Theory of continuous-flow amplifiers and resonators

Камчатнов, А. М.; Chernyakov, A. L.

doi:10.1070/qe1982v012n05abeh012379

Cited by 14 publications

(18 citation statements)

References 4 publications

(4 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We can estimate the soliton lifetime by dividing the energy by dE/dt, calculated before any energy dissipation [7]. Since this is the maximum rate of energy dissipation, we can obtain a lower bound on the time it takes for the total energy to dissipate.…”

Section: Finite Conductivity and Soliton Lifetimementioning

confidence: 99%

“…[7], 2 we study the two scaled quantities of the system-the length scale R, which corresponds to the size of the soliton, and B 0 , which is the magnetic field strength at the origin. (The length scale R is also the radius of the sphere S 3 before stereographic projection.)…”

Section: Stability Analysismentioning

confidence: 99%

“…Hopfions have been shown to represent localized topological solitons in many areas of physics-as a model for particles in classical field theory [2], fermionic solitons in superconductors [3], particle-like solitons in superfluid-He [4], knotlike solitons in spinor Bose-Einstein (BE) condensates [5] and ferromagnetic materials [6], and topological solitons in magnetohydrodynamics (MHD) [7]. The Hopf fibration can also be used in the construction of finite-energy radiative solutions to Maxwell's equations and linearized Einstein's equations [8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Constructing a class of topological solitons in magnetohydrodynamics

et al. 2014

View full text Add to dashboard Cite

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, n t and n p , respectively. The special case of n t = 1 and n p = 1 corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for n t ∈ Z + and n p = 1, these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity, and we estimate the soliton lifetime in such a medium as a function of the toroidal winding number.

show abstract

Section: Finite Conductivity and Soliton Lifetimementioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Constructing a class of topological solitons in magnetohydrodynamics

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Solution of the equations of ideal magnetohydrodynamics describes a localized topological soliton with use of Hopf mapping shown by Kamchatnov (1982). Example of introducing the Euler's potential into a topological MHD soliton which has non-trivial helicity called MHD Kamchatnov-Hopf soliton was described by Semenov et al (2001).…”

Section: Introductionmentioning

confidence: 99%

MHD Kamchatnov-Hopf soliton in the model of primordial solar nebula

Salmin

2008

Proc. IAU

View full text Add to dashboard Cite

Abstract. Stereographic projection of Hopf field on the 3-sphere into Euclidean 3-space is used as a model of 3D steady flow of ideal compressible fluid in MHD. In such case, flow lines are Villarceau circles lying on tori corresponding to the levels of Bernoulli function. Existence of an optimal torus with minimal relative surface free energy is shown. Beat of oscillations with wave numbers corresponding to structural radii of optimal torus leads to scaling of optimal tori. Spatial intersection of homothetic tori within one torus result in formation of cluster with the size depending on scaling factor. Optimal tori are considered as precursors of planetary orbits.

show abstract

“…Since our solutions are based on the Bateman construction, it follows from a recent result by Goulart [29] that they are also exact solutions of nonlinear electrodynamics. We expect that the implementation of knot theory to generate topologically nontrivial structures in electromagnetism introduced here will lead to generalizations in linearized gravity [12,30], Bose-Einstein condensate configurations [31], and plasma configurations [32,33].…”

mentioning

confidence: 99%

Knotted optical vortices in exact solutions to Maxwell's equations

et al. 2017

View full text Add to dashboard Cite

We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred to as optical vortices, and their topology are preserved as time evolves and the fields have finite energy. To derive explicit expressions for these new electromagnetic fields that satisfy the nullness property, we make use of the Bateman variables for the Hopf field as well as complex polynomials in two variables whose zero sets give rise to algebraic links. The class of algebraic links includes not only all torus knots and links thereof, but also more intricate cable knots. While the unknot has been considered before, the solutions presented here show that more general knotted structures can also arise as optical vortices in exact solutions to Maxwell's equations.

show abstract

Theory of continuous-flow amplifiers and resonators

Cited by 14 publications

References 4 publications

Constructing a class of topological solitons in magnetohydrodynamics

Constructing a class of topological solitons in magnetohydrodynamics

MHD Kamchatnov-Hopf soliton in the model of primordial solar nebula

Knotted optical vortices in exact solutions to Maxwell's equations

Contact Info

Product

Resources

About