A Laboratory Experiment of Magnetic Reconnection: Outflows, Heating and Waves in Chromospheric Jets
N. Nishizuka, Y. Hayashi, H. Tanabe, A. Kuwahata, Y. Kaminou, Y. Ono, M. Inomoto, T. Shimizu
aa r X i v : . [ a s t r o - ph . S R ] D ec A Laboratory Experiment of Magnetic Reconnection: Outflows,Heating and Waves in Chromospheric Jets
N. Nishizuka , Y. Hayashi , H. Tanabe , A. Kuwahata , Y. Kaminou , Y. Ono , M.Inomoto , T. Shimizu ABSTRACT
Hinode observations have revealed intermittent recurrent plasma ejec-tions/jets in the chromosphere. These are interpreted as a result of non-perfectlyanti-parallel magnetic reconnection, i.e. component reconnection, between atwisted magnetic flux tube and the pre-existing coronal/chromospheric mag-netic field, though the fundamental physics of component reconnection is unre-vealed. In this paper, we experimentally reproduced the magnetic configurationand investigated the dynamics of plasma ejections, heating and wave generationtriggered by component reconnection in the chromosphere. We set plasma pa-rameters as in the chromosphere (density 10 cm − , temperature 5-10 eV, i.e.(5-10) × K, and reconnection magnetic field 200 G) using argon plasma. Ourexperiment shows bi-directional outflows with the speed of 5 km s − at maximum,ion heating in the downstream area over 30 eV and magnetic fluctuations mainlyat 5-10 µ s period. We succeeded in qualitatively reproducing chromospheric jets,but quantitatively we still have some differences between observations and exper-iments such as jet velocity, total energy and wave frequency. Some of them canbe explained by the scale gap between solar and laboratory plasma, while theothers probably by the difference of microscopy and macroscopy, collisionalityand the degree of ionization, which have not been achieved in our experiment. Subject headings:
Magnetic reconnection — Sun: chromosphere — Sun: activity— Plasmas — Methods: laboratory — Magnetic fields
1. Introduction
Solar jets are ubiquitous phenomena both in the corona and the chromosphere. Theysometimes show cusp-like structure which is thought to be evidence of magnetic reconnection Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Yoshinodai, Sagami-hara, Kanagawa 229-8510, Japan; [email protected] Graduate School of Frontier Sciences, University of Tokyo, Tokyo, Japan §
2, we explain the apparatus of the reconnection experiment of laboratory plasmaand the method of measurements. In §
3, we show experimental results such as reconnectionjets, plasma heating and wave generation. Finally, in §
4, we discuss the experimental resultscomparing with solar observations of chromospheric jets.
2. The TS-4 Experiment2.1. Apparatus of the TS-4 Experiment
The Tokyo Spheromak (TS) toroidal plasma merging experiments have been conductedto study plasma heating effects of magnetic reconnection since 1986 (e.g. Ono et al. 1993,1997; Yamada et al. 1997). As shown in Figure 2, the instrument of TS-4 device is composedof the axisymmetric toroidal vacuum vessel with length of 2.5 m and diameter of 2.0 m andthe two flux cores of poloidal field (PF) and toroidal field (TF) coils for poloidal/toroidalflux injections (see more details in Kawamori & Ono 2005; Kawamori et al. 2007). Thecylindrical coordinate is adopted: Z-axis in the axial direction, R-axis in the radial directionand T-axis in the toroidal direction. TS-4 also contains a center solenoid coil called OH coil(originally named ohmic heating coil) along the Z-axis with the radius of 90 mm, outsideof which is filled with fully ionized plasma and inserted by three kinds of probe arrays:the 2D magnetic field probe array, the magnetic fluctuation probe array and the Machprobe. Locations of the probe arrays are overlaid in Figure 2. The vacuum vessel hasa window, through which the Doppler spectroscopy measurements are performed. Withthese instruments, we performed four different measurements simultaneously for the plasmadiagnostics in TS-4 device.Figure 3 shows the schematic pictures of our experimental scenario. The time profiles 4 –of electrical current induced in TF, PF and OH coils are shown in Figure 4. Initially thevacuum vessel is kept in the vacuum state less than 10 − Torr and then filled with argongas. The reasons for the selection of argon gas are reproductivity and emissivity comparedwith hydrogen. At first, argon plasma was fully ionized (more than 90%) and two toroidalplasmas with the radius of 0.5 m