Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons

Geraldini, Alessandro; Parra, Felix; Militello, F.

doi:10.1017/s0022377819000771

Cited by 5 publications

(14 citation statements)

References 36 publications

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“…for any prescribed value of τ , where Θ is the Heaviside step function defined in (3.6) and e z is a unit vector in the z direction. The family of velocity distributions (7.1) is the same as used in Geraldini et al (2019) to study the dependence of the magnetic presheath solution on ion temperature, and is chosen to satisfy the marginal kinetic Chodura condition (Geraldini et al 2018…”

Section: Boundary Conditions At the Magnetic Presheath Entrancementioning

confidence: 99%

“…As sputtering predictions depend on the distribution of kinetic energy and angle of impact of ions reaching the target, it is useful to calculate the energy-angle distribution of ions 5 For τ 1, enlarging ion gyro-orbits make this analysis insufficient (Geraldini et al 2019).…”

Section: Energy-angle Distributions At the Targetmentioning

confidence: 99%

“…This inaccuracy is unimportant if τ is sufficiently large that the asymptotic theory correctly describes the majority of ion orbits. It was shown inGeraldini, Parra & Militello (2019) that when τ α 1/3 , the asymptotic theory fails for an appreciable fraction of the ions.…”

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confidence: 99%

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Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

Geraldini

2021

J. Plasma Phys.

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A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

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Section: Boundary Conditions At the Magnetic Presheath Entrancementioning

confidence: 99%

Section: Energy-angle Distributions At the Targetmentioning

confidence: 99%

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Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

Geraldini

2021

J. Plasma Phys.

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“…The trajectories defined by equations (14)(15)(16), as in [14,15], can be solved for α = 0, giving the constants of the motions U ⊥ , U and x defined by…”

Section: The α = 0 Problem and Quasi-periodicitymentioning

confidence: 99%

“…Given that the cutoff potential is a parameter of the problem, it is natural to ask whether solutions exist for all φ cut and whether they have φ(0) = φ cut or φ(0) > φ cut . We can answer these questions by appealing to the hot ion theory developed in [23] and [16]. The hot ion theory models the limit T e T i in which the potential cannot substantially distort the ion orbits.…”

Section: The Limits Of Hot and Cold Ion Temperaturementioning

confidence: 99%

Sheath collapse at critical shallow angle due to kinetic effects

Ewart,

Parra,

Geraldini

2021

Preprint

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The Debye sheath is shown to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of the finite ion orbit width effects, which are not captured by fluid models. The wall potential with respect to the bulk plasma at which the Debye sheath vanishes is calculated. Above this wall potential, it is possible that the Debye sheath will invert.

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Three-dimensional cross-field flows at the plasma-material interface in an oblique magnetic field

et al. 2020

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This article describes experimental evidence that the magnetic presheath is a fully three-dimensional structure modified by ion–neutral collisions. Velocity distributions of both ions and neutrals, obtained via laser-induced fluorescence, show that cross field ion drifts do not result from entrainment of ions in a flowing neutral background. Ion flows parallel to E×B arise and accelerate to as much as 0.2cs within several ion gyroradii of the boundary surface, where cs is the sound speed. Within measurement resolution, the onset of the E×B aligned flow occurs at the same distance to the surface that ions begin to deflect from travel along magnetic field lines. Collisional fluid and particle-in-cell simulations of the boundary region are compared to the experimental measurements. We find that, in contrast to the classical collisionless Chodura model, collisional effects between the ions and the non-flowing neutral population are essential to quantitatively predict the observed ion drift velocities. No momentum coupling between ions and neutrals, separable from noise and other effects, is observed in either signal. We discuss several explanations and implications of this observation.

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Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons

Cited by 5 publications

References 36 publications

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

Sheath collapse at critical shallow angle due to kinetic effects

Three-dimensional cross-field flows at the plasma-material interface in an oblique magnetic field

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