Dynamics of an Erupting Arched Magnetic Flux Rope in a Laboratory Plasma Experiment

Transcription

1 Solar Phys DOI /s Dynamics of an Erupting Arched Magnetic Flux Rope in a Laboratory Plasma Experiment S.K.P. Tripathi W. Gekelman Received: 1 June 2012 / Accepted: 12 February 2013 Springer Science+Business Media Dordrecht 2013 Abstract A laboratory plasma experiment has been built to study the eruption of arched magnetic flux ropes (AMFRs) in the presence of a large magnetized plasma. This experiment simulates the eruption of solar AMFRs in two essential steps: i) it produces an AMFR (n = cm 3, T e = 14 ev, B 1 kilo-gauss, L = 0.51 m) with a persistent appearance that lasts several Alfvén transit times using a lanthanum hexaboride (LaB 6 )plasma source, and ii) it generates controlled plasma flows from the footpoints of the AMFR using laser beams. An additional LaB 6 plasma source generates a large magnetized plasma in the background. The laser-generated flows trigger the eruption by injecting dense plasma and magnetic flux into the AMFR. The experiment is highly reproducible and runs continuously with a 0.5 Hz repetition rate; hence, several thousand identical loop eruptions are routinely generated and their spatio-temporal evolution is recorded in three-dimensions using computer-controlled movable probes. Measurements demonstrate striking similarities between the erupting laboratory and solar arched magnetic flux ropes. Keywords Coronal mass ejections, initiation and propagation Flares, dynamics Waves, plasma 1. Introduction The dynamics of the magnetic structures that confine plasma plays an important role in constituting the solar atmosphere and affecting its energetics (Lang, 2001). Solar magnetic structures can be broadly divided into two categories i) open magnetic structures that extend beyond the solar corona from darker extreme ultra-violet (EUV) regions that are called coronal holes and continuously transport material into interplanetary space (Krieger, Timothy, and Roelof, 1973; Timothy, Krieger, and Vaiana, 1975), and ii) closed magnetic S.K.P. Tripathi ( ) W. Gekelman Physics & Astronomy, University of California at Los Angeles, Los Angeles, CA 90095, USA tripathi@physics.ucla.edu W. Gekelman gekelman@physics.ucla.edu

2 S.K.P. Tripathi, W. Gekelman structures that more efficiently confine plasma and magnetic energy from days to weeks and then suddenly erupt (Abbot, 1911; Rosner, Tucker, and Vaiana, 1978). The pre-eruption phase of the closed magnetic structures is relatively stable and lasts for several Alfvén transit times (time taken by the shear Alfvén wave to travel from one footpoint to the other). In this paper, we use the term arched magnetic flux rope (AMFR) for closed magnetic structures that are essentially current-carrying plasmas confined by an arched magnetic field. The self magnetic field generated by the current gives the characteristic rope-like twisted magnetic structure to the AMFR. The presence of an electrical current in solar magnetic flux ropes has been implied in vector magnetograph measurements, which show significant twist and associated helicity in the magnetic structures emanating from the photosphere (Alfvén and Carlqvist, 1967; Pevtsov, Canfield, and Metcalf, 1995; Leka et al., 1996; Wheatland, 2000; Burnette, Canfield, and Pevtsov, 2004). We also use the term stable AMFR to signify the persistent appearance of the AMFR structure without any significant changes in its morphology. This term does not indicate the absence of waves or microscopic plasma instabilities in the AMFR. Erupting solar AMFRs lead to an impulsive release of the stored energy and trigger solar energetic events such as coronal mass ejections (CMEs) and flares (Dennis and Schwartz, 1989; Kosovichev and Zharkova, 1999; Lang, 2001; Low, 2001; Cremades and Bothmer, 2004; Chen and Kunkel, 2010; Hudson, 2011). The exact nature of the instability that drives the CME flux rope eruption is a matter of intense debate. Contemporary models of the CME flux rope eruptions rely on either the storage-and-release or on the magnetic-flux-injection paradigm. The storage-and-release models of CME flux ropes have a two-phase process in which magnetic energy slowly builds up in the corona during the pre-eruption phase. Once the stored magnetic energy reaches a certain threshold, the configuration becomes unstable and erupts impulsively. Three examples of the candidate mechanisms related to the storage-and-release paradigm are the loss of the flux-rope equilibrium (Forbes and Isenberg, 1991), the onset of breakout reconnection (Antiochos, DeVore, and Klimchuk, 1999), and the ideal kink-instability of AMFRs (Török, Kliem, and Titov, 2004). The magnetic-flux-injection model of the CME eruption (Chen, 1996; Chen and Kunkel, 2010) relies on the dynamical injection of magnetic flux associated with the AMFR current to drive the CME eruptions. Other examples of solar AMFRs are coronal loops, filaments, and small-scale structures in the lower solar atmosphere. The twist in the magnetic field lines in coronal and photospheric loops may not be always significant, which is why the term magnetic-flux-tube is associated with these structures. However, the term magnetic-flux-rope can still be used in a general sense for such structures because magnetic flux ropes become magnetic flux tubes in the limit of low magnetic-field-line twist. It is unlikely that there is a universal mechanism of solar AMFR eruptions because solar observations reveal a great variety of AMFR structures that cover wide spatial and energy scales. Although our laboratory experiment can simulate both drive mechanisms of solar AMFR eruptions, this work focusses on the dynamical injection of magnetic flux and plasma into an AMFR to trigger its eruption. In the recent past, improvements in the remote sensing and imaging capabilities of spacecraft and ground-based observations have advanced our knowledge of the evolution of solar plasma structures and energetic particle release. However, it is still not possible to capture the complex events in the solar atmosphere with a good spatio-temporal resolution or to directly measure solar plasma parameters (e.g., the magnetic field in the upper solar atmosphere) to develop a clear understanding of solar AMFR eruptions. A laboratory study of AMFR eruptions has unique advantages since it enables us to systematically vary plasma parameters, control the boundary conditions, and perform a detailed study of the AMFR

