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Putin and Vladimir Fortov (below)
HIGH MAGNETIC FIELDS – by Vladimir Fortov
Excerpt from “EXTREME STATES OF MATTER” – Springer 2016
Production of ultrahigh magnetic field generation is an interesting and vigorously developing line of research…
Different mechanisms of magnetic filed generation in the interaction of high-intensity laser radiation with solid targets give rise to magnetic fields with a magnetic induction of up to 1 GGs, which are produced in the interaction of high-intensity laser radiation with dense plasmas. These fields are localized near the critical surface, where there occurs the main absorption of laser energy. Several main mechanism have been proposed responsible for the generation of the quasistatic magnetic fields: (1) the difference in directions of the plasma temperature and density gradients; (2) the flux of fast electrons accelerated by ponderomotive forces along and across the laser pulse direction; (3) collisionless Weibel instability.
The generation of magnetic fields with an induction of about 1 GGs in relativistic dense plasma was first predicted by R.N. Sudan in a paper ‘Mechanism for the generation of [10 to the 9th G] magnetic fields in the interaction of ultra intense short laser pulse with an overdense plasma target’ 1993. According to the theory proposed in this source of quasistationary magnetic field is the ponderomotive force acting on electrons. It generates radial electron current away from the axis of the laser beam towards its periphery until the beginning of a combined vibrational motion of ions and electrons caused by the requirement of electroneutrality.
The Weibel instability mechanism in the plasma arises from the anisotropy [not uniform, not consistent] of electrons in their velocity directions. This anisotropy emerges in the course of ionization of atoms and atomic ions by superhighway laser field.
The majority of electrons escapes along the direction of the electric intensity vector of a linearly polarized laser wave. The number of electrons escaping in the transverse velocities are defined by the energy-time uncertainty relations.
[In 1959] Weibel was the first to show that the presence of electron current anisotropy gives rise to instability in Maxwell equations relative to a spontaneous buildup of quasi static magnetic field.
The thermoelectric mechanism, unlike the previous one, is realized in a collisional plasma in which there are gradients of the electron density and electron temperature directed at an angle to each other. The density gradient is directed along the radius of the electron beam. It is caused by the nonuniformity of laser radiation intensity across the focal spot.
As a result, the number of electrons on the axis of the laser beam is far greater than at the beam periphery owing to a strong difference in the degree of ionization of the atoms of the medium. The temperature gradient is evidently directed along the normal to the target surface. The growth increment of spontaneous magnetic field is proportional both to the temperature gradient and the velocity gradient. In this case the magnetic field possesses toroidal symmetry: its circular lines of force embrace the laser beam.
In the passage of a laser pulse of relativistic intensity, the plasma electrons are accelerated along the direction of laser pulse propagation by the magnetic part of the Lorentz force. This gives rise to a magnetic field, which is also annular in character.
There also exists more sophisticated methods of magnetic generation in a laser plasma.
Vladimir Yevgenyevich Fortov (Russian: Владимир Евгеньевич Фортов, born 23 January 1946 in Noginsk, Moscow Oblast) is a Russian physicist and a member of the Russian Academy of Sciences; on 29 May 2013 he was elected its president. Prior to the election, Fortov was the director of the Joint Institute for High Temperatures. On 22 March 2017, Fortov resigned as a President.
The Weibel instability is a plasma instability present in homogeneous or nearly homogeneous electromagnetic plasmas which possess an anisotropy in momentum (velocity) space. This anisotropy is most generally understood as two temperatures in different directions. Burton Fried showed that this instability can be understood more simply as the superposition of many counter-streaming beams. In this sense, it is like the two-stream instability except that the perturbations are electromagnetic and result in filamentation as opposed to electrostatic perturbations which would result in charge bunching. In the linear limit the instability causes exponential growth of electromagnetic fields in the plasma which help restore momentum space isotropy. In very extreme cases, the Weibel instability is related to one- or two-dimensional stream instabilities.
Consider an electron-ion plasma in which the ions are fixed and the electrons are hotter in the y-direction than in x or z-direction.
To see how magnetic field perturbation would grow, suppose a field B = B cos kx spontaneously arises from noise. The Lorentz force then bends the electron trajectories with the result that upward-moving-ev x B electrons congregate at B and downward-moving ones at A. The resulting current j = -en ve sheets generate magnetic field that enhances the original field and thus perturbation grows.
Weibel instability is also common in astrophysical plasmas, such as collisionless shock formation in supernova remnants and -ray bursts.