Page 9 - Global simulation of ion temperature gradient instabilities in a field-reversed configuration

Physics of Plasmas ARTICLE
FIG. 7. (a) Ion temperature and density gradients at outer midplane Z 1⁄4 0, where Ti is normalized by electron temperature at the axis Tea 1⁄4 80.0 eV, ni is normalized by electron density at the axis nea 1⁄4 2.44 􏰁 1013 cm􏰂3, and r is normalized by R0 1⁄4 26.8 cm. (b) Magnetic field strength B, rB, and r 􏰁 B scale length along the parallel direction at field line w 1⁄4 wðR 1⁄4 2:02R0 ; Z 1⁄4 0Þ.
FIG. 8. (a) Electrostatic potential of the ITG mode in FRC. The circles represent the separatrix. The mode structures of real and imaginary parts (b) along the radial direction at the outer midplane (Z 1⁄4 0) as shown by the black dotted line in (a), and the separatrix radial location is R/R0 1⁄4 1.42, and (c) along the parallel direction [field line with wðR 1⁄4 2:02R0 ; Z 1⁄4 0Þ as shown by the black dashed line in (a)].
􏰁 􏰂2 2􏰀􏰈 Tie2ne0
x􏰈i
􏰂gi niZðniÞ
01⁄4 1􏰂C0 k?qi þ
Te Zi2ni0 􏰏􏰊x􏰈i􏰋 x􏰈i2
x
􏰁 􏰁􏰂1 􏰂 k2?q2i 􏰀C0􏰂k2?q2i 􏰀 þ k2?q2i C1􏰂k2?q2i 􏰀􏰈
1􏰂 niZðniÞþgi ni 1⁄21þniZðniÞ􏰃 xx
Next, in order to compare with theory Eq. (35) in the slab limit, we
carry out simulations in the domain of Fig. 1: Z=R0 2 1⁄2􏰂0:2; 0:2􏰃 and
w ranges from wðR 1⁄4 1:702R0; Z 1⁄4 0Þ to wðR 1⁄4 1:705R0; Z 1⁄4 0Þ,
where the magnetic field variation is small and magnetic drift effect
can be ignored. In the simulation, jTi 1⁄4 1 @Ti jZ1⁄40 1⁄4 5:0; jTe 1⁄4 1 Ti @R Te
@Tej 1⁄40:0; j 1⁄4j 1⁄41@nij 1⁄42:5; g1⁄4j =j 1⁄42:0, @R Z1⁄40 ni ne Ti @R Z1⁄40 i Ti ni
and the parallel vector kjj is fixed: kjjqi 1⁄4 1:08 􏰁 10􏰂2, and the per- pendicular vector is determined by the toroidal component: k? 1⁄4 kf. We first fixed s 1⁄4 Te/Ti 1⁄4 0.35 and scanned k?qi (we use deuterium as ion species in the simulation) by increasing kf; and the simulation results agree well with theory as shown in Figs. 5(a) and 5(b). Then,
􏰂 􏰂1􏰂 3 x􏰈i
􏰐 􏰂2 2􏰀 niZðniÞ C0 k?qi :
scitation.org/journal/php
􏰂 gi 2x
(35)
Phys. Plasmas 26, 042506 (2019); doi: 10.1063/1.5087079 Published under license by AIP Publishing
26, 042506-9