3 Magnetic Flux Rope in a Laboratory Experiment dynamics. When used in association with solar observations and numerical codes, laboratory experiments can test theoretical models and identify processes relevant to solar AMFR eruptions. To the best of our knowledge, the first laboratory experiment that simulated solar AMFRs was reported by Bostick (1956). Bostick s experiment was primitive, yet it demonstrated that by driving an electrical current along an arched magnetic field one can create a laboratory AMFR. The next generation of laboratory plasma experiments on AMFRs was developed several decades later by the Caltech group (Hansen, 2001; Hansen, Tripathi, and Bellan, 2004; Tripathi, Bellan, and Yun, 2007), followed by AMFR experiments conducted at the FlareLab (Arnold et al., 2008). The kink instability of an AMFR that does not erupt due to dominant and axially-uniform arched magnetic field has been studied by the MRX group (Oz et al., 2011). Interaction of multiple straight flux ropes has been studied in a great detail in laboratory experiments at the UCLA and LANL (Gekelman, Maggs, and Pfister, 1992; Intrator et al., 2009). The UCLA group has identified a quasi-separatrix layer in the reconnection region (Lawrence and Gekelman, 2009). Traditionally, a magnetized plasma arc is produced in laboratory experiments to mimic the behavior of solar AMFRs. The electrical current in such plasma arcs rises to several tens of kilo-amperes within a few Alfvén transit times (t A ). Hence, a relatively stable pre-eruption phase of AMFRs (characteristic feature of solar AMFRs) is not observed in the magnetized plasma arc experiments that simulate AMFR eruption. Moreover, solar AMFRs evolve in the presence of a background magnetized-plasma that plays an important role in wave excitation and energy transport. To capture the essential features of solar AMFR eruptions, a laboratory plasma experiment has been constructed at UCLA (Tripathi and Gekelman, 2010, 2011), which introduces a new approach that uses two independent plasma sources to produce the AMFR and background plasma, and a laser source to generate controlled plasma flows from the footpoints of the AMFR to trigger the eruption. The experiment has the following unique features: i) The laboratory AMFR erupts in the presence of a background magnetized-plasma. The relative magnitude of parameters in the AMFR and background plasma can be varied and the magnetic field direction can be reversed. ii) Plasma flow from the footpoints of the AMFR is generated using jets of plasma produced by laser beams. Hence, it is independent of the plasma production mechanism. iii) The electrical current in the AMFR can be kept below the kink-instability threshold for alongtime(> 50t A ). Therefore, a relatively stable pre-eruption phase of the AMFR can be maintained for a long time and a source of instability can be applied at a desired time to trigger the eruption. iv) The experiment operates with a 0.5 Hz repetition rate and is highly reproducible (normalized shot-to-shot variation in plasma density: n/n 0.005). Thus, several thousand identical eruptions can be generated and their spatio-temporal evolution can be recorded by performing a high-resolution three-dimensional (3-D) measurement of plasma parameters. The remainder of this paper proceeds with a discussion on the relevance of our laboratory plasma experiment to actual solar eruptions in Section 2. Details of the experimental set-up are presented in Section 3, which is followed by results from the experiment in Section 4. The main points of the paper are summarized at the end in Section 5.

