Astrophysical Magnetic Field Understanding Continues To Benefit From Plasma Laboratory Experiments

Image of coronal mass ejection successfully produced in laboratory experiment, in 2016.

For decades astrophysicists have had to contend with investigating their objects of inquiry from a distance, using instruments such as powerful telescopes, spectroscopes, and vector magnetographs.   But in the past 17 years that frustration has given way to laboratory experiments that have exposed astrophysical magnetic phenomena in hitherto unknown ways.

For example, in December, 2016 solar physicists, for the first time,   replicated an artificial coronal mass ejection in the laboratory as part of a plasma experiment. The researchers, Ha and Bellan, used a plasma gun in concert with an artificial strapping field to create their own flux ropes in their lab and from these CME-eruptions inside a vacuum chamber (see image).   Read more details of their work here, in the abstract to the Ph.D. thesis of Bao N. Quoc Ha:
http://thesis.library.caltech.edu/9061/

The strapping field itself  (that field which secures or holds back any emerging flux ropes) had to be carefully computed so that it decayed as a precise function of height. The reason is that the pair needed to generate the most likely instability - called the "torus instability". This is believed to occur in the Sun's upper atmosphere - namely the corona- when the growth of a flux rope is held back by a magnetic field structure that subsequently decays with increasing altitude.

Before this, in 2001, Agris Gailitis and colleagues achieved the first laboratory amplification of a self-exciting magnetic field in a turbulent flow of liquid sodium. Then, in 2012, Gianluca Gregori generated shock waves in a laboratory plasma with a laser  and showed that asymmetric shocks, like those occurring in gamma ray bursts and supernova remnants, e.g. like this one in Cygnus:

produced seed magnetic fields.  Most recently, laboratory experiments have moved into the domain of astrophysical dynamos.  In fact, for the first time we have first hand evidence from such experiments they can exist.   

 I refer to the latest work by Gianluca Gregori and Petros Tzeferacos et al who have measured the amplification of a turbulent laboratory plasma and demonstrated the first physical evidence of a dynamo resulting from turbulent motion.  Their study,  an overview of which was reported in Physics Today, e.g.

https://physicstoday.scitation.org/doi/10.1063/PT.3.3891

 Shows, in fact, that the turbulent dynamo could be a viable mechanism for magnetic field amplification, in the lab and in astrophysical settings.

To sustain a dynamo a fluid needs to be electrically conductive and its motion can't be too symmetric. Dynamo conditions also require magnetic lines stay in the plasma (e.g. "frozen in") rather than diffusing away.

In the classical solar  dynamo theory - which explains how sunspots originate-  we are looking at the process by which the solar magnetic field is generated through a combination of rotation and convection. We refer to the two parts of the dynamo process the a-effect and w- effect.

In the latter, the shear flows are able to stretch the photospheric magnetic field lines in the direction of the shear while in the former, helical flows are able to lift and twist field lines into orthogonal planes. The basic equation for solar dynamo theory is given below - which is constructed from Maxwell’s equations and the solar form of Ohm’s law:

¶B / ¶ t =     Ñ X (v X B)    +    h  Ñ ²  B

Where B is the magnetic induction, v is the velocity and h is the magnetic diffusivity.  A key condition for a dynamo to emerge is a high enough value for a dimensionless quantity called  the magnetic Reynolds number  Â_m   . If   Â_m   >> 1 then diffusion can be ignored, otherwise it can’t. It is commonly expressed:

Â_m  =  L V_A / h

Where L is a typical length scale for a given solar environment, V_A   is the Alfven velocity and h  is the magnetic diffusivity. The infinitely conducting condition applies for  h   -> 0.  This implies zero electrical resistance, so the field lines must be frozen into the plasma. Hence, the frozen-in condition, high magnetic Reynolds number and infinite conductivity all mean the same condition for solar plasma.

In the work by Gregori,  Tzeferacos et al a value for Â_m  of 600 was achieved, consistent with modeled intergalactic plasmas  which have much lower density than solar plasma. (Mathematically, one needs  Â_m  > 200 for a magnetic fluid to remain a good conductor and hence have any chance of generating a dynamo.)

As summarized in Physics Today, Gregori,  Tzeferacos et al irradiated two fixed targets of penny-sized pieces of chlorine-doped polystyrene foil with a series of progressively stronger UV laser pulses to deliver a total of 5 kJ to each target. This experiment was conducted at the Omega Laser Facility at the University of Rochester.

The foils faced each other 8 mm apart, and the laser quickly stripped and ionized each foil's atoms generating two hot plasma jets that were directed toward each other through a grid of holes.  The grids, having been offset from each other, created interpenetrating fingers of plasma that sheared when they collided, generating a strongly turbulent region.  Images then taken by an x-ray framing camera confirmed the experiment reached the turbulent region.

