Velocity Distribution Function

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Andrey Shagayda - One of the best experts on this subject based on the ideXlab platform.

  • analytic non maxwellian electron Velocity Distribution Function in a hall discharge plasma
    2017
    Co-Authors: Andrey Shagayda, Alexey Tarasov
    Abstract:

    The electron Velocity Distribution Function in the low-pressure discharges with the crossed electric and magnetic fields, which occur in magnetrons, plasma accelerators, and Hall thrusters with a closed electron drift, is not Maxwellian. A deviation from equilibrium is caused by a large electron mean free path relative to the Larmor radius and the size of the discharge channel. In this study, we derived in the relaxation approximation the analytical expression of the electron Velocity Distribution Function in a weakly ionized Lorentz plasma with the crossed electric and magnetic fields in the presence of the electron density and temperature gradients in the direction of the electric field. The solution was obtained in the stationary approximation far from boundary surfaces, when diffusion and mobility are determined by the classical effective collision frequency of electrons with ions and atoms. The moments of the Distribution Function including the average Velocity, the stress tensor, and the heat flux w...

  • stationary electron Velocity Distribution Function in crossed electric and magnetic fields with collisions
    2012
    Co-Authors: Andrey Shagayda
    Abstract:

    Analytical studies and numerical simulations show that the electron Velocity Distribution Function in a Hall thruster discharge with crossed electric and magnetic fields is not Maxwellian. This is due to the fact that the mean free path between collisions is greater than both the Larmor radius and the characteristic dimensions of the discharge channel. However in numerical models of Hall thrusters, a hydrodynamic approach is often used to describe the electron dynamics, because discharge simulation in a fully kinetic approach requires large computing resources and is time consuming. A more accurate modeling of the electron flow in the hydrodynamic approximation requires taking into account the non-Maxwellian character of the Distribution Function and finding its moments, an approach that reflects the properties of electrons drifting in crossed electric and magnetic fields better than the commonly used Euler or Navier-Stokes approximations. In the present paper, an expression for the electron Velocity Distribution Function in rarefied spatially homogeneous stationary plasma with crossed electric and magnetic fields and predominance of collisions with heavy particles is derived in the relaxation approximation. The main moments of the Distribution Function including longitudinal and transversal temperatures, the components of the viscous stress tensor, and of the heat flux vector are calculated. Distinctive features of the hydrodynamic description of electrons with a strongly non-equilibrium Distribution Function and the prospects for further development of the proposed approach for calculating the Distribution Function in spatially inhomogeneous plasma are discussed.

  • stationary electron Velocity Distribution Function in crossed electric and magnetic fields with collisions
    2012
    Co-Authors: Andrey Shagayda
    Abstract:

    Analytical studies and numerical simulations show that the electron Velocity Distribution Function in a Hall thruster discharge with crossed electric and magnetic fields is not Maxwellian. This is due to the fact that the mean free path between collisions is greater than both the Larmor radius and the characteristic dimensions of the discharge channel. However in numerical models of Hall thrusters, a hydrodynamic approach is often used to describe the electron dynamics, because discharge simulation in a fully kinetic approach requires large computing resources and is time consuming. A more accurate modeling of the electron flow in the hydrodynamic approximation requires taking into account the non-Maxwellian character of the Distribution Function and finding its moments, an approach that reflects the properties of electrons drifting in crossed electric and magnetic fields better than the commonly used Euler or Navier-Stokes approximations. In the present paper, an expression for the electron Velocity dist...

A I Smolyakov - One of the best experts on this subject based on the ideXlab platform.

  • on limitations of laser induced fluorescence diagnostics for xenon ion Velocity Distribution Function measurements in hall thrusters
    2018
    Co-Authors: Yevgeny Raitses, Igor D Kaganovich, Ivan Romadanov, A Diallo, Kentaro Hara, A I Smolyakov
    Abstract:

    Hall thruster operation is characterized by strong breathing oscillations of the discharge current, the plasma density, the temperature, and the electric field. Probe- and laser-induced fluorescence (LIF) diagnostics were used to measure temporal variations of plasma parameters and the xenon ion Velocity Distribution Function (IVDF) in the near-field plasma plume in regimes with moderate (<18%) external modulations of applied DC discharge voltage at the frequency of the breathing mode. It was shown that the LIF signal collapses while the ion density at the same location is finite. The proposed explanation for this surprising result is based on a strong dependence of the excitation cross-section of metastables on the electron temperature. For large amplitudes of oscillations, the electron temperature at the minimum enters the region of very low cross-section (for the excitation of the xenon ions); thus, significantly reducing the production of metastable ions. Because the residence time of ions in the chan...

