Magnetic Feedback Control of Plasma Shape and Turbulence via PID LQR Hall Effect Sensors
March 19, 2026 Submitted and Accepted to American Physical Society
Magnetic confinement fusion will require novel Hall effect coil feedback systems located at the centimeter scale to adequately mitigate turbulence and shape density functions in H mode plasmas. Plasma shape and turbulence must be controlled on the scale of the turbulent eddies that form within the closed magnetic field lines; the scale is unfortunately that of centimeters. The startup environment for nuclear fusion is ripe for a revolution in magnetic feedback systems that are built from adequate circuit components and plasma sensors. Hall effect probes are used in the detection of varying magnetic fields which are changing in position space. A magnetic field from the plasma will change the flux through the Hall probe, causing a voltage difference orthogonal to the calibrating Hall current. Controlling coils in the magnetic confinement reactor connected to these Hall effect sensors through sensitive feedback loops will be able to accurately stop Alfven eigenmodes (AEs) and edge localized modes (ELMs). Circuits will have to be robust as the production of 1 T scale controlling currents will require a copper wire setup. Superconducting wires will be investigated but their ability to provide real-time feedback is limited by ramp up current Andreev reflections at the superconducting and conducting interface. Circuit elements controlling copper coils connected to Hall sensors will be able to detect subtle changes in plasma density and power field coils to shape plasma and prevent neoclassical transport. Neutron bombardment and modeling of heat flux will also be necessary to accurately uncover embrittlement and temperature considerations in a real world fusion reactor. A good proportional integral derivative (PID) controller will be able to set a calibrated plasma field set point for output controlling current. In addition a linear quadratic regulator (LQR) controller might be better suited to control non-linear phenomena.
Tunnel-ase Proteins Involved in the Creation of Quantum Consciousness
March 4, 2024 Accepted to American Physical Society
Neuroscience involves the description of consciousness from coarse grained action potentials to the neural network of cognition. Philosophers have expounded on quantum mechanics as the basis for free will but no mechanism of quantum mechanics has been thoroughly investigated as the harbinger of this. Perhaps glutamine synthetase and proteins like it are involved in the formation of quantum corrals in neurons which then couple through quantum tunneling to regions where the action potential fires. Thus, the creation of an action potential is linked directly to the collapse of a quantum state, here nestled within the central region of the glutamine synthetase active site.. Philosophically, this is called biological realism, and it involves quantum tunneling inside glutamine synthetase to couple the quantum states of charged species held within the Debye shielded region of interest in the protein. The age old battle between monism and dualism again surfaces with the biological world being the firm foundation of free will with this new class of tunnel-ase proteins involved in the creation of decision making. It would be good to briefly discuss generative A.I., neural networks, and models of free will in order to put this theoretical discovery into context, or at least to suggest a new area of research. It is likely that the role of all proteins in the brain has not been discovered and this is just one of the many mysteries left in the field of quantum mechanics as it related to quantum consciousness.
Determinism, Muonium, Regge Beta Decay, Yang-Mills Unification, Anti-Matter Plasmas, and Endothermic Ordering Entropy Escape Quark Fusion
July 1, 2019 Submitted and Accepted to American Physical Society
Predestination is a philosophy attributed to eras of the past, however, deterministic geodesics generate Hamilton-Jacobi equations. Laplace and Poincaré believed, a sufficient intelligence predicts the universe. As such, the production of exotic materials, like a muon orbiting a proton, anti-hydrogen, and the DT plasma seem like tangible classical problems. This means that the uncertainty principle is neglected in the MHD, relativity, and Fokker-Planck relations. Extrapolating this analytic dissonance to new Regge theory, the beta decay is explained by a spectrum of rotational energy, non-negligible in the production of a Fermi-Curie deconvolution. Yang-Mills frequencies further angular corrections of an old theory. Mathematical tools that describe rotation, symmetry, abstract amplitude functions, and strings in the spacetime Riemann metric unify. Analysis leads to prime number distributions in Dirac’s gamma matrix dimensions generating the simplified standard model as the surface of a quantum observable. Unification simplifies expressions, helpful for analyzing turbulent motion. Unified physics promises a utopia; fusion through endothermic quark ordering can be done in theory.