were generated by the flux cores (Fig. 3a). Two toroidalplasmas were merged together in the axial (Z) direction under magnetic compression providedby the pair of PF coils or acceleration coils (Fig. 3b). The magnetic reconnection occursat the contacting point of the two toroidal plasmas, causing high-power plasma heatingby magnetic reconnection. The merged toroidal plasma, i.e. spheromak, has the helicalmagnetic configuration with toroidal and poloidal components. Then we induced a newpoloidal field anti-parallel to the poloidal field of the spheromak by the OH coil (Fig. 3c).The spheromak and the anti-parallel OH field were merged together in the radial (R) directionvia magnetic reconnection. As the reconnection proceeds, the spheromak becomes smallerand smaller and the reconnection point moves upward (in positive R -direction) under controlby the separation coils (Fig. 3d).The experimental parameters were selected similar to the chromospheric parametersin the sun such as ion and electron temperatures T i = T e =10 eV ( ∼ K), electron density n e ∼ cm − , and toroidal and poloidal magnetic fields are B p /B t = 400G/220G at thesurface of the spheromak (plasma beta β ∼ µ s (100-300 G), ion Larmor radius 7 cm, local sound speed 7 km s − (T=10 K) and ionAlfv´en velocity 13 km s − (B=200 G) for argon ion we used, respectively. Therefore, inthis experiment, we see microscopic phenomena around the reconnection region occurringin the solar chromosphere, which cannot be seen neither in Hinode observations nor inmagnetohydrodynamic simulations. The two sets of the 10 × R − Z plane of the vessel to measure directly the 2D magnetic field profile. Its spatial resolution is80 mm in the radial direction and 90 or 135 mm in the axial direction. Its time resolution is1 µ s. The poloidal flux contours and current density profiles, based on the axial symmetryassumption, were calculated from the measured B z and B t components of 2D magnetic fieldprofiles. The current sheet was identified by the measured toroidal current density profile J t and the X-line structure. More in detail, physical parameters of B r , J t and E t were 5 –calculated from B z by the following equations, B r ( r, z ) = − πr ∂ Ψ ∂z (1) J t ( r, z ) = ∂B r ∂z − ∂B z ∂r = − πr ∂ Ψ ∂z − ∂B z ∂r (2) E t ( r, z ) = − πr ∂ Ψ ∂t , (3)where Ψ( r, z, t ) = R rr min πr ′ B z dr ′ is magnetic flux ( r min =92 mm at the surface of the OHcoil). Since magnetic field is almost negligible in the current sheet, the effective resistivity isderived by η =E t /J t , although it is slightly affected by the magnetic flux inside the OH coil.An array of 27 magnetic pickup coils (Kuwahata et al. 2011) was also inserted on themid-plane (z=0), but with much shorter distances of 10 mm, to measure the 1D magneticfluctuation profile in R-direction ( δB z ). The magnetic fluctuation probe array is digitizedby 200 M sampling s − with the 8 bit analog to digital converters (ADCs). The integrationof measured δ B z at the same location gives us B z value, and the toroidal current density iscalculated by J t = - ∂ B z / ∂ r, on the assumption that B r is negligible on the mid-plane.The ion Doppler velocity V i and temperature T i diagnostics was performed by the fiberoptic multi-channel imaging spectroscopy system (Tanabe et al. 2010). 23 sets of multi-chord line spectra of Ar II at 434.8 nm are collected to optical fibers. Each of them arecollimated by f=50 mm and F=1.2 camera lens and measured by ICCD imaging spectrometerwith 256 pixel wavelength resolution (0.024 nm pixel − ). At first, each Doppler width of thespectral line is calculated by using Gaussian function fitting algorithm to plot the 1D profileof V i and T i along the axial (Z) direction in the current sheet. Its spatial resolution is 20mm in the axial direction, and its time resolution is 20 µ s.The 1D ion velocity profile V i was also directly measured by the Mach probe arrayinserted along the current sheet near the OH coil at r =190 mm. Its axial spatial resolutionis 50 mm and its time resolution is 0.5 µ s. The probe was used to directly measure Machnumber of the ion flow, which is calculated from the difference of the two current densitiesentering into the probe through the sheath, such as exp( KM ) = J up / J down . Since a paper onthe K-value calibration for the Mach probe concluded K=2.0-2.5 for SSX parameters (T e =7eV, T i =20 eV Zhang et al. 2011), we adopted K=2.5 in this paper.
