Comment on “Mathematical and physical aspects of Kappa velocity distribution” [Phys. Plasmas 14, 110702 (2007)]

Hellberg, M. A.; Mace, R. L.; Baluku, T. K.; Kourakis, Ioannis; Saini, N. S.

doi:10.1063/1.3213388

Cited by 350 publications

(247 citation statements)

References 55 publications

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“…The physical meaning of the Debye length 343 2001; Saito et al 2000;Leubner 2004;Raadu and Shafiq 2007;Hellberg et al 2009;Livadiotis and McComas 2009, 2010a-c, 2011a, 2011b, 2012, 2013aTribeche et al 2009;Le Roux et al 2010;Eslami et al 2011;Kourakis et al 2012;Yoon 2012;Yoon et al 2012;Bains et al 2013;Saberian and Esfandyari-Kalejahi 2013).…”

Section: And Zelenyi 2000mentioning

confidence: 99%

Electrostatic shielding in plasmas and the physical meaning of the Debye length

Livadiotis

McComas

2014

J. Plasma Phys.

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This paper examines the electrostatic shielding in plasmas, and resolves inconsistencies about what the Debye length really is. Two different interpretations of the Debye length are currently used: (1) The potential energy approximately equals the thermal energy, and (2) the ratio of the shielded to the unshielded potential drops to 1/e. We examine these two interpretations of the Debye length for equilibrium plasmas described by the Boltzmann distribution, and non-equilibrium plasmas (e.g. space plasmas) described by kappa distributions. We study three dimensionalities of the electrostatic potential: 1-D potential of linear symmetry for planar charge density, 2-D potential of cylindrical symmetry for linear charge density, and 3-D potential of spherical symmetry for a point charge. We resolve critical inconsistencies of the two interpretations, including: independence of the Debye length on the dimensionality; requirement for small charge perturbations that is equivalent to weakly coupled plasmas; correlations between ions and electrons; existence of temperature for nonequilibrium plasmas; and isotropic Debye shielding. We introduce a third Debye length interpretation that naturally emerges from the second statistical moment of the particle position distribution; this is analogous to the kinetic definition of temperature, which is the second statistical moment of the velocity distribution. Finally, we compare the three interpretations, identifying what information is required for theoretical/experimental plasma-physics research: Interpretation 1 applies only to kappa distributions; Interpretation 2 is not restricted to any specific form of the ion/electron distributions, but these forms have to be known; Interpretation 3 needs only the second statistical moment of the positional distribution.

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Section: And Zelenyi 2000mentioning

confidence: 99%

Electrostatic shielding in plasmas and the physical meaning of the Debye length

Livadiotis

McComas

2014

J. Plasma Phys.

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“…first and second kinds, and forms where either the "temperature" or "thermal velocity" is kappa dependent e.g. Lazar et al (2016), Livadiotis (2015Livadiotis ( , 2014, Livadiotis & McComas (2009), Hellberg et al (2009), Leubner (2004. The physical interpretation of the value of κ obtained from the line fitting, in terms of the ion velocity distribution, therefore depends on the form of the ion kappa distribution used.…”

Section: Non-thermal Ion Motionmentioning

confidence: 99%

First evidence of non-Gaussian solar flare EUV spectral line profiles and accelerated non-thermal ion motion

Jeffrey

Fletcher

Labrosse

2016

A&A

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Context. The properties of solar flare plasma can be determined from the observation of optically thin lines. The emitting ion distribution determines the shape of the spectral line profile, with an isothermal Maxwellian ion distribution producing a Gaussian profile. Non-Gaussian line profiles may indicate more complex ion distributions. Aims. We investigate the possibility of determining flare-accelerated non-thermal ion and/or plasma velocity distributions. Methods. We study EUV spectral lines produced during a flare SOL2013-05-15T01:45 using the Hinode EUV Imaging Spectrometer (EIS). The flare is located close to the eastern solar limb with an extended loop structure, allowing the different flare features: ribbons, hard X-ray (HXR) footpoints and the loop-top source to be clearly observed in UV, EUV and X-rays. EUV line spectroscopy is performed in seven different regions covering the flare. We study the line profiles of the isolated and unblended Fe XVI lines (λ262.9760 Å ) mainly formed at temperatures of ∼2 to 4 MK. Suitable Fe XVI line profiles at one time close to the peak soft X-ray emission and free of directed mass motions are examined using: 1. a higher moments analysis, 2. Gaussian fitting, and 3. by fitting a kappa distribution line profile convolved with a Gaussian to account for the EIS instrumental profile. Results. Fe XVI line profiles in the flaring loop-top, HXR footpoint and ribbon regions can be confidently fitted with a kappa line profile with an extra variable κ, giving low, non-thermal κ values between 2 and 3.3. An independent higher moments analysis also finds that many of the spectral line kurtosis values are higher than the Gaussian value of 3, even with the presence of a broad Gaussian instrumental profile. Conclusions. A flare-accelerated non-thermal ion population could account for both the observed non-Gaussian line profiles, and for the Fe XVI "excess" broadening found from Gaussian fitting, if the emitting ions are interacting with a thermalised ∼4 MK electron population, and the instrumental profile is well-approximated by a Gaussian profile.

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“…1 The authors point out that v th 2 in Eq. ͑1͒ ought to have dependence on and v th 2 should be replaced with ͑ −3/ 2͒v th 2 , while k B T in Eq.…”

Section: ͑6͒mentioning

confidence: 99%

Response to “Comment on ‘Mathematical and physical aspects of Kappa velocity distribution’ ” [Phys. Plasmas 16, 094701 (2009)]

Hau

Chuang

2009

Physics of Plasmas

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The comment questions the formulation of the κ velocity distribution function used in our paper as compared to a slightly different form used by the authors. The difference in the distribution function necessarily leads to different number densities, thermal pressures, etc. We show that the restriction with their distribution function is that the macroscopic temperature (or average kinetic energy) is the same for all spatially uniform systems with a family of κ distributions including the Maxwellian case. The distribution function used in our paper and widely adopted in various studies of nonthermal systems, however, does not impose such a constraint; in particular, the temperature has κ dependence reflecting the kinetic nature of different statistical systems. The points made in the comment are trivial and misleading.

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Comment on “Mathematical and physical aspects of Kappa velocity distribution” [Phys. Plasmas 14, 110702 (2007)]

Cited by 350 publications

References 55 publications

Electrostatic shielding in plasmas and the physical meaning of the Debye length

Electrostatic shielding in plasmas and the physical meaning of the Debye length

First evidence of non-Gaussian solar flare EUV spectral line profiles and accelerated non-thermal ion motion

Response to “Comment on ‘Mathematical and physical aspects of Kappa velocity distribution’ ” [Phys. Plasmas 16, 094701 (2009)]

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