Structure and Dynamics of Current Sheets in 3D Magnetic Fields with the X Line and Manifestations of Two-Fluid

Structure and Dynamics of Current Sheets in 3D Magnetic Fields with the X Line and Manifestations of Two-Fluid

Plasma Properties A.G. Frank1, S.Yu. Bogdanov1, S.G. Bugrov1, G.V. Dreiden2, V.S. Markov1, and G.V. Ostrovskaya2

1A.M. Prokhorov Institute of General Physics of the Russian Academy of Sciences, Moscow, Russia
2A.F. Ioffe Physical-Technical Institute of the Russian Academy of Sciences, St.-Petersburg, Russia

Abstract.Two novel phenomena are revealed in the current sheets formed in 3D magnetic fields with the X line. One is the deterioration of plasma compression due to enhancement of the guide field inside the sheet. Another is generation of the Hall currents, which manifests itself both in plasma sheet deformation in the presence of the guide field, and in transformation of the 2D magnetic configuration to the 3D one in the absence of the guide field. Keywords: Magnetic Reconnection; Current Sheet; Plasma Dynamics; Hall Current; Holographic Interferometry. PACS: 52.35.Vd; 52.30.-q; 42.40.Kw The formation of a current sheet (CS), which separates differently directed magnetic field lines, is a key prerequisite to magnetic reconnection processes [1,2]. In complex 3D magnetic configurations CS can form in some distinct regions, and of a crucial importance is the presence of a singular line of X type. The magnetic field in a vicinity of a simplest X line can be presented as follows: B={-hy; -hx; BZ}. Here, the X line is aligned with the zaxis; the gradient in the (x, y) plane h.const, the guide field is uniform, BZ . const, so that the field B is zindependent. The transverse magnetic field B. = h ..r. vanishes at the z-axis increasing linearly with the distance away from this axis. This field can be treated as an element of more complex magnetic configurations. We report on experimental results on the CS formation and evolution in 3D magnetic fields with the X line. An analysis of spatial distributions of plasma density, electric currents and magnetic fields gives an insight into the key processes governing CS structure and dynamics. Characteristics of the initial 3D magnetic configuration can have a pronounced effect on the CS structure. Plasma density inside the sheet decreases in the presence of the guide field, displaying the transition to the behavior of uncompressible plasma. We discuss the guide field amplification in CS, and an influence of the Hall currents on plasma dynamics. FIGURE 1. Experimental device CS-3D: side view and cross-section. The experiments are carried out in the CS-3D device, Figure 1 [3,4]. The initial 3D magnetic configuration is formed by a combination of two fields: one is the transverse 2D field with the null line at the z-axis, the field lines in the (x,y) plane, and the transverse gradient h . 600 G/cm; the second field is almost uniform guide field BZ . 6 kG aligned with the null line. The strength and direction of each field can be changed independently allowing the formation of various magnetic configurations. The cylindrical quartz vacuum chamber 18 cm in diameter and 100 cm in length is filled with Ar or Kr at a pressure of 20 mTorr. The initial plasma in the magnetic field is produced by an auxiliary .-discharge with strong preionization. Then, a pulsed voltage is applied in z-direction, thus initiating plasma flows, excitation of plasma current JZ, and the CS formation. The electron density distributions in the (x, y) plane (z-averaged) are obtained with the interference-holographic method (see [5,6] for details). Three components of the magnetic field in a vicinity of CS are measured simultaneously with small magnetic probes, which are moving along the directions shown as dotted lines in Figure 1.

The plasma current JZ aligned with the X line attains the shape of a sheet, which has two different dimensions in
the (x, y) plane: the CS width exceeds the thickness by a factor of .10, Figure 2. The tangential component BX near the CS surface is increased in .7 times as compared to its initial value, while the normal component BY and its derivative .BY / .x go down to .30% of the values in the vacuum magnetic field. The current density in the middle of CS reaches its peak .5.5 kA/cm2. CS formation is accompanied by effective plasma compression, so that the electron density in the sheet is usually much higher than that in the surrounding space, Figure 3. The steep plasmadensity profile in the direction perpendicular to the sheet surface is typical for the CS plasma.

It was found that the distributions of the both electron density and current are rather sensitive to the magnetic field topology. We observe the effect of progressive decrease of the plasma compression ratio in response to increasing guide field [6]. This effect has two basic manifestations: a decrease of the maximum plasma density, and an enlargement of the sheet thickness, Figure 4, and it also displays a gradual transition to the behavior of uncompressible plasma. Based on the experimental data we advanced a concept that the deterioration of plasma compression is due to enhancement of the guide field in CS over its initial value, and to exciting the currents in the (x, y) plane perpendicular to the X line and to the original current JZ [6]. This concept is confirmed by direct measurements of the excessive guide field .BZ .1.3 kG inside the CS, Figures 5, 6.

The analysis of spatial distributions of the plasma density allowed revealing another novel and important effect. We observe formation of plasma sheets, which assume an unusual asymmetric and tilted shape in the presence of the guide field BZ, see Figure 2, and such plasma sheets differ noticeably from the sheets formed in the 2D magnetic
fields (BZ = 0) [7]. One can see that the angle of the sheet tilting changes the sign when the direction of the guide field is reversed, while in the absence of the guide field the sheet is symmetrical enough, without any tilting, Figure 7. It was proposed that the sheet asymmetry is an evidence of the two-fluid plasma properties and excitation of the Hall currents in the (x, y) plane perpendicular to the X line. Interaction of the Hall currents with the guide field BZ produces additional dynamic effects, which result in deformation of plasma sheets [7]. At the same time, an
analysis of typical plasma parameters suggests that the Hall currents should appear in the planar CS formed in the 2D magnetic configuration in the absence of the guide field (BZ = 0). Magnetic measurements confirm this suggestion and show generation of the longitudinal magnetic field component .BZ in such CS, Figure 8. This result
makes it evident that the two-fluid plasma effects and excitation of the Hall currents bring about a conversion of the initial 2D magnetic field to the 3D one.
Hence two novel phenomena are revealed in CS formed in 3D magnetic fields with the X line. One is the deterioration of plasma compression due to enhancement of the guide field inside CS. Another is generation of the Hall currents, which manifests itself both in plasma sheet deformation in the presence of the guide field, and in transformation of the 2D magnetic configuration to the 3D one in the absence of the guide field.

ACKNOWLEDGMENTS
The work is supported in part by the Russian Foundation for Basic Research (Project No. 06-02-17011), and by the Presidential Program “Governmental Support of the Leading Scientific Schools” (Project No. 5382.2006.2).
REFERENCES
1. S.I. Syrovatskii, Annu. Rev. Astron. Astrophys. 19, 163-229 (1981). 2. E.R. Priest, T. Forbes, Magnetic reconnection. MHD theory and applications, Cambridge University Press, Cambridge, United Kingdom, 2000, 600 pp. 3. A.G. Frank, Plasma Physics & Control. Fusion 41 Suppl. 3A, A687-A697 (1999). 4. S.Yu. Bogdanov, N.P. Kyrie, V.S. Markov, A.G. Frank, JETP Lett. 71, 53-57 (2000). 5. S.Yu. Bogdanov, V.S. Markov, A.G. Frank et al., Plasma Physics Reports 28, 549-558 (2002) 6. A.G. Frank, S.Yu. Bogdanov, V.S. Markov et al., Phys. Plasmas 12, 052316 (2005). 7. A.G. Frank, S.Yu. Bogdanov, G.V. Dreiden et al., Phys. Letters A 348, 318-325 (2006).

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