3. Experimental Results
Figures 5(a) and 5(b) show the poloidal flux contours in the poloidal (R-Z) plane of twomerging toroidal plasmas (B p =400 G, B t =220 G at the surface of the spheromak). These two 6 –toroidal plasmas were merged together during 380-400 µ s (Fig. 5a and illustrations in Figs.3a-3b). Magnetic reconnection between the spheromak and the OH field occurred during450-560 µ s (Fig. 5b and Figs.3c-3d). At that time, negative J t region (blue color in Fig. 5b),that is a current sheet, was observed between the spheromak and the OH coil (92 mm < r < § z component measuredby the magnetic fluctuation probe array, the reconnection point between the spheromak andthe OH field moved upward as the spheromak became smaller and smaller. The reconnectionpoint is located in the undetectable area below the wall of the vacuum vessel in the earlyphase, where reconnection occur partially in vacuum and partially in plasma leading to themorphology change of the global magnetic field to accelerate the plasma by sling-shot effectdue to magnetic tension force. In the later phase, we directly observed the reconnectionpoint with the 2D magnetic probe array, when it moved upward as reconnection proceeds.Figure 6 shows the axial (Z) profiles of ion velocities during 380-560 µ s measured bythe fiber optic multi-channel imaging spectroscopy system. To distinguish 2-dimensionalflow from the integrated line spectra in the line-of-sight direction, the system has 3 differentviews, from left-hand side, right-hand side and just above the mid-plane. Their line-of-sightdirections are shown in Figure 6(a). Since they are set to avoid the center solenoid coil,each spectrum contain toroidal velocity, but it is less than 3 km s − estimated from thebias velocity in view 3 and removed. Finally, the residual data of view 1 and 2 in Figure6(b) show outflow velocities in the poloidal (R-Z) plane stereoscopically. Positive Dopplervalues mean ion flow in the direction opposite to each camera lens. Initially plasma velocitywas 0 km s − . Reconnection outflow was detected for 80 µ s after 480 µ s, during which ionflow was gradually accelerated to 3-4 km s − in the line-of-sight direction (almost positiveR-direction) at the fiber channel numbers 2, 7 and 13 in Figure 6(a) (near z= ±
400 mm).The bi-directional outflow was observed at around the fiber channel numbers 4 and 10, whichmay correspond to the reconnection X-point. The reconnection outflow was accelerated intime and with distance from the X-point.Figure 7 shows the axial (Z) profiles of ion velocity V i in Z-direction during 380-560 µ s,directly measured by the Mach probe at six positions z =100, 150, 200, 250, 300, 400 mm byturns. This is a complementary measurement for the previous Doppler spectroscopy. Theion velocity is presented in Mach number (local ion sound speed C s ∼ − for T i =10eV). Before the reconnection, the ion velocity is detected to be zero. Positive velocity meansrightward flow (outflow) from the mid-plane or the X-point. A reconnection X-point, i.e. thezero velocity point, existed between z=100-170 mm before 460 µ s and then moved inwardless than z=100 mm as reconnection proceeds. The maximum velocity was 0.4 C s (soundspeed) at z=200 mm. Inside the velocity peak, ion flow was accelerated proportional to the 7 –distance from the X-point. Outside z=200 mm, ion velocity gradually decreased. These areconsistent with the previous Doppler spectroscopy measurement.Additionally we derived ion temperature from the Doppler spectroscopy measurements.Figure 6(c) shows the axial (Z) profile of the 1D ion temperature T i during the spheromakand the OH field merging (420-560 µ s). The initial ion temperature was uniformly 5-10 eV.The ion temperature at the left downstream area was preliminary heated up to 13-25 eV atfirst (400-440 µ s). After that, the ion plasma was further heated up to 18-32 eV (440-480 µ s) at maximum. It is gradually cooled down to 15-20 eV during 480-520 µ s and then to5-15 eV during 520-560 µ s. The locations of the highest ion temperature and the largest ionvelocity are almost the same in the left downstream area in view 1, though the other side inview 1 and both in view 2 were not.Associated with magnetic reconnection, magnetic fluctuation of B z component ( δB z )was also observed by the magnetic fluctuation probe array at around the current sheetduring 450-550 µ s. The locations of the fluctuation probe array and the corresponding2D poloidal flux contours measured by the 2D magnetic probe array are shown in Figure8(a). Figure 8(b) shows the time slice image of the magnetic