Characteristics of Plasma Dynamics in Current Sheets Formed in Helium Plasma

The characteristic features of plasma acceleration in the current sheets are discussed on the basis of an analysis of the structure of electrodynamic forces at successive stages of the evolution of the current sheets formed in the plasma with helium ions. Of particular interest is the generation of reverse currents at the side edges of the sheet and the appearance of forces, which are braking previously accelerated plasma flows.


Introduction
The formation of current sheets with high concentration of magnetic energy in spatially separated regions of magnetized plasma and the possibility of a rapid release of energy via magnetic reconnection have been intensively studied over the past decades. According to modern concepts, the dynamics of current sheets provide a basis for various flare-type phenomena including Solar flares and flares on other stars, substorms in the magnetospheres of the Earth and other planets, and disruption instability in tokamak plasma [1][2][3][4][5].
Along with the theoretical research, the dynamics of current sheets and magnetic reconnection are studied in dedicated laboratory experiments. These experiments, among other factors, can provide laboratory modeling of non-stationary astrophysical phenomena [6][7][8][9][10][11][12]. Laboratory experiments are carried under highly controlled and reproducible conditions and use modern methods of plasma diagnostics, which allows for the relation of plasma dynamics to the evolution of magnetic fields, currents, and electrodynamic forces in current sheets [11][12][13][14][15][16].
The initial conditions for the formation of current sheets in laboratory experiments can be established within a relatively wide range, therefore providing the current sheets of different structures, much like the current sheets in natural conditions (for example, in the Earth's magnetosphere). In particular, by changing the mass of ions in plasma, we can bring about changes in both the relative thickness of the sheet and the role of the Hall effect in plasma dynamics [14,15]. In plasma with heavy ions, we obtain "thin" sub-ionic current sheets with a thickness of the order of the ion inertial length. In the lighter-ions plasma, "thick" current sheets are usually formed with a thickness exceeding several times the ion inertial length [14,15,17].
Magnetic energy accumulated in the vicinity of the metastable current sheet can be transformed into thermal energy and into the energy of high-speed flows of plasma [18][19][20]. Plasma is accelerated along the surface of the current sheet mainly under the action of the Ampère forces that are initially directed from the central region of the sheet to its edges on both sides [11,21]. In some cases, plasma acceleration can be spatially in-homogeneous in the normal direction to the sheet, and higher acceleration can be at some distance from the middle plane of the sheet, in regions of low plasma density [11,22,23].
Accelerated plasma flows along the current sheet surface can result in exciting the reverse currents at the sheet edges. This effect can significantly change the dynamic processes in the current sheets, including the process of plasma acceleration [24]. This paper is focused on the experimental research of plasma dynamics in current sheets produced in helium plasma in two-dimensional magnetic fields with a null line of the X-type. The basic parameters of plasma and current sheets were obtained by spectroscopic methods and magnetic measurements. The energy of accelerated plasma flows is correlated with the structure of electrodynamic forces at successive stages of the current sheet evolution. Of particular interest is the first registration of the reverse currents in current sheets formed in the helium plasma. Excitation of reverse currents gives rise to additional Ampère forces that slow down previously accelerated plasma flows.

