Magnetic dynamics of simple collective modes in a two-sphere plasma model

Essén, Hanno

doi:10.1063/1.2149349

Cited by 8 publications

(9 citation statements)

References 24 publications

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“…It is also in accord with Woltjer's [52] assumption that self organized states of a plasma should correspond to maxima of magnetic energy. Mehra and De Luca [53], on the other hand, made computer simulations of a plasma minimizing the velocity space form of the Darwin energy (30). They then found surprising results indicating that anti-parallel currents attracted each other.…”

Section: On the Nature Of Magnetic Energymentioning

confidence: 99%

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From least action in electrodynamics to magnetomechanical energy—a review

Essén

2009

Eur. J. Phys.

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The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative and one can study them in a Hamiltonian formalism. The central concepts of generalized capacitance and inductance coefficients are introduced and explained. The problem of gauge independence of self-inductance is considered. Our main interest is in magnetomechanics, i.e. the study of systems where there is exchange between mechanical and magnetic energy. This throws light on the concept of magnetic energy, which according to the literature has confusing and peculiar properties. We apply the theory to a few simple examples: the extension of a circular current loop, the force between parallel wires, interacting circular current loops, and the rail gun. These show that the Hamiltonian, phase space, form of magnetic energy has the usual property that an equilibrium configuration corresponds to an energy minimum.

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Section: On the Nature Of Magnetic Energymentioning

confidence: 99%

“…In case of doubt the safe method is to start with the Darwin Lagrangian (11) and introduce relevant constraints and idealizations. A couple of examples of this procedure can be found in Essén [29,30]. Electromechanical systems are treated e.g.…”

Section: Electromechanical Systemsmentioning

confidence: 99%

From least action in electrodynamics to magnetomechanical energy—a review

Essén

2009

Eur. J. Phys.

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“…In order to interpret our data, we developed a simple model in which we assume that the electron cloud moves as a whole in response to an applied external field within a Gaussian ion density distribution [25]. While this would be a poor model under many cycles of applied RF because the non-solid nature of the electron cloud will cause the cloud to de-phase, for 2-cycles it is more applicable.…”

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Density-dependent response of an ultracold plasma to few-cycle radio-frequency pulses

2013

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Ultracold neutral plasmas exhibit a density-dependent resonant response to applied radiofrequency (RF) fields in the frequency range of several MHz to hundreds of MHz for achievable densities. We have conducted measurements where short bursts of RF were applied to these plasmas, with pulse durations as short as two cycles. We still observed a density-dependent resonant response to these short pulses, but the timescale of the response is too short to be consistent with local heating of electrons in the plasma from collisions under a range of experimental parameters. Instead, our results are consistent with rapid energy transfer from collective motion of the entire electron cloud to individual electrons. This collective motion was also observed by applying two sharp electric field pulses separated in time to the plasma. These measurements demonstrate the importance of collective motion in the energy transport in these systems.

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“…The magnetic interaction described by the Darwin Lagrangian is essential in relativistic many-electron calculations as noted by Breit and others [12][13][14][15]. It has found applications in nuclear physics [16,17], and especially in plasma physics, for numerical simulation [18][19][20][21][22], thermodynamics and kinetics [23][24][25][26][27], as well fundamental theory [28][29][30]. Barcons and Lapiedra [31] noted that the Darwin approach is not valid for a relativistic plasma and therefore used a different approach to its statistical mechanics.…”

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The exact Darwin Lagrangian

Essén

2007

Europhys. Lett.

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Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in v/c keeping terms up to order (v/c) 2 . Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.PACS numbers: 03.50. De, 11.10.Ef When radiation can be neglected the Lagrangian of classical electrodynamics, putting β = v/c, can be written,(1) In 1920 Darwin [1] expanded the Liénard-Wiechert potentials to second order in β = v/c and thus found that,and (hats are used for unit vectors),give the correct Lagrangian to this order. More recent derivations can be found in a few textbooks [2][3][4]. In particular Jackson [4] notes that using the Coulomb gauge (∇ · A = 0) makes the electrostatic Coulomb potential φ exact and moves all approximation to the vector potential A which obeys the inhomogeneous wave equation with the transverse (divergence free) current as source. [7]), and it is useful in various fundamental studies of electrodynamics [8][9][10][11]. The magnetic interaction described by the Darwin Lagrangian is essential in relativistic many-electron calculations as noted by Breit and others [12][13][14][15]. It has found applications in nuclear physics [16,17], and especially in plasma physics, for numerical simulation [18][19][20][21][22], thermodynamics and kinetics [23][24][25][26][27], as well fundamental theory [28][29][30]. Barcons and Lapiedra [31] noted that the Darwin approach is not valid for a relativistic plasma and therefore used a different approach to its statistical mechanics.Corrections to the Darwin Lagrangian have been discussed. Since a system of particles with identical charge to mass ratio does not dipole radiate a higher order expansion should be meaningful for such systems [32][33][34]. To that order, however, acceleration inevitably enters and must be handled in some way. Others have argued that since radiation is due to acceleration, v/c expansion is irrelevant, and further that radiation can be negligible even if the particle speeds are considerable (Trubnikov and Kosachev [35], Frejlak [36]). We will pursue that lead here.One frequently encounters the statement that the Darwin approach neglects retardation. This may be due to the fact that the, nowadays best known, elegant derivation by Jackson [4] hides the complications due to retardation. Nevertheless it is wrong. The derivations by Darwin [1] and by Landau and Lifshitz [2] show that the contribution of retardation to the Coulomb potential in the Lorenz gauge, is quite large. The main acceleration dependent part, however, vanishes either, as in Darwin's derivation, because it gives a total time derivative term in the Lagrangian, or, as in Landau ...

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Magnetic dynamics of simple collective modes in a two-sphere plasma model

Cited by 8 publications

References 24 publications

From least action in electrodynamics to magnetomechanical energy—a review

From least action in electrodynamics to magnetomechanical energy—a review

Density-dependent response of an ultracold plasma to few-cycle radio-frequency pulses

The exact Darwin Lagrangian

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