A detailed investigation of the properties of a Vlasov–Maxwell equilibrium for the force-free Harris sheet

Neukirch, T.; Wilson, Fiona; Harrison, M.

doi:10.1063/1.3268771

Cited by 40 publications

(81 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Ions are initialized with a Maxwellian distribution function, with plasma beta β i = 0.5. For the plasma conditions chosen, we have verified that evolutionary differences which arise from the use of non-Maxwellian distribution functions required at kinetic scales (see Neukirch, Wilson & Harrison 2009;Wilson & Neukirch 2011) are negligible. In addition to the initial conditions described above, referred to hereafter as the 'anti-parallel' or AP case, two variations are also described in this study.…”

Section: Simulationsmentioning

confidence: 96%

Three-dimensional simulations of sheared current sheets: transition to turbulence?

et al. 2017

View full text Add to dashboard Cite

Systems of multiple current sheets arise in various situations in natural plasmas, such as at the heliospheric current sheet in the solar wind and in the outer heliosphere in the heliosheath. Previous three-dimensional simulations have shown that such systems can develop turbulent-like fluctuations resulting from a forward and inverse cascade in wave vector space. We present a study of the transition to turbulence of such multiple current sheet systems, including the effects of adding a magnetic guide field and velocity shears across the current sheets. Three-dimensional hybrid simulations are performed of systems with eight narrow current sheets in a triply periodic geometry. We carry out a number of different analyses of the evolution of the fluctuations as the initially highly ordered state relaxes to one which resembles turbulence. Despite the evidence of a forward and inverse cascade in the fluctuation power spectra, we find that none of the simulated cases have evidence of intermittency after the initial period of fast reconnection associated with the ion tearing instability at the current sheets. Cancellation analysis confirms that the simulations have not evolved to a state which can be identified as fully developed turbulence. The addition of velocity shears across the current sheets slows the evolution in the properties of the fluctuations, but by the end of the simulation they are broadly similar. However, if the simulation is constrained to be two-dimensional, differences are found, indicating that fully three-dimensional simulations are important when studying the evolution of an ordered equilibrium towards a turbulent-like state.

show abstract

Section: Simulationsmentioning

confidence: 96%

Three-dimensional simulations of sheared current sheets: transition to turbulence?

et al. 2017

View full text Add to dashboard Cite

show abstract

“…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%

“…As demonstrated in Harrison & Neukirch (2009a) and Neukirch et al (2009), the assumption of summative separability (the first option in (2.1)) determines the components of the pressure according to…”

mentioning

confidence: 99%

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

et al. 2016

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…So far only a small number of one-dimensional (1D) collisionless force-free plasma equilibria is known, of which most belong to the class of linear force-free fields [4][5][6][7][8] . So far, analytical self-consistent distribution functions have been found only for one example of non-linear force-free fields, the force-free Harris sheet [9][10][11][12] . Finding self-consistent force-free collisionless equilibria is difficult, because one is dealing with an inverse problem, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In order to find the relativistic generalization of the collisionless distribution function for the force-free Harris sheet, we shall use the relativistic version [22][23][24] of the distribution function of the normal Harris sheet 25 as a guide, together with the non-relativistic distribution function for the force-free Harris sheet. 9,11 The paper is structured as follows: section II summarizes the mathematical framework of the non-relativistic force-free Harris sheet 9 . Section III then uses this as a basis for determining the distribution function for the relativistic force-free Harris sheet, and Section IV we present a discussion and our conclusions.…”

Section: Introductionmentioning

confidence: 99%

Collisionless distribution function for the relativistic force-free Harris sheet

Stark

Neukirch

2012

Physics of Plasmas

Self Cite

View full text Add to dashboard Cite

A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)] as it has the same dependence on the particle energy and canonical momenta.We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed.

show abstract

A detailed investigation of the properties of a Vlasov–Maxwell equilibrium for the force-free Harris sheet

Cited by 40 publications

References 13 publications

Three-dimensional simulations of sheared current sheets: transition to turbulence?

Three-dimensional simulations of sheared current sheets: transition to turbulence?

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

Collisionless distribution function for the relativistic force-free Harris sheet

Contact Info

Product

Resources

About