Experimental Setup and Methods of Diagnostics
Plasma dynamics in the current sheets were studied with the experimental setup CS-3D ( Figure 1) [7,25,26]. A quartz vacuum chamber (18 cm in diameter, 100 cm long) was filled with helium gas up to pressure of 320 mTorr. A system of straight current-carrying conductors placed outside the vacuum chamber excited a quasistationary 2D magnetic field with the null line of the X-type at the z axis: The null line was aligned with the chamber axis. The magnetic field gradient h in the xy-plane was established equal to 0.5 kG/cm. The initial plasma in the magnetic field (1) was produced using the Θ-discharge with strong preliminary ionization, and the initial plasma was almost homogeneous in the z direction. Then, the plasma current Z J was excited by applying the impulsive voltage Z U between two grid electrodes that were arranged at the chamber ends on the distance of Δz = 60 cm from each other. The time dependence of the plasma current ) (t J Z was close to sinusoid, with the amplitude ≈ 45 kA and the half-period T/2 = 6.3 μs. The current Z J initiated 2D plasma flows in the magnetic field B  , and gave rise to the current sheet formation during the first 1-1.5 μs. The typical transverse sizes of the current sheet were: 2δx ≈ 12-17 cm (width) and 2δy ≈ 1.5-3.5 cm (thickness), at the level of 0 1 . 0 z j ⋅ ; here, 0 z j is the current density at the middle plane of the sheet [27,28].
The sheet length along the direction of the current was equal to Δz.
Plasma flows in the xy-plane resulted in increasing the electron density in the middle plane of the current sheet. This density exceeded several times the densities of both the initial plasma and the surrounding plasma [29,30].
The velocities of the helium ions and the electron densities were obtained by registration of the profiles of two spectral lines: the He II 468.6 nm (the n = 3 → n = 2 transition, α P ) and the He II 320.3 nm (the n = 4 → n = 2 transition, β P ). Analyzing the spectral data, we took into account that the broadening of the He II α P spectral line was caused by both the Doppler and Stark effects, while the broadening of the He II β P line was due mainly to the Stark effect [31,32]. The difference between the constants of the Doppler and Stark broadenings of these spectral lines allowed for calculation of the plasma parameters in the sheet; for details see [20,33]. The optical part of the setup included two channels for simultaneous registration of plasma emission in two mutually perpendicular directions. In the "z-channel," the radiation was collected from the central quasi-cylindrical region D1 (Ø ~ 1.5 cm), extended along the direction of the plasma current, shown in Figure 1. This channel was used to determine the plasma density and the ions' thermal velocities in the central region of the current sheet, since the directed plasma motions occur predominantly in the xy-plane.
The "x-channel" collected the plasma radiation along the width of the current sheet (region D2, Ø ~ 2.5 cm, Figure 1). This channel was used to determine the ions' velocities in the x-direction and the plasma density, both averaged along the sheet width. Plasma emission from two channels was transmitted via the quartz light guides on the entrance slit of the monochromator MDR-3 (diffraction grating 1200 grooves/mm, inverse linear dispersion D = 1.3 nm/mm). The monochromator was completed with the Nanogate 1-UF programmed electro-optical detector. The profiles of the spectral lines were recorded in one pulse of the experimental setup with an integration time of ≈ 0.8 μs.   are shown in the panel (a) by the dashed lines with the arrows; 2-cylindrical vacuum chamber, its axis is aligned with the null line; 3-system of coils of the Θ discharge used to create the initial plasma; 4-current sheet formed after excitation of the plasma current Z J ; 5-grid electrodes; 6-quartz windows; 7-quartz lenses; 8-quartz waveguides; 9-monochromator; 10-Nanogate 1UF electro-optical camera; 11-computer. AA', BB', and CC' are the lines of displacement of the magnetic probes. 1 D , 2 D -quasi-cylindrical regions from which plasma radiation was detected in the z and x channels, respectively.
In order to investigate the magnetic fields of the current sheets, we recorded the time dependences of three mutually perpendicular components of the magnetic field measured by the system of magnetic probes. The probes could be moved in the xy-plane either along the width of the current sheet, at a distance of ≈ 1.2 cm from the x-axis (line AA'), or across the current sheet, at the distances of -0.8 cm and -5.0 cm from the y-axis (lines BB' and CC', respectively). The measured data were then analyzed and processed to obtain the spatial distributions of the magnetic fields, current densities, and the Ampere forces [11,16,21].