fluctuations on the mid-plane,and Figure 8(c) shows three examples of δ B z fluctuations. Since the current sheet and thereconnecting magnetic field lines are located in the axial (Z) direction, δB z fluctuationsindicate longitudinal oscillation (magnetoacoustic sausage mode) or projected transverseoscillation with toroidal (guide) field to the poloidal (R-Z) plane. Here we can not distinguishstanding waves from propagating waves with the current data. We applied wavelet analysisto these data. Details of the procedure are given by Torrence & Compo (1998). Figure9 displays the wavelet power spectra of magnetic fluctuations at different locations r =92,112 and 182 mm on the mid-plane. In the wavelet spectrum diagrams, regions with 95%significance level are outlined. The power spectra show a peak in the period of 4-20 µ s, inwhich there exists sub-structure at 5, 6, 10, 15-20 and 30 µ s. The spectrum at 5 µ s periodalso show two peaks at 440 µ s and 480 µ s in time variation (Fig. 9b). The oscillation lastsfor 90 µ s from 430 µ s, containing 16 periods for the shortest frequency. Here we note thatthese oscillations are not affected by the magnetic fluctuations produced by the spheromakformation from 330-390 µ s, because the detection times are completely different and thefrequencies are slightly different from each other.
4. Discussion and Conclusions
We reproduced magnetic configuration of a twisted flux tube and chromospheric plasmaejections by component reconnection with laboratory experiment. Here we focused on the 8 –similarity between magnetic configurations of the spheromak in the laboratory plasma andof the emerging flux rope in the solar atmosphere. We performed two toroidal fully ionizedargon plasmas merging experiment, followed by the magnetic reconnection driven by the OHfield emergence. We measured 2D magnetic field configuration, ion flow, ion temperatureand magnetic fluctuations at the same time during the reconnection process.
Reconnection outflows were independently measured by the fiber optic multi-channelimaging spectroscopy system and the Mach probe. Both measurements show consistentresults; the ion flow was accelerated proportional to the distance from the reconnectionpoint and then decelerated by the accumulated magnetic flux at the outflow region. Themaximum velocity in the line of sight direction (R-direction) v r was 4 km s − by the Dopplermeasurement and the velocity in axial (Z) direction v z was 0.4 C s (sound speed) at maximumby the Mach probe, meaning 2.8 km s − on the assumption that the local ion sound speedis 7 km s − . These values are about 40% of the local Alfv´en velocity. In the later phase,plasma velocity near the mid-plane (z=100 mm) increased as well as in the outer region (Fig.7b). At the same time, reconnection point, that is the transition of positive and negative(rightward and leftward) velocities, moved inward; it is located at z=150 mm at 420 µ s andmoved to z=100 mm at 460 µ s and less than 100 mm later. This may suggest two possibleinterpretations: the one is that reconnection with a long current sheet transits to the X-type fast reconnection as shown in the illustration of Figure 10(a). The other one is thatthe reconnection point moves upward to the detectable region by the Mach probe, which isshown in Figure 10(b) for comparison.Here we note that the current sheet thickness is 10 cm, while ion skin depth and ionLarmor radius are 14-70 cm and 7-14 cm (20 eV, 20 mT), respectively. Therefore, the currentsheet thickness is comparable to or a little smaller than the ion skin depth or the ion Larmorradius. However, the electron and ion mean free paths are 1 cm, which are smaller thanthe current sheet thickness, so that the Hall current is not detected in our experiment. Thereconnection rate is estimated as v in / v out =0.13-0.33 for v in =0.5-1.0 km s − and v out =3-4 km s − , respectively, while the Sweet-Parker reconnection rate is 1/ R m / =0.05-0.1 for R m =100-400. Hence, the reconnection in our experiment is slightly faster than the Sweet-Parker reconnection. Here we can say that collisionality suppresses the Hall effect and leadsto the Sweet-Parker reconnection or slightly faster reconnection, though physical mechanismdriving reconnection faster without the Hall effect is not revealed.Generally, the plasma flow is accelerated by plasma pressure and magnetic tension force. 9 –However, no enhancements of temperature and density of ions and electrons were detected atthe center of the current sheet in this experiment, so that it is expected that the plasma flowwas not accelerated by plasma pressure but magnetically accelerated. Figure 11(a) showsthe Lorentz force in Z-direction (J × B) z =J t B r . Near the mid-plane (-300 mm < z <
