Clementson, J.

Grulke, O.

Klinger, T.

Lewerentz, L.

Schneider, R.

Sydora, R.

English

MPG.PuRe

Gyrokinetic simulations of magnetic reconnection in non-uniform plasmasJ. Clementson1, L. Lewerentz2, O. Grulke1, R. Schneider2, R. D. Sydora3, and T. Klinger1,21Max-Planck/Princeton Center for Plasma Physics,Max Planck Institute for Plasma Physics, DE-17491 Greifswald, Germany2Department of Physics, University of Greifswald, DE-17487 Greifswald, Germany3Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1AbstractA two-dimensional gyrokinetic particle-in-cell (2D-gyroPIC) model, designed to simulatedriven magnetic reconnection in the VINETA-II experiment, has been employed to study theinfluence of plasma resistivity on the reconnection rate in non-uniform plasmas.IntroductionThe transfer of magnetic to kinetic energy during magnetic reconnection in low-collisionalitysystems, such as tokamaks and solar flares, proceeds orders of magnitude faster than expectedfrom MHD theory. In order to have predictive models for the quantitative spatial and temporalevolutions of reconnection it is necessary to understand the influence of plasma parameters onthe reconnection process [1, 2].magnetic X-pointpublic fluxprivate fluxseparatricesprivate fluxBgFigure 1: The magnetic geometry ofthe model is illustrated with flux sur-faces of constant Az. Perpendicular tothe azimuthal field is a guide field Bg.Based on a Vlasov–Ampère–Poisson gyrokineticparticle-in-cell code (gyroPIC) [3], a two-dimensional pe-riodic slab model for studies of magnetic reconnectionin low-beta plasmas [4] has been implemented to sup-port the experimental efforts at the VINETA-II linear de-vice [5, 6]. The experiment is designed to produce plas-mas and magnetic-field configurations over a wide param-eter range, thereby allowing for 3D-studies of slow colli-sional to fast collisionless reconnection. As illustrated inFig. 1 the prescribed magnetic geometry consists of anazimuthal separatrix field and an axial guide field. Pri-vate flux is driven toward the magnetic X-point to initiatereconnection. The plasmas, with profiles peaking at theX-point, have densities ranging over n = 1016−19 m−3,electron temperatures Te = 2 – 6 eV, and ion temperaturesof Ti ≈ 0.1 eV.41st EPS Conference on Plasma Physics P4.118Reconnection RateThe magnetic geometry of the model is described by A = Azẑ and ∂Az∂ z = 0 so the inductionin the system is∂Az∂ t=−vAz ·∇⊥Az +η∗µ0∇2⊥Az, (1)where η∗ denotes the plasma resistivity. Magnetic flux thus propagates through the plasma atvAz =∣∣∣∂Az∂ t −η∗µ0∇2⊥Az∣∣∣|∇⊥Az|2∇⊥Az, (2)with the velocity depending linearly on the local resistivity. At the X-point, where the gradientof Az is zero, the flux reconnects at a rate ofR =∣∣∣∣∂Az∂ t∣∣∣∣= η∗µ0 ∣∣∇2⊥Az∣∣= |Ez|. (3)In a plasma it is therefore the local X-point resistivity together with the divergence of the gra-dient of Az (current density) that determines R.Plasma ResistivityWhere the driven flux penetrates the plasma the inductive electric field Ez will follow thereconnection drive frequency ω = 2π fD. The resistivity parallel to the field lines can be de-scribed in terms of η∗|| = ηc|| + jηi|| where the collisional resistivity ηc|| accounts for electron–ionCoulomb collisions and the π/2 phase-shifted inductive resistivity η i|| is due to electron inertia.Applying Spitzer resistivity for the collisional term, the parallel Ohm’s law may be writtenÊz cosωt =πζ e2√me lnΛ(4πε0)2T3/2eĴe cosωt + jmeωnee2Ĵe cosωt =√(ηc||)2 +(η i||)2Ĵe cos(ωt +ϕ). (4)The resistive term ηc|| is independent of density, but a strong function of electron temperature.The inductive term, on the other hand, is independent of temperature and instead scales linearlywith drive frequency and inversely with electron density. Figure 2 displays the complex resis-tivity terms as function of