Page 7 - Suppressed ion-scale turbulence in a hot high-β plasma

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13860
ARTICLE
a4
3
2
1
0 b 20
10
0
0.06 0.57
SOL R/Ln= 6.7
k s = 4.1
a 0.6 0.4
ne (1019 m–3) 2.3
1.9 1.5 1.1 0.7
R 0.4 Rs 0
r/Rs=1.1 r/Rs=0.9
r/Rs=1.1 r/Rs=0.9
f
r (cm) ExB, D (106 rad/s) R/Ln ñ/n (au) r (m)
R/cs, veiR/cs R/cs
w/ coll. wo/ coll. VeiR/cs
b
c
d
0.2 0 0.2
0.4
0.6
0.14 0.07 0
6 4 2
1.0
0.5
0
1.42 2.85 Vei*
5.70
Figure 8 | Effect of scrape-off layer collisionality on stability. The effect of including finite collisionality in the SOL linear growth rate calculations is demonstrated in this figure, for a sample toroidal wavenumber kyrs 1⁄4 4.1. The normalized electron collisionality is defined as n 1⁄4 n =ðvth=2L Þ,
R/Ln crit
ei ei e c where nei is the electron-ion collision rate, and Lc is the distance from the
midplane to the axial boundary in the scrape-off layer (fieldline
length 1⁄4 2Lc). Other simulation parameters are as stated above.
(a) normalized linear growth rate versus collisionality in comparison to the collisionless case; (b) normalized frequency as a function of collisionality. Collisions are seen to have a stabilizing effect and reduce the normalized growth rate substantially. The frequency of the mode investigated here is also greatly reduced with increasing electron-ion collision rate.
3.0 1.5 0
(cm) r
the linear growth rate spectrum. The accessible wavenumber range in the measured saturated SOL density fluctuation spectrum (Fig. 4b) however clearly points towards an instability source at low toroidal wavenumber, in the range where the calculated linear growth rate spectrum is peaked.
Critical SOL density gradient. We now examine the interaction of the plasma density gradient and the turbulence dynamics in more detail. Figure 9a shows a contour/cross-sectional plot of the plasma density evolution during a C-2 discharge (#36691). The null-field radius R (corresponding to the radius of highest plasma density) and the FRC excluded flux radius Rs are indicated by dashed lines. The evolution of the measured rms density fluctuation level n˜/n is given in Fig. 9b both for the SOL and for the FRC core plasma. The value of n˜/n is relatively low for 0.2msoto0.4ms after the initial high turbulence period likely related to FRC translation and merging. The normalized radial density gradient (Fig. 9c) increases substantially during the first 1 ms, in particular in the SOL. We attribute this effect to parallel loss that dissipates/evacuates the SOL plasma produced during FRC formation and merging. The characteristic parallel loss time t8, for the case of collisionless ions can be estimated via the pitch angle scattering time t8 into the mirror loss cone t8 1⁄4 t8log10(Lm) (ref. 42), where Lm is the primary mirror ratio. This estimate is expected to hold when the pitch angle scattering time of mirror-trapped ions exceeds the collisional parallel mirror confinement time43 t8c 1⁄4 LSOLLm/2(0.3cs)B0.5 ms. Here, LSOL is the distance from the FRC midplane to the axial endplates. For typical SOL parameters in C-2, t8Bt8c. The observed depletion timescale of the SOL plasma (B0.7 ms) is comparable to t8c and t8. At higher ion temperature the pitch angle scattering time is expected to set the parallel loss time. Within the available measurement resolution, the radial ion and electron temperature gradients are not observed to change substantially as the density gradient evolves and steepens. The electron temperature gradient scale length LTe (from Thomson scattering) is similar to Ln after 1.2 ms within diagnostic uncertainty.
1.5 1.0 0.5
0 0
–10 0 10 r-Rs (cm)
NATURE COMMUNICATIONS | 7:13860 | DOI: 10.1038/ncomms13860 | www.nature.com/naturecommunications 7
e –0.5
0.5
1.0
1.5 Time (ms)
2.0 2.5
Figure 9 | Evolution of plasma density fluctuation level and E B shearing rate. (a) Time evolution of the plasma density profile shown as a contour plot. The null-field radius R (corresponding to the radius of highest plasma density) and the field reversed configuration (FRC) excluded flux radius Rs are indicated by dashed lines. (b) density fluctuation level n˜/n in the scrape-off layer (SOL) and in the closed flux surface region inside the field reversed configuration (FRC) separatrix. (c) normalized radial density gradient in the SOL and inside the separatrix. (d) E B shearing rate oE B and turbulence decorrelation rate oD in the SOL. The E B shearing rate is shown to exceed the turbulence decorrelation rate after tB1 ms; this condition is a prerequisite for the sheared flow to substantially reduce turbulence. (e) the time evolution of the radial turbulence correlation length in the shear flow region several centimeters outside the separatrix shows a gradual reduction indicating reduced radial extent of turbulent structures/ eddies. (f) insert: radial profile of the radial turbulence (density fluctuation) correlation length, averaged from 1.2 to 2 ms. A dip in the correlation length just outside the FRC separatrix is indicative of the formation of a radial transport barrier. The error bars in Fig. 9 (e) and (f) represent the standard deviation (s.d.) of the measurements.
As shown in more detail in Fig. 9c, the initial increase in SOL fluctuation level for t 40.4ms occurs as the density gradient exceeds a critical level or instability threshold44,45. The density gradient then relaxes somewhat during the remainder of the discharge but remains higher than the initial critical value. The SOL fluctuation level also decreases and returns to levels slightly above the early minimum.
We explain this behaviour by an upshift of the critical gradient in the presence of sheared E B rotation analogous to