Separatrix Crossings Research Articles

The reversibility of magnetic reconnection

The reversibility of the transfer of energy from the magnetic field to the surrounding plasma during magnetic reconnection is examined. Trajectories of test particles in an analytic field model demonstrate that irreversibility is associated with separatrix crossings and passages through regions of weaker magnetic field. Inclusion of a guide field enhances the magnetization of particles and the extent to which forward and reverse trajectories overlap. Full kinetic simulations with a particle-in-cell code support these results and demonstrate that while time-reversed simulations at first “un-reconnect,” they eventually evolve into a reconnecting state.

Wave Activity in a Dynamically Evolving Reconnection Separatrix

AbstractWaves driven by electron beams are frequently observed within the narrow separatrices of magnetic reconnection. Strong plasma instabilities can grow from mixing between the reconnection inflow and outflow, resulting in electron heating which ultimately influences the reconnection process. Observations of a separatrix encounter by the Magnetospheric MultiScale mission on July 11, 2017 feature an anti‐parallel electron beam accelerated in a sub‐ion‐scale layer containing high amplitude (>50 mV/m) electrostatic waves. In two consecutive separatrix crossings, one exhibits faster electron beams, greater magnetic shear, higher amplitude waves, and more electron heating than the other. The observations suggest that variable reconnection outflow pressure is associated with these changes. Coincident with lower hybrid waves are Buneman and beam‐mode instabilities, likely responsible for parallel heating of electrons. Dissipation (J⋅E) within the mixing layer is found to be negative where wave activity is strongest, indicating a slowing of electrons and growth of electromagnetic fields likely related to local thinning of the separatrix. Calculation of momentum balance via the generalized Ohm's law indicates an overall imbalance of >40 mV/m in the more extreme separatrix crossing, requiring a significant dissipative term or error in the electron inertial term to make up the remainder. Finally, an analysis of quasi‐viscous heating shows that active heating of electrons is more prevalent in the presence of a high speed electron inflow and increased magnetic shear.

The Reversibility of Magnetic Reconnection

The reversibility of the transfer of energy from the magnetic field to the surrounding plasma during magnetic reconnection is examined. Trajectories of test particles in an analytic model of the fields demonstrate that irreversibility is associated with separatrix crossings and regions of weaker magnetic field. Inclusion of a guide field increases the degree of reversibility. Full kinetic simulations with a particle-in-cell code support these results and demonstrate that while time-reversed simulations at first un-reconnect, they eventually evolve into a reconnecting state.

Superfast ion scattering by solar wind discontinuities.

Large-amplitude fluctuations of the solar wind magnetic field can scatter energetic ions. One of the main contributions to these fluctuations is provided by solar wind discontinuities, i.e., rapid rotations of the magnetic field. This study shows that the internal configuration of such discontinuities plays a crucial role in energetic ion scattering in pitch angles. Kinetic-scale discontinuities accomplish very fast ion pitch-angle scattering. The main mechanism of such pitch-angle scattering is the adiabatic invariant destruction due to separatrix crossings in the phase space. We demonstrate that efficiency of this scattering does not depend on the magnetic field component across the discontinuity surface, i.e., both rotational and almost tangential discontinuities scatter energetic ions with the same efficiency. We also examine how the strong scattering effect depends on the deviations of the discontinuity magnetic field from the force-free one.

Plasma Heating due to Cyclic Diffusion across a Separatrix.

We observe plasma heating due to collisional diffusion across a separatrix when a magnesium ion column in a Penning-Malmberg trap is cyclically pushed back and forth across a partial trapping barrier. The barrier is an externally applied axisymmetric "squeeze" potential, which creates a velocity separatrix between trapped and passing particles. Weak ion-ion collisions then cause separatrix crossings, leading to irreversible heating. The heating rate scales as the square root of the oscillation rate times the collision frequency and thus can be dominant for low-collisionality plasmas. The particle velocity distribution function is measured with coherent laser induced fluorescence and shows passing and trapped particles having an out-of-phase response to the forced plasma oscillations.

Separatrix Crossing in Rotation of a Body with Changing Geometry of Masses

We consider free rotation of a body whose parts move slowly with respect to each other under the action of internal forces. This problem can be considered as a perturbation of the Euler--Poinsot problem. The dynamics has an approximate conservation law---an adiabatic invariant. This allows us to describe the evolution of rotation in the adiabatic approximation. The evolution leads to an overturn in the rotation of the body: the vector of angular velocity crosses the separatrix of the Euler--Poinsot problem. This crossing leads to a quasirandom scattering in body's dynamics. We obtain formulas for probabilities of capture into different domains in the phase space at separatrix crossings.