4 S.K.P. Tripathi, W. Gekelman 2. Relevance of Laboratory Plasma Results to Solar Observations Relevance of a laboratory plasma experiment for solar observations and its limitations using a dimensionless form of the two-fluid magnetohydrodynamical (MHD) induction equation (Hansen, 2001), which can be written as (U B) B 1 t S B c ( ) ( B) B }{{} ω pi L n }{{} MHD induction Hall + c ( ) ( ( )) 1 ω pi L β e c2 d B = 0, (1) n ωpe 2 L2 dt n }{{}}{{} hydrostatic electron inertia where B = B/B 0, U = U/v A, n = n/n 0, t = t/t A,and =L are the normalized magnetic field, plasma velocity, density, time, and length scales with respect to the maximum magnetic field B 0, the Alfvén speed v A = B 0 / μ 0 nm i, the maximum plasma density n 0, the Alfvén transit time t A, and the length L of the AMFR. The Alfvén transit time is the time taken by the Alfvén wave to travel the length L. n, m i, ω pe,andω pi are the plasma density, ion mass, electron plasma frequency, and ion plasma frequency. The dimensionless parameter S = v A Lμ 0 /η is the Lundquist number, which is the ratio between the resistive diffusion time and the Alfvén transit time. A high value of S indicates a highly conducting plasma where plasma dynamics is primarily dictated by the magnetic J B force and the cross-field diffusion is relatively unimportant. Essentially, the plasma is frozen to the magnetic field when S is high. The primary requirement from the experiment is that the laboratory AMFR retains the geometry of solar AMFRs. This is fulfilled by driving an electrical current with two electrodes (as shown in Figure 1(a)) along an arched vacuum (potential) Figure 1 (a) Basic geometry of the laboratory AMFR is depicted in this simplified 2-D view. Electrodes and laser-generated jets are also indicated. The footpoints of the AMFR are anchored on the electrodes. An external power supply, connected to the electrodes, drives current I along the arched magnetic field B 0 and sustains the AMFR. (b) Arrangement of the AMFR, laser, and ambient plasma sources in a cylindrical vacuum chamber to achieve the conditions depicted in (a). The z-direction is along the axis of the vacuum chamber and the ambient magnetic field B 0a is in the opposite direction to the z-axis. The AMFR is formed in the xy-plane at z = 0. The origin of the Cartesian coordinates (x,y,z) is on the vacuum chamber axis and its approximate location is indicated in panel (a). The footpoints of the AMFR are at x = 11.5 cmand y =±11.5 cm.

5 Magnetic Flux Rope in a Laboratory Experiment Table 1 Comparison between laboratory and solar plasma parameters. Typical plasma parameters of an erupting helium laboratory AMFR are used in the table. Lower corona Coronal loops Laboratory AMFR n (m 3 ) T (K) ( 24 ev) L (m) B (G) r (m) r i (m) r/r i β S c ω pi L β e c ω pi L c 2 ωpel magnetic field. The footpoints of the laboratory AMFR are anchored to the electrodes. Following the onset of an instability, the AMFR can expand away from the footpoints without being affected by the wall of the vacuum chamber. Details of the experimental arrangements are described in Section 3. Typical plasma parameters of the laboratory and solar AMFRs are presented in Table 1. Parameters of a coronal loop (Lang, 2001; Chen and Kunkel, 2010) are presented in the table to represent solar AMFRs. Even though the absolute plasma parameters (n, T, L, and B) for laboratory and solar AMFRs significantly differ, the laboratory studies retain the essential physics of solar AMFRs. This can be explained by examining the terms in Equation (1). The MHD induction is the dominant term for both laboratory and solar AMFRs because it is on the order of unity. The resistive term in the MHD induction is on the order of 1/S, which is on the Sun and in the experiment. In both systems the resistive term is usually ignorable. However, the data presented in Table 1 do not represent localized regions of the plasma where L is much smaller and the effective resistivity η is orders of magnitude higher than the Spitzer resistivity. Therefore, S is relatively small and the resistive term cannot be ignored in these regions. Such a scenario is known to exist in the magneticreconnection regions on the Sun (Lin et al., 2007) and in the laboratory (Stenzel, Gekelman, and Wild, 1982; Kulsrudet al., 2005), and they strongly affect the dynamics of the AMFRs. The Hall ( c/ω pi L), hydrostatic ( cβ e /ω pi L), and electron inertia ( c 2 /ω 2 pe L2 )terms for solar coronal loops are on the order of 10 7,10 9, and In the same sequence, these terms for the laboratory AMFR are on the order of 10 1,10 3, and The magnitude of these three terms (especially the Hall term) with respect to the MHD-induction term is not as small in the experiment as on the Sun. Therefore, they can play a more active role in the experiment than on the Sun. Moreover, the ratio between the AMFR radius and the ion gyroradius (r/r i ) is orders of magnitude higher on the Sun. Hence, laboratory measurements of waves and structures that are smaller in size than the ion gyro-radius size ( 2 mm) may not be directly relevant to solar AMFRs. This analysis shows that the MHD induction is the dominant term in both solar and laboratory plasmas and hence the laboratory AMFR studies are relevant to the Sun. There are regimes where non-mhd effects can play an important role in the experiment and on the

