Arrayás, Fontelos, and Trueba Reply:

Arrayás, Manuel; Fontelos, Marco A.; Trueba, José L.

doi:10.1103/physrevlett.101.139502

Cited by 20 publications

(64 citation statements)

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“…A different, extensive analysis with different results can be found in [5]. Below we show that the expansion and calculation in [1] are inconsistent, that the result contradicts a known analytical asymptote, and that it does not fit the cross-checked numerical results presented in [5]. Furthermore, we find in [5] that the most unstable wavelength does not scale as D 1=3 e as claimed in [1], but as D…”

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confidence: 60%

“…In [1], ionization fronts are only considered in the limit jE 1 j ) 1 ahead of the front which amounts to a saturating impact ionization cross section ðEÞ ! 1.…”

Section: =4mentioning

confidence: 99%

“…For negative streamers in pure gases like nitrogen or argon, electron diffusion D e > 0 should be included into the discharge model. This is attempted in [1] (8) reproduces the diffusive layer for large jE 1 j, but the nonlinear term is incomplete. Then the dispersion relation is calculated by the expansion (11)-(13) about the planar ionization front.…”

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confidence: 99%

“…The Letter [1] therefore aims to calculate the temporal growth rate sðkÞ of modes with wave number k, when the electric field far ahead of the ionization front is E 1 . In earlier work [2][3][4], sðkÞ was determined in a pure reaction-drift model for the free electrons, i.e., in the limit of vanishing electron diffusion D e ¼ 0.…”

mentioning

confidence: 99%

“…For negative streamers in pure gases like nitrogen or argon, electron diffusion D e > 0 should be included into the discharge model. This is attempted in [1] in the limit of large field jE 1 j ahead of the front. A different, extensive analysis with different results can be found in [5].…”

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confidence: 99%

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Comment on “Mechanism of Branching in Negative Ionization Fronts”

Ebert

Derks

2008

Phys. Rev. Lett.

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When the fingers of discharge streamers emerge from a planar ionization front due to a Laplacian instability, their initial spacing is determined by the band of unstable transversal Fourier perturbations and generically dominated by the fastest growing modes. The Letter [1] therefore aims to calculate the temporal growth rate sðkÞ of modes with wave number k, when the electric field far ahead of the ionization front is E 1 . In earlier work [2][3][4], sðkÞ was determined in a pure reaction-drift model for the free electrons, i.e., in the limit of vanishing electron diffusion D e ¼ 0. For negative streamers in pure gases like nitrogen or argon, electron diffusion D e > 0 should be included into the discharge model. This is attempted in [1] (8) reproduces the diffusive layer for large jE 1 j, but the nonlinear term is incomplete. Then the dispersion relation is calculated by the expansion (11)-(13) about the planar ionization front. Here the expansion of the electron density n e starts in order 2 (where is the small expansion parameter), while the expansions of ion density n p and field E start in order . The absence of order in the expansion of n e is unexpected, not explained, and in contradiction with the calculation for D e ¼ 0 in [4].Jumping to the result of [1], the dispersion relation in Eq. (21) Furthermore, in [5], dispersion curves sðkÞ for a range of fields E 1 and diffusion constants D e are derived as an eigenvalue problem for s; they are plotted in Fig. 1. In one case, the curve is confirmed by numerical solutions of an initial value problem; the curves are also consistent with the analytical small k asymptote. The results for positive s are conveniently fitted as sðkÞ ¼ c (23)] for the spacing of emergent streamers does not hold; rather our physical arguments and the numerical data in [5] suggest that the fastest growing mode is

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confidence: 60%

“…In [1], ionization fronts are only considered in the limit jE 1 j ) 1 ahead of the front which amounts to a saturating impact ionization cross section ðEÞ ! 1.…”

Section: =4mentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Comment on “Mechanism of Branching in Negative Ionization Fronts”

Ebert

Derks

2008

Phys. Rev. Lett.

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On topology and electromagnetism

Rañada

2012

Annalen der Physik

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Arrayás and Trueba [1] recently obtained an exact solution of Maxwell's equations in empty space with non trivial topology of the force lines, in which there is an exchange of helicity between its electric and magnetic fields. The two helicities were different at time zero, but in the limit of infinite time they are equal, their sum being conserved. Although not widely known, there are topological solutions of Maxwell equations with the surprising property that any pair of electric lines and any pair of magnetic lines are linked except for a zero measure set. These solutions, baptized "electromagnetic knots", discovered and developed in references [2-4] building on the Hopf fibration [5], allowed the basis for a topological model of electromagnetism (TME) to be proposed, in which the force lines play a prominent role. In reference [6] a review is presented of the work done on that model (see also [7]). The paper by Arrayás and Trueba is an important step in its development.The principal aim of this line of research is to complete the TME that, in its present form, is locally equivalent to Maxwell's theory, is based on the topology of the electric and magnetic lines and has topological constants of motion as the electric charge or the total helicity. The force lines are the level curves of two complex scalar fields φ(r, t ), θ(r, t ) with only one value at infinity, that can be interpreted as maps between two spheres S 3 → S 2 ,

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Surface behavior based on ion-induced secondary electron emission from semi-insulating materials in breakdown evolution

Koç

Karaköse

Salamov

2013

Phys. Status Solidi A

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This study focuses on analyses of secondary electron emission (SEE) at semiconductor surfaces when the sufficient conditions of space–time distribution occur. Experimental measurements and calculations with the approach of Townsend coefficients, which include the evaluations of ionization coefficient (α) and SEE coefficient (γ) were performed in high‐ohmic InP, GaAs, and Si semiconductor cathodes with argon and air environments in a wide range of E/N (300–10 000 Td). The direct calculations of γ were carried out to determine the behavior of cold‐semiconductor cathode current in a wide range of microgaps (45–525 μm). Paschen curves are interpreted in the dependence of large pd range on breakdown voltage through γ and α/N. Ion‐induced secondary electrons exhibit the direct behaviors affecting the timescale of breakdown evolution in the vicinity of the Paschen minimum during the natural bombardment process with ions of semiconductor cathodes. Also, when α/N rapidly drops and the excitations of gas atoms densely occupy the gas volume, we determined that the photoelectric effect provides a growth for electron emission from semiconductor surfaces at the breakdown stage at the reduced values of E/N. At all pressures, the emission magnitudes of electrons liberated by semiconductor cathodes into vacuum are found as γInP > γGaAs > γSi in breakdown evolution.

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Arrayás, Fontelos, and Trueba Reply:

Cited by 20 publications

References 6 publications

Comment on “Mechanism of Branching in Negative Ionization Fronts”

Comment on “Mechanism of Branching in Negative Ionization Fronts”

On topology and electromagnetism

Surface behavior based on ion-induced secondary electron emission from semi-insulating materials in breakdown evolution

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