arXiv subjects

Allen H Boozer

Publications and source records attributed to Allen H Boozer.

27 records · Page 2Linked to original sources

arXiv2022

Local analysis of fast magnetic reconnection

Fast magnetic reconnection is defined by the topology of the magnetic field lines changing on a timescale that is approximately an order of magnitude longer than the topology-conserving ideal-evolution timescale. Fast reconnection is an intrinsic property of Faraday's law when the evolving magnetic field depends non-trivially on all three spatial coordinates and is commonly observed -- even when the effects that allow topology breaking are arbitrarily small. The associated current density need only be enhanced by a factor of approximately ten and flows in thin but broad ribbons along the magnetic field. These results follow from the variation in the separation of neighboring pairs of magnetic field lines, which in an ideal evolution typically increases exponentially with time, and the existence of a spatial scale below which magnetic field lines freely change their identities due to non-ideal effects such as resistivity. Traditional reconnection theory ignores exponentially large variations and relies on the current density reaching a magnitude that is exponentially larger than is actually required. Here, an analysis of the behavior of magnetic field lines in the neighborhood of an arbitrarily chosen line is used to obtain more precise and rigorous results on intrinsic reconnection. The maximum parallel kinetic energy of collisionless charged particles is shown to have an exponential increase in time during a generic magnetic evolution.

physics.plasm-ph↗

arXiv2022

The rapid destruction of toroidal magnetic surfaces

The operation of ITER will require reliable simulations in order to avoid major damage to the device from disruptions. Disruptions are the sudden breakup of magnetic surfaces across the plasma volume -- a fast magnetic reconnection. This reconnection can be caused by the growth of perturbations outside of the plasma core causing an ideal perturbation to the core. This causes an increasing ratio of the maximum to the minimum separation, $Δ_{max}/Δ_{min}$, between neighboring magnetic surfaces. Magnetic reconnection becomes a dominant process when magnetic field lines can quickly interchange connections over a spatial scale $a_r$. This occurs when $Δ_{max}/Δ_{min}\gtrsim a_r/Δ_d$, where $Δ_d$ is the scale over which non-ideal effects make magnetic field lines indistinguishable. Traditional reconnection theory is fundamentally different. It is a study of the steady-state cancellation of oppositely directed magnetic field components across a thin layer. During more than sixty years, mathematical implications of Faraday's Law have been derived that clarify and constrain the physics of fast magnetic reconnection. These are reviewed because they are not commonly known but are needed to understand and to place in context how an ideal magnetic evolution can cause reconnection to quickly become a dominant process no matter how small $Δ_d/a_r$ may be.

physics.plasm-ph↗

arXiv2021

Carbon Dioxide, Fusion, and Stellarators

Much emotion is expended on the dangers of carbon dioxide, but solutions require reason and recognition of facts: (1) The cost of developing options is approximately a thousand times less than their deployment. (2) Timescales involve two questions: (a) How quickly can an option be demonstrated? (b) How quickly can the required equivalent of thousands of units be built. Two questions are implied: (1) What options would most fundamentally change the carbon-dioxide problem? (2) For each option, how could it be demonstrated most quickly? An option of fundamental importance is direct air capture of carbon dioxide. The option that appears most attractive for carbon-free energy production is the stellarator fusion concept, which is poised for a rapid demonstration.

physics.plasm-ph↗

arXiv2021

Stellarators as a Fast Path to Fusion

This paper is focused on three points: (1) Overcoming obstacles to tokamak power plants may require a configuration modification as large as that of a stellarator. (2) The demonstrated reliability of the computational design of stellarators should change fusion strategy. (3) Deployment of carbon-free energy sources is mandated by the thirty-year doubling of carbon dioxide emissions. Carbon-free energy options must be developed and fully deployed within a few doubling times. Unit size and cost of electricity are only relevant in comparison to alternative worldwide energy solutions. Intermittency, site specificity, waste management, and nuclear proliferation make fusion attractive as the basis for a carbon-free energy system compared to the alternatives. Nonetheless, fusion is not an option for deployment until a power plant has successfully operated. A critical element in a minimal time and risk program is the use of computational design as opposed to just extrapolation. Only the stellarator has an empirical demonstration of the reliable computational design through large changes in configuration properties and scale. The computational design of stellarators should proceed while the inventions necessary for a more tokamak-like power plant are sought. The cost of computational design is extremely small, but adequate time is required for the development of ideas that maximize attractiveness and minimize risk. Rapid power-plant construction without many intermediate steps may seem risky, but the price is small compared to the cost of trillions of dollars for each year's delay in addressing carbon-dioxide emissions.