6 S.K.P. Tripathi, W. Gekelman Sun, and they could be relevant to each other. Hence, one should be careful in only stressing the importance of MHD effects and focusing on plasmas with high S in all situations. 3. Experimental Set-up The experiment was conducted in a 4.9 m long, 1.0 m diameter cylindrical vacuum chamber that has external electromagnets to produce an axial magnetic field B 0a of up to 300 gauss (G) (see Figure 1(b)). The vacuum chamber was filled with neutral helium gas at torr pressure. A rectangular lanthanum hex-boride (LaB 6 ) cathode (size: 20 cm 20 cm) and a molybdenum wire-mesh anode, separated by 27 cm, were placed at one end of the chamber. The LaB 6 cathode was indirectly heated to 1700 C to obtain an efficient thermionic emission of primary electrons that are accelerated away from the cathode when 100 V discharge voltage is applied between the electrodes. The primary electrons produce a cylindrical plasma 0.6 m in diameter and 4 m long by ionizing the neutral gas. Details of the plasma production by this mechanism is described by Cooper et al. (2010). The cylindrical plasma fills the vacuum chamber and serves as an ambient magnetized plasma in which the AMFR evolves. For the results reported in this paper, the ambient plasma parameters are density n a = cm 3, electron temperature T ea 4.0 ev, discharge current I a 600 A, and B 0a = 0 75G. The experimental conditions of the AMFR are shown in a simplified 2-D view in Figure 1(a). The AMFR is produced in the middle of the chamber with two additional electrodes that are mounted on two radial shafts, as shown in Figure 1(b). The AMFR cathode is circular disk-shaped LaB 6 (7.6 cm diameter) that is indirectly heated to 1825 C. The AMFR anode is made of copper and is identical to the cathode in shape. The footpoints of the AMFR are anchored to the electrodes, which are separated by 23 cm. Each AMFR electrode is surrounded by an electromagnet to produce an arched magnetic field B 0 along the axis of the AMFR (see the direction of B 0 and AMFR electrodes in Figure 1). The AMFR is produced when 200 V discharge voltage is applied between the electrodes from an external power supply. After producing the AMFR, most of the discharge voltage drops near the electrodes in a thin sheath region (size < 0.1 mm AMFR length) and the bulk of the AMFR dynamics is not directly affected by the voltage at the footpoints. A stable laboratory AMFR (as evident from its persistent appearance and stationary n and T profiles) is produced in 140 µs after applying the voltage on the electrodes. The initial current I,drivenbythe power supply, rises to 60 A in 140 µs and remains stationary until a source of instability is applied to disrupt the persistent appearance of the AMFR. This is accomplished by firing two identical infrared laser beams (wavelength = 1064 nm, pulse-duration = 8 12ns,beam energy 0.8 J/pulse for each beam) toward the footpoints of the AMFR. Each AMFR electrode has a small orifice and a carbon rod placed behind the electrode. The laser beams pass through the orifices and ablate the carbon targets to produce two plasma jets that emanate from the footpoints of the AMFR as shown in Figure 1(a). The injection of the plasma jets into the AMFR causes a sudden increase in the current I and density n of the AMFR, which results in an impulsive eruption of the AMFR. The injection of the plasma and current I into the laboratory AMFR is analogous to the plasma and poloidal magnetic flux injection from the convection zone into the solar AMFRs. The plasma parameters of the stable AMFR are density n = cm 3, electron temperature T e 14 ev, discharge current I 60 A, and B 0 = 1000 G at the footpoints. Following the injection of the laser jets, n and T e rise to a maximum value of cm 3 and 24 ev. At the beginning of the experiment, the vacuum chamber is evacuated to a base pressure of torr and electromagnets for the ambient magnetic field are turned on. Over

