Physics of the Advanced Plasma Source: a review of recent experimental and modeling approaches

Brinkmann, Ralf Peter; Harhausen, J.; Lapke, Martin; Storch, Robert; Styrnoll, Tim; Awakowicz, Peter; Foest, Rüdiger; Hannemann, M.; Loffhagen, Detlef; Ohl, A.

doi:10.1088/0741-3335/58/1/014033

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…The ion gyroradius, in contrast, amounts to at least several cm and is therefore of the same magnitude as L and λ. All scales, however, exceed the Debye length l = 1 is higher than all other frequencies, except the electron plasma frequency w = pe --10 10 s 11 12 1 , while the gyrofrequencies of the ions are negligibly small. Such plasmas must be described in the frame of kinetic theory: each participating species s (of mass m s and charge q s ) is represented by a phase space distribution function ( )…”

Section: Introductionmentioning

confidence: 89%

“…Partially magnetized plasmas play an important role in numerous technological applications. Examples reach from magnetically enhanced glow discharges over various types of magnetron sources to Hall effect thrusters [1][2][3][4]. The physical regimes of these plasmas are quite similar: the magnetic field in the active region is around = -B 10 100 mT, and they are operated at relatively low pressure, = p 0.1 1 Pa, and high plasma density, = -n 10 10 m e 18 20 3 .…”

Section: Introductionmentioning

confidence: 99%

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Interaction of magnetized electrons with a boundary sheath: investigation of a specular reflection model

Krüger

Brinkmann

2017

Plasma Sources Sci. Technol.

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This publication reports analytical and numerical results concerning the interaction of gyrating electrons with a plasma boundary sheath, with focus on partially magnetized technological plasmas. It is assumed that the electron Debye length l D is much smaller than the electron gyroradius r L , andr L in turn much smaller than the mean free path λ and the gradient length L of the fields. Focusing on the scale of the gyroradius, the sheath is assumed as infinitesimally thin (l  0 D ), collisions are neglected (l  ¥), the magnetic field is taken as homogeneous, and electric fields (=potential gradients) in the bulk are neglected (  ¥ L ). The interaction of an electron with the electric field of the plasma boundary sheath is represented by a specular reflection  -• v v v e e 2 z z of the velocity v at the plane z=0 ofa naturally oriented Cartesian coordinate system ( ) x y z , , . The electron trajectory is then given as sequences of helical sections, with the kinetic energy ò and the canonical momenta p x and p y conserved, but not the position of the axis (base point R 0 ), theslope (pitch angle χ), and the phase (gyrophase j). A 'virtual interaction' which directly maps the incoming electrons to the outgoing ones is introduced and studied in dependence of the angle γ between the field and the sheath normal e z . The corresponding scattering operator is constructed, mathematically characterized, and given as an infinite matrix. An equivalent boundary condition for a transformed kinetic model is derived.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Interaction of magnetized electrons with a boundary sheath: investigation of a specular reflection model

Krüger

Brinkmann

2017

Plasma Sources Sci. Technol.

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“…Magnetized low temperature plasmas such as Hall effect thrusters, DC or RF magnetrons, and magnetically enhanced glow discharges are widely used in technology and industry [1][2][3][4][5][6]. They operate at low pressures, p = 0.1-1 Pa, and high plasma densities, n e = 10 18 -10 20 m −3 .…”

Section: Introductionmentioning

confidence: 99%

Collisionless dissipation at the boundary sheath of magnetized low temperature plasmas

Krüger

Köhn

et al. 2023

Plasma Sources Sci. Technol.

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In partially magnetized technological plasmas like magnetron discharges or Hall-eﬀect thrusters, the interaction of gyrating electrons with the plasma boundary sheath plays an important role. This study shows that the interaction can be described as a dissipative process. It is assumed that the Debye length λD is much smaller than the electron gyroradius rL, and rL in turn much smaller than the mean free path λ and the ﬁeld gradient length l. Focusing on the scale of the gyroradius, the sheath is assumed as thin (λD → 0), collisions are neglected (λ → ∞), the magnetic ﬁeld is taken as homogeneous, and electric ﬁelds (= potential gradients) in the bulk are neglected (l →∞). The interaction of an electron with the electric ﬁeld of the plasma boundary sheath is represented by specular reﬂection, v → v −2 v·nn, where v is the electron velocity and n is the sheath normal. A previous study showed that this set-up leads to a scattering process where gyrophase invariant incoming velocity distributions are scattered into outgoing distributions with fractal dependence on the gyrophase [D. Krüger, R.P. Brinkmann, Plasma Sources Sci. Technol. 26, 115009 (2017)]. The present research focuses on the subsequent evolution. It is shown that the gyromotion results in fast phase mixing with respect to the gyrophase which quickly restores the gyrophase invariance. In combination, the two phases of the sheath interaction constitute a mapping within the space of gyrophase invariant distributions. This combined process is dissipative and leads to isotropization. As an explicit comparison shows, it acts similarly to elastic electron-neutral collisions and can even dominate the latter in low pressure plasmas. A simpliﬁed version of the operator that applies for weakly anisotropic distributions is suited for practical simulation work.

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“…Partially magnetized plasmas, using external magnetic field B perpendicular to applied electric field E to confine electrons and generate high plasma density in low pressures, represent an advanced plasma source in technology and industry, such as magnetrons, Hall effect thrusters and magnetically enhanced glow/arc discharges [1,2,3,4,5]. These discharges feature magnetized electrons subject to the E×B confinement (electron Larmor radius ρ e is smaller than the plasma size L, ρ e < L) and non-or weakly magnetized ions (ion Larmor radius ρ i L), which are accelerated almost collisionlessly in the applied electric field for the application purpose.…”

Section: Introductionmentioning

confidence: 99%

Formation mechanism of the rotating spoke in partially magnetized plasmas

Li¹,

Eremin²,

Smolyakov³

et al. 2022

Preprint

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Rotating spokes commonly occur in partially magnetized plasmas devices. In this paper, the driving mechanism behind the formation of an m=1 rotating spoke mode in a magnetically enhanced hollow cathode arc discharge is investigated by means of 2D radial-azimuthal particle-in-cell/Monte Carlo collision simulations with a uniform axial magnetic field. We find that the formation of the spoke potential hump region can be explained as a result of the positive anode sheath collapse due to the lower hybrid type instability evolving into the long wavelength regime. It is shown that an initial short-wavelength instability in the non-neutral anode sheath undergoes a sequence of transitions into the large scale mode. The sheath non-neutrality effect on the instability is considered and incorporated in the two-fluid linear theory of the lower hybrid instability. The unstable modes predicted by the theory in the linear phase and nonlinear evolution are in good agreement with the fluctuation modes developed in the particle simulations.

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Physics of the Advanced Plasma Source: a review of recent experimental and modeling approaches

Cited by 5 publications

References 12 publications

Interaction of magnetized electrons with a boundary sheath: investigation of a specular reflection model

Interaction of magnetized electrons with a boundary sheath: investigation of a specular reflection model

Collisionless dissipation at the boundary sheath of magnetized low temperature plasmas

Formation mechanism of the rotating spoke in partially magnetized plasmas

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