Page 2 - Global simulation of ion temperature gradient instabilities in a field-reversed configuration

Physics of Plasmas ARTICLE
FIG. 1. Contour plot of w=jwOj for global FRC geometry, where wO is the poloidal magnetic flux value at the magnetic axis as shown by the green star. The black solid lines represent the different field lines (contour line of w), and the red line represents the separatrix. The arrows denote the directions of cylindrical coordinates.
large orbit size, magnetic well geometry, and short electron transit
length. Meanwhile, a new global particle-in-cell FRC code, ANC, has
been developed by incorporating core and SOL regions across the
separatrix. ANC simulations show that ion scale turbulence can spread
33,34
divertor region for FRC, a new GTC family code, gyrokinetic toroidal code-X (GTC-X), is developed in this work by refactoring the coordi- nate system and geometry of the original GTC code, i.e., change the Boozer coordinates to cylindrical coordinates and change the geome- try from tokamak and stellarator to FRC. GTC-X enables the cross- separatrix simulation with a field aligned mesh covering the whole geometry of the FRC. Compared to the original GTC code, both the particle trajectory and the Poisson solver are newly written as well as the simulation grids in the GTC-X code. The GTC mixed-model OpenMP-MPI parallelization35 is adopted in GTC-X. This paper mainly presents the numerical developments, code verification, and initial results of ion temperature gradient (ITG) modes in the global FRC geometry. GTC-X global simulations show that ITG is unstable in the SOL and stable in the core, which is consistent with previous local simulations and experimental observations. We find that the ITG mode grows along the field line direction in the SOL and shows an axial variation. The maximum amplitude of the ITG mode is in the formation region with bad curvature, while the mode amplitude is small in the central FRC region. The mode structure in the SOL is sen- sitive to the parallel domain size, which experiences a transition from even parity to odd parity when increasing the domain size.
This paper is organized as follows. In Sec. II, we introduce the global FRC geometry implementation. The gyrokinetic particle simu- lation model for FRC is described in Sec. III. The benchmark simula- tion results are shown in Sec. IV. In Sec. V, the global simulation of ITG modes is described. The conclusion is discussed in Sec. VI.
II. GLOBAL FRC GEOMETRY IMPLEMENTATION
In order to avoid the singularity of magnetic coordinates at the
separatrix,22,36 we adapt the cylindrical coordinate system for global
from the SOL to the core.
In order to study the turbulent transports globally up to the
plasma-gun electrodes to improve the confinement. In this section, based on the characteristics of FRC equilibrium, we will introduce the algorithms used in GTC-X for global particle-in-cell modeling of FRC.
FRC simulation with (R, f, Z), where the 3 independent unit vectors ^^^
satisfy the right hand rule: R 􏰂 f 􏰁 Z 1⁄4 1. The poloidal magnetic flux
w of FRC equilibrium and cylindrical coordinates used in GTC-X is
shown in Fig. 1, which is calculated by an axisymmetric force balance
FRC equilibrium solver: LR_eqMI code.
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The equilibrium box size is
ulation containing different geometric topologies with a separatrix. Thus, we apply the cylindrical coordinate system as the basic coordi- nates. In order to guarantee the free divergence property for the mag- netic field in cylindrical coordinates, we use the poloidal magnetic flux w to calculate the magnetic field components and their derivatives and, thus, enforce the consistency between each component. In FRC, the equilibrium magnetic field B has no toroidal component and can
^^
1 @w
BR 1⁄4 􏰃 (1)
1@w
BZ 1⁄4 : (2)
From equilibrium calculated by the LR_eqMI code, we can get the value of poloidal magnetic flux w over the whole FRC geometry on the equal space grids in the (R, Z) plane as shown in Fig. 1, and LSR 1⁄4 150 and LSZ 1⁄4 401 are the equilibrium radial and axial grid numbers, respectively. By using the value on coarse equilibrium grids, we can use the quadratic spline function to calculate w at the arbitrary loca- tion (R, Z) inside the equilibrium domain as
and
R@R
scitation.org/journal/php
et al.
10,27
shows that the drift wave is stable in the FRC core due to the
normalized by the radial position of magnetic axis: R 1⁄4 R0 1⁄4 26.8 cm,
i.e., the distance between the magnetic axis and the cylinder axis.
There are several mirror plugs in the SOL region aiming at decreasing
the particle end loss, and the expanded divertors are located at the
ends of open field lines, where we can apply the edge biasing via the
4
A. Magnetic field representation in cylindrical coordinates
The magnetic field and associated derivatives commonly appear
in the particle dynamic equations for the simulation of magnetized
plasmas; thus, it is important that the magnetic field satisfies r 􏰁 B
1⁄4 0 numerically. The magnetic coordinates enable the free divergence
representation for the magnetic field as B 1⁄4 ra 􏰂 rb, where a and b
are coordinates which vary along the directions orthogonal to the
magnetic field. However, magnetic coordinates fail to address the sim-
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be expressed as B1⁄4rw􏰂rf1⁄4BRRþBZZ. The magnetic field strength in radial and axial directions can then be derived as
R@Z
Phys. Plasmas 26, 042506 (2019); doi: 10.1063/1.5087079 Published under license by AIP Publishing
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