7 Magnetic Flux Rope in a Laboratory Experiment Figure 2 Timing sequence of the computer-controlled events that form an erupting laboratory AMFR. This sequence is repeated every 2 s to generate thousands of identical loop eruptions. The displayed timings may be adjusted to achieve the desired boundary conditions within the experimental limits. a period of one to two days, the temperature of the two LaB 6 cathodes is slowly raised to the desired value, while a base pressure < 10 5 torr is maintained in the chamber. After the pressure drops to below 10 6 torr, the chamber is filled with helium gas at the desired neutral pressure. At this stage, the ambient and AMFR plasmas can be formed in a pulsed mode with a 0.5 Hz repetition rate with the timing sequence displayed in Figure 2. During each pulse the following sequence is executed i) discharge voltage pulse for the ambient plasma is applied, ii) pulsed magnetic field B 0 (not shown in Figure 2) fortheamfris turned on, iii) discharge voltage pulse for the AMFR is applied in the afterglow of the ambient plasma ( B 0 /B 0 during AMFR < 0.01), iv) the laser beams are fired in the middle of the AMFR pulse, and v) data are recorded and the diagnostic probe is moved to a new location in the plasma. After every AMFR pulse, the laser targets are moved by 1 mm. This ensures that a fresh target surface is ablated by the laser beams in the following AMFR pulse. This is critical for maintaining a good reproducibility of the experiment. The experiment and data acquisition system are automated using computer controls. Hence, several thousand identical AMFR eruptions are routinely generated and data of high spatio-temporal resolution are recorded during the course of the experiment, which lasts several hours. Langmuir and magnetic-loop probes are used to measure the plasma parameters (n, T e,andb). A fast CCD-intensifier camera (5 ns minimum exposure time, pixels, forced air cooling, 12 bit digital converter) records images of the AMFR evolution. 4. Results and Discussion The time evolution of a helium laboratory AMFR is shown in Figure 3. The time t was measured with respect to the laser trigger at t = 0 µs. Two different intensity scales (one for the top panel and the other for the bottom panel) were used to display the frames in Figure 3. This way, the relative intensities of the frames in each panel can be compared. After application of the discharge voltage pulse at t = 1000 µs on the electrodes, the AMFR begins to form in 40 µs (see the first frame in Figure 3(a)). During this plasma breakdown phase, primary electrons ionize the neutral gas and plasma density begins to build up. After 140 µs at t = 860 µs, the AMFR exhibits a persistent appearance and the discharge current attains a steady-state value of 60 A. This initiates the stable phase of the AMFR. The Alfvén transit time τ A = L/v A in the stable AMFR is 1.2 µs (using L = 0.51 m, B 0 = 1000 G, n = cm 3, v A = ms 1 ). The resistive diffusion time τ d is μ 0 L 2 /η, whereη = η /2andη is transverse Spitzer resistivity. The value of τ d for the

8 S.K.P. Tripathi, W. Gekelman Figure 3 (a) Formation of a helium laboratory AMFR after application of the voltage on the electrodes at t = 1000 µs is displayed in these unfiltered images recorded by a fast CCD camera with 1 µs exposure time. The laser beams are triggered at t = 0 µs. It takes about 140 µs (t = 1000 µs to 860 µs) to form an AMFR with a persistent appearance. (b) Escape of plasma from the AMFR after the laser-generated flows, shown on a fast time-scale (2.5µs 2 Alfvén transit time). The exposure time of the fast camera is 50 ns. laboratory AMFR is 22 ms (using T e = 14 ev, charge state Z = 1, Coulomb logarithm ln = 15, η = m). It can be shown that the value of τ d in the transverse direction (μ 0 r 2 /η ) is in the µs range. The stable phase of the AMFR persists from t = 860 µs to t = 0µs( t = 717t A ), mimicking the behavior of solar AMFRs that remain stable for several Alfvén transit times before erupting (Abbot, 1911). The evolution of the laboratory AMFR following the laser trigger is displayed in Figure 3(b). The AMFR current rises to 500 A within 0.7 µs after the laser trigger. Our previous study of an argon laboratory AMFR (Tripathi and Gekelman, 2010) has demonstrated that an order of magnitude increase in the current leads to a significant twist in the magnetic structure of the AMFR (I = 500 A average twist (r) π) andit becomes kink unstable (Hood and Priest, 1979; Török, Kliem, and Titov, 2004). It was also confirmed that the laser plasma is primarily composed of C ++ ions. The motion of the laser plasma in the AMFR was observed by attaching a 460 nm narrow-passband filter to the CCD camera. The filter blocks the light from the helium plasma and transmits the C ++ emission from the laser plasma. The time-of-flight measurements indicate that the laser plasma jets propagate with an average speed v jet ms 1. The ion acoustic speed c s in the AMFR is ms 1 and v A near the footpoints is ms 1. Hence, the jets are supersonic and sub-alfvénic (c s <v jet <v A ) near the footpoints. A comparison of the bright regions in the t = 0.2 µs and 0.7 µs frames implies that the increase in the current leads to an outward motion of the AMFR and its minor radius decreases significantly. The outward motion is understood to be caused by the increase in the hoop force, and the decrease in the plasma radius is generated by the pinch force (Chen, 1996). Our previous study on an argon AMFR (Tripathi and Gekelman, 2010) was performed in the presence of a positive B 0a, which causes a somewhat stronger outward motion because of the outward J B 0a force. For the results reported here, B 0a is 10 G and the J B 0a force is in the inward direction. In this configuration, the plasma β value at the leading edge of the AMFR rapidly increases from 0.1 to 1.3 within 1.4 µs after the laser flows are produced. Magnetic field measurements (to be discussed below) evince ejection of an axial current from the AMFR at t 1.4 µs.