Evolution of Plasma Parameters in Current Sheets Formed in the Helium Plasma
In the context of the presented research, one of the most important characteristics of the current sheet is the energy of plasma flows that are accelerated along the sheet width. The evolution of this energy, along with the evolution of the ion temperature and plasma density, was obtained by analyzing the profiles of the spectral lines: He II 468.6 nm and He II 320.3 nm. It was found that the broadenings of these lines registered in the x-direction ( x λ Δ ) were usually several times larger than the broadenings measured in [20,33]. For example, at t ≈ 3.3 μs, the ratio of the half-widths was   [20]. The abscissa axis shows the radiation wavelength (100 pixels = 1.25 nm) and the radiation intensity is given on the ordinate axis in arbitrary units. The parameters of the experiment are h = 0.5 kG/cm, p = 320 mTorr, The quantitative characteristics of the plasma parameters were derived from the experimental data with the use of the Stark constants for the spectral lines He II β P [34] and He II α P [35]; in this case, the calculations were carried out by the method of the successive approximations (for details see [33]). The revealed difference between the data from the x-and z-channels proves that helium ions receive an excess energy of directed motion along the width of the current sheet (along the x-axis) [20,33]. We defined the energy of the directed ions' motion x W as the difference between the total ion energy measured by the x-channel, and the ion thermal energy i T measured by the z-channel at the same time. We also associate the difference between plasma densities One can see from the Figure 3 that, at the early times (t ≈ 1.2 μs), the electron density was practically uniform along the current sheet,

Ampère Forces in Current Sheets and Plasma Acceleration
Excitation of the plasma current Z J parallel to the null line of the magnetic field  [21].
Typical distributions of the current sheet parameters along the sheet width (along the x-direction), shortly after the sheet formation, are shown in the Figure 4a. The presented parameters are the tangential magnetic field component Here, , The Ampère forces ) , ( t x F x shown on Figure 4 are the integrals of  x W starts with a delay which is due mainly to the inertia of the ions [24,28], and, to some extent, to the increase in the Ampère forces with time. As we have shown above, the energy of plasma flows peaks at t ≈ 4.3 μs, when x W ≈ 400 eV, and then goes down.
In accordance with the structure of the Ampère forces

Generation of Reverse Currents
At the later stages of the current sheet evolution, the distributions of the parameters shown in Figure 4 change significantly: see Figures 4b-d. A distinctive feature of these distributions is the appearance of reverse currents at the side edges of the current sheet. The reverse currents flow in the direction opposite to the main current in the central region of the sheet. Simultaneously, the current sheet becomes thicker and the current density rapidly decreases at a considerable distance from the null line along the x-axis, (compare Figures 5b and 5a).
The possibility of the appearance of reverse currents in current sheets has been predicted theoretically by S.I. Syrovatsky [36], and, subsequently, reverse currents have been revealed experimentally [11,21]. The generation of reverse currents is closely connected with the motion of plasma flows in the magnetic field of the current sheet, as we have demonstrated for current sheets formed in plasmas with heavy ions-Ar and Kr [24,37]. In this paper we present results related to phenomena that occur in current sheets formed in plasma containing the He ions. We consider the excitation of reverse currents, as well as the effect of reverse currents on the dynamics of plasma flows.
It is known that plasma motion in a magnetic field gives rise to the excitation of inductive electric fields. This effect should also come into play when plasma flows move along the width of the current sheet across the transverse magnetic field  Moreover, a faster decrease in the current density 0 Z j and increase in the current sheet thickness, 2δy, at the considerable distance from the null line along the x-axis, Figure 5b, are also due to the appearance of reverse currents, but of a smaller value than at the sheet edges; see also [24].

