arXiv subjects

Allen H. Boozer

Publications and source records attributed to Allen H. Boozer.

17 recordsLinked to original sources

arXiv2025

The subtlety of the outermost stellarator magnetic surface

An analytic model of the magnetic field line behavior in a stellarator is used to study the subtlety of the concept of an outermost magnetic surface. The analytic model that we use has a central region of nested magnetic surfaces. The outermost perfectly confining surface has a toroidal flux of 0.86 of the toroidal flux of the outermost confining surface. The field lines in the annulus between these surfaces strike a distant wall, but they make tens of thousands of transits through a period of the stellarator before doing so. The number of transits is so large that this region can probably be viewed as having confining surfaces. Between the outermost confining surface and a surface at 1.02 times the toroidal flux field lines go to the walls in four flux tubes: two with inward flux and two with outward flux. One of the inward-outward pairs of flux tubes are adjoining and the other pair is separated. When the toroidal flux is greater than 1.02 of that of the outermost confining surface approximately 85% of the field lines strike the wall before transiting a single period. The loss of plasma from this region is so fast compared to cross-field plasma diffusion that they are probably irrelevant to the study of divertors. In addition to the two inward-outward flux tube pairs that escape from the region inside 1.02 times the flux of the confining region, the outer region has two new inward-outward of flux-tube pairs; one adjoining and one separated.

nlin.CD↗

arXiv2022

Magnetic field evolution and reconnection in low resistivity plasmas

The mathematics and physics of each of the three aspects of magnetic field evolution -- topology, energy, and helicity -- is remarkably simple and clear. When the resistivity $\eta$ is small compared to an imposed evolution, $a/v$, timescale, which means $R_m\equiv\mu_0va/\eta>>1$, magnetic field line chaos dominates the evolution of field-line topology in three-dimensional systems. Chaos has no direct role in the dissipation of energy. A large current density, $j_\eta\equiv vB/\eta$, is required for energy dissipation to be on a comparable time scale to the topological evolution. Nevertheless, chaos plus Alfv\'en wave damping explain why both timescales tend to be approximately an order of magnitude longer than the evolution timescale $a/v$. Magnetic helicity is injected onto tubes of field lines when boundary flows have vorticity. Chaos can spread but not destroy magnetic helicity. Resistivity has a negligible effect on helicity accumulation when $R_m>>1$. Helicity accumulates within a tube of field lines until the tube erupts and moves far from its original location.

physics.plasm-ph↗

arXiv2021

A new type of stellarator divertor: the hybrid stellarator divertor

A new type of stellarator divertor is found. It has features of both a nonresonant divertor (A. Punjabi and A. H. Boozer, Phys. Plasmas 27, 012503 (2020)) as well as a resonant divertor. It has the outermost confining surface with sharp edges and large islands outside the outermost surface. For this reason, we have called it hybrid divertor. This divertor can be configured by adjusting the currents in external coils which produce nonresonant perturbations. We have simulated this divertor using the method developed in (A. H. Boozer and A. Punjabi, Phys. Plasmas 25, 092520 (2018)). The simulation shows that the footprints have fixed locations on the wall and are stellarator symmetric. The magnetic field lines leave and enter the outermost surface through three magnetic turnstiles. The probability exponents of the three turnstiles are 2.1, 2.25, and 4.3. The hybrid divertor confines larger plasma volume, has higher average shear, larger footprints, lower average density of strike points, lower maximum density of strike points, and longer loss-times than the nonresonant stellarator divertor. The hybrid divertor is robust against small changes in the rotational transform and large changes in the shape parameter that controls the sharp edges on the outermost confining surface.

physics.plasm-ph↗

arXiv2021

Simulation of non-resonant stellarator divertor

An efficient numerical method of studying nonresonant stellarator divertors was introduced in Boozer and Punjabi [Phys. Plasmas 25, 092505 (2018)]. This method is used in this paper to study a different magnetic field model of a nonresonant divertor. The most novel and interesting finding of this study is that diffusive magnetic field lines can be distinguished from lines that exit through the primary and the secondary turnstile, and that below some diffusive velocity, all lines exit through only the primary turnstile. The footprints of each family are stellarator symmetric and have a fixed location on the wall for all velocities. The probability exponent of the primary turnstile is d1 = 9/4 and that of the secondary turnstile is d2 = 3/2. This study also addresses the issues of an inadequate separation of the chamber walls from the outermost confining magnetic surface and a marginal step size of the numerical integrations that could compromise the interpretation of the earlier results [Boozer and Punjabi, Phys. Plasmas 25, 092505 (2018)]. The previous value of d1 = 2 is within the error bar of d1 = 9/4 estimated here.

physics.plasm-ph↗

arXiv2021

Magnetic turnstiles in nonresonant stellarator divertor

Non-resonant stellarator divertors have magnetic flux tubes, called magnetic turnstiles, that cross cantori, which are fractal remnants of destroyed invariant tori with holes, that lie outside the outermost confining surface. The exiting and entering flux tubes can be adjacent as is generally expected but can also have the unexpected feature of entering or exiting at separate locations of the cantori. Not only can there be two types of turnstiles, but pseudo turnstiles can also exist. A pseudo turnstile is formed when a cantorus has a sufficiently large, although limited, radial excursion to strike a surrounding chamber wall. The existence of non-adjacent and adjacent turnstiles and pseudo turnstiles resolves issues that arose in earlier simulations of nonresonant stellarator divertors [A. Punjabi and A. H. Boozer, Phys. Plasmas 27, 012503 (2020)].

