determined in terms of other dependent variables. This permits to reduce the number of equations. It appears however, that the new system can have complex characteristics in some regions. This in turn implies instability of certain modes with frequencies lower than ωc.Using the fluid equations of Hall thruster plasma we analyze the influence of the electron energy balance on the stability of ion sound modes. For frequencies lower than ωc = 107 s−1 the gains and losses in the source term are approximately equal, thus the temperature can be in principle determined in terms of other dependent variables. This permits to reduce the number of equations. It appears however, that the new system can have complex characteristics in some regions. This in turn implies instability of certain modes with frequencies lower than ωc.

Cauchy problem for quasilinear hyperbolic systems with coeffcients functionally dependent on solutions

Abstract The mixed problem for quasilinear hyperbolic system with coefficients functionally dependent on the solution is studied. We assume that the coefficients are continuous nonlinear operators in the Banach space C1(ℝ) satisfying some additional assumptions. Under these assumptions we prove the uniqueness and existence of local in time C1 solution, provided that the initial data are also of class C1.

High Frequency Oscillations In 2‐D Fluid Model Of Hall Effect Thrusters

2‐D linearised plasma dynamics equations for Hall Thruster plasmas are examined with special attention focused on the effect of spatial non‐uniformity of the unperturbed state. Introducing fast and slow (separated) scales of plasma parameter variation, the stability conditions for HF modes are discussed.