Electric field induced crossings of energy terms of a Rydberg quasi molecule enhancing charge exchange and ionization

Kryukov, Nikolay; Oks, Eugene

doi:10.1139/p2012-059

Cited by 7 publications

(6 citation statements)

References 23 publications

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“…The last term in equation (11) containing the exponential function is small and can be neglected, leading to the possibility of an analytical solution. This equation can then be solved for p, which can then be substituted into equations ( 18) and ( 17), thus obtaining the equilibrium equations for ε and r. Also, from the scaling formulas we see that E=−(Z/L) 2 ε/r, so that if we denote ε/r=ε 1 , then ε 1 and r will have the same scaling.…”

Section: Analytical Calculations Of Classical Energy Termsmentioning

confidence: 99%

“…Equation (17), after being squared, is a fourth-degree polynomial with respect to p and has a real positive analytical solution for p which depends on r: p 0 =p(w, b, r). Substituting k and the solution for p into equations ( 18) and (11), we obtain the formula for energy ε(w, b, r, Z, L, N, n) and equation (11) bearing the same variables. Then we solve the resulting equation (11) for w (it may have up to 3 solutions) and substitute them into ε(w, b, r, Z, L, N, n).…”

Section: Analytical Calculations Of Classical Energy Termsmentioning

confidence: 99%

“…Substituting k and the solution for p into equations ( 18) and (11), we obtain the formula for energy ε(w, b, r, Z, L, N, n) and equation (11) bearing the same variables. Then we solve the resulting equation (11) for w (it may have up to 3 solutions) and substitute them into ε(w, b, r, Z, L, N, n). Also, from the scaling formulas we see that E=−(Z/L) 2 ε/r, so if we denote ε/r=ε 1 , then ε 1 and r will have the same scaling.…”

Section: Analytical Calculations Of Classical Energy Termsmentioning

confidence: 99%

“…Later applications of these results included the following studies: the magnetic stabilization of such one-electron Rydberg quasimolecules (hereafter, RQ1) [10], the electric-fieldcaused enhancement of the ionization of the RQ1 and of charge exchange [11,12], the effect of the screening by plasma electrons on the classical energy terms of RQ1 [13,14], the application to the problem of continuum lowering in plasmas [13][14][15], the effect of a laser field on RQ1 [16], and the attachment of an electron to a muonic hydrogen atom [17,18] or to a muonic hydrogenic ion [19]. All these studies were summarized in review [20].…”

Section: Introductionmentioning

confidence: 99%

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Classical description of charge exchange involving He-like or Li-like ions in Rydberg states in plasmas

Kryukov¹,

Oks²

2016

J. Phys. B: At. Mol. Opt. Phys.

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A purely classical description of energy terms of one-electron Rydberg quasimolecules (hereafter, RQ1) consisting of one electron and two fully stripped ions of charges Z and Z′, where Z′≠Z, had been previously published by one of us. The analysis of the crossings of the energy terms led to a classical description of charge exchange either between a hydrogen-like ion of the nuclear charge Z with a fully stripped ion of the charge Z′ or between a hydrogen-like ion of the nuclear charge Z′ with a fully stripped ion of the charge Z. Later applications included, e.g., the influence of electric and magnetic fields, as well as of the screening by plasma electrons. In the present paper we extend the classical description of energy terms to two-electron Rydberg quasimolecules (RQ2), consisting of two electrons and two fully stripped ions of charges Z and Z′, and to three-electron Rydberg quasimolecules (RQ3), consisting of three electrons and two fully stripped ions of charges Z and Z′. We show that classical energy terms of RQ2 and RQ3 also exhibit crossings like the energy terms of RQ1. The crossing of terms of RQ2 occurs at a larger internuclear distance compared to the crossing of the corresponding terms of RQ1, so that the cross-section of the charge exchange for RQ2 is larger than the corresponding cross-section for RQ1. The crossing of terms of RQ3 occurs at an even larger internuclear distance compared to the crossing of the corresponding terms of RQ2, so that the cross-section of the charge exchange for RQ3 is even larger than the corresponding cross-section for RQ2. Thus, the classical roots of charge exchange are revealed not only by the example of RQ1 systems, but also by the examples of RQ2 and RQ3 systems. Our results contribute to advance the understanding of the quantum-classical correspondence and can be used in applications where charge exchange plays the key role.