physics.plasm-ph↗

arXiv2021

Plasma steering to avoid disruptions in ITER and tokamak power plants

Steering tokamak plasmas is commonly viewed as a way to avoid disruptions and runaway electrons. Plasma steering sounds as safe as driving to work but will be shown to more closely resemble driving at high speed through a dense fog on an icy road. The long time required to terminate an ITER discharge compared to time over which dangers can be foreseen is analogous to driving in a dense fog. The difficulty of regaining plasma control if it is lost resembles driving on an icy road. Disruptions and runaways are associated with three issues -- a solution to one tends to complicate the solution to the other two: loss of plasma position control, excessive heat deposition, and wall melting due to runaway electrons. All three risks must be addressed for ITER to achieve its mission and essentially eliminated before tokamak power plants can be deployed.

physics.plasm-ph↗

arXiv2020

The interaction of the ITER first wall with magnetic perturbations

Mitigation of the multiple risks associated with disruptions and runaway electrons in tokamaks involves competing demands. Success requires that each risk be understood sufficiently that appropriate compromises can be made. Here the focus is on the interaction of short timescale magnetic-perturbations with the structure in ITER that is closest to the plasma, blanket modules covered by separated beryllium tiles. The effect of this tiled surface on the perturbations and on the forces on structures are subtle. Indeterminacy can be introduced by tile-to-tile shorting. A determinate subtlety is introduced because electrically separated tiles can act as a conducting surface for magnetic perturbations that have a normal component to the surface. A practical method for including this determinate subtlety into plasma simulations is developed. The shorter the timescales and the greater the localization, particularly in the toroidal direction, the more important the magnetic effects of the tiles become.

physics.plasm-ph↗

arXiv2020

Magnetic nulls in interacting dipolar fields

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field-lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance $\Delta_d$. Electron inertia ensures $\Delta_d\gtrsim c/\omega_{pe}$. The lines that lie within a magnetic flux tube of radius $\Delta_d$ at the place where the field strength $B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$,vanishes, then distinguishable lines come no closer to the null than $\approx (a^2c/\omega_{pe})^{1/3}$, where $a$ is a characteristic spatial scale of the magnetic field. The behavior of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

physics.plasm-ph↗

arXiv2019

Magnetic reconnection with null and X-points

Null and X-points are not themselves directly important to magnetic reconnection because distinguishable field lines do not approach them closely. Even in a collision-free plasma, magnetic field lines that approach each other on a scale $c/\omega_{pe}$ become indistinguishable during an evolution. What is important is the different regions of space that can be explored by magnetic field lines that pass in the vicinity of null and X-points. Traditional reconnection theories made the assumption that the reconnected magnetic flux must be dissipated or diffused by an electric field. This assumption is false in three dimensional systems because an ideal evolution can cause magnetic field lines that cover a large volume to approach each other within the indistinguishability scale $c/\omega_{pe}$. When the electron collision time $\tau_{ei}$ is short compared to the evolution time of the magnetic field $\tau_{ev}$, the importance of $c/\omega_{pe}$ is replaced by the resistive time scale $\tau_\eta=(\eta/\mu_0)L^2$ with $L$ the system scale. The magnetic Reynolds number is $R_m\equiv\tau_\eta/\tau_{ev}$ is enormous in many reconnection problems of interest. Magnetic flux diffusion implies the current density required for reconnection to compete with evolution scales as $R_m$ while flux mixing implies the required current density to compete scales as $\ln R_m$.

physics.plasm-ph↗

arXiv2019

Curl-free magnetic fields for stellarator optimization

This paper describes a new and efficient method of defining an annular region of a curl-free magnetic field with specific physics and coil properties that can be used in stellarator design. Three statements define the importance: (1) Codes can follow an optimized curl-free initial state to a final full-pressure equilibrium. The large size of the optimization space of stellarators, approximately fifty externally-produced distributions of magnetic field, makes success in finding a global optimum largely determined by the starting point. (2) The design of a stellarator is actually improved when the central region of the plasma has rapid transport with the confinement provided by a surrounding annulus of magnetic surfaces with low transport. (3) The stellarator is unique among all fusion concepts, inertial as well as magnetic, in not using the plasma itself to provide an essential part of its confinement concept. This permits reliable computational design, which opens a path to faster, cheaper, and more certain achievement of fusion energy.

physics.plasm-ph↗

arXiv2019

Problematic nature of plasmoid theory of magnetic reconnection

Plasmoid theory uses two-coordinate models to explain fast magnetic reconnection, which occurs on an Alfvénic, not a resistive time scale, in plasmas that are evolving in the near-ideal limit. The primary application has been to three-dimensional naturally-occurring plasmas. A magnetic field representation that applies to all magnetic fields allows features of magnetic evolution in toroidal and natural plasmas to be compared. This comparison illustrates why plasmoid models of magnetic field evolution are not robust solutions to Maxwell's equations. Despite five-hundred papers on plasmoid models, they provide a problematic description of fast magnetic reconnection.

