Paul Bellan

Experimental identification of the kink instability as a poloidal flux amplification mechanism for coaxial gun spheromak formation.

The magnetohydrodynamic kink instability is observed and identified experimentally as a poloidal flux amplification mechanism for coaxial gun spheromak formation. Plasmas in this experiment fall into three distinct regimes which depend on the peak gun current to magnetic flux ratio, with (I) low values resulting in a straight plasma column with helical magnetic field, (II) intermediate values leading to kinking of the column axis, and (III) high values leading immediately to a detached plasma. Onset of column kinking agrees quantitatively with the Kruskal-Shafranov limit, and the kink acts as a dynamo which converts toroidal to poloidal flux. Regime II clearly leads to both poloidal flux amplification and the development of a spheromak configuration.

Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates

It is demonstrated that (i) the postulate of infinite differentiability in Cartesian coordinates and (ii) the physical assumption of regularity on the axis of a cylindrical coordinate system provide significant simplifying constraints on the coefficients of Fourier expansions in cylindrical coordinates. These constraints are independent of any governing equations. The simplification can provide considerable practical benefit for the analysis (especially numerical) of actual physical problems. Of equal importance, these constraints demonstrate that if A is any arbitrary physical vector, then the only finite Fourier terms of A_r and A_θ are those with m=1 symmetry. In the Appendix, it is further shown that postulate (i) may be inferred from a more primitive assumption, namely, the arbitrariness of the location of the cylindrical axis of the coordinate system.

Three-dimensional Model of the Structure and Evolution of Coronal Mass Ejections

We present a new three-dimensional magnetohydrodynamic (MHD) model that describes the evolution of coronal magnetic arcades in response to photospheric flows. The dynamics of the system is discussed, and it is shown that the model reproduces a number of features characteristic of coronal mass ejection (CME) observations. In particular, we propose explanations for the three-part structure of CMEs observed at the solar limb and the formation and evolution of sigmoids and overlaying arcades. The model includes the effects of finite resistivity in the system and morphological changes induced by reconnection are studied. Reconnection is found to prevent the formation of highly twisted magnetic structures if the magnitude of photospheric velocity is close to the observed values. In addition, we suggest a novel explanation for the splitting of the CMEs core prominence material observed in some eruptions. The distinguishing features of the model are the novel numerical methods used to evolve the MHD system and the formulation of the boundary conditions. The stiffness of the resistive MHD equations constitutes a major difficulty for numerical simulations. Calculations in our model are performed using recently introduced exponential propagation techniques that allow efficient integration of the equations with time steps far exceeding the CFL bound that constrains explicit schemes.

On the jets, kinks, and spheromaks formed by a planar magnetized' coaxial gun

Measurements of the various plasma configurations produced by a planar magnetized coaxial gun provide insight into the magnetic topology evolution resulting from magnetic helicity injection. Important features of the experiments are a very simple coaxial gun design so that all observed geometrical complexity is due to the intrinsic physical dynamics rather than the source shape and use of a fast multiple-frame digital camera which provides direct imaging of topologically complex shapes and dynamics. Three key experimental findings were obtained: (1) formation of an axial collimated jet [Hsu and Bellan, Mon. Not. R. Astron. Soc. 334, 257 (2002)] that is consistent with a magnetohydrodynamic description of astrophysical jets, (2) identification of the kink instability when this jet satisfies the Kruskal-Shafranov limit, and (3) the nonlinear properties of the kink instability providing a conversion of toroidal to poloidal flux as required for spheromak formation by a coaxial magnetized source [Hsu and Bellan, Phys. Rev. Lett. 90, 215002 (2003)]. An interpretation is proposed for how the n = 1 central column instability provides flux amplification during spheromak formation and sustainment, and it is shown that jet collimation can occur within one rotation of the background poloidal field.

Magnetic reconnection from a multiscale instability cascade

Magnetic reconnection, the process whereby magnetic field lines break and then reconnect to form a different topology, underlies critical dynamics of magnetically confined plasmas in both nature and the laboratory. Magnetic reconnection involves localized diffusion of the magnetic field across plasma, yet observed reconnection rates are typically much higher than can be accounted for using classical electrical resistivity. It is generally proposed that the field diffusion underlying fast reconnection results instead from some combination of non-magnetohydrodynamic processes that become important on the ‘microscopic’ scale of the ion Larmor radius or the ion skin depth. A recent laboratory experiment demonstrated a transition from slow to fast magnetic reconnection when a current channel narrowed to a microscopic scale, but did not address how a macroscopic magnetohydrodynamic system accesses the microscale. Recent theoretical models and numerical simulations suggest that a macroscopic, two-dimensional magnetohydrodynamic current sheet might do this through a sequence of repetitive tearing and thinning into two-dimensional magnetized plasma structures having successively finer scales. Here we report observations demonstrating a cascade of instabilities from a distinct, macroscopic-scale magnetohydrodynamic instability to a distinct, microscopic-scale (ion skin depth) instability associated with fast magnetic reconnection. These observations resolve the full three-dimensional dynamics and give insight into the frequently impulsive nature of reconnection in space and laboratory plasmas.

