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

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

Dual-Species Plasmas Illustrate MHD Flows

Plasma loops created in the laboratory strongly resemble structures observed in the solar corona. For example, both solar coronal loops and experimental loops exhibit remarkably uniform axial cross sections. A magnetohydrodynamic theory that was proposed to explain this phenomenon predicts that a plasma loop whose axial magnetic field is constricted at both footpoints will experience bulk flows into the loop from both ends. To test this theory, dual-species plasma loops were formed by supplying a different neutral gas to each of the two footpoints. Optical filters were then used to separately image the motion of different sections of the plasma. Bulk flows were, in fact, observed

Model for how an accretion disk drives astrophysical jets and sheds angular momentum

Clumps of ions and neutrals in the weakly ionized plasma in an accretion disk are shown to follow trajectories analogous to those of fictitious 'metaparticles' having a charge to mass ratio reduced from that of an ion by the ionization fraction. A certain class of meta-particles have zero-canonical angular momentum and so spiral in towards the star. Accumulation of these meta-particles establishes a radial electric field that drives the electric current that flows in bidirectional astrophysical jets lying along the disk axis and provides forces that drive the jets. The entire process converts gravitational potential energy into jet energy while absorbing angular momentum from accreting material and shedding this angular momentum at near infinite radius

Fast, purely growing collisionless reconnection as an eigenfunction problem related to but not involving linear whistler waves

If either finite electron inertia or finite resistivity is included in 2D magnetic reconnection, the two-fluid equations become a pair of second-order differential equations coupling the out-of-plane magnetic field and vector potential to each other to form a fourth-order system. The coupling at an X-point is such that out-of-plane even-parity electric and odd-parity magnetic fields feed off each other to produce instability if the scale length on which the equilibrium magnetic field changes is less than the ion skin depth. The instability growth rate is given by an eigenvalue of the fourth-order system determined by boundary and symmetry conditions. The instability is a purely growing mode, not a wave, and has growth rate of the order of the whistler frequency. The spatial profile of both the out-of-plane electric and magnetic eigenfunctions consists of an inner concave region having extent of the order of the electron skin depth, an intermediate convex region having extent of the order of the equilibrium magnetic field scale length, and a concave outer exponentially decaying region. If finite electron inertia and resistivity are not included, the inner concave region does not exist and the coupled pair of equations reduces to a second-order differential equation having non-physical solutions at an X-point