Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence

Abstract

A field theory and the associated structure-preserving geometric Particle-In-Cell (PIC) algorithm are developed to study low frequency electrostatic perturbations with fully kinetic ions and adiabatic electrons in magnetized plasmas. The algorithm is constructed by geometrically discretizing the field theory using discrete exterior calculus, high-order Whitney interpolation forms, and non-canonical Hamiltonian splitting method. The discretization preserves the non-canonical symplectic structure of the particle-field system, as well as the electromagnetic gauge symmetry. As a result, the algorithm is charge-conserving and possesses long-term conservation properties. Because drift wave turbulence and anomalous transport intrinsically involve multi time-scales, simulation studies using fully kinetic particle demand algorithms with long-term accuracy and fidelity. The structure-preserving geometric PIC algorithm developed adequately servers this purpose. The algorithm has been implemented in the \textsl{SymPIC} code, tested and benchmarked using the examples of ion Bernstein waves and drift waves. We apply the algorithm to study the Ion Temperature Gradient (ITG) instability and turbulence in a 2D slab geometry. Simulation results show that at the early stage of the turbulence, the energy diffusion is between the Bohm scaling and gyro-Bohm scaling. At later time, the observed diffusion is closer to the gyro-Bohm scaling, and density blobs generated by the rupture of unstable modes are the prominent structures of the fully developed ITG turbulence.

References in corpus (6)

• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Variational approach to low-frequency kinetic-MHD in the current coupling scheme
• Toroidal regularization of the guiding center Lagrangian
• Gauge-free electromagnetic gyrokinetic theory
• Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities

Cited by in corpus (8)

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• Geometric Electrostatic Particle-In-Cell Algorithm on Unstructured Meshes
• Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms
• A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus
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• Symplectic particle-in-cell methods for hybrid plasma models with Boltzmann electrons and space-charge effects