physics.plasm-ph↗

arXiv2019

Fast magnetic reconnection and the ideal evolution of a magnetic field

Regardless of how small non-ideal effects may be, phenomena associated with changes in magnetic field line connections are frequently observed to occur on an Alfvénic time scale. Since it is mathematically impossible for magnetic field line connections to change when non-ideal effects are identically zero, an ideal evolution must naturally lead to states of unbounded sensitivity to non-ideal effects. That such an evolution is natural is demonstrated using Lagrangian coordinates based on the flow velocity of the magnetic field lines. The Lagrangian representation of an evolving magnetic field is highly constrained when neither the magnetic field strength nor the forces exerted by the magnetic field increase exponentially with time. The development of a state of fast reconnection consistent with these constraints (1) requires a three-dimensional evolution, (2) has an exponentially increasing sensitivity to non-ideal effects, and (3) has a parallel current density, which lies in exponentially thinning but exponentially widening ribbons, with a magnitude that is limited to a slow growth. The implication is that exponential growth in sensitivity is the cause of fast magnetic reconnection when non-ideal effects are sufficiently small. The growth of the non-ideal effect of the resistivity multiplied by the parallel current density is far too slow to be competitive.

physics.plasm-ph↗

arXiv2019

Particle acceleration and fast magnetic reconnection

Mathematics demonstrates that an ideally evolving magnetic field has an exponentially increasing sensitivity to non-ideal effects for all but truly exceptional evolutions. On a time scale that depends only logarithmically on the magnitude of non-ideality, an evolving magnetic field will generally reach a state of fast magnetic reconnection. The effects of fast magnetic reconnection proceed at a rate determined by Alfv\'enic, not resistive, physics. The best known of these effects are associated with the transfer of magnetic field energy to the plasma and the conservation of magnetic helicity, which limits the energy transfer. As will be shown, weak non-ideality implies helicity conservation in regions bounded by magnetic surfaces or rigid perfect conductors. But, weak non-ideality makes the rapid transfer of energy subtle. This transfer can be understood by the drive for Alfv\'en waves and two other effects, which are present even in an ideal evolution, an effective parallel electric field $\mathcal{E}_{||}$, which can accelerate particles despite the particle acceleration due to the true parallel electric field $E_{||}$ being negligible, and a coefficient $\nu_K$, which gives a rate for exponentiation of the kinetic energy of particle motion along the magnetic field. Classical theories of reconnection are two-dimensional and exclude the exponentially increasing sensitivity that is robustly present for magnetic fields in three-dimensional space.

physics.plasm-ph↗

arXiv2016

Adjoint Fokker-Planck equation and runaway electron dynamics

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energyelectrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.

physics.plasm-ph↗

arXiv2014

Rapid Change of Field Line Connectivity and Reconnection in Stochastic Magnetic Fields

Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are found in the process of resistive relaxation. During the quasi-static phase, rapid change of field line connectivity and strong induced flow are found in regions of high field line exponentiation. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of field line mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold, leading to formation of intense current filaments and rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity is more appropriately designated as magnetic reconnection. Our results show that rapid change of field line connectivity appears to be a necessary, but not a sufficient condition for fast reconnection.

astro-ph.SR↗

arXiv2002

The Onset of Dissipation in the Kinematic Dynamo

The kinematic regime of the magnetic dynamo neglects the backreaction of the magnetic field on the flow. For small magnetic diffusivity, in the early stage of evolution, there is an ideal phase where dissipative effects can also be neglected. We estimate the magnitude of the energy dissipation term (Ohmic heating), taking into account differential constraints on chaotic flows. We find that the period of ideal evolution is roughly doubled over an estimate without constraints. The helicity generation terms are exponentially smaller than the energy dissipation, so that large quantities of energy are dissipated before any helicity can be created. Helicity flow is exponentially larger than net helicity generation. The constraints also lead to the existence of a singular initial condition for the magnetic field for which sizable amounts of helicity can potentially be created.

nlin.CD↗

arXiv2001

Geometrical Constraints on Finite-time Lyapunov Exponents in Two and Three Dimensions

Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditions (the Lagrangian coordinates) to the state of the system at a later time (the Eulerian coordinates). This coordinate transformation naturally defines a metric tensor, from which the Lyapunov exponents and characteristic directions are obtained. By requiring that the Riemann curvature tensor vanish for the metric tensor (a basic result of differential geometry in a flat space), differential constraints relating the finite-time Lyapunov exponents to the characteristic directions are derived. These constraints are realized with exponential accuracy in time. A consequence of the relations is that the finite-time Lyapunov exponents are locally small in regions where the curvature of the stable manifold is large, which has implications for the efficiency of chaotic mixing in the advection-diffusion equation. The constraints also modify previous estimates of the asymptotic growth rates of quantities in the dynamo problem, such as the magnitude of the induced current.

nlin.CD↗