Space Time Algebra Formulation of Cold Magnetized Plasmas

TL;DR

This paper introduces a novel space-time algebra formulation for modeling cold magnetized plasmas, enabling efficient numerical solutions of Maxwell's equations and potentially facilitating quantum computing applications in plasma physics.

Contribution

The paper develops a Clifford algebra-based, Dirac-type evolution equation for cold magnetized plasmas, simplifying computational approaches and enabling direct transfer to quantum computers.

Findings

Formulation yields a Hermitian evolution operator.

Suitable for large spatial systems and quantum computing.

Simplifies numerical solutions of plasma electromagnetic behavior.

Abstract

The propagation and scattering of electromagnetic waves in magnetized plasmas in a state where a global mode has been established or is in turbulence, are of theoretical and experimental interest in thermonuclear fusion research. Interpreting experimental results, as well as predicting plasma behavior requires the numerical solutions of the underlying physics, that is, the numerical solution of Maxwell equations under various initial conditions and, under the circumstances, complex boundary conditions. Casting, the underlying equations in a coordinate free form that exploits the symmetries and the conserved quantities in a form that can easily encompass a variety of initial and boundary conditions is of tantamount importance. Pursuing this task we utilize the advantages the Clifford Algebras can possibly provide. For simplicity we deal with a cold multi-species lossless magnetized plasma. The formulation renders a Dirac type evolution equation for am augmented state that consists of the electric and magnetic field bivectors as well as the polarizations and their associated currents for each species. This evolution equation can be dealt with a general spatial lattice disretization scheme. The evolution operator that dictates the temporal advancement of the state is Hermitian. This formulation is computationally simpler whatever the application could be. However, small wavelength capabilities (on the Debye length scale) for spatially large systems (magnetic confinement devices) is questionable even for conventional super-computers. However, the formulation provided in this work it is entirely suitable and it can be directly transferred in a quantum computer. It is shown that the simplified problem in the present work could be suitable for contemporary rudimentary quantum computers.