9 Magnetic Flux Rope in a Laboratory Experiment Figure 4 Plasma density n and electron temperature T e profiles of a stable helium AMFR are measured along the x-axis at t = 840 µs. As shown in Figure 1(a), the positive and negative x-directions are toward the inboard and outboard of the AMFR, respectively. Following this phase, the AMFR current drops to the steady-state value (40 60 A), the outward expansion is inhibited, and plasma from the AMFR escapes to the background. The escape of plasma from the AMFR leads to the disappearance of the bright regions of the AMFR, as seen in the last two panels of Figure 3(b). The panels in Figure 3 are unfiltered and the discharge source is kept on during the entire period. Hence, the light emission from the newly formed low-density plasma appears in the last two panels in a faint blue color. The measurement of the plasma density profiles provides more details of the eruption that are discussed in the following paragraphs. These observations suggest that the laboratory AMFR erupts on a time scale τ exp such that τ A <τ exp τ d. Density and electron temperature profiles of a stable AMFR were measured with a Langmuir probe and are displayed in Figure 4. The AMFR profile was measured off-axis at z = 5 cm to ensure that the probes are not destroyed by the laser beams in the z = 0cm plane. The maximum in the n-profile exists near the AMFR axis, where n = cm 3 and T e = 14 ev. A steep decay of n and T e in the inboard region reflects the steep B 0 gradient there. Away from the AMFR axis at x = 10 cm, the ambient plasma parameters are n a = cm 3 and T ea = 4 ev. In our experiment, the time-resolution of the T e measurement is 50 µs, which is too slow to capture the evolution of T e during the eruption. However, the ion-saturation current density j i n T e can be recorded by the Langmuir probe with a fast time response ( t = 1/25 µs) and the AMFR density can be extracted from the measurements of j i using an average value T e = 10 ev. The density fluctuation spectra of the AMFR were sampled in three different time-ranges that characterize the ambient plasma (t = 1290 to 1140 µs), stable AMFR (t = 400 to 250 µs), and unstable AMFR (t = 5 to 155 µs). The spectra were averaged over an xy-plane that intersects the AMFR and is presented in Figure 5. A significant increase in the fluctuation level in the lower frequency range (f <1.0 MHz) and appearance of a peak at 171 khz (labeled global kink mode oscillation ) are highlights of the unstable AMFR spectrum. The currently obtained results are not adequate to characterize the broad lowfrequency spectrum of the unstable AMFR. Although this broad low-frequency spectrum appears to have characteristics of turbulence modes, the absence of a multitude of coherent modes cannot be ruled out without performing a more detailed measurement using a fixed and a moving Langmuir probe pair. The spectra of the stable and unstable phases of the AMFR above 1.0 MHz frequency are identical, and both indicate the presence of peaks near the lower hybrid frequency. An analysis of these high-frequency fluctuations reveals associated modes at the edge of the AMFR, where plasma parameters have steep gradients. A detailed discussion of these high-frequency modes is beyond the scope of this paper. The AMFR density profiles with a good spatio-temporal resolution ( x = 5 mm, t = 1/25 µs) were produced from the measurements of j i and are presented in Figure 6(a). As

10 S.K.P. Tripathi, W. Gekelman Figure 5 Normalized density fluctuation spectra of the AMFR are displayed for the ambient plasma, stable arched magnetic flux rope (AMFR), and unstable AMFR. The spectra have been averaged over 615 equidistant points in an xy-plane (x = 10 to 10 cm, y = 3.5 to3.5cm,z = 5 cm). Prominent features of the unstable AMFR spectra are a significant increase in the fluctuation level in the lower frequency range (f <1.0 MHz) and the appearance of a low-frequency peak at 171 khz (labeled global kink mode oscillation ). Figure 6 (a) Time evolution of the density profile of an erupting helium laboratory AMFR (see the x-axis in Figure 1). The striking features are the outward expansion of the AMFR during the eruption and the damped oscillations with a khz frequency in the post-eruption phase. (b) Phase-fronts of a fast magnetosonic wave are detected in the post-eruption AMFR and presented on an expanded xt-plane. The data have been processed using a MHz digital passband filter before plotting.