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Section: Analytical Calculations Of Classical Energy Termsmentioning

confidence: 99%

Section: Analytical Calculations Of Classical Energy Termsmentioning

confidence: 99%

Section: Analytical Calculations Of Classical Energy Termsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Classical description of charge exchange involving He-like or Li-like ions in Rydberg states in plasmas

Kryukov¹,

Oks²

2016

J. Phys. B: At. Mol. Opt. Phys.

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“…Using the value of the scaled energy of the electron in the TCC system given in equation ( 5) of paper [20] with the substitution of the numeric or approximate solution for p from (10) into ( 5) and ( 7) and the further substitution of from ( 7) into (5) (all equations are from [20]), we obtain the dependence of the scaled energy on the scaled coordinate w in the situation where the electric field is parallel to the internuclear axis:…”

Section: Electric Field Effects On the Continuum Lowering In The Ioni...mentioning

confidence: 99%

Ionization channel of continuum lowering in plasmas: effects of plasma screening, electric and magnetic fields

Kryukov

Oks

2013

J. Phys. B: At. Mol. Opt. Phys.

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Calculations of continuum lowering (CL) in plasmas evolved from ion sphere models to dicentre models of the plasma state. One of such theories—a percolation theory—calculated CL defined as an absolute value of energy at which an electron becomes bound to a macroscopic portion of plasma ions (a quasi-ionization). Previously one of us derived analytically the value of CL in the ionization channel which was disregarded in the percolation theory. In the present paper we study how the value of CL in the ionization channel is affected by plasma screening, electric and magnetic fields. We show that the screening and the magnetic field decrease the value of CL, inhibiting the ionization, while the electric field increases the value of CL, promoting the ionization. These results should be important for inertial fusion, x-ray lasers, powerful Z-pinches, astrophysics and other applications of high-density plasmas. We also show that the screening stabilizes the nuclear motion of the corresponding Rydberg quasimolecules in some cases and destabilizes it in other cases.

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Classical analytical description of negative hydrogen ions

Oks

2021

Can. J. Phys.

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Studies of negative hydrogen ions (hereafter, NHI), such as, H– and D–, are important from both practical and fundamental points of view. One of the reasons for practical importance has to do with heating tokamak plasmas by external beams of NHI. Another practical use is the injection of NHI in high power proton accelerator facilities – for enhancing their performance. In addition, NHI are also important for studies of opacities of the atmospheres of the Sun and of the A-type stars. We present a classical analytical description of NHI in the situation where the underlying hydrogen (or deuterium) atom constitutes a rapid subsystem while the outer electron represents a slow subsystem. We focus at the case where the inner electron is in a circular state, so that the subsystem “nucleus plus inner electron” does not have the average electric dipole moment – in distinction to previous studies where the presence of the average dipole moment was the crucial requirement. By using the separation of rapid and slow subsystems, we show analytically that there is a classical bound state in such system and studied its parameters. In particular, we calculate analytically the primary frequency of the radiation of such system. This could be used for its experimental detection. The states that we found for the above systems could be considered as classical counterparts of the double-excited states of NHI previously studied in the literature in frames of quantum mechanics. The existence of classical counterparts of the double-excited states of NHI is a counterintuitive result.

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Electric field induced crossings of energy terms of a Rydberg quasi molecule enhancing charge exchange and ionization

Cited by 7 publications

References 23 publications

Classical description of charge exchange involving He-like or Li-like ions in Rydberg states in plasmas

Classical description of charge exchange involving He-like or Li-like ions in Rydberg states in plasmas

Ionization channel of continuum lowering in plasmas: effects of plasma screening, electric and magnetic fields

Classical analytical description of negative hydrogen ions

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