Equilibrium theory of cylindrical discharges with special application to helicons

Curreli, Davide; Chen, Francis F.

doi:10.1063/1.3656941

Cited by 45 publications

(39 citation statements)

References 43 publications

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“…Most theory on gas discharges do not tackle the problem of equilibrium profiles; rather, they are about distribution functions and collision cross sections, which are peripheral to the problem of central peaking though they may have small effects on the details. This paper is a short version of our complete paper 1 , published earlier, which contains the appropriate references A previous attempt 2 had been made to solve this problem. The orbit of an electron in a cylinder with rf applied only at the circumference was traced through many rf cycles with the nonlinear radial Lorentz force L e = − F v B   × included.…”

Section: Introductionmentioning

confidence: 99%

Central peaking of magnetized gas discharges

Chen

Curreli

2013

Physics of Plasmas

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Partially ionized gas discharges used in industry are often driven by radiofrequency (rf) power applied at the periphery of a cylinder. It is found that the plasma density n is usually flat or peaked on axis even if the skin depth of the rf field is thin compared with the chamber radius a. Previous attempts at explaining this did not account for the finite length of the discharge and the boundary conditions at the endplates. A simple 1D model is used to focus on the basic mechanism: the short-circuit effect. It is found that a strong electric field (E-field) scaled to electron temperature T e , drives the ions inward. The resulting density profile is peaked on axis and has a shape independent of pressure or discharge radius. This "universal" profile is not affected by a dc magnetic field (B-field) as long as the ion Larmor radius is larger than a.

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Section: Introductionmentioning

confidence: 99%

Central peaking of magnetized gas discharges

Chen

Curreli

2013

Physics of Plasmas

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“…Consistent calculations of the equilibrium conditions of helicon and ICP discharges [10] show that the power deposition occurs at the edge of the plasma cylinder for all the cases when the Knudsen number (ratio of the mean free path and the characteristic size) of the discharge is much smaller than one. In those cases, the absorption of RF power happens thanks to the collisional TrivelpieceGould mode, which is rapidly absorbed in a region near the external boundary of the plasma cylinder.…”

Section: Transition To Centered Depositionmentioning

confidence: 99%

Transition from edge-localized to center-localized power deposition in helicon discharges

Curreli

2011

Eur. Phys. J. Appl. Phys.

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Abstract. In radiofrequency (RF) helicon discharges the electromagnetic power is transferred from the RF field irradiated by the antenna to the plasma medium by means of plasma-wave coupling of the electromagnetic wave with the electrons. For the common industrial frequencies of tens of MHz, and for typical pressures of few Pascals, the power deposition occurs mostly at the edge of the discharge. In these conditions, ionization and electron heating occurs in a layer close to the chamber walls, where a consistent fraction of the plasma is rapidly lost by diffusion toward the surface. The remaining fraction of plasma diffuses inward toward the center of the discharge, setting up a uniform and almost flat density profile, used in applications. A one-dimensional model considering both the plasma-wave coupling of the electrons with the RF wave and the macroscopic transport of ions and neutrals along the radial dimension of a cylindrical processing chamber has been derived, and used to evaluate the profiles at equilibrium. The model has been validated through Langmuir probe measurements in helicon processing chambers. The numerical model has then been used to study the power-coupling behavior of the discharge when the pressure of the neutral gas is decreased. When the Knudsen number of the neutral gas approaches the unity and in conditions of slightly magnetized discharge, the power deposition shifts from being edge-localized to center-localized, thus reducing the particle fluxes toward the walls and increasing the efficiency of the coupling.

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“…Identifying the physical mechanisms of power deposition of the fast-wave in helicon sources has been a point of interest in literature [14][15][16][17][18][19][20]. Most authors attribute the efficient ionization of helicon sources in heavy ion discharges to the collisional damping of the Trivelpiece Goulde mode (TG) [16,[21][22][23][24]. The TG mode, slow-wave, is typically excited through non-resonant mode conversion of the helicon-mode, fast-wave, that occurs at the periphery of the plasma [25], therefore power deposition is typically edge dominated in helicon sources using heavy ions.…”

Section: Introductionmentioning

confidence: 99%

Helicon normal modes in Proto-MPEX

Piotrowicz

Caneses

Green

et al. 2018

Plasma Sources Sci. Technol.

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The Proto-MPEX helicon source has been operating in a high electron density 'helicon-mode'. Establishing plasma densities and magnetic field strengths under the antenna that allow for the formation of normal modes of the fast-wave are believed to be responsible for the 'heliconmode'. A 2D finite-element full-wave model of the helicon antenna on Proto-MPEX is used to identify the fast-wave normal modes responsible for the steady-state electron density profile produced by the source. We also show through the simulation that in the regions of operation in which core power deposition is maximum the slow-wave does not deposit significant power besides directly under the antenna. In the case of a simulation where a normal mode is not excited significant edge power is deposited in the mirror region.

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Equilibrium theory of cylindrical discharges with special application to helicons

Cited by 45 publications

References 43 publications

Central peaking of magnetized gas discharges

Central peaking of magnetized gas discharges

Transition from edge-localized to center-localized power deposition in helicon discharges

Helicon normal modes in Proto-MPEX

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