11 Magnetic Flux Rope in a Laboratory Experiment expected, the density profile before the laser trigger at t = 0 µs appears to be persistent and is identical to the density profile in Figure 4. Following the laser trigger, the AMFR expands in the outward direction (see the Expanding AMFR label) and a low-density plasma remains at the location of the stable AMFR. The discharge and magnetic field power supplies for the AMFR are kept on during the entire period. Hence, a new AMFR quickly forms and exhibits a damped oscillation in the frequency range khz. These oscillations are also observed on the discharge current and magnetic-field signal, and appear as a 171 khz peak in the density spectrum of the unstable AMFR (see Figure 5). With a striking similarity, the existence of such damped oscillations in post-flare loops on the Sun has been reported by several groups and has been interpreted as characteristics of global kink modes (Nakariakov et al., 1999; Chen and Schuck, 2007; Ofman and Wang, 2008). The frequency f of this mode is given by f = v ( ) A 2 1/2, (2) 2L 1 + n a /n i where n a and n i are the ambient plasma and AMFR plasma densities, respectively. The AMFR magnetic field decays away from the footpoints, and its average value in the AMFR is 321 G. Hence, the average v A in the AMFR is ms 1.WeusedL = 0.51 m and n a /n i = 1/3 to estimate a 171 khz frequency for the global kink mode in our experiment. This estimate agrees well with the observed frequency of the oscillations. The oscillation amplitude decays with an e-folding time of 51 µs, which is much slower than the axial resistive time and comparable to the transverse resistive time of the AMFR. Detailed measurements are planned in the future to identify the damping mechanism of the global kink modes in our experiment. The time evolution of the AMFR density also contains a signal at a 4.7 MHz frequency with n/n The nature of this high-frequency oscillation was analyzed by applying a MHz digital passband filter to the data and plotting them on an expanded xt scale in Figure 6(b). The density wave at 4.7 MHz frequency and 3.0 cm wavelength is confirmed from the measurement of the phase fronts displayed in Figure 6(b). The amplitude of the 4.7 MHz peak in Figure 5 is identical for the stable and unstable AMFR. Hence, the density wave exists even during the stable phase. The wave propagates across the AMFR magnetic field with a phase speed v φ ms 1, which is comparable to v A ms 1 and much faster than the ion acoustic speed c s ms 1. Moreover, the wave frequency is lower than the lower hybrid frequency ( 10.5 MHz). These observations indicate that the density wave is a fast magnetosonic wave (Habbal, Holzer, and Leer, 1979). The global kink mode oscillations and fast waves are also detected in the magnetic fields of the AMFR. The global kink mode oscillations damp in 51 µs, which is followed by a significant increase in the electron temperature (from 14 ev to 24 ev) of the AMFR. After t 120 µs, the plasma oscillations disappear, the electron temperature drops to 14 ev, and the AMFR density profile resembles the density profile of the stable AMFR at t<0µs. Magnetic-field vectors of the AMFR were measured with a magnetic-loop probe during the eruption in an xy-plane and are presented in Figure 7. The magnetic loop probe measures the time-varying magnetic field during the eruption and is not sensitive to the vacuum (potential) magnetic fields. The t = 0.6 µs panel shows a relatively stronger inboard magnetic field of the AMFR, which links the AMFR footpoints. Following the laser trigger, the observation of O -points in the t = 1.4 and 2.3 µs panels are the main features in Figure 7. The O -points are surrounded by an azimuthal magnetic field, indicating the emergence of an axial current from the leading edge of the AMFR. Measurement of the B z profile (not

12 S.K.P. Tripathi, W. Gekelman Figure 7 Evolution of the AMFR magnetic field at four distinct times is displayed in an xy-plane at z = 5cm.The approximate location of the plane is indicated by the dotted rectangle in Figure 1(a). The vectors are drawn using the B x and B y components of the magnetic field. Appearance of the O -points in the 1.4 and 2.3 µs panels indicates the ejection of an out-of-plane current (along the z-direction) from the AMFR. The inboard point α and outboard point β are marked here and in Figure 1(a) to guide us in approximately locating the O -point in the schematic view of the AMFR. presented here) in the xy-plane of Figure 7 shows that the magnitude of B z is comparable to B x and B y around the O -point. This implies that the emerging axial current-channel is a large flux rope with a significant twist. The appearance of this axial current channel at t = 1.4 µs is concurrent with the escape of plasma from the AMFR in Figure 3(b). However, the large flux rope that contains the low-density plasma released from the AMFR is not visible in the camera images. To verify the presence of this large flux rope, Langmuir and magnetic loop probes were placed at z =±32 cm and unambiguously detected the flux rope in the xy-planes away from the AMFR. The emergence of a large flux rope from an erupting laboratory AMFR is relevant to the flux rope models of CMEs (Gibson and Low, 2000), since it demonstrates the transport of magnetic flux into the ambient plasma from the AMFR. The large flux rope quickly grows to the size of the vacuum chamber. Hence, its evolution cannot be directly compared with the evolution of CMEs to large spatial scales. 5. Conclusions A comparison of the solar and laboratory plasma parameters using the dimensionless form of the two-fluid MHD induction equation in Section 2 has demonstrated that the laboratory AMFR studies are relevant to the solar AMFRs because the MHD induction is the dominant term in both plasmas. However, certain non-mhd effects (e.g., the role of the Hall term, the appearance of structures smaller in size than the ion gyro-radius, and the dynamics of the plasma on a time scale slower than the resistive diffusion time) can play more active roles in the laboratory experiments than on the Sun. The experimental results confirmed that a stable