300 mm),the Lorentz force plays a role in accelerating the plasma outward in the opposite directionsfrom the mid-plane (z=0). Beyond 300 mm apart from the mid-plane, the Lorentz forcechanges to the deceleration force due to the surrounding closed magnetic field. The absolutevalue of the Lorentz force increases in time and spatially in the axial and radial directions.If we assume the average value of the Lorentz force (J × B) z =10 N calculated from Figure11(a), the acceleration is estimated 1.6 × km s − and the accelerated velocity 15.9 kms − with the acceleration time of 100 µ s. This is comparable to but slightly larger than themeasured values.Next we show the moving velocity of the magnetic field lines at r=146 mm in Figures11(b)-11(d), to compare with the measured ion flow. It is estimated from the Ohm’s lawwith the 2D magnetic probe data B =(B r , B t , B z ) and E =(0, E t , 0). The three componentsof the magnetic field velocity are given by v ⊥ = E × B | B | = ( E t B z | B | , , − E t B r | B | ) , (4)which is derived from the Ohm’s law, E = − v × B . The z-component of v ⊥ in Figure 11(b)indicates the outward velocity of reconnected filed lines in the axial (Z) direction, wherepositive (negative) value means rightward (leftward) velocity. Similarly, the r-componentof v ⊥ in Figure 11(c) indicates the inward velocity of the field lines to the current sheet inthe radial (R) direction, where negative value means the inflow to the current sheet. Figure11(d) shows the absolute value of the field line velocity. It shows the velocity peak at around3-4 km s − near z=200 mm. We can also find that the velocity peak moves inward from 420 µ s to 540 µ s, consistent with the Mach probe measurement of the ion flow, though argongas is not completely frozen in to the magnetic field lines.Our experimental results show the ion velocity with both axial and radial components,which means reconnection outflow is in the direction apart from the parallel direction tothe surrounding stratified (vertical) magnetic field lines. This is consistent with the factthat magnetic tension force works obliquely to the stratified field with the angle of 45 ◦ asshown in Figure 5(b). However, in solar observations, it looks that plasma ejections overthe light bridge occur along the vertical magnetic field lines. This is probably because thereconnection outflow is redirected to the parallel direction of the surrounding straight fieldlines after the collision of the plasma flow and the magnetic field lines. Therefore, evenin the laboratory experiment, it would be reproduced in much larger spatial scale wheremagnetohydrodynamic behavior becomes dominant. 10 – Figure 12(a) shows the relationship between the resistivity enhancement and the outflowacceleration in time. The effective resistivity is measured at r=119 mm on the mid-plane(z=0 mm) and peaks at 450-480 µ s. The outflow velocities at two different locations z=200mm and 300 mm are overlaid on it. The acceleration of reconnection outflow occurs justafter the enhancement of effective resistivity. The peak of the outflow velocity at z=300 mmis earlier and smaller than the one at z=200 mm. Time variations of the ion temperaturemeasured by the Doppler spectroscopy measurement with fiber channel 1, roughly at z =-300 mm and r =90-200 mm, and the power spectrum of magnetic fluctuations of 5 µ s periodat r =112 mm on the mid-plane (dotted line in Fig. 9b) are shown in Figure 12(b). Themagnetic fluctuation shows three peaks at 445, 480 and 500 µ s. The first one correspondsto the beginning of the resistivity enhancement, and the second one is at the peak time ofthe effective resistivity.Ion heating occurred in the left downstream area close to the surrounding closed mag-netic field. The ion temperature increased to 20-30 eV. The heating by reconnection isexpected T / β in magnetohydrodynamic theory, where T is the initial temperature and β is the plasma beta (Yokoyama & Shibata 1995). Assuming β is 0.25, heating occurs from 10eV to 40 eV. This is comparable to the measurement. The fact that ion heating occurs at theedge of the downstream area is consistent with the previous merging experiment (Ono et al.2011), though the distance of the heating spot from the X-point is larger (approximatelyfour times). This is probably because the distance from the X-point to the obstacle maydetermine the heating spot. Ono et al. (2011) suggested ion heating mechanisms by the fastshock and