  • kinetic effects in a hall thruster discharge
    2007
    Co-Authors: Igor Kaganovich, Dmytro Sydorenko, Yevgeny Raitses, A I Smolyakov
    Abstract:

    Recent analytical studies and particle-in-cell simulations suggested that the electron Velocity Distribution Function in E×B discharge of annular geometry Hall thrusters is non-Maxwellian and anisotropic. The average kinetic energy of electron motion in the direction parallel to the thruster channel walls (across the magnetic field) is several times larger than that in the direction normal to the walls. Electrons are stratified into several groups depending on their origin (e.g., plasma or channel walls) and confinement (e.g., lost on the walls or trapped in the plasma). Practical analytical formulas are derived for the plasma flux to the wall, secondary electron fluxes, plasma potential, and electron cross-field conductivity. Calculations based on these formulas fairly agree with the results of numerical simulations. The self-consistent analysis demonstrates that the elastic electron scattering in collisions with atoms and ions plays a key role in formation of the electron Velocity Distribution Function ...

  • effects of non maxwellian electron Velocity Distribution Function on two stream instability in low pressure discharges
    2007
    Co-Authors: Dmytro Sydorenko, Igor Kaganovich, A I Smolyakov, Yevgeny Raitses
    Abstract:

    Electron emission from discharge chamber walls is important for plasma maintenance in many low-pressure discharges. The electrons emitted from the walls are accelerated by the sheath electric field and are injected into the plasma as an electron beam. Penetration of this beam through the plasma is subject to the two-stream instability, which tends to slow down the beam electrons and heat the plasma electrons. In the present paper, a one-dimensional particle-in-cell code is used to simulate these effects both in a collisionless plasma slab with immobile ions and in a cross-field discharge of a Hall thruster. The two-stream instability occurs if the total electron Velocity Distribution Function of the plasma-beam system is a nonmonotonic Function of electron speed. Low-pressure plasmas can be depleted of electrons with energy above the plasma potential. This study reveals that under such conditions the two-stream instability depends crucially on the Velocity Distribution Function of electron emission. It is...

Yevgeny Raitses - One of the best experts on this subject based on the ideXlab platform.

  • on limitations of laser induced fluorescence diagnostics for xenon ion Velocity Distribution Function measurements in hall thrusters
    2018
    Co-Authors: Yevgeny Raitses, Igor D Kaganovich, Ivan Romadanov, A Diallo, Kentaro Hara, A I Smolyakov
    Abstract:

    Hall thruster operation is characterized by strong breathing oscillations of the discharge current, the plasma density, the temperature, and the electric field. Probe- and laser-induced fluorescence (LIF) diagnostics were used to measure temporal variations of plasma parameters and the xenon ion Velocity Distribution Function (IVDF) in the near-field plasma plume in regimes with moderate (<18%) external modulations of applied DC discharge voltage at the frequency of the breathing mode. It was shown that the LIF signal collapses while the ion density at the same location is finite. The proposed explanation for this surprising result is based on a strong dependence of the excitation cross-section of metastables on the electron temperature. For large amplitudes of oscillations, the electron temperature at the minimum enters the region of very low cross-section (for the excitation of the xenon ions); thus, significantly reducing the production of metastable ions. Because the residence time of ions in the chan...

  • kinetic effects in a hall thruster discharge
    2007
    Co-Authors: Igor Kaganovich, Dmytro Sydorenko, Yevgeny Raitses, A I Smolyakov
    Abstract:

    Recent analytical studies and particle-in-cell simulations suggested that the electron Velocity Distribution Function in E×B discharge of annular geometry Hall thrusters is non-Maxwellian and anisotropic. The average kinetic energy of electron motion in the direction parallel to the thruster channel walls (across the magnetic field) is several times larger than that in the direction normal to the walls. Electrons are stratified into several groups depending on their origin (e.g., plasma or channel walls) and confinement (e.g., lost on the walls or trapped in the plasma). Practical analytical formulas are derived for the plasma flux to the wall, secondary electron fluxes, plasma potential, and electron cross-field conductivity. Calculations based on these formulas fairly agree with the results of numerical simulations. The self-consistent analysis demonstrates that the elastic electron scattering in collisions with atoms and ions plays a key role in formation of the electron Velocity Distribution Function ...