Nonlocal adiabatic theory. I. The action distribution function

In this paper, we address the motion of charged particles acted upon by a sinusoidal electrostatic wave, whose amplitude and phase velocity vary slowly enough in time for neo-adiabatic theory to apply. Moreover, we restrict to the situation when only few separatrix crossings have occurred, so that the adiabatic invariant, I, remains nearly constant. We insist here on the fact that I is different from the dynamical action, I. In particular, we show that I depends on the whole time history of the wave variations, while the action is usually defined as a local function of the wave amplitude and phase velocity. Moreover, we provide several numerical results showing how the action distribution function, f(I), varies with time, and we explain how to derive it analytically. The derivation is then generalized to the situation when the wave is weakly inhomogeneous.

Probabilistic eccentricity bifurcation for stars around shrinking massive black hole binaries

Based on the secular theory, we discuss the orbital evolution of stars in a nuclear star cluster to which a secondary massive black hole is infalling with vanishing eccentricity. We find that the eccentricities of the stars could show sharp transitions, depending strongly on their initial conditions. By examining the phase-space structure of an associated Hamiltonian, we show that these characteristic behaviours are partly due to a probabilistic bifurcation at a separatrix crossing, resulting from the retrograde apsidal precession by the cluster potential. We also show that separatrix crossings are closely related to realization of a large eccentricity and could be important for astrophysical phenomena such as tidal disruption events or gravitational wave emissions.

Averaging method for systems with separatrix crossing

The averaging method provides a powerful tool for studying evolution in near-integrable systems. The existence of separatrices in the phase space of the underlying integrable system is an obstacle for the application of standard results that justifies the use of averaging. We establish estimates that allow us to use the averaging method when the underlying integrable system is a system with one rotating phase, and the evolution leads to separatrix crossings.

Violation of adiabaticity in magnetic billiards due to separatrix crossings.

We consider dynamics of magnetic billiards with curved boundaries and strong inhomogeneous magnetic field. We investigate a violation of adiabaticity of charged particle motion in this system. The destruction of the adiabatic invariance is due to the change of type of the particle trajectory: particles can drift along the boundary reflecting from it or rotate around the magnetic field at some distance from the boundary without collisions with it. Trajectories of these two types are demarcated in the phase space by a separatrix. Crossings of the separatrix result in jumps of the adiabatic invariant. We derive an asymptotic formula for such a jump and demonstrate that an accumulation of these jumps leads to the destruction of the adiabatic invariance.

Neoclassical transport processes in weakly collisional plasmas with fractured velocity distribution functions

Ripples in magnetic or electrostatic confinement fields give rise to trapping separatrices, and conventional neoclassical transport theory describes the collisional trapping/detrapping of particles with fractured distribution function. Our experiments and novel theory have now characterized a new kind of neoclassical transport processes arising from chaotic (nominally collisionless) separatrix crossings, which occur due to E × B plasma rotation along θ−ruffled or wave-perturbed separatrices. This chaotic neoclassical transport becomes dominant at low collisionality when the collisional spreading of particle energy during the dynamical period is less than the separatrix energy ruffle.

Chaotic Neoclassical Separatrix Dissipation in Parametric Drift-Wave Decay

Experiments and theory characterize a parametric decay instability between plasma drift waves when the nonlinear coupling is modified by an electrostatic barrier. Novel mode coupling terms representing enhanced dissipation and mode phase shifts are caused by chaotic separatrix crossings on the wave-ruffled separatrix. Experimental determination of these coupling terms is in broad agreement with new chaotic neoclassical transport analyses.

Enhanced superbanana transport caused by chaotic scattering across an asymmetric separatrix

This paper discusses a novel “chaotic” form of superbanana transport and compares the theory to experiments on non-neutral plasmas. Superbanana transport is caused by particles that cross local trapping separatrices (magnetic or electric ripples) in the presence of field “errors” such as toroidal magnetic curvature. Traditionally, collisions (at rate ν) cause separatrix crossings, with resulting transport that scales as ν1/2B-1/2. The “chaotic” transport of interest here occurs when the separatrix is “ruffled” in the direction of plasma drift; then, collisionless particle orbits give random trapping and detrapping. Prior theory assumed a “stellarator symmetry” and suggested that these orbits give reduced transport scaling as νp with p∼1. Here, we fully characterize chaotic transport and show that the transport is enhanced rather than reduced, scaling as ν0B-1. Experiments on pure electron plasmas provide quantitative transport measurements, with precise control of the overall field error, and of the trapping separatrix with and without ruffles. The experiments show close agreement with theory over a decade in B, for both collisional neoclassical transport, and for the distinctive chaotic transport. At low magnetic fields, transport scaling as B-p with p>rsim2 becomes dominant, showing preliminary agreement with bounce-resonant theory.

