EX/P5-17 1

Evidence for Trapped Electron Mode Turbulence in MST Improved Confinement RFP Plasmas D.L. Brower1, J. Duff2, Z. Williams2, B.E. Chapman2, W.X. Ding1, L. Lin1, E. Parke1, M.J. Pueschel2, J.S. Sarff2, