Quantum Calculation of Classical Kinetic Equations: A Novel Approach for Numerical Analysis of 6D Boltzmann-Maxwell Equations in Collisionless Plasmas Using Quantum Computing
Hayato Higuchi, Juan William Pedersen, Akimasa Yoshikawa
A novel quantum algorithm for solving the Boltzmann-Maxwell equations of the 6D collisionless plasma is proposed. The equation describes the kinetic behavior of plasma particles in electromagnetic fields and is known for the classical first-principles equations in various domains, from space to laboratory plasmas. We have constructed a quantum algorithm for a future large-scale quantum computer to accelerate its costly computation. This algorithm consists mainly of two routines: the Boltzmann solver and the Maxwell solver. Quantum algorithms undertake these dual procedures, while classical algorithms facilitate their interplay. Each solver has a similar structure consisting of three steps: Encoding, Propagation, and Integration. We conducted a preliminary implementation of the quantum algorithm and performed a parallel validation against a comparable classical approach. IBM Qiskit was used to implement all quantum circuits.
Strong collisionless damping of the low-velocity branch of electromagnetic wave in plasmas with Maxwellian-like electron velocity distribution function
A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.
A lattice Boltzmann method (LBM) approach to the Charney-Hasegawa-Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas, is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (mo…
Vlasov-Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields, and the Vlasov equation for the phase-space dynamics of particle distributions in a collisionless plasma. These two systems (macroscopic and microscopic) are coupled via the source terms in Maxwell's equations, which are sums of velocity-space 'moment' integrals of the particle distribution function. This paper considers 'the inverse problem for collisionless equilibria' (IPCE), viz. "given information regarding the real-space…
Self-consistent system of equations for a kinetic description of the low-pressure discharges accounting for the nonlocal and collisionless electron dynamics
The head-on collision of ion-acoustic solitary waves in a collisionless plasma with cold ions and Boltzmann electrons is studied. It is shown that solitary waves of sufficiently large amplitudes do not retain their identity after a collision. Their amplitudes decrease and their forms change. Dependences of amplitudes of the potential and densities of ions and electrons after a head-on collision of identical solitary waves on their initial amplitude are presented.
We study the theory of Vlasov-Maxwell equilibria in one spatial dimension, as well as its application to current sheet and flux tube models. The 'inverse problem' is that of determining a Vlasov-Maxwell equilibrium distribution function self-consistent with a given magnetic field. We develop the theory of inversion using expansions in Hermite polynomials of the canonical momenta. Sufficient conditions for the convergence of a Hermite expansion are found, given a pressure tensor. For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisati…
The mechanism of heating for hot, dilute, and turbulent plasmas represents a long-standing problem in space physics, whose implications concern both near-Earth environments and astrophysical systems. In order to explore the possible role of interparticle collisions, simulations of plasma turbulence -- in both collisionless and weakly collisional regimes -- have been compared by adopting Eulerian Hybrid Boltzmann-Maxwell simulations, being proton-proton collisions explicitly introduced through the nonlinear Dougherty operator. Although collisions do not significantly influence the statistical c…
A new class of exact electrostatic solutions of the Vlasov-Maxwell equations based on the Jeans's theorem is proposed for studying the evolution and properties of two-dimensional anisotropic plasmas that are far from thermodynamic equilibrium. In particular, the free expansion of a slab of electron-ion plasma into vacuum is investigated.
Ion acceleration due to the interaction between a short high-intensity laser pulse and a moderately overdense plasma target is studied using Eulerian Vlasov-Maxwell simulations. The effects of variations in the plasma density profile and laser pulse parameters are investigated, and the interplay of collisionless shock and target normal sheath acceleration is analyzed. It is shown that the use of a layered-target with a combination of light and heavy ions, on the front and rear side respectively, yields a strong quasi-static sheath-field on the rear side of the heavy-ion part of the target. Thi…
We develop first-principles theory of kinetic plasma turbulence governed by the Vlasov-Maxwell-Landau equations in the limit of vanishing collision rates. Following an exact renormalization-group approach pioneered by Onsager, we demonstrate the existence of a "collisionless range" of scales (lengths and velocities) in 1-particle phase space where the ideal Vlasov-Maxwell equations are satisfied in a "coarse-grained sense". Entropy conservation may nevertheless be violated in that range by a "dissipative anomaly" due to nonlinear entropy cascade. We derive "4/5th-law" type expressions for the …