physics.plasm-ph↗

arXiv2021

The tritium burn-fraction in DT fusion

The fraction of the tritium that is burned during one pass through a DT fusion system, $f_{tb}$, is a central issue for success of fusion energy. Reducing the tritium fraction, $f_t$, in a $DT$ burning plasma below a half increases the burn fraction, $f_{tb}\propto1/f_t$ but also the required confinement to achieve a burn $nTτ_E\propto1/f_t(1-f_t)$. A doubling of the fractional burn entails only a 4/3 enhancement of the required $nTτ_E$. The energy confinement time $τ_E$ in tokamaks and stellarators is empirically gyro-Bohm with an approximate factor of two between the best and worse results used to construct scaling laws. Gyro-Bohm is also the approximate level of transport needed in a power plant. What has received little study are $τ_t/τ_E$, the ratio of the tritium to the energy confinement time, and $τ_α/τ_E$, the ratio of the alpha particle to the energy confinement time. The tritium burn fraction is proportional to $τ_t/τ_E$, so the larger the better. The contamination of the plasma by helium ash is proportional to $τ_α/τ_E$, so the smaller the better.

physics.plasm-ph↗

arXiv2021

Example of exponentially enhanced magnetic reconnection driven by a spatially-bounded and laminar ideal flow

In laboratory and natural plasmas of practical interest, the spatial scale $Δ_d$ at which magnetic field lines lose distinguishability differs enormously from the scale $a$ of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives $a/Δ_d\sim10^{12}$, which is the magnetic Reynold number $R_m$. The traditional resolution of the paradox of disparate scales is for the current density $j$ associated with the reconnecting field $B_{rec}$ to be concentrated by a factor of $R_m$ by the ideal evolution, so $ j\sim B_{rec}/μ_0Δ_d$. A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, $Δ_{max}/Δ_{min}$, when calculated at various points in time. Reconnection becomes inevitable where $Δ_{max}/Δ_{min}\sim R_m$. A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for $Δ_{max}/Δ_{min}$. Reconnection occurs on a time scale and with a current density enhanced by only $\ln(a/Δ_d)$ from the ideal evolution time and from the current density $B_{rec}/μ_0a$. In both resolutions, once a sufficiently wide region, $Δ_r$, has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfvénic time scale. The Alfvénic evolution is intrinsically ideal but expands the region in which $Δ_{max}/Δ_{min}$ is large.

physics.plasm-ph↗

arXiv2020

Flattening of the tokamak current profile by a fast magnetic reconnection with implications for the solar corona

During tokamak disruptions the profile of the net parallel current is observed to flatten on a time scale that is so fast that it must be due to a fast magnetic reconnection. After a fast magnetic reconnection has broken magnetic surfaces, a single magnetic field line covers an entire volume and not just a magnetic surface. The current profile, given by $K\equivμ_0j_{||}/B$, relaxes to a constant within that volume by Alfvén waves propagating along the chaotic magnetic field lines. The time scale for this relaxation determines the commonly observed disruption phenomena of a current spike and a sudden drop in the plasma internal inductance. An efficient method for studying this relaxation is derived, which allows a better understanding of the information encoded in the current spike and the associated sudden drop in the plasma internal inductance. Implications for coronal heating are also discussed.

physics.plasm-ph↗

arXiv2020

Why carbon dioxide makes stellarators so important

The increasing level of atmospheric carbon dioxide has driven public discourse throughout the world. An immediate implementation of carbon-free energy sources is demanded with little discussion of costs, technical constraints on the sources, or implications of high residual levels of carbon dioxide. Residual carbon-dioxide can be removed from the air, but the cost to remove the carbon-dioxide produced by human activity during a year is thought to be trillions of dollars---otherwise it remains in the atmosphere for centuries. Economic considerations may limit wind and solar sources to less than 40\% of the electricity production. Fission or fusion may be the only choice for most of the rest. Development costs are orders of magnitude smaller than implementation costs, which are tens of trillions of dollars for fission. A needless delay in the development of fusion has enormous financial implications. As will be shown stellarators are better positioned than any other concept for a fast path to fusion. A computationally derived conceptual design for a stellarator reactor may allow final design and construction to be initiated without the delay of intermediate generations of experiments. The most urgent issue is the development of conceptual designs.

physics.plasm-ph↗

arXiv2020

Changed paradigm of fast magnetic reconnection

Although magnetic reconnection takes place in three-dimensional space, reconnection theory has focused on two-dimensional models for more than sixty years. Well-posed three-dimensional mathematics associated with the theory of fluid mixing provides a predictive and compelling explanation for why fast magnetic reconnection is prevalent---exponentially large variations in the separations between magnetic field lines. The proofs have been simplified to remove any rational reason to maintain a focus on two dimensional models, which fail to represent the mathematical properties of three-dimensional space.

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