An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

Allanson, Oliver; Neukirch, T.; Wilson, Fiona; Troscheit, Sascha

doi:10.1063/1.4934611

Cited by 35 publications

(123 citation statements)

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“…In § 3.4 we calculate DFs corresponding to the 're-gauged' FFHS, that are multiplicative. These 're-gauged' DFs are essentially equivalent to those derived in Allanson et al (2015), as functions of z and v. However they are different as functions of p s . The involved calculations that prove the necessary properties of convergence and boundedness of the above DFs, by using techniques established in this paper, are included in appendix A.…”

Section: 2mentioning

confidence: 82%

“…In particular, forcefree current sheets are relevant for the solar corona (Priest & Forbes 2000), Jupiter's magnetotail (Artemyev, Vasko & Kasahara 2014), the Earth's magnetotail Petrukovich et al 2015) and the Earth's magnetopause (Panov et al 2011). Further relevant theoretical works on distribution functions (DFs) for (nonlinear) forcefree current sheets are, for example, Harrison & Neukirch (2009a,b), Neukirch, Wilson & Harrison (2009), Wilson & Neukirch (2011), Abraham-Shrauner (2013), Allanson et al (2015) and Kolotkov, Vasko & Nakariakov (2015).…”

Section: O Allanson T Neukirch S Troscheit and F Wilsonmentioning

confidence: 99%

“…In § 3 we present non-trivial examples to demonstrate the application of the inversion method to a recently derived force-free DF (Allanson et al 2015) as well as to DFs that correspond to the same magnetic field, but in a different gauge. This work is motivated by numerical reasons, and should allow easier calculation and visualisation of the DFs.…”

Section: O Allanson T Neukirch S Troscheit and F Wilsonmentioning

confidence: 99%

“…In a recent paper, Allanson et al (2015) used the pressure transformation techniques described above, resulting in a pressure tensor of 'multiplicative form'…”

Section: 2mentioning

confidence: 99%

“…Usually one would expect that solving (1.8) for g s is much more difficult after the transformation toP zz . This pressure transformation theory is important for the derivation of the low-β DF for the nonlinear FFHS (Allanson et al 2015). As explained therein, if the pressure transformation…”

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confidence: 99%

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From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials

et al. 2016

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We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' theorem, the equilibrium distribution functions are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite polynomials. A sufficient condition on the pressure tensor is found which guarantees the convergence and the boundedness of the candidate solution, when satisfied. This condition is obtained by elementary means, and it is clear how to put it into practice. We also argue that for a given pressure tensor for which our method applies, there always exists a positive distribution function solution for a sufficiently magnetised plasma. Illustrative examples of the use of this method with both force-free and non-force-free macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the force-free Harris sheet (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116). In the effort to model equilibria with lower values of the plasma β, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for β pl = 0.05.

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Section: 2mentioning

confidence: 82%

Section: O Allanson T Neukirch S Troscheit and F Wilsonmentioning

confidence: 99%

Section: O Allanson T Neukirch S Troscheit and F Wilsonmentioning

confidence: 99%

“…In a recent paper, Allanson et al (2015) used the pressure transformation techniques described above, resulting in a pressure tensor of 'multiplicative form'…”

Section: 2mentioning

confidence: 99%

mentioning

confidence: 99%

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From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials

et al. 2016

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Electron currents supporting the near‐Earth magnetotail during current sheet thinning

Artemyev

Angelopoulos

Liu

et al. 2017

Geophysical Research Letters

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Formation of intense, thin current sheets (i.e., current sheet thinning) is a critical process for magnetospheric substorms, but the kinetic physics of this process remains poorly understood. Using a triangular configuration of the three Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft at the end of 2015 we investigate field‐aligned and transverse currents in the magnetotail current sheet around 12 Earth radii downtail. Combining the curlometer technique with direct measurements of ion and electron velocities, we demonstrate that intense, thin current sheets supported by strong electron currents form in this region. Electron field‐aligned currents maximize near the neutral plane Bx∼0, attaining magnitudes of ∼20 nA/m2. Carried by hot (>1 keV) electrons, they generate strong magnetic shear, which contributes up to 20% of the vertical (along the normal direction to the equatorial plane) pressure balance. Electron transverse currents, on the other hand, are carried by the curvature drift of anisotropic, colder (<1 keV) electrons and gradually increase during the current sheet thinning. In the events under consideration the thinning process was abruptly terminated by earthward reconnection fronts which have been previously associated with tail reconnection further downtail. It is likely that the thin current sheet properties described herein are similar to conditions further downtail and are linked to the loss of stability and onset of reconnection there. Our findings are likely applicable to thin current sheets in other geophysical and astrophysical settings.

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Exact Vlasov‐Maxwell equilibria for asymmetric current sheets

Allanson

Wilson

Neukirch

et al. 2017

Geophysical Research Letters

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The NASA Magnetospheric Multiscale mission has made in situ diffusion region and kinetic‐scale resolution measurements of asymmetric magnetic reconnection for the first time, in the Earth's magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle‐in‐cell simulations. Many particle‐in‐cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris‐type magnetic field but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the Vlasov‐Maxwell system that are self‐consistent with one‐dimensional asymmetric current sheets, with an asymmetric Harris‐type magnetic field profile, plus a constant nonzero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution and has different bulk flow properties.

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An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

Cited by 35 publications

References 35 publications

From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials

From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials

Electron currents supporting the near‐Earth magnetotail during current sheet thinning

Exact Vlasov‐Maxwell equilibria for asymmetric current sheets

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