Using Laboratory Experiments to Study Solar Corona Physics P

White Paper: Using Laboratory Experiments to Study Solar Corona Physics P. M. Bellan MC 128-95 Caltech, Pasadena CA 91125; [email protected] 1 Recommendation

It is recommended that the Solar and Space Physics Decadal Survey include the statement:

"Because of recent demonstrations that certain laboratory plasma experiments can simulate essential three dimensional MHD properties of solar coronal loops, the next decade of heliospheric research should include advanced laboratory plasma experiments designed speciﬁcally to address important outstanding issues relevant to the solar corona."

In support of this recommendation this white paper lists important current issues in solar corona physics, reviews recent lab experiments at Caltech that have addressed some of these issues, and con- cludes with an example of a future experiment designed to address a specific and important solar corona issue. 2 Issues in solar corona physics 1. The coronal heating problem - why does the solar corona blatantly violate the second law of ther- modynamics by having a temperature over two orders of magnitude hotter than the photosphere? 2. The coronal loop uniformity problem - why is the cross-section of a coronal loop approximately constant along the length of a loop? 3. The triggering problem - why do coronal loops erupt suddenly? Are eruptions triggered by some slight internal change or by an external event? 4. The power supply problem - what is the energy source for the non-potential magnetic fields in the solar corona? Twisted magnetic fields have more internal energy than non-twisted (i.e., potential) fields satisfying the same boundary conditions. It is conventionally assumed in numerical magnetohydrodynamic (MHD) simulations that the twisting of coronal loops results from differ- ential motion at the photospheric surface but recent measurements (Pevtsov et al., 2003) show that actual photospheric footpoint motion is insufficient to account for the observed twist. 5. The particle acceleration problem - what accelerates particles to high energies in an eruption? Solar coronal physics is traditionally modeled using ideal MHD which has the essential feature that no electric field component exists parallel to the magnetic field. As a consequence of this feature, MHD is fundamentally incapable of predicting the generation of energetic particles. In stark contrast to this, observations show that a considerable fraction of the stored magnetic energy in twist is transformed into energetic particles and x-rays. 6. The scale height and particle source problem - why is the plasma density in coronal loops greater than the surroundings? If the coronal loop magnetic fields were potential or force-free, there would be no force other than gravity. Isothermal loops would therefore be in hydrostatic equilibrium in which case the plasma density in the loop would decay exponentially with altitude as exp( ) where  =  3 107 m is the gravitational scale height. However, actual loops− are uniformly filled with plasma∼ × to altitudes exceeding 3 The density at the apex of these high loops is thus more than 20 times greater than predicted by hydrostatic equilibrium models. This indicates the presence of strong upward forces that overwhelm gravity; neither force-free nor potential magnetic fields can explain such forces. 1 3 Lab experiments as a means for studying solar corona physics

A great similarity exists between solar corona magnetic structures and a magnetic fusion confinement plasma concept known as the spheromak (Bellan, 2000). The author is neither the first nor the only person to note this similarity which has been exploited in theoretical models (Kliem and Torok, 2006), numerical simulations (Gibson and Fan, 2008), and in the interpretation of ground and space-based observations (Nandy et al., 2003). However, the author has gone a step further than merely noting a similarity. The author has purposely adapted spheromak technology to create lab experiments designed to be explicitly relevant to solar physics. This adaptation consists of locating the vacuum chamber wall far from the plasma to mimic the solar situation and changing the symmetry of boundary conditions to conform to the solar situation. As with solar plasmas, plasma dynamics in the experiments is subject to the constraint that E + U B =0 i.e., magnetic flux is frozen into the frame of the plasma. Thus as with solar plasmas, dynamics× is determined by the MHD equation of motion giving the evolution of the plasma velocity as a function of the magnetic field while simultaneously the induction equation gives the magnetic field evolution as a function of the plasma velocity.

