Reply to the Comment by Wu on “Quantum telegraph: is it possible?” by B.B. Kadomtsev (Phys. Lett. A 210 (1996) 371)

Kadomtsev, M. B.

doi:10.1016/s0375-9601(99)00097-3

Cited by 53 publications

(77 citation statements)

References 7 publications

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“…This reflects the fact that the electronic cloud has a more and more pronounced needle-like form oriented along the magnetic line, as was predicted in the classical papers [1][2]. The behavior of < ρ > itself does not display any unusual properties, smoothly decreasing with magnetic field, quickly approaching the cyclotron radius for small inclinations and large magnetic fields.…”

Section: Resultssupporting

confidence: 68%

“…Many years have passed since the moment when theoretical qualitative arguments were given that show that in the presence of a strong magnetic field the physics of atoms and molecules exhibits a wealth of new, unexpected phenomena even for the simplest systems [1,2]. In particular, a chance that unusual chemical compounds may be formed which do not exist without magnetic field was mentioned.…”

Section: Introductionmentioning

confidence: 99%

“…Let us fix a vector potential in (1). Assume that we have solved the spectral problem exactly and have found the ground state eigenfunction.…”

Section: Introductionmentioning

confidence: 99%

“…One can easily show that for a system possessing axial (rotational) symmetry [37] the optimal gauge is the symmetric gauge ξ = 1/2 with arbitrary d. This is precisely the gauge which has been overwhelmingly used (without any explanations) in the majority of the previous research on H + 2 in the parallel configuration [1] - [30]. However, this is not the case if θ = 0 • .…”

Section: Introductionmentioning

confidence: 99%

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H2+molecular ion in a strong magnetic field: Ground state

Turbiner

Vieyra

2003

Phys. Rev. A

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A detailed quantitative analysis of the system (ppe) placed in magnetic field ranging from 0 − 4.414 × 10 13 G is presented. The present study is focused on the question of the existence of the molecular ion H + 2 in a magnetic field. As a tool, a variational method with an optimization of the form of the vector potential (optimal gauge fixing) is used. It is shown that in the domain of applicability of the non-relativistic approximation the system (ppe) in the Born-Oppenheimer approximation has a well-pronounced minimum in the total energy at a finite interproton distance for B 10 11 G, thus manifesting the existence of H + 2 . For B 10 11 G and large inclinations (of the molecular axis with respect to the magnetic line) the minimum disappears and hence the molecular ion H + 2 does not exist. It is shown that the most stable configuration of H + 2 always corresponds to protons situated along the magnetic line. With magnetic field growth the ion H + 2 becomes more and more tightly bound and compact, and the electronic distribution evolves from a two-peak to a one-peak pattern. The domain of inclinations where the H + 2 ion exists reduces with magnetic field increase and finally becomes 0 o − 25 o at B = 4.414 × 10 13 G. Phase transition type behavior of variational parameters for some interproton distances related to the beginning of the chemical reaction H +

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Section: Resultssupporting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

“…Let us fix a vector potential in (1). Assume that we have solved the spectral problem exactly and have found the ground state eigenfunction.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

H2+molecular ion in a strong magnetic field: Ground state

Turbiner

Vieyra

2003

Phys. Rev. A

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“…Previous papers 1,2,3 have outlined the requirements for "plasma physics identity experiments" between different devices. They regard, in addition to the identity of trivially dimensionless parameters fixing the plasma geometry and the poloidal/ toroidal field ratio ( .. , , , q a R o δ κ ), the prescription of heating power, magnetic field strength, density and plasma dimension so as to keep constant 4 na , or combinations of these parameters.…”

Section: Dimensionless Engineering Variablesmentioning

confidence: 99%

Dimensionless Engineering Variables for Measuring the ITER and Reactor Relevance of Tokamak Experiments

Lackner

2008

Fusion Science and Technology

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a 5/4 and P heat . a 3/4 are proposed as dimensionless engineering parameters to measure the reactor relevance of existing and planned confinement devices. These quantities -together with a density parameter that can be written as n . a 3/4 /B t -have to be conserved in plasma physics identity experiments on different size devices to respect the so-called Kadomtsev similarity constraints, and offer a coordinate system to map the approach to the reactor regime. Theoretical and semi-empirical models can be used in this coordinate space to produce isocontours for different dimensionless physics quantities, like the usual parameters ρ * ,ν * ,β, but also for the intensity of collisional coupling, the excess of heating power over the L-H transition threshold, and the ratio of current redistribution to energy confinement time to visualize the distance to the regime of a fusion reactor.

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Fluctuation‐dissipation‐dispersion relations for a nonuniform plasma

Belyi

2003

Contrib. Plasma Phys.

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Using the Langevin approach and the multiscale technique, a kinetic theory of the time and space nonlocal fluctuations in the collisional plasma is constructed. In local equilibrium a generalized version of the CallenWelton theorem is derived. It is shown that not only the dissipation but also the time and space derivatives of the dispersion determine the amplitude and the width of the spectrum lines of the electrostatic field fluctuations, as well as the form factor. There appear significant differences with respect to the non-uniform plasma. In the kinetic regime the form factor is more sensible to space gradient than the spectral function of the electrostatic field fluctuations. As a result of the inhomogeneity, these proprieties became asymmetric with respect to the inversion of the frequency sign. The differences in amplitude of peaks could become a new tool to diagnose slow time and space variations in the plasma.Fluctuations play an essential role in the plasma diagnostics. Indeed, plasma parameters such as temperature, mean velocity, density can be determined by incoherent (Thomson) scattering diagnostics [1], i.e. by the proper interpretation of data obtained from the scattering of a given electromagnetic field interacting with the system. The key point of interpreting them is the knowledge of the intensity of the dielectric function fluctuations or equally of the electron form factor (δn e δn e ) ω,k . Here ω and k are respectively the frequency and wavevector of the autocorrelations. Due to the Poisson equation the electron form factor in the spatially homogeneous system is directly linked to the electrostatic field fluctuations, which have been the object of active study since the early 1960s [1]. In the thermodynamic equilibrium, the electrostatic field fluctuations satisfy the famous Callen-Welton fluctuation-dissipation theorem [2]:linking their intensity to the imaginary (dissipative) part of the dielectric function ε(ω, k), and the temperature Θ in energy units. The spectral function has peaks, corresponding to proper plasma frequencies. The matter becomes more tricky in the non-equilibrium case. When the state of the plasma is given by Maxwell distributions characterized by different constant temperatures and velocities per species (Θ a , V a ; a = e, i), it is generally admitted that the spectral function of the electron density for a two component system takes the form [1]:(δn e δn e ) ωk =2 . k D is the Debye number and χ a (a = e, i) is the complex dielectric susceptibility of the a-th component. This formula has been extensively used to interpret the scattering data mentioned above. We have indeed shown [3], that, in the collisional regime equations this formula should be revisited. We stressed the fact that a kinetic approach should be taken. Introducing fluctuations by the Langevin method, we have elaborated a "revisited" Callen-Welton formula containing new terms explicitly displaying dissipative non equilibrium contributions. It is however not evident that the plasma parameters -tempera...

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Reply to the Comment by Wu on “Quantum telegraph: is it possible?” by B.B. Kadomtsev (Phys. Lett. A 210 (1996) 371)

Cited by 53 publications

References 7 publications

H2+molecular ion in a strong magnetic field: Ground state

H2+molecular ion in a strong magnetic field: Ground state

Dimensionless Engineering Variables for Measuring the ITER and Reactor Relevance of Tokamak Experiments

Fluctuation‐dissipation‐dispersion relations for a nonuniform plasma

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