the viscosity in the downstream area, but the fast shock may not in this experi-ment because the measured Mach number is always less than unity. Rather it is interestingto see that the enhancement of magnetic resistivity and waves are in association with iontemperature enhancement. The locations of enhanced resistivity and hot ion spot is differ-ent from each other, so the association of ion heating and waves may indicate some physicalrelationship among them. In solar observations, it is impossible to detect µ s order waves.However, this experimental result may suggest that such high frequency waves are generatedthrough the magnetic reconnection process and contribute to the ion (and electron) heating.Figures 13 shows the different magnetic configurations of the simple spheromak mergingexperiment and the OH field merging experiment. The former experiment confines hotplasma at the center of the spheromak with closed field lines, but the latter does not. Inthe OH field merging experiment, the hot plasma spot is not maintained for a long time anddiffused along the surrounding straight open magnetic field lines. This would also affect thewave generation associated with magnetic reconnection. 11 – Experimental measurements of ion temperature and velocity enable us to estimate ther-mal and kinetic energies converted from the released magnetic energy. Assuming plasmadensity n = 10 cm − , the thermal energy is E th =nk B TV=1.1 × erg ( V =3.8 × cm and T i =30 eV) and the kinetic energy is E kin =Vnm i v i /2=3.2 × erg (V=2.3 × cm and v i =4 km s − ), leading to the total converted energy 1.1 × erg. It seems that kinetic energyis much smaller than thermal energy converted from magnetic energy in this experiment.On the other hand, the reconnection rate of the total magnetic flux ∂ Ψ/ ∂t is of theorder of (2-3) × Mx s − . By assuming two dimensional steady magnetic reconnection,the released magnetic energy can be estimated at the Poynting flux entering from both sidesinto the reconnecting region using the relation, dE mag dt = 2 B π v in A, (5)where dE mag /dt is the magnetic energy release rate due to magnetic reconnection, B ismagnetic flux density in the spheromak, v in is an inflow velocity to the reconnection site, A is the surface area of the current sheet ( A = 2 πrL z =2500 cm ; for r =10 cm, L z =40cm). Since we cannot know the actual inflow velocity v in , we use a perpendicular velocityto the magnetic field lines assuming zero resistivity outside the current sheet, such that( v ⊥ ) r = E t B r / | B | as an assumption. Figure 11(c) shows ( v ⊥ ) r profile in Z-direction at r=146mm, thus ( v ⊥ ) z =0.5-1.0 km s − and the resulting energy release rate d E mag /dt=6 × ergs − , with the total energy release 3 × erg for the duration of magnetic reconnection, 50 µ s.These are comparable to the estimated total energy of thermal and kinetic energies 10 erg.As for the energy gap between laboratory experiments (10 − erg) and solar observations(10 erg), it would be explained by the scale gap between laboratory and solar plasmas,because stored magnetic energy E mag ∝ B L under the condition that B is constant. Sincespatial scale of solar plasma is 4-5th orders larger than laboratory plasma, stored energy isself-similarly enlarged to E mag,solar =10 − E mag,lab ∼ − erg, corresponding to nanoflareenergy regime of solar observations, that is, chromospheric jets. Similarly, reconnectiontime scale is determined by τ rec = √ τ A τ d ∝ L / , where Alfv´en time scale is τ A =4.5 µ s anddiffusion time scale is τ d =316 µ s by assuming the current sheet width L=10 cm in labora-tory experiment, and then τ rec,lab =38 µ s. The reconnection time scale in solar atmospherewould be, therefore, self-similarly enlarged to τ rec,solar =10 − . τ rec,lab ∼ § Magnetic fluctuations of B z component, i.e. waves, were detected in the current sheet(negative J t region) during magnetic reconnection. They show multiple frequencies, mainlyat 5-6 µ s and 10 µ s. Since the measured frequencies are lower than the lower hybrid (LH)frequency ( f LH = p f c,i f c,e =2 MHz, f − LH =0.5 µ s) and rather close to the ion cyclotron fre-quency ( f c,i =50-150 kHz, f − c,i =6-20 µ s), the measured fluctuations may not be explained bythe lower hybrid instability (Bale et al. 2002; Carter et al. 2002) nor the modified two-fluidinstability (Ji et al. 2004), but by some kind of the drift (kink) instability (Zhu & Winglee1996; Kuwahata et al. 2011) or shear Alfv´en mode, though it cannot be identified with thecurrent data set. If we consider the oscillation driven by the restoring magnetic