Dynamic and Stagnating Plasma Flow Leading to Magnetic-Flux-Tube Collimation

Highly collimated, plasma-filled magnetic-flux tubes are frequently observed on galactic, stellar, and laboratory scales. We propose that a single, universal magnetohydrodynamic pumping process explains why such collimated, plasma-filled magnetic-flux tubes are ubiquitous. Experimental evidence from carefully diagnosed laboratory simulations of astrophysical jets confirms this assertion and is reported here. The magnetohydrodynamic process pumps plasma into a magnetic-flux tube and the stagnation of the resulting flow causes this flux tube to become collimated.

Laboratory simulations of solar prominence eruptions

Spheromak technology is exploited to create laboratory simulations of solar prominence eruptions. It is found that the initial simulated prominences are arched, but then bifurcate into twisted secondary structures which appear to follow fringing field lines. A simple model explains many of these topological features in terms of the trajectories of field lines associated with relaxed states, i.e., states satisfying [del] × B = lambda B. This model indicates that the field line concept is more fundamental than the flux tube concept because a field line can always be defined by specifying a starting point whereas attempting to define a flux tube by specifying a starting cross section typically works only if lambda is small. The model also shows that, at least for plasma evolving through a sequence of force-free states, the oft-used line-tying concept is in error. Contrary to the predictions of line-tying, direct integration of field line trajectories shows explicitly that when lambda is varied, both ends of field lines intersecting a flux-conserving plane do not remain anchored to fixed points in that plane. Finally, a simple explanation is provided for the S-shaped magnetic structures often seen on the sun; the S shape is shown to be an automatic consequence of field line arching and the parallelism between magnetic field and current density for force-free states.

Multielement magnetic probe using commercial chip inductors

A 60-element magnetic probe array has been constructed using miniature commercial chip inductors. The array consists of twenty clusters of three coils each mounted on a linear fixture. The coils are oriented in orthogonal directions to yield three-dimensional information. The array has been used to investigate magnetic properties of spheromaks.

Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result

Suppose an electric current I flows along a magnetic flux tube that has poloidal flux psi and radius a = a(z), where z is the axial position along the flux tube. This current creates a toroidal magnetic field Bphi. It is shown that, in such a case, nonlinear, nonconservative J×B forces accelerate plasma axially from regions of small a to regions of large a and that this acceleration is proportional to [partial-derivative]I2/[partial-derivative]z. Thus, if a current-carrying flux tube is bulged at, say, z = 0 and constricted at, say, z = ±h, then plasma will be accelerated from z = ±h towards z = 0 resulting in a situation similar to two water jets pointed at each other. The ingested plasma convects embedded, frozen-in toroidal magnetic flux from z = ±h to z = 0. The counterdirected flows collide and stagnate at z = 0 and in so doing (i) convert their translational kinetic energy into heat, (ii) increase the plasma density at z[approximate]0, and (iii) increase the embedded toroidal flux density at z[approximate]0. The increase in toroidal flux density at z[approximate]0 increases Bphi and hence increases the magnetic pinch force at z[approximate]0 and so causes a reduction of a(0). Thus, the flux tube develops an axially uniform cross section, a decreased volume, an increased density, and an increased temperature. This model is proposed as a likely hypothesis for the long-standing mystery of why solar coronal loops are observed to be axially uniform, hot, and bright. It is furthermore argued that a small number of tail particles bouncing between the approaching counterstreaming plasma jets should be Fermi accelerated to extreme energies. Finally, analytic solution of the Grad–Shafranov equation predicts that a flux tube becomes axially uniform when the ingested plasma becomes hot and dense enough to have 2µ0nkappaT/B pol 2 = (µ0Ia(0)/psi)2/2; observed coronal loop parameters are in reasonable agreement with this relationship which is analogous to having betapol = 1 in a tokamak.

Experimental Demonstration of How Strapping Fields Can Inhibit Solar Prominence Eruptions

It has been conjectured that the eruption of a solar prominence can be inhibited if a much larger scale, arched magnetic field straddles the prominence and effectively straps it down. We have demonstrated this effect in a laboratory experiment where a vacuum strapping field acts on a scaled simulation of a solar prominence. The required magnitude of the strapping field is in good agreement with a theoretical model that takes into account the full three-dimensional magnetic topology.