Page 8 - Suppressed ion-scale turbulence in a hot high-β plasma

ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13860
the upshift in ion temperature gradient observed in gyrokinetic simulations of tokamak plasmas46. It is well known from tokamak experiments as well as linear plasma devices that sheared E B flow strongly affects the growth and radial correlation of turbulent eddies, if the E B shearing rate exceeds the ambient turbulence decorrelation rate, as discussed in detail elsewhere47. Figure 9d shows the evolution of the E B shearing rate, determined via DBS from two radially adjacent probing radii, according to oE B 1⁄4 1⁄2vE Bðr2Þ vE Bðr1Þ =ðr2 r1Þ together with the turbulence decorrelation rate oD. The decorrelation rate clearly exceeds the flow shearing rate initially, so that the E B shear cannot quench or reduce the turbulence via eddy shearing/decorrelation47. Later in the discharge, at tB1ms, the E B shear due to plasma gun biasing26,27 increases significantly. The shearing rate transiently exceeds the turbulence decorrelation rate oD and then remains close to oD. Further evidence for the effect of E B shear is provided by a decrease in the radial turbulence correlation length lr (Fig. 9e), which decreases steadily throughout the discharge. A radial profile of lr shows a distinct dip just outside the separatrix at the location of maximum shear (see insert, Fig. 9f). This is the first observation of a radial transport barrier in an FRC (with entirely different magnetic geometry compared to a tokamak) formed at/outside the separatrix on open field lines. In contrast, tokamak transport barriers form inside the separatrix in the closed flux surface region48.
To elucidate the role of the critical density gradient, Fig. 10a shows a plot of the measured fluctuation level versus the local density gradient. Well into the FRC core (r/Rs 1⁄4 0.85), the density gradient remains moderate (R/Lnr3.1), fluctuation levels are very low and no nonlinear increase of n˜/n with gradient has been observed. Just inside the separatrix (r/Rs 1⁄4 0.95), a critical gradient around R/LnB3.5 is found experimentally. In the SOL, a pronounced critical gradient R/LcnritB3.8–4 is measured during the early discharge phase (to0.6 ms). For the SOL the linear GTC simulation yields a linear threshold R/LnB2.7 (Fig. 10b) for toroidal wavenumbers 2.7rkyrso4.2 within the most unstable part of the growth rate spectrum. The measured SOL critical gradient is somewhat higher than the calculated linear threshold, as expected if local flow shear resulting from the equilibrium radial electric field or from zonal flow components effectively upshifts the nonlinear critical gradient. This effect is typically observed in nonlinear gyrokinetic simulations45,46. A lower linear threshold is found here for high toroidal wavenumber; however, the energy density in the higher-k part of the spectrum is substantially lower, and the associated radial transport rates are expected to be low. Importantly, a further upshift of the measured SOL density gradient is clearly detected experimentally for t 41.2ms when the E B shear is fully developed (Fig. 9c). A moderately large SOL critical gradient, as measured here, is favourable for achieving a sufficiently narrow SOL for reactor-like FRC parameters. This is significant, as a narrow SOL minimizes the required device radius and is advantageous for achieving a compact fusion core. The increased parallel heat flux in a narrow SOL can be exhausted in an axisymmetric FRC via radial magnetic flux expansion, and the heat load to plasma facing components can be kept within safe limits. In contrast, the flux expansion in tokamak poloidal divertors is geometrically limited, and a narrow SOL is problematic as it increases the divertor peak heat load.
Discussion
In conclusion, we have presented experimental evidence that ion- scale fluctuations with toroidal scale length on the order of or larger than the ion gyroradius are stable in the core of a large FRC
a
R/Cs ñ/n
8 NATURE COMMUNICATIONS | 7:13860 | DOI: 10.1038/ncomms13860 | www.nature.com/naturecommunications
0
b 1.6
1.2
2
34 R/Ln
0.04
0.02
r/Rs ~ 1.15 r/Rs = 0.95
r/Rs ~ 0.85 kθρs ~ 5–20
(SOL) (Core)
k s= k s= 2.67 k s= 4.16 k s= 8.05
1.37
i= e=1 0.8
0.4
0
Figure 10 | Density fluctuation level and calculated instability growth rate versus normalized density gradient. (a) Measured fluctuation level n˜/n versus the normalized density gradient in the field-reversed configuration (FRC) core (in red), near the separatrix (r/RsB0.95, orange), and in the scrape-off layer (SOL), (r/RsB1.15, green); the data sets taken near the separatrix and in the SOL show a clear increase at a critical density gradient. (b) calculated linear growth rate from the Gyrokinetic Toroidal Code (GTC) versus normalized density gradient R/Ln in the SOL (r/Rs 1⁄4 1.2, Z 1⁄4 1), for different normalized toroidal wavenumbers as indicated in the figure. Characteristic perpendicular fluctuation scale lengths observed in the C-2 FRC are in between the ion and electron Larmor radii, corresponding to the electron mode regime. The linear instability threshold for kyrs 1⁄4 1.37 and kyrs 1⁄4 2.67 is similar to the (nonlinear) critical gradient observed in the fluctuation level measurements.
configuration. The observed ion-scale drift-wave/interchange stability is a new discovery that is expected to hold generically in FRCs, independently of the specific C-2 machine parameters explored here. This result is highly encouraging because both ion and electron thermal transport are most strongly driven by low-k (ion-scale) fluctuations.
Only weak unstable electron-mode fluctuations with toroidal scale lengths smaller than the ion gyroradius are observed in the C-2 FRC core plasma, leading to an inverted toroidal wavenumber spectrum for kyrsr7. The observed absence of low-k fluctuations is ascribed to Finite Larmor radius effects due to the large bulk ion orbits in the FRC core. In addition, the radially increasing magnetic field (with rB opposing rp), and
0246 R/Ln
R/Ln crit
R/Ln crit SOL