force dueto magnetic reconnection, Alfv´en time scale determines the oscillation time period, that is, t A = L / V A =10 µ s ( L /25 cm)( V A /22 km s − ) − , assuming the scale length as the half radiusof the spheromak (25 cm). This is comparable to the measured frequencies. Furthermore,if we consider Alfv´en waves generated by magnetic reconnection in the solar atmosphere,the wave period would be enlarged to t A,solar =10 − t A,lab =10-100 s by considering the scalegap between the laboratory and solar plasmas. This is comparable to the solar observa-tions of wave periods 200 s as observed in solar chromospheric jets (Nishizuka et al. 2008;Liu et al. 2009), an X-ray jet (Cirtain et al. 2007) and spicules (De Pontieu et al. 2007;Okamoto & De Pontieu 2011).The energy fluxes carried by the transverse (Alfv´en) wave along the guide field in thecurrent sheet in toroidal and axial directions are described by F A,t = 14 π [ − δB z δv z B t − δB z δv t B z ] (6) F A,z = 14 π [ − δB t δv z B t − δB t δv t B z ] . (7) 13 –Here we assume that magnetic fluctuations occur only in the 2-dimensional Z-T plane, i.e. δB r = δv r =0, resulting to the relationships δv z = δB z B r v r and δv t = δB t B r v r . Since the fluctuationsoccur perpendicular to the guide field, we derive δB z =- B t B z δB t . Furthermore, by using equa-tions such as δB z δB t = δv z δv t and v z B z = v r B r = v t B t , we estimate the energy fluxes in the toroidaldirection F A,t ∼ × erg cm − s − and in the axial direction F A,z ∼ × erg cm − s − ,respectively. This leads to the total energy flux 3.8 × erg cm − s − and the total energy3 × erg for the duration of reconnection, 50 µ s. This is 1-10% of the estimated releasedmagnetic energy and comparable to the previous expectations from numerical simulationssuch that 3% in Yokoyama (1998) and 40% at maximum in Kigure et al. (2010). We experimentally investigated fundamental physics of chromospheric jets observed inthe solar atmosphere and succeeded in qualitatively reproducing the jets with componentmagnetic reconnection. As an advantage of laboratory experiments, we could directly mea-sure magnetic field strength in 2D plane, plasma (ion) flows, ion temperature, effectivemagnetic resistivity and high frequency waves in association with magnetic reconnection.These measurements are impossible in solar telescope observations and partly in magneto-hydrodynamic simulations.However, on the other hand, qualitatively we found some differences between the lab-oratory experiment and the solar observations. For example, jet velocity is much smallerthan Alfv´en velocity (40%) in our laboratory experiment, while in solar observations it iscomparable to the one. The direction of reconnection jet in laboratory experiment is obliqueto the parallel direction to the surrounding straight magnetic field lines, while in solar atmo-sphere it looks parallel to the surrounding vertical magnetic field. The total release energy,the reconnection time scale and the wave frequency are also different in laboratory and solarplasmas with several orders.Here it is useful to consider the differences between microscopic and macroscopic scales,collisionality (collisional and collisionless), which may come from not only the instrumen-tal size but also the selection of argon gas, and the degrees of ionization (fully ionized andpartially ionized) in solar chromospheric and laboratory plasmas. The reasons for the selec-tion of argon gas are reproductivity and emissivity compared with hydrogen, but it makesion mass and Larmor radius larger than hydrogen which is the majority of gas in the solaratmosphere. We expect that MHD scale physics may play an important role in acceleratereconnection jet to the local Alfv´en speed. This would be impossible to investigate in rel-atively small scale laboratory experiments compared with the solar atmosphere. The scale 14 –gap between laboratory and solar plasmas may also explain the differences of the releaseenergy, the reconnection time scale and the wave frequency by the scaling-law. Furthermore,recent studies of chromospheric anemone jets suggest that neutral particles in partially ion-ized plasma, such as chromospheric plasma, may drive fast reconnection (Nishizuka et al.2011; Singh et al. 2011), though plasma is fully ionized enough during the reconnectionevent in our current experiment so that it seems that the effect of partial ionization doesnot appear. The experiment with partially ionized hydrogen plasma is an interesting topicin the future work.TS-4 is the two toroidal plasma merging device in Tokyo University.
