Energy conservation and Poynting's theorem in the homopolar generator

Chyba, Christopher F.; Hand, K. P.; Thomas, Paul J.

doi:10.1119/1.4895389

Cited by 8 publications

(6 citation statements)

References 26 publications

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“…The luminosity of the disc is very different in prograde and retrograde discs, being negligible for the latter cases, but significant for the former ones. An estimate of the flow of energy emerging from an isolated AD can be found in the so-called Faraday disc (e.g., Feynman et al 2011;Chyba et al 2015, and references therein). A disc-shaped electrical generator of height h F rotating with angular velocity ω F in a uniform magnetic field B F relies on the energy conversion from the magnetic field to the induced electric current I F by the mechanical rotation.…”

Section: Appendix D: Energy Outflow From the Discmentioning

confidence: 99%

Striped Blandford/Znajek jets from advection of small-scale magnetic field

Mahlmann

Levinson

Aloy

2020

Monthly Notices of the Royal Astronomical Society

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ABSTRACT Black hole – accretion disc systems are the central engines of relativistic jets from stellar to galactic scales. We numerically quantify the unsteady outgoing Poynting flux through the horizon of a rapidly spinning black hole endowed with a rotating accretion disc. The disc supports small-scale, concentric, flux tubes with zero net magnetic flux. Our general relativistic force-free electrodynamics simulations follow the accretion on to the black hole over several hundred dynamical time-scales in 3D. For the case of counter-rotating accretion discs, the average process efficiency reaches up to 〈ϵ〉 ≈ 0.43, compared to a stationary energy extraction by the Blandford/Znajek process. The process efficiency depends on the cross-sectional area of the loops, i.e. on the product l × h, where l is the radial loop thickness and h its vertical scale height. We identify a strong correlation between efficient electromagnetic energy extraction and the quasi-stationary setting of ideal conditions for the operation of the Blandford/Znajek process (e.g. optimal field line angular velocity and fulfillment of the so-called Znajek condition). Remarkably, the energy extraction operates intermittently (alternating episodes of high and low efficiency) without imposing any large-scale magnetic field embedding the central object. Scaling our results to supermassive black holes, we estimate that the typical variability time-scale of the system is of the order of days to months. Such time-scales may account for the longest variability scales of TeV emission observed, e.g. in M87.

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Section: Appendix D: Energy Outflow From the Discmentioning

confidence: 99%

Striped Blandford/Znajek jets from advection of small-scale magnetic field

Mahlmann

Levinson

Aloy

2020

Monthly Notices of the Royal Astronomical Society

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“…Since the shell is being carried by Earth, it is clear that electrical power in our system derives ultimately from the kinetic energy of Earth's rotation. This is analogous to the Poynting theorem analysis of the homopolar generator [12].…”

Section: Analysis In the Laboratory Framementioning

confidence: 76%

“…In any frame at least part of C is in motion. A Poynting theorem analysis of the Faraday disk shows that the energy for the electric current flowing between axle and rim in the disk comes from the disk's kinetic energy of rotation [12]. Taking into account the small magnetic perturbations to the applied B due to the current that flows in C does not change these conclusions [12].…”

Section: Historical Background and Definitionsmentioning

confidence: 99%

Electric Power Generation from Earth’s Rotation through its Own Magnetic Field

Chyba

Hand

2016

Phys. Rev. Applied

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We examine electric power generation from Earth's rotation through its own non-rotating magnetic field (that component of the field symmetric about Earth's rotation axis). There is a simple general proof that this is impossible. However, we identify a loophole in that proof and show that voltage could be continuously generated in a low-magnetic-Reynolds number conductor rotating with Earth, provided magnetically permeable material were used to ensure curl(v × B 0) = 0 within the conductor, where B 0 derives from the axially symmetric component of Earth's magnetic flux density and v is Earth's rotation velocity at the conductor's location. We solve the relevant equations for one laboratory realization, and from this solution predict voltage magnitude and sign dependence on system dimensions and orientation relative to Earth's rotation. The effect, which would be available nearly globally with no intermittency, requires testing and further examination to see if it could be scaled to practical emission-free power generation.

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“…In C&HSec. XI, in a further promotion of the assumed existence of an intrinsic velocity of quasi static B fields, the authors claim that clear conclusions concerning this velocity can be deduced from highly respected experimental results that are one century old (C&H references [1], [15], and [19]), although these experimental results are also in perfect agreement with predictions from today's electromagnetism which ignores and rejects the notion of intrinsic velocity of B fields. The elaborate discussion of the electromagnetic state of the isolated ferrite device presented in C&HSec.…”

Section: A Intrinsic Velocity Of Quasi-static Magnetic Fields Axisymentioning

confidence: 93%

Comment on “Electric Power Generation from Earth’s Rotation Through its own Magnetic Field”

Jeener

2020

Phys. Rev. Applied

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In a recent article [Phys. Rev. Applied 6, 014017 (2016)], Chyba and Hand propose a new scheme to generate electric power continuously at the expense of Earth's kinetic energy of rotation, by using an appropriately shaped cylindrical shell of a well chosen conducting ferrite, rigidly attached to the Earth. No experimental confirmation is reported for the new prediction. In the present Refutation, I first use today's standard electromagnetism and essentially the same model as Chyba and Hand to show in a very simple way that no device of the proposed type can produce continuous electric power, whatever its configuration or size, in agreement with widespread expectation. Next, I show that the prediction of nonzero continuous power by Chyba and Hand results from a confusion of frames of reference at a critical step of their derivation. When the confusion is clarified, the prediction becomes exactly zero and the article under discussion appears as pointless. At the end, I comment about the persistent invocation by Chyba and Hand of the misleading legacy notion that quasi-static magnetic fields have an intrinsic velocity, and other questionable concepts.

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Energy conservation and Poynting's theorem in the homopolar generator

Cited by 8 publications

References 26 publications

Striped Blandford/Znajek jets from advection of small-scale magnetic field

Striped Blandford/Znajek jets from advection of small-scale magnetic field

Electric Power Generation from Earth’s Rotation through its Own Magnetic Field

Comment on “Electric Power Generation from Earth’s Rotation Through its own Magnetic Field”

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