A paper in the journal “Nature Physics: Linked and knotted beams of light by William T. M. Irvine and Dirk Bouwmeester appears like it would be related to the goals of Lawrenceville Plasma Physics, Inc to make Focus Fusion. Because knotted light beams have both beamlike properties and unique unexplored properties, the physicists (Irvine and Bouwmeester) predict that creating the beams could have applications in several areas. These could include applications in plasma confinement, atomic particle trapping, manipulating cold atomic ensembles, and generating soliton-like solutions in nonlinear media. Plasma confinement with knots is what dense plasma focus fusion is about.
In some little-known solutions to Maxwell’s equations, all the electric and magnetic field lines form circles that are all linked to each other. These loops of field lines can be used to construct the donut shape of a torus. In such a scenario, each circle wraps around the torus once, and no two circles cross each other. Smaller tori could then be nested within larger ones, filling three-dimensional space with circles of light beams.
After investigating knotted light’s properties, the physicists determined that they could use laser fields to create the structures. Starting with a single-pulsed beam of circularly polarized light, and tightly focusing the beam, it should be possible to create various shapes of looped light beams. By using holographic techniques and a spatial light modulator, the shape and profile of the looped light could also be controlled. These same techniques have recently been used to produce Airy beams, which are light beams that don’t spread out as they propagate.
Currently the physicists are preparing for an experimental realization of the new solutions either using electromagnetic radiation in the optical regime, i.e. light, or in the microwave regime. The main challenge will be to deal with ultra-short pulses of radiation in order to create a broad spectrum of frequencies as needed for the construction of the light knots.
Maxwell’s equations allow for curious solutions characterized by the property that all electric and magnetic field lines are closed loops with any two electric (or magnetic) field lines linked. These little-known solutions, constructed by Rañada, are based on the Hopf fibration. Here we analyse their physical properties to investigate how they can be experimentally realized. We study their time evolution and uncover, through a decomposition into a spectrum of spherical harmonics, a remarkably simple representation. Using this representation, first, a connection is established to the Chandrasekhar–Kendall curl eigenstates, which are of broad importance in plasma physics and fluid dynamics. Second, we show how a new class of knotted beams of light can be derived, and third, we show that approximate knots of light may be generated using tightly focused circularly polarized laser beams. We predict theoretical extensions and potential applications, in fields ranging from fluid dynamics, topological optical solitons and particle trapping to cold atomic gases and plasma confinement.
2. The plasma sheet bends inwards to the hole in the anode.
Plasma filaments are formed in counter rotating pairs.
3. The plasma sheet and filaments contract towards the center. The focus forms.
The filament pairs merge like a zipper. Energy is transferred from the outside to the central region
4. The plasma sheet and filaments continue contracting into the center
5. A rotating plasma vortex is formed in the center, carrying all the current
7. The filament forms a tight plasma helix
8. the helix starts to kink
9. And it becomes unstable and …
11. The magnetic field of the plasmoid causes it to shrink
12. The shrinking plasmoid rotates.
The electron beam that the plasmoid generates heats it up.
13. The temperature becomes high enough for some colliding protons and boron nuclei to overcome their electric repulsion
14. Protons and boron nuclei fuse and create unstable carbon-12 nuclei
15. The nucleus breaks up to form helium nuclei (alpha particles).
Energy is released as the kinetic energy of the alpha particles
16. The fast alpha particles heat the plasma and the fusion reactions occur faster and faster
17. An electric field creates a beam of fast ions (nuclei) that carry most of the fusion energy (shown in blue). An electron beam (shown in red) goes in the opposite direction
18. The plasmoid is evacuated by the beams
19. The energy in the ion beam is collected by a solenoid.
This direct conversion to electricity is very efficient and economical
Time evolution of the Hopf field lines: Magnetic field lines
Quicktime movie file (620 KB): Supplementary video 1.mov
Summary: Animation showing the time evolution of the Hopf Magnetic field lines
Time evolution of the Hopf field lines: Electric field lines
Quicktime movie file (772 KB): Supplementary video 2.mov
Summary: Animation showing the time evolution of the Hopf Electric field lines
Time evolution of the Hopf field lines: Electric and Magnetic field lines
Quicktime movie file (852 KB): Supplementary video 3.mov
Summary: Animation showing the time evolution of the Hopf Electric and Magnetic field