  • effects of non maxwellian electron Velocity Distribution Function on two stream instability in low pressure discharges
    2007
    Co-Authors: Dmytro Sydorenko, Igor Kaganovich, A I Smolyakov, Yevgeny Raitses
    Abstract:

    Electron emission from discharge chamber walls is important for plasma maintenance in many low-pressure discharges. The electrons emitted from the walls are accelerated by the sheath electric field and are injected into the plasma as an electron beam. Penetration of this beam through the plasma is subject to the two-stream instability, which tends to slow down the beam electrons and heat the plasma electrons. In the present paper, a one-dimensional particle-in-cell code is used to simulate these effects both in a collisionless plasma slab with immobile ions and in a cross-field discharge of a Hall thruster. The two-stream instability occurs if the total electron Velocity Distribution Function of the plasma-beam system is a nonmonotonic Function of electron speed. Low-pressure plasmas can be depleted of electrons with energy above the plasma potential. This study reveals that under such conditions the two-stream instability depends crucially on the Velocity Distribution Function of electron emission. It is...

Yasushi Suto - One of the best experts on this subject based on the ideXlab platform.

  • modeling a pairwise peculiar Velocity Distribution Function of dark matter from halo density profiles
    2002
    Co-Authors: Takeshi Kuwabara, Atsushi Taruya, Yasushi Suto
    Abstract:

    We derive the pairwise peculiar Velocity Distribution Function of dark matter particles by applying a dark-matter halo approach. Unlike previous work, we do not assume a Gaussian Velocity Distribution Function of dark matter in a single halo, but compute it self-consistently with the assumed density profile for the dark-matter halo. The resulting Distribution Function is well approximated by an exponential Distribution which is consistent with the previous observational, numerical, and theoretical results. We also compute the pairwise peculiar Velocity dispersion for different density profiles, and provide a practical fitting formula. We apply an empirical biasing scheme into our model and present a prediction for a pairwise peculiar Velocity dispersion of galaxies, and reproduce the previous results of simulations using our semi-analytical method.

Igor D Kaganovich - One of the best experts on this subject based on the ideXlab platform.

  • on limitations of laser induced fluorescence diagnostics for xenon ion Velocity Distribution Function measurements in hall thrusters
    2018
    Co-Authors: Yevgeny Raitses, Igor D Kaganovich, Ivan Romadanov, A Diallo, Kentaro Hara, A I Smolyakov
    Abstract:

    Hall thruster operation is characterized by strong breathing oscillations of the discharge current, the plasma density, the temperature, and the electric field. Probe- and laser-induced fluorescence (LIF) diagnostics were used to measure temporal variations of plasma parameters and the xenon ion Velocity Distribution Function (IVDF) in the near-field plasma plume in regimes with moderate (<18%) external modulations of applied DC discharge voltage at the frequency of the breathing mode. It was shown that the LIF signal collapses while the ion density at the same location is finite. The proposed explanation for this surprising result is based on a strong dependence of the excitation cross-section of metastables on the electron temperature. For large amplitudes of oscillations, the electron temperature at the minimum enters the region of very low cross-section (for the excitation of the xenon ions); thus, significantly reducing the production of metastable ions. Because the residence time of ions in the chan...

  • anomalous skin effect for anisotropic electron Velocity Distribution Function
    2004
    Co-Authors: Igor D Kaganovich, Edward A Startsev, Gennady Shvets
    Abstract:

    The anomalous skin effect in a plasma with a highly anisotropic electron Velocity Distribution Function (EVDF) is very different from the skin effect in a plasma with isotropic EVDF. An analytical solution was derived for the electric field penetrated into plasma with the EVDF described as a Maxwellian with two temperatures Tx≫Tz, where x is the direction along the plasma boundary and z is the direction perpendicular to the plasma boundary. The skin layer was found to consist of two distinct regions of width of order vTx/ω and vTz/ω, where vTx,z=Tx,z/m is the thermal electron Velocity and ω is the incident wave frequency.

  • anomalous skin effect for anisotropic electron Velocity Distribution Function
    2004
    Co-Authors: Igor D Kaganovich, Edward A Startsev, Gennady Shvets
    Abstract:

    The anomalous skin effect in a plasma with a highly anisotropic electron Velocity Distribution Function (EVDF) is very different from skin effect in a plasma with the isotropic EVDF. An analytical solution was derived for the electric field penetrated into plasma with the EVDF described as a Maxwellian with two temperatures Tx >> Tz, where x is the direction along the plasma boundary and z is the direction perpendicular to the plasma boundary. The skin layer was found to consist of two distinctive regions of width of order nTx/w and nTz/w, where nTx,z/w = (Tx,z/m)1/2 is the thermal electron Velocity and w is the incident wave frequency.