Toroidal Polynomials Isomorphic to Ignition Scattering Functions in Fusion Conditions
November 5, 2018 Submitted and Accepted to American Physical Society
Nuclear fusion is achieved through the self-sustaining chain reaction of particles in various geometries. One of the most interesting and novel structures developing fusion is the tokamak. Solving the Poisson equation and the Lagrangian for geodesics in the toroidal geometry requires the development of a new function called the toroidal elliptic function. As the coordinate system has problems with skewness, the components of the differential equation solution cannot be separated. Thus, the dot product is modified to account for overlapping coordinates. The importance of finding analytic solutions to fusion scattering and geodesic problems has implications in supersymmetry/standard model predictions and practical energy production in the H mode. This work is an effort to create polynomials of infinite order and recursion relations that define coefficients that completely describe a set of eigenfunctions in a toroidal shape. Denoted by a special letter, these toroidal elliptic functions are written in spherical, cylindrical, and Cartesian polynomials to simplify the difficult task of finding an isomorphic analytic and computational model for particles moving along geodesics in a tokamak.
Developing the Polynomial Expressions for Fields in the ITER Tokamak
July 16, 2017 Submitted and Accepted to American Physical Society
The two most important problems to be solved in the development of working nuclear fusion power plants are: sustained partial ignition and turbulence. These two phenomena are the subject of research and investigation through the development of analytic functions and computational models. Ansatz development through Gaussian wave-function approximations, dielectric quark models, field solutions using new elliptic functions, and better descriptions of the polynomials of the superconducting current loops are the critical theoretical developments that need to be improved. Euler-Lagrange equations of motion in addition to geodesic formulations generate the particle model which should correspond to the Dirac dispersive scattering coefficient calculations and the fluid plasma model. Feynman-Hellman formalism and Heaviside step functional forms are introduced to the fusion equations to produce simple expressions for the kinetic energy and loop currents. Conclusively, a polynomial description of the current loops, the Biot-Savart field, and the Lagrangian must be uncovered before there can be an adequate computational and iterative model of the thermonuclear plasma.
Mathematical Foundations for Fields of Toroidal Current Loops
August 9, 2016 Submitted and Accepted to American Physical Society
Motivating the functions that define electromagnetic fields for a toroidal shaped current loop are centered around three main isomorphisms: fundamental additions to solutions of differential equations, solving for the geodesics of thermonuclear magnetic reactors, and constructing accurate computational combinatoric models for fusion plasmas. Thermonuclear plasmas in tokamaks are essentially loops of current where the ions and electrons create two current densities which contribute to the magnetic field of the electricity generating current loop. The toroidal shaped current loop necessitates, however, new calculus. In the Biot Savart circular loop, off axis solutions are generated from an integral of a line segment. The non circular shape's differing eccentricity is in corner regions and the linear section and requires new integration and coordinates. The solution of the incremental loop elements in the toroidal shaped coil case are now loops considered parts of semicircles and step functions. When constructing a field, new elliptic functions are going to be generated and a new polynomial function---called an elliptic function of the first and second kind---must be uncovered.
Introduction to Electromagnetic Fields and Geodesics in a Tokamak
November 5, 2015 Submitted and Accepted to American Physical Society
Photons mediate electromagnetic radiation such that electric and magnetic particles obey the principle of least action from the applied fields. Elastic and inelastic collisions arise after summation of Lagrangian geodesics. In the case of reacting tritium and deuterium, energy is released in the form of electromagnetic radiation, neutrons, and alpha particles. Within fusion tokamaks, alpha particle energies determine if a self sustaining reaction---or ignition---will proceed. If particle mean free path is confined by electric and magnetic fields, then fusion occurs at higher frequencies. If temperature is increased and particle velocity is increased, then collision frequency increases. Modeling the nucleons as polarizable quark dielectric liquid drops increases differentiation between scattering events and fusion. When the cross section of two reactant liquid drops is coincident, fusion occurs. If cross sections do not overlap sufficiently, Coulomb scattering occurs. One strives for understanding of geometric approaches to solving for reactants' cross sections and fusion collision frequency in order to determine power output per particle and critical density of reactants.