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Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field  

Oliver Allanson   Submitted: 2016-09-15 08:29

We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the ?force-free? Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly force-free, but by reducing its magnitude, the departure from force-free can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely, the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's equation and Ampère's law are solved exactly, and the solution allows either electrically neutral or non-neutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space, and astrophysical contexts, as well as in the laboratory.

Authors: O. Allanson, F. Wilson & T. Neukirch
Projects: None

Publication Status: Physics of Plasmas, 23, 092106 (2016) [13 pages, Open Access]
Last Modified: 2016-09-17 07:04
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From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials  

Oliver Allanson   Submitted: 2016-09-08 07:04

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 βpl=0.05.

Authors: O. Allanson, T. Neukirch, S. Troscheit and F. Wilson
Projects: None

Publication Status: Journal of Plasma Physics, 82, 905820306 (2016) [28 pages, Open Access] )
Last Modified: 2016-09-10 13:40
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An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta  

Oliver Allanson   Submitted: 2016-09-08 07:01

We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.

Authors: O. Allanson, T. Neukirch, F. Wilson and S. Troscheit
Projects: None

Publication Status: Physics of Plasmas, 22, 102116 (2015) [11 pages, Open Access])
Last Modified: 2016-09-10 13:41
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Abstracts by Author
Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field
From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials
An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

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