Abstract
In the Earth’s magnetosphere, sunspots and magnetic cusp fusion devices, the boundary between the plasma and the magnetic field is marked by a diamagnetic current layer with a rapid change in plasma pressure and magnetic field strength. First principles numerical simulations were conducted to investigate this boundary layer with a spatial resolution beyond electron gyroradius while incorporating a global equilibrium structure. The boundary layer thickness is discovered to be on the order of electron gyroradius scale due to a self-consistent electric field suppressing ion gyromotion at the boundary. Formed at the scale of the electron gyroradius, the electric field plays a critical role in determining equilibrium structure and plasma transport. The discovery highlights the necessity to incorporate electron gyroradius scale physics in studies aimed at advancing our understanding of fusion devices, the magnetosphere and sunspots.
Main Text:
In many plasma systems, the plasma is surrounded by magnetic fields leading to afascinating array of natural and manmade phenomena. Plasma jet formation from accretion disks,Earth’s magnetosphere, sunspots and magnetic fusion devices are examples of plasma interactionwith magnetic fields. At the boundary between the plasma and the magnetic field, if there is achange in plasma pressure or magnetic field strength, gyromotions of electrons and ions generatecurrent, known as diamagnetic current, separating the plasma and magnetic field [1]. Amongexamples of plasma diamagnetic effects are the magnetopause in the Earth’s magnetosphere,sharp boundary layers in magnetic cusp fusion devices, and the dark patches of sunspots [2-8]. Inthese systems, a diamagnetic current layer marks the boundary across which plasma penetrationor loss to the magnetic field region is greatly reduced. The diamagnetic effect in these systemshas been studied extensively, leading to the development of magnetohydrodynamics (MHD), thestandard model for many solar, astrophysics and fusion plasmas over the past 50 years [9,10].
However, an ab initio solution of plasma diamagnetic effects had remained elusive withsome of the most fundamental questions yet to be answered [11]. For example, there has beenno definitive answer to the thickness of the diamagnetic current layer. Also unknown are therespective contributions of ions and electrons to the plasma diamagnetic current since there issignificant difference in their gyroradii, a factor of 43 in the case of hydrogen ions at the sametemperature as electrons. The lack of understanding remains because we are still trying tounderstand plasma dynamics at the scale of the electron the gyroradius, the fundamental, yetsmallest, length scale of plasma diamagnetism. While there have been many theoretical and numerical studies to investigate the boundary layer structure, these studies have been limited dueto geometrical complexities and technical challenges and have been unable to resolve electrongyroradius scale physics while incorporating the global equilibrium structure [12-16]. At thesame time, a number of observations indicate the importance of electron scale phenomena at theboundary such as formation of electron scale ion flow in laboratory magnetic cusp experiments[17]. The recently launched Magnetospheric Multiscale (MMS) mission, designed to makeelectron scale plasma measurements, has started to generate observational data in themagnetopause demonstrating the importance of electron dynamics in magnetic reconnection andturbulence [18-21].
To explore the diamagnetic current layer on the electron gyroradius scale, we utilized afirst-principles particle-in-cell (PIC) code, called the Energy Conserving semi-implicit model(ECsim), using its cylindrical coordinate implementation [22-24]. The ECsim simulates acollisionless plasma by solving Newton’s equation for particle motion and Maxwell’s equationsfor electric and magnetic fields, while conserving system energy. The simulations wereconducted for a cylindrically symmetric magnetic cusp system known as the “Picket Fence” thatwas proposed as a magnetic confinement system for fusion energy, as shown in Figure S1 [25].The magnetic field configuration of the picket fence is topologically identical to the daysideEarth magnetosphere, with the convex curvature of the Earth’s dipole magnetic field facing thesolar wind as well as the magnetic field in sunspots [6, 15, 26]. PIC simulations were conductedto investigate the boundary layer as a function of plasma pressure and ion mass with a spatialresolution beyond electron gyroradius while incorporating the global equilibrium structure. Theexploration led to the discovery of a localized electric field at the electron gyroradius scale thattransforms our understanding of plasma diamagnetic effects. Further details of the ECsim codeand simulation method are given in the Method section in supplemental materials includingTable ST1 summarizing the unit conversion between simulations and physical systems and TableST2 summarizing simulation parameters used in the present study.
