Closed-form expressions for the magnetic fields of rectangular and circular finite-length solenoids and current loops

Hampton, S.; Lane, Ryan A.; Hedlof, R. M.; Phillips, R. E.; Ordonez, C. A.

doi:10.1063/5.0010982

Cited by 14 publications

(7 citation statements)

References 14 publications

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“…0:5S, because smaller values of d were not considered. For a confined plasma with a Maxwellian velocity distribution, the condition can be satisfied by particles other than those in the tail of the distribution by writing the condition as r th ( 0:5d; (32) where…”

Section: Discussionmentioning

confidence: 99%

“…A closed-form expression for the magnetic field B l ðr; h; zÞ produced by such a current loop centered at the coordinate origin with radius R k is obtained from Ref. 32. The magnetic field for a set of N loops evenly distributed on a toroidal surface with constant minor radius a and major radius R is given by…”

Section: Axisymmetric Configurationmentioning

confidence: 99%

“…A closed-form expression for the field of a rectangular current loop is obtained from Ref. 32. For the current loop in Fig.…”

Section: Magnetic Plasma Expulsionmentioning

confidence: 99%

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Magnetic confinement of effectively unmagnetized plasma particles

Ordonez

2020

Physics of Plasmas

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A purely magnetic applied field may provide plasma confinement under conditions where the bulk of the plasma is effectively free of the applied magnetic field. The applied magnetic field surrounds the bulk of the plasma, and plasma particles that are incident on the applied magnetic field can be reflected back into the effectively unmagnetized region of plasma. The concept belongs to a class of magnetic plasma confinement approaches studied long ago, for which some experimental results indicated that classical (collision-based) cross-magnetic-field transport may occur. However, multiple magnetic coils are required to be immersed within the confined plasma, and rapid plasma loss may occur if material structures are present, which pass through the plasma (e.g., to hold the immersed coils in place). In the work reported, the concept is studied in combination with magnetic plasma expulsion [R. E. Phillips and C. A. Ordonez, Phys. Plasmas 25, 012508 ( 2018)], which would be employed to keep plasma away from material structures that pass through the plasma. A planar model is used for the study. A classical trajectory Monte Carlo simulation is carried out on particles that are independently incident on the applied magnetic field. With monoenergetic incident particles, the results indicate that the applied magnetic field can reflect all independently incident particles in certain regions of parameter space. Prospects for achieving three-dimensional magnetic confinement of an effectively unmagnetized plasma with a Maxwellian velocity distribution are discussed.

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Section: Discussionmentioning

confidence: 99%

Section: Axisymmetric Configurationmentioning

confidence: 99%

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Magnetic confinement of effectively unmagnetized plasma particles

Ordonez

2020

Physics of Plasmas

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“…The sources in Eq. ( 5) are the free-space field H s components that do not depend on the media and can be computed analytically for rectangular coils as we did in this work [41]. Then, Eq.…”

Section: B Computation Of the Forward Problemmentioning

confidence: 95%

Imaging of Magnetic Nanoparticles with Permeability Tomography

Veiga¹,

Fernandez-Corazza²,

Raap³

et al. 2022

Preprint

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<div>Magnetic nanoparticles are being increasingly used in numerous biomedical applications for diagnosis and therapy. During the course of these applications nanoparticle biodegradation and body clearance may occur.</div><div>In this context, a portable, non-invasive, non-destructive and contactless imaging device can be relevant to trace the nanoparticle distribution before and after the medical procedure. </div><div>We present a method for $in\:vivo$ imaging the nanoparticles based on the magnetic induction technique, and we show how to properly tune it for magnetic permeability tomography, maximizing the permeability selectivity. </div><div>A tomograph prototype was designed and built to demonstrate the feasibility of the proposed method. It includes data collection, signal processing and image reconstruction.</div><div>Useful selectivity and resolution are achieved on phantoms and animals, proving that the device can be used to monitor the presence of magnetic nanoparticles without requiring any particular sample preparation. By this way, we show that magnetic permeability tomography may become a powerful technique to assist medical procedures.</div>

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“…In the present literature, analytical solutions for the circular loop problem exist, but only a small part of the literature focuses on deriving expressions for an arbitrarily shaped arc filament. A series of papers have derived analytical expressions for a finite arc segment of a filament and other cross sections [28][29][30][31][32][33]. The expressions derived in these papers are written in terms of Jacobian elliptic functions and elliptic integrals.…”

Section: Introductionmentioning

confidence: 99%