Work of the Ampère Forces and Slow Down of Plasma Flows
The kinetic energy of plasma flows can change (either increase or decrease) due to the work of the Ampère forces at the distances where these forces act. Below, we estimate the work of the Ampère forces ) (x F x at the half-width of the current sheet ( Here, c R is the radius of the vacuum chamber, i.e., the largest possible half-width of the sheet. The values of the work A(t) are calculated separately for two different regions. The first is the central region ( where the main (direct) currents are concentrated, and we denote the work of Ampère forces at this region as D A ; Figure   6a. At the second region ( , the reverse currents are concentrated, and this work is denoted as R A ; Figure 6a is also shown in Figure 6a; it is evident that At the first stage of the current sheet evolution (t < 4.0 μs), the work of the Ampère forces is positive, Figure 6a, and plasma can be effectively accelerated along the sheet surface. Then, the situation changes dramatically, since the absolute value of the work | | R A sharply increases due to the excitation of reverse currents. Simultaneously, the D A value slightly decreases; so that the total work T A goes down and, moreover, it even becomes negative after t ≈ 5.0 μs. Based on these results, we can conclude that, at the later stages of the current sheet evolution, the plasma flows should slow down. The data presented in Figure 6a allow us to give an interpretation for experimental results related to the evolution of the kinetic energy of plasma flows; see Figure 6b  The appearance of braking forces makes it possible to explain the nature of the temporal changes in the energy of plasma flows, when the energy achieves the super-thermal value and then reduces quite quickly [20,23,24,33].
It can be assumed that the generation of reverse currents and, as a result, the appearance of braking forces, can also affect the characteristics of high-speed plasma flows that extend from the tail region of the magnetosphere towards the Earth. Indeed, as shown by direct measurements carried out with the help of various satellite missions, the deceleration of plasma flows directed to the Earth has been recorded at distances from the Earth about (10-20) E R [38][39][40][41] (here, E R is the radius of the Earth). We believe that the excitation of the reverse currents and the appearance of additional forces directed towards high-speed plasma flows can be a significant factor leading to slowing down plasma flows in the Earth's magnetosphere.

Conclusions
In this paper, we present experimental results on the dynamics of plasma with the helium ions in the current sheets formed in two-dimensional magnetic fields with the null-line of the X-type. The research was carried out using the CS-3D experimental setup at the Prokhorov General Physics Institute of the Russian Academy of Sciences. The parameters of the plasma in the current sheets were investigated by the spectroscopic methods using two various spectral lines of the helium ion that were registered along two mutual perpendicular directions. The structure and evolution of the magnetic fields, electric currents, and the Ampère forces in the current sheets were studied using a system of magnetic probes.
We demonstrate an appearance of plasma flows accelerated along the width (the larger transverse size) of the current sheet. The energy of the flows increases rapidly and peaks at 400 eV, whereas the temperature of the helium ions is about 50 eV. Immediately upon reaching its maximum, the energy of the plasma flows decreases very quickly.
We analyze the structure of the Ampère forces that can accelerate plasma along the current sheet width. At the early stage of the current sheet evolution, the Ampère forces are directed from the middle of the sheet to both of its side edges, and build up the kinetic energy of directed flows of the helium ions.
The plasma flows that are moving in the magnetic field of the current sheet excite the inductive electric fields and the electric currents of the opposite directions relative to the main current in the sheet. The reverse currents reveal themselves primarily at the side edges of the current sheet, and bring about the Ampère forces that are directed oppositely to the forces in the sheet central region. These forces modify plasma dynamics in the current sheet, initiating deceleration of previously accelerated plasma flows. Comparison of the work of the multidirectional Ampère forces in the current sheet with the evolution of the energy of the accelerated plasma flows demonstrates a satisfactory time correlation.
The appearance of braking forces makes it possible to explain the nature of the temporal changes in the energy of plasma flows, when the energy has achieved the super-thermal value and then reduces quite quickly.
It should be emphasized that phenomena related to the excitation of reverse currents in the current sheets represent a manifestation of the general Lenz's rule. According to this rule, the induction current always results in decreasing the impact of the cause that has excited this current.
It seems reasonable that the excitation of the reverse currents and the appearance of the Ampère forces directed towards high-speed plasma flows can be a significant factor leading to braking plasma flows in the Earth's magnetosphere.