The laboratory method has its share of advantages and disadvan- tages and, like any other new idea, care is re- quired to avoid over- selling it. Advantages include the ability to replicate the topology and dynamics of observed solar structures in a highly reproducible manner, the ability to diagnose all physical parameters in principle, the ability to control initial conditions, and the ability to observe how MHD physics connects to non-MHD physics such as generation of energetic particles and x-rays. The use of a real Figure 1: Sequence: (a) potential field established, neutral gas injected, (b) breakdown, upflows, (c) collimation, (d) expansion, kink, possible plasma means that the kinetic jet laboratory simulation is inherently self-consistent and correct. The main shortcoming is that the lab plasma is not an exact scale model of a solar phenomenon so while what is observed in the lab can give useful insights into solar behavior, the lab plasma results cannot be simply scaled up. Furthermore, setting up a successful experiment involves significant challenges such as designing and building apparatus that provide unam- biguous reproducible results, developing suitable diagnostics, and relating measurements to theoretical models in a useful way.

2 The controlled nature of the experiments means that proposed models can be subjected to stringent tests. In particular, because basic parameters such as magnetic ﬁeld strength and electric current can be adjusted, the credibility of a model can be quickly tested. This experimental approach to solar physics gives an intuitive ‘hands-on’ feel for the various physical phenomena. Laboratory experiments can also test numerical MHD simulations which at least should be able to simulate the MHD aspects of a lab experiment.

The author initiated the experiments described here in 1995 and has been continuing since. Several other groups have begun similar experiments in the last ﬁve years and so laboratory simulation of solar physics can now be considered to be an emerging discipline rather than just the effort of a single group. Other groups who have laboratory simulations of solar phenomena underway include the University of Bochum, Germany (Soltwisch et al., 2010), the LAPD group at UCLA (Tripathi and Gekelman, 2010), the MRX group at Princeton (Williams et al., 2008), and the Naval Research Lab (Dahlburg et al., 2010). 4 Outline of basic method

Figure 1 sketches the typical sequence of Caltech experiments while Fig. 2 showsimagesofactualconfigurations. In the first step of the sequence, a quasi- static ‘horseshoe’ electromagnet (Fig.1a) produces an initial arch-shaped potential magnetic field with field strength of the order of 1-3 kG at the footpoints. Next, sufficient neutral gas to enable breakdown is puffed via high-speed electromagnetic pulsed gas valves into the region between the magnet poles. After the gas puff, a high-energy capacitor bank charged to several kilovolts is connected across the magnet poles [see Fig.1(b)] and breaks down the neutral gas in about 0.1 sto form a low density plasma as indicated in Fig. 1(b).

The initial current flowing through the tenuous plasma produced at breakdown is small and follows the arched vacuum field lines [Fig. 1(b)]. As the high-voltage ca- Figure 2: Left: configuration for creating single coronal pacitor discharges, this current increases loop (D-shaped electrode removed on RHS). Right: typical to a peak value of 40-80 kiloamps in about experimental lab simulations of single coronal loop 5-10 s. The MHD J B force associ- ated with the current is observed× to drive upflowing Alfvenic velocity plasma jets from both footpoints [see Fig. 1(b)]. These fast upflowing plasma jets quickly collide at the apex of the arched loop and fill the flux tube with plasma. The flux tube collimates as the two jets collide and then writhes to form a kink-like dip in the middle.

3 All the while, the magnetic hoop force causes an expansion of the major radius of the arch [see Fig. 1(d) and Fig. 2(right)]. The jet upflows and collimation were both unexpected effects that instigated development of a theoretical model (Bellan, 2003). This model motivated further experiments (You et al., 2005) and these experiments provided verification for the flow/collimation model.

The sequence shown in Figs. 1 and 2(right) occurs only if neutral gas is provided at the nozzle; the gas is ionized at the nozzle and so provides a plasma source at the nozzle. Plasma density in the bright loop results from the flux loop being filled with plasma by the jet upflows. The magnetic configuration thus depends on a mass flux boundary condition (i.e., plasma ingestion) as well as on the normal magnetic field and the normal electric current boundary conditions. 5Significant results to date

A single loop system as described in Fig. 1 was constructed. This experiment showed (i) physics long thought to occur only on the sun could, in fact, be reproduced in the laboratory, (ii) the loop self-collimated almost instantly, (iii) the loop axis writhed in a helix, (iv) the surface projection was sigmoidal, (v) the major radius increased with time [see Fig. 2(right)], and (vi) plasma upflow from the electrodes affected magnetic field behavior. 5.1 Strapping field

A second, independent magnetic field system was arranged to provide a horizontal magnetic field B passing through the simulated coronal loop (see Fig. 3 top). The vertically directed J B force × could, depending on the polarity of B, aid or inhibit the tendency of the loop major radius to expand. Studies (Hansen and Bellan, 2001) of this multiflux system showed that loop eruption could be slowed or halted by application of a suitably strong B with appropriate polarity (see Fig. 3 bottom). 5.2 Spider legs The early stages of a configurationusedforastro- physical jet simulations involved an arcade of eight coronal loops (You et al., 2005) arranged like the legs of a spider (see Fig. 4). These loops have the same helicity and merge to form a coaxial jet which then undergoes a dramatic kink instability (Hsu and Bellan, 2003). As seen in Fig. 4, these spider legs are very collimated in contrast to the dipole potential field existing before their formation. 5.3 Tracking flows using two gas species High speed movies indicate that the morphology of the simulated coronal loop depends on the mass flux of plasma upflowing from the footpoints; these observations motivated the ‘gobble’ model (Bellan, 2003). Since mass flux is an important behavior which is not generally appreciated and which has caused a certain amount of controversy, significant efforts have Figure 3: Strapping magnetic field (top, been devoted to check whether the prediction of plasma turquoise) inhibits upward expansion of upflow from footpoints is indeed real. Flow from loop (bottom right) footpoints has been measured using Doppler spectroscopy and strong blue shifts are observed (Tripathi 4 et al., 2007) indicating suprathermal mass upflows.

A conclusive demonstation of mass upflowing from footpoints is provided as follows: By using two distinct gases the optical line emission of the plasma originating from the two footpoints is arranged to be distinct, i.e., the plasma is color-coded according to its originating footpoint if in fact it originates from a footpoint. By placing atomic line filters in front of the camera the two different colors are resolved and so the trajectories of footpoint- originating plasma is established, e.g., red plasma upflows from one footpoint while green plasma upflows from the other. Figure 4: Spider legs: eight arched plasma-filled magnetic flux tubes Experiments using two gases Stenson and Bellan (Stenson and Bellan, 2008) have clearly shown these upflows from each footpoint, with the flow velocity dependent on the gas mass. Figure 5 shows results where hydrogen (red) is supplied at the upper footpoint and nitrogen (green) at the lower footpoint. The hydrogen travels faster than the nitrogen and the loop is constituted by the identifiable flows from the two footpoints.

1 s4.53 s

Figure 5: Two-gas experimental results: Composite photo made by superimposing line-ﬁltered images of hydrogen plasma (top, red) and nitrogen plasma (bottom, green). Hydrogen gas is supplied at the top footpoint and nitrogen at the bottom footpoint (Stenson and Bellan, 2008).

6 Impact to date

The experiments described above have made an impact on both observational and theoretical solar physics. As examples, Meshalkina et al. (Meshalkina et al., 2009) have cited our merging experiments in interpreting observed solar eruptions, while Kliem (Kliem and Torok, 2006) and Olmedo (Olmedo and Zhang, 2010) have used results from our experiments in the development of the torus instability model for eruptive instability. 7 The next decade

The experiments described above have demonstrated the feasibility of laboratory experiments and their relevance to solar corona research. Future experiments will exploit the infrastructure/expertise that 5 has been developed to investigate reconnection in three dimensions, x-ray production, Alfven wave propagation, triggering of instabilities, effect of magnetic nulls, jet flows, and plasma heating mechanisms. Improved diagnostics will measure the 3D evolution of the magnetic, electric, and velocity fields, the particle velocity distribution, and mechanisms by which magnetic energy is converted into particle energy. Figure 6 sketches a 3D magnetic reconnection experiment now under construction. This experiment has been motivated by discussions with solar observer S. Martin who has proposed that long solar filaments (prominences) form by repeated reconnections as shown in Fig. 6.

y (a)

x M2 P2 M1 P1 x=L, y=b x=-a, y=-b x=a, y=b x=-L, y=-b

y (b)

x M1 M2 P2 P1 reconnection to form long filament from P1 to M2; also short structure from P2 to M1 y (c)

x M1 M2 P2 P1

Figure 6: Sketch showing layout and expected sequence of 3D magnetic reconnection experiment now under construction. This sequence is believed to be the mechanism by which the long ﬁlamentary structures in prominences starting with much shorter structures.

Acknowledgement: The work described here has been supported by USDOE, NSF, and AFOSR.

6 References

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