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Articles With Citations to Z. Abou-Assaleh

Theoretical Plasma Physics

Controlled Thermonuclear Fusion Energy

2012

Plasma Sources Sci. Technol. 21 (2012) 063001 (47pp)

https://iopscience.iop.org/

article/10.1088/0963-0252/21/6/063001/meta

doi:10.1088/0963-0252/21/6/063001

"Mach probes"

Kyu-Sun Chung

Department of Electrical Engineering, Hanyang University, Seoul 133-791, Republic of Korea

Received 4 February 2008, in final form 6 August 2012

Published 16 November 2012 Online at stacks.iop.org/PSST/21/063001

Abstract

A Mach probe (MP) is an electric probe system to deduce the plasma flow velocity from the ratio of ion saturation currents. Generally, a typical MP is composed of two directional electric probes located at opposite sides of an insulator, which is mostly used as a parallel MP, but there are other MPs such as perpendicular MP (PMP), Gundestrup probe (GP) or rotating probe (RP), and visco-MP (VMP), depending on the shape of the probe holder, location of different probes or the method of collecting ions. For the parallel MP (to be called simply an MP), the relation between the ratio of the upstream ion saturation current density (Jup) to the downstream (Jdn) and the normalized drift velocity (M∞ = vd/√Te/mi) of the plasma has generally been fitted into an exponential form (R = Jup/Jdn ≈ exp[KM∞]). For the GP or RP, with oblique ion collection, the relation becomes R = exp[K(M −M⊥ cot θ)], where K  2.3–2.5, M = M∞, M⊥ is the normalized perpendicular flow to the magnetic field, and θ is the angle between the magnetic field and the probe surface. The normalized drift velocity of flowing plasmas is deduced from the ratio (Rm) measured by an MP as M∞ = ln[Rm]/K, where K is a calibration factor depending on the magnetic flux density, collisionality of charged particles and neutrals, viscosity of plasmas, ion temperature, etc. Existing theories of MPs in unmagnetized and magnetized flowing plasmas are introduced in terms of kinetic, fluid and particle-in-cell models or self-consistent and self-similar methods along with key physics and comments. Experimental evidence of relevant models is shown along with validity of related theories. Calibration and error analysis are also given. For probes other than the typical parallel MP, the relation between the ratio of ion saturation currents and M∞ can be expressed as a combination of the functional forms: exponential and/or polynomial form of M∞ for PMP; two Rs of two separate MPs for VMP. Collisions of ions/electrons/neutrals, asymmetries of ion temperatures and the existence of hyperthermal electrons, existence of ion beam, supersonic flow and negative ions can affect the deduction of flow velocities by an MP.

References

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[142]  Gulick S L, Stansfield B L, Z. Abou-Assaleh, Boucher C, Matte J P, Johnston T W and Marchand R 1990 J. Nucl. Mater. 176–177 1059

Home > Physics of Plasmas > Volume 19, Issue 10 > 10.1063/1.4754004

Physics of Plasmas 19, 102103 (2012); https://doi.org/10.1063/1.4754004

Multi-temperature representation of electron velocity distribution functions. I. Fits to numerical results

A. A. Haji Abolhassani^a) and J.-P. Matte^b)

INRS-Énergie, Matériaux et Télécommunications, Université du Québec, Varennes, Québec J3X 1S2, Canada.

ABSTRACT

Electron energy distribution functions are expressed as a sum of 6–12 Maxwellians or a sum of 3, but each multiplied by a finite series of generalized Laguerre polynomials. We fitted several distribution functions obtained from the finite difference Fokker-Planck code “FPI” [Matte and Virmont, Phys. Rev. Lett. 49, 1936 (1982)] to these forms, by matching the moments, and showed that they can represent very well the coexistence of hot and cold populations, with a temperature ratio as high as 1000. This was performed for two types of problems: (1) the collisional relaxation of a minority hot component in a uniform plasma and (2) electron heat flow down steep temperature gradients, from a hot to a much colder plasma. We find that the multi-Maxwellian representation is particularly good if we accept complex temperatures and coefficients, and it is always better than the representation with generalized Laguerre polynomials for an equal number of moments. For the electron heat flow problem, the method was modified to also fit the first order anisotropy f 1 (x,v,t) f1(x,v,t), again with excellent results. We conclude that this multi-Maxwellian representation can provide a viable alternative to the finite difference speed or energy grid in kinetic codes.

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