density, temperature, and drive frequency. The relative importanceof the collisional and inductive parts of the complex resistivity strongly depends on the plasmaparameter regime.41st EPS Conference on Plasma Physics P4.11810151016101710181019102010−1010−810−610−410−2100ne[m−3]η[Ωm]1 kHz10 kHz100 kHz1 MHz10 MHz100 MHz1 eV10 eV100 eV1 keV10 keVηiηcFigure 2: Complex plasma resistivity η∗ = ηc + jη i as function of ne, Te, and fD.Simulations of Collisionless ReconnectionThe reconnection rates R for plasmas with flat temperature profiles of Te = 4 eV,Ti = 0.2 eVand Gaussian density profiles with peak densities at the X-point in the 1014−17 m−3 range andwidths of σ = 11 – 57 mm and have been calculated for fD = 50 and 100 kHz. Accordingto Fig. 2 the inductive resistivity for these plasmas is larger than the collisional resistivity. Anexample of the time evolution of Az, Ez, Je, and Ji at the X-point, where the inductive field isparallel to the magnetic field, is shown in Fig. 3. The quantities follow the drive frequency and,as expected, there is a phase shift of the currents relative the electric field. The current sheet isdominated by electron flow.Calculated reconnection rates for a distribution of σ = 42 mm for the two drive frequenciesare shown in the top panel of Fig. 4. R shows the same frequency dependence as the inductiveresistivity term. The bottom panel of the same figure shows how the rate normalized to vacuumreconnection, R ′ =R/R0, varies with distribution widths for fD = 100 kHz. At high densities,where the skin depth δe = cωpe gets small, the flux is prohibited to fully penetrate to the X-pointdue to the generation of currents at the plasma edge. Current sheets for four plasmas subject tothe same drive of fD = 50 kHz are displayed in Fig. 5.Summary and DiscussionIn ideal plasmas the time scale of the fluctuation initiating reconnection determines the re-sistivity together with the plasma density. The influence of these parameters on the resultingreconnection rates for high-guide-field non-uniform plasmas are investigated using a gyroki-netic slab model tailored to the experimental conditions of the VINETA-II device. A full 3Dmodel with logical sheath boundaries, where also non-uniformites along the magnetic field canbe included, is currently being developed [4].41st EPS Conference on Plasma Physics P4.118Figure 3: Az, Ez, Je, and Ji at the X-pointas function of drive current for a plasmawith n = 7.8×1014 m−3 and σ = 27 mm.1014101510161017101810−1100ne[m−3]σ = 11 mmσ = 27 mmσ = 42 mmσ = 57 mm02468[V/m]f = 50 kHzf = 100 kHzf = 100 kHzσ = 42 mmFigure 4: Top: R as function of fD and neBottom: R ′ as function of σ and neI II III IVFigure 5: Generated electron current sheets for fD = 50 kHz. I n = 2.0×1016 m−3, σ = 11 mmII n = 2.0×1016 m−3, σ = 27 mm III n = 3.1×1017 m−3, σ = 11 mm IV n = 3.1×1017 m−3, σ = 27 mmAcknowledgementsThis project has received funding from the EURATOM research and training program 2014 –2018. The authors wish to thank H. Bohlin, K. Rahbarnia, H. M. Smith, and A. von Stechowfor valuable discussions.References[1] M. Yamada, J. Geophys. Res. 104(A7), 14,529 (1999)[2] D. Biskamp, Magnetic Reconnection in Plasmas, Cambridge University Press (2000)[3] R. D. Sydora, Phys. Plasmas 8(5), 1929 (2001)[4] L. Lewerentz, J. Clementson, R. Schneider, et al., Europhys. Conf. Abs. 38, P1.144 (2014)[5] H. Bohlin, A. von Stechow, K. Rahbarnia, et al., Rev. Sci. Instrum. 85(2), 023501 (2014)[6] A. von Stechow, H. Bohlin, K. Rahbarnia, et al., Europhys. Conf. Abs. 38, P4.111 (2014)41st EPS Conference on Plasma Physics P4.118

Gyrokinetic simulations of magnetic reconnection in non-uniform plasmas

http://hdl.handle.net/21.11116/0000-0008-86A3-8

Gyrokinetic simulations of magnetic reconnection in non-uniform plasmas

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