Hinode is aJapanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic part-ner and NASA and STFC (UK) as international partners. It is operated by these agenciesin co-operation with ESA and NSC (Norway). This work was supported by the JSPS Core-to-Core Program 22001.
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This preprint was prepared with the AAS L A TEX macros v5.2.
17 –Fig. 2.— TS-4 (Tokyo Spheromak) toroidal plasma merging experiment device. Largeand small gray circles show flux cores composed by PF and TF coils and separation coils,respectively. White circles show two spheromak plasmas merging on the mid-plane. Thedirection parallel to the cylindrical axis is Z-direction, based on which other radial andtoroidal directions are determined. Dots (or lattice points) show the 2D magnetic probearray and the locations of the magnetic fluctuation probe array and the Mach probe areshown with gray colored squares. 18 –Fig. 3.— Illustration of light bridge reconnection in the double annular plasma configurationin R-Z plane. Thick line shows magnetic field lines and arrows show plasma flows. Graycolor means dense plasma inside the spheromak. The large spheromak is formed throughmerging process (c) and reconnects with the new emerging straight magnetic field inducedby the center solenoid (OH) coil (d). 19 –Fig. 4.— Typical current wave forms for TF, PF and OH coils, respectively. 20 –Fig. 5.— Snapshot images of (a) two toroidal argon plasma merging and (b) merging ofspheromak and OH field. Thick contours show magnetic field lines at regular intervals andthin contours are complementary to emphasize reconnecting field lines. Color bar indicatestoroidal current density measured by the 2D magnetic probe array. (c) The radial profile of B z component and (d) the toroidal current J t on the mid-plane. 21 –Fig. 6.— (a) The fanned line-of-sight directions of the fiber optic multi-channel imaging spec-troscopy system overlaid on a snapshot image of magnetic configuration of the spheromakat 535 µ s with toroidal current density in color. (b) 1D axial profiles of ion Doppler veloc-ity in the line-of-sight direction (almost r-direction) with compensation of toroidal velocitycomponent and (c) ion Doppler temperature. 22 –Fig. 7.— (a) The locations of the Mach probe shifted along the current sheet at r=190 mmand z=100, 150, 200, 250, 300 and 400 mm. (b) The axial (Z) profile of ion velocity in axialdirection in units of Mach number ( C s ∼ − ) at 420, 460, 500 and 540 µ s. 23 –Fig. 8.— (a) The location of the magnetic fluctuation probe array overlaid on snapshotimages of plasma merging experiment with poloidal field contours and toroidal current incolor. (b) Time slice image and (c) time plots of magnetic fluctuations δB z measured by themagnetic fluctuation probe array at r =90, 240, 380 mm, whose positions are overlaid on(a) and (b). 24 –Fig. 9.— Wavelet power spectrum of magnetic fluctuations δB z , which is reduced by thesmoothed long-term variation larger than 40 µ s from the raw data, measured by the magneticfluctuation probe array on the mid-plane at r =92, 112, 182 mm (nearby the OH coil).Fig. 10.— Interpretation of accelerated outflow in the inner region of a current sheet: (a)transition from the Sweet-Parker reconnection to X-type reconnection and (b) the movementof the reconnection point and outflow up to the detectable area. 25 –Fig. 11.— The axial (Z) profiles of estimated Lorentz force and plasma velocity perpendicularto the magnetic field lines at r=146 mm: (a) Lorentz force in Z-direction (J × B) z =J t B r , (b)axial velocity v ⊥ ,z =-(E t B r )/ | B | (outflow in Z-direction), (c) radial velocity v ⊥ ,r =E t B z / | B | (inflow at the center and outflow in R-direction outside) and (d) the absolute value of ionvelocity | v ⊥ | =E t p B t + B r / | B | . 26 –Fig. 12.— (a) Time variation of the effective resistivity η =E t /J t and the ion velocitiesat r=190 mm and z=200 and 300 mm. (b) Time variation of power spectra of magneticfluctuations with 5 µµ