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Neutral and nonneutral collisionless plasma equilibria for twisted flux tubes: The GoldHoyle model in a background field 

Oliver Allanson Submitted: 20160915 08:29
We calculate exact onedimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the ?forcefree? GoldHoyle magnetic flux tube embedded in a uniform and antiparallel 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 forcefree, but by reducing its magnitude, the departure from forcefree 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 nonneutral 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: 20160917 07:04



From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials 

Oliver Allanson Submitted: 20160908 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 forcefree and nonforcefree macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the forcefree 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.
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: 20160910 13:40



An exact collisionless equilibrium for the ForceFree Harris Sheet with low plasma beta 

Oliver Allanson Submitted: 20160908 07:01
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a onedimensional nonlinear forcefree magnetic field, namely, the forcefree Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear forcefree 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 nonnegativity 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: 20160910 13:41




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