Jumps of adiabatic invariant at the separatrix of a degenerate saddle point

We consider a slow-fast Hamiltonian system with two degrees of freedom. One degree of freedom corresponds to slow variables, and the other one corresponds to fast variables. A characteristic ratio of the rates of change of slow and fast variables is a small parameter κ. For every fixed value of the slow variables, in the phase portrait of the fast variables there are a saddle point and separatrices passing through it. When the slow variables change, phase points may cross the separatrices. The action variable of the fast motion is an adiabatic invariant of the full system as long as a trajectory is far from the separatrices: value of the adiabatic invariant is conserved with an accuracy of order of κ on time intervals of order of 1/κ. A passage through a narrow neighborhood of the separatrices results in a jump of the adiabatic invariant. We consider a case when the saddle point is degenerate. We derive an asymptotic formula for the jump of the adiabatic invariant which turns out to be a value of order of κ(3/4) (in the case of a non-degenarate saddle point a similar jump is known to be a value of order of κ). Accumulation of these jumps after many consecutive separatrix crossings leads to the "diffusion" of the adiabatic invariant and chaotic dynamics. We verify the analytical expression for the jump of the adiabatic invariant by numerical simulations. We discuss application of the obtained results to the description of charged particle dynamics in the Earth magnetosphere.

Overview of Transport, Damping, and Wave Couplings from Separatrix Dissipation in an Axisymmetric Plasma

Axial variations in magnetic or electrostatic confinement fields create local trapping separatrices, and traditional neo-classical theory analyzes the effects from collision-induced separatrix crossings. Recent experiments and theory have characterized the distinctive neo-classical effects from chaotic separatrix crossings, induced by equilibrium plasma rotation across θ-ruffled separatrices, or by wave-induced separatrix fluctuations. Experiments on nominally-symmetric pure electron plasmas with controlled separatrices agree quantitatively with theory in 3 broad areas: 1) radial particle transport is driven by a static z- and θ-asymmetry; 2) both E × B drift waves and Langmuir waves are damped; and 3) novel dissipative wave-wave couplings are observed. The new chaotic neo-classical effects scale as ν0B-1, whereas traditional plateau-regime collisional effects scale as ν1/2B-1/2.

Chaotic Neoclassical Transport at Azimuthally Perturbed or Wave-Mingled Separatrix

Variations in magnetic or electrostatic confinement fields give rise to trapping separatrices, and standard neoclassical transport theory analyzes effects from collision-induced separatrix crossings. Experiments and theory have now characterized novel transport effects arising from “chaotic“ separatrix crossings, which occur due to equilibrium plasma rotation across θ-ruffled separatrices, and/or due to wave-induced separatrix fluctuations.

Chaotic Transport and Damping fromθ-Ruffled Separatrices

Variations in magnetic or electrostatic confinement fields give rise to trapping separatrices, and neoclassical transport theory analyzes effects from collision-induced separatrix crossings. Experiments on pure electron plasmas now quantitatively characterize a broad range of transport and wave damping effects due to "chaotic" separatrix crossings, which occur due to equilibrium plasma rotation across θ-ruffled separatrices, and due to wave-induced separatrix fluctuations.

Regular and chaotic charged particle dynamics in low frequency waves and role of separatrix crossings

We consider interaction of charged particles with an electromagnetic (electrostatic) low frequency wave propagating perpendicular to a uniform background magnetic field. The effects of particle trapping by the wave and further acceleration of a surfatron type are discussed in details. Method for this analysis based on the adiabatic theory of separatrix crossing is used. It is shown that particle can unlimitedly accelerate in the trapping in electromagnetic waves and energy of particle does not increase for the system with electrostatic wave.

Regular and chaotic charged particle dynamics in low frequency waves and role of separatrix crossings

Regular and chaotic charged particle dynamics in low frequency waves and role of separatrix crossings

Breakdown of autoresonance due to separatrix crossing in dissipative systems: From Josephson junctions to the three-wave problem

Optimal energy amplification via autoresonance in dissipative systems subjected to separatrix crossings is discussed through the universal model of a damped driven pendulum. Analytical expressions of the autoresonance responses and forces as well as the associated adiabatic invariants for the phase space regions separated by the underlying separatrix are derived from the energy-based theory of autoresonance. Additionally, applications to a single Josephson junction, topological solitons in Frenkel-Kontorova chains, as well as to the three-wave problem in dissipative media are discussed in detail from the autoresonance analysis.