13 Magnetic Flux Rope in a Laboratory Experiment arched magnetic flux rope with a persistent appearance lasting several Alfvén transit times can be generated in the laboratory and that the eruption of the stable AMFR can be triggered by injecting a dense plasma and magnetic flux into the AMFR. The experiment operates with a 0.5 Hz repetition rate; hence details of the eruption can be captured by recording data with a good spatio-temporal resolution. Highlights of the laboratory AMFR eruption are i) the outward motion of the AMFR due to the hoop force, ii) the decrease of the minor radius of the AMFR due to the pinch force, iii) the development of a highly twisted magnetic structure in the kink-unstable AMFR, iv) the appearance of global kink mode oscillations and a fast magnetosonic wave in the post-eruption phase, v) the ejection of a large magnetic flux rope from the leading edge of the AMFR, and vi) the observation of strong heating in the inboard region of the AMFR. We showed that these results resemble the observations of solar AMFR eruptions. Our future studies will be focused on simulating the storage-andrelease model of the eruption. In these experiments, the AMFR eruption will be triggered by a programmed increase of the discharge current in the absence of the laser plasma source and the AMFR force balance will be examined in a variety of scenarios. Acknowledgements The experiment was conducted at the Basic Plasma Science Facility (BaPSF) at the University of California, Los Angeles, which is jointly funded by National Science Foundation and Department of Energy. The authors thank James Chen, Alexander Kosovichev, and Steven Spangler for useful discussions and P. Pribyl, Z. Lucky, and M. Drandell for technical assistance. One of the authors (SKPT) thanks Paul Bellan for his valuable suggestions in deriving the two-fluid MHD induction equation. References Abbot C.: 1911, The Sun, D. Appleton and Company, New York, 128. Alfvén, H., Carlqvist, P.: 1967, Solar Phys. 1, 220. Antiochos, S.K., DeVore, C.R., Klimchuk, J.A.: 1999, Astrophys. J. 510, 485. Arnold, L., Dreher, J., Grauer, R., Soltwisch, H., Stein, H.: 2008, Phys. Plasmas 15, Bostick, W.H.: 1956, Phys. Rev. 104, Burnette, A.B., Canfield, R.C., Pevtsov, A.A.: 2004, Astrophys. J. 606, 565. Chen, J.: 1996, J. Geophys. Res. 101, Chen, J., Kunkel, V.: 2010, Astrophys. J. 717, Chen, J., Schuck, P.: 2007, Solar Phys. 246, 145. Cooper, C.M., Gekelman, W., Pribyl, P., Lucky, Z.: 2010, Rev. Sci. Instrum. 81, Cremades, H., Bothmer, V.: 2004, Astron. Astrophys. 422, 307. Dennis, B.R., Schwartz, R.A.: 1989, Solar Phys. 121, 75. Forbes, T.G., Isenberg, P.A.: 1991, Astrophys. J. 373, 294. Gekelman, W., Maggs, J., Pfister, H.: 1992, IEEE Trans. Plasma Sci. 20, 614. Gibson, S.E., Low, B.C.: 2000, J. Geophys. Res. 105, Habbal, S.R., Holzer, T.E., Leer, E.: 1979, Solar Phys. 64, 287. Hansen J.F.: 2001, Laboratory Simulations of Solar Prominences. Ph.D. thesis, California Institute of Technology. Hansen, J.F., Tripathi, S.K.P., Bellan, P.M.: 2004, Phys. Plasmas 11, Hood, A.W., Priest, E.R.: 1979, Solar Phys. 64, 303. Hudson, H.: 2011, Space Sci. Rev. 158, 5. Intrator, T., Sun, X., Lapenta, G., Dorf, L., Furno, I.: 2009, Nat. Phys. 5, 521. Kosovichev, A., Zharkova, V.: 1999, Solar Phys. 190, 459. Krieger, A.S., Timothy, A.F., Roelof, E.C.: 1973, Solar Phys. 29, 505. Kulsrud, R., Ji, H., Fox, W., Yamada, M.: 2005, Phys. Plasmas 12, Lang K.: 2001, The Cambridge Encyclopedia of the Sun, 1st edn., Cambridge University Press, Cambridge, 106. Lawrence, E.E., Gekelman, W.: 2009, Phys.Rev.Lett.103, Leka, K.D., Canfield, R.C., McClymont, A.N., van Driel-Gesztelyi, L.: 1996, Astrophys. J. 462, 547. Lin, J., Li, J., Forbes, T.G., Ko, Y.K., Raymond, J.C., Vourlidas, A.: 2007, Astrophys. J. Lett. 658, L123. Low, B.C.: 2001, J. Geophys. Res. 106,

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