The mirror mode: a “superconducting” space plasma analogue

Treumann, Rudolf A.; Baumjohann, Wolfgang

We examine the physics of the magnetic mirror mode in its final state of saturation, the thermodynamic equilibrium, to demonstrate that the mirror mode is the analogue of a superconducting effect in a classical anisotropic-pressure space plasma. Two different spatial scales are identified which control the behaviour of its evolution. These are the ion inertial scale inline-formulaλim(τ) based on the excess density inline-formulaNm(τ) generated in the mirror mode, and the Debye scale inline-formulaλD(τ). The Debye length plays the role of the correlation length in superconductivity. Their dependence on the temperature ratio inline-formula M4inlinescrollmathml italic τ = T / T < normal 1 65pt16ptsvg-formulamathimg6f0098f1c0ce091c450e1250feb01172 angeo-36-1015-2018-ie00001.svg65pt16ptangeo-36-1015-2018-ie00001.png is given, with inline-formulaT the reference temperature at the critical magnetic field. The mirror-mode equilibrium structure under saturation is determined by the Landau–Ginzburg ratio inline-formula M6inlinescrollmathml italic κ D = italic λ normal im / italic λ D 60pt14ptsvg-formulamathimg96d7e353bc57f05697978a485e7e6d14 angeo-36-1015-2018-ie00002.svg60pt14ptangeo-36-1015-2018-ie00002.png , or inline-formula M7inlinescrollmathml italic κ italic ρ = italic λ normal im / italic ρ 54pt16ptsvg-formulamathimg526a170b1edc6a8ce1329f3a4513ca55 angeo-36-1015-2018-ie00003.svg54pt16ptangeo-36-1015-2018-ie00003.png , depending on whether the Debye length or the thermal-ion gyroradius inline-formulaρ – or possibly also an undefined turbulent correlation length inline-formulaℓturb – serve as correlation lengths. Since in all space plasmas inline-formulaκD≫1, plasmas with inline-formulaλD as the relevant correlation length always behave like type II superconductors, naturally giving rise to chains of local depletions of the magnetic field of the kind observed in the mirror mode. In this way they would provide the plasma with a short-scale magnetic bubble texture. The problem becomes more subtle when inline-formulaρ is taken as correlation length. In this case the evolution of mirror modes is more restricted. Their existence as chains or trains of larger-scale mirror bubbles implies that another threshold, inline-formula M13inlinescrollmathml V normal A > italic υ normal th 45pt12ptsvg-formulamathimg4baf05af3b783d2f083a94f5cd7de086 angeo-36-1015-2018-ie00004.svg45pt12ptangeo-36-1015-2018-ie00004.png , is exceeded. Finally, in case the correlation length inline-formulaℓturb instead results from low-frequency magnetic/magnetohydrodynamic turbulence, the observation of mirror bubbles and the measurement of their spatial scales sets an upper limit on the turbulent correlation length. This might be important in the study of magnetic turbulence in plasmas.

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Treumann, Rudolf A. / Baumjohann, Wolfgang: The mirror mode: a “superconducting” space plasma analogue. 2018. Copernicus Publications.

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Rechteinhaber: Rudolf A. Treumann

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