Inhomogeneities developed in a region more than 1 mm across after the plasma collided (see Fig. 2a below). Note that the intensity fluctuations are directly related to the electron density fluctuations which in turn indicate the plasma turbulence.   This is depicted in frame 2b below, verifying the x-ray imagery captured the associated turbulence:

  Now down to some sobering measurement reality. Because the experiments lasted only tens of nanoseconds, with the amplified magnetic fields lasting only a fraction of that, it was necessary to use numerical simulations, i.e. to measure the magnetic field produced by the plasma. Basically, these simulations were needed to determine when to run the diagnostic tools.  In one method, the researchers measured the polarization of light passing through the plasma. This is based on a technique used by astronomers to measure the magnetic fields of distant objects, see e.g.  https://en.wikipedia.org/wiki/Faraday_effect

This and an additional method using focused protons determined the magnetic field in the turbulent region several times during the experiment.  It was found that in less than 10 ns the field amplified by a factor of 25-30.  To put this into perspective, on galactic spatial and temporal scales the same amplification mechanism could 'grow' a tiny seed field to the observed values.  (The initially weak fields then evolve according to Maxwell's equations, e.g.
http://brane-space.blogspot.com/2015/03/solar-electrodynamics-part-3-of-3.html

While these results, including in the associated papers, are exciting, it is important now that they be replicated in other labs, universities. It is especially important to nail down the same time and intensity parameters given the same basic experimental setup.  For example, is there the same field amplification factor of 25-30 in less than 10 ns?  Also, does the magnetic energy of the plasma saturate at about 4 % of its kinetic energy as the Univ. of Rochester experiments found?

Given there is now a lot of hullaballoo about experiments- claims being confirmed, e.g.
https://blogs.scientificamerican.com/doing-good-science/evaluating-scientific-claims-or-do-we-have-to-take-the-scientists-word-for-it/

This is an important next step in securing the validity of astrophysical experiments.

Coronal Mass Ejections Successfully Reproduced in Laboratory

Image of  artificial CME successfully produced in laboratory experiment

For the first time ever solar researchers have successfully replicated an artificial coronal mass ejection in the laboratory as part of a plasma experiment. The researchers, Ha and Bellan, used a plasma gun in concert with an artificial strapping field to create their own flux ropes in their lab and from these CME-eruptions inside a vacuum chamber (see image).   Read more details of their work here, in the abstract to the Ph.D. thesis of Bao N. Quoc Ha:

http://thesis.library.caltech.edu/9061/


The strapping field itself  (that field which secures or holds back any emerging flux ropes) had to be carefully computed so that it decayed as a precise function of height. The reason is that the pair needed to generate the most likely instability - called the "torus instability". This is believed to occur in the Sun's upper atmosphere - namely the corona- when the growth of a flux rope is held back by a magnetic field structure that subsequently decays with increasing altitude.  With ultimate dissipation of the overlying field the eruption of the flux rope and CME then becomes imminent.  One such theoretical model proposed by DeMoulin and Titov exhibits a geometry such as depicted below:

Fig. 1

The plane can be visualized as the Sun's photosphere and the entire "ring" as a solar loop structure with the shaded part extending into the solar atmosphere (e.g. corona) and the lower part submerged. In many respects it is reflective of the solar loop structure shown below:
















Fig. 2

The loop circuit analog shown is for a line-tied arch(loop). By "line tied" I mean that the loop feet are firmly anchored in the photosphere at the level where the plasma beta approaches or exceeds 1. This can engender a "dynamo effect" whereby convective motions spawn electric currents which in turn create powerful magnetic fields in the loop of the solar loop what we call the "force free" region is depicted in cross section with the loop bearing magnetically-confined x-ray plasma.  In the model geometry, above (Fig. 1), the force free coronal magnetic field above the photosphere is constructed using 3 sources: a circular flux rope with thin total current, I,  a pair of charges q and (-q), the latter the image charge of the first below the photosphere, and a line current Io below the surface.  

One model type for a loosened strapping field giving rise to a disrupted prominence, which might have a CME associated with it,  is shown below, after Tsuneta:

Fig. 3

Visible is a pre-existing flux rope (now in 2D) which loses stability and causes a plasma eruption. The CME is then "blown off" via the rising plasmoid. In like manner, the two researchers recreated the conditions in the lab, demonstrating a transition from slow rise to rapid acceleration.  Assume then the detailed toroidal structure is initially in equilibrium, what happens to trigger the torus instability? Well, according to one variation proposed by Yuhong Fan, the configuration becomes unstable to an expansion  D R, when the toroidal radius R attains a critical dimension relative to the separation of the charges +q and -q.

Specifically, one will be looking at the decline of the potential field   B _q  with R and when it becomes critically deep.   This is evaluated using a decay index with torus instability occurring when the condition holds:

n = - d ln B _q   / d ln R > 1.5

In respect of their CME -generating experiment, Ha and Bellan would likely have taken these considerations into account to a suitable scale to create their strapping magnetic field that decays with increasing altitude (e.g. z).  It is important to note that the experimentally generated CMEs followed the pattern of slow rise giving way to rapid acceleration.(In the case of the mini-CME  the distance between the plasma footpoints, e.g. +y to -y from the toroid geometry, was 8.0 cm.

These results as they stand inspire confidence that similar - and perhaps larger scale experiments in the future - could improve predictions of potentially destructive CMEs.

An encouraging aspect of the current work is an earlier finding that, indeed, the torus instability can be a trigger mechanism for CMEs. See, for example, the paper:

https://arxiv.org/pdf/1401.5936v1.pdf


Again, further demonstrations in the laboratory setting, particularly for the confined plasma under progressively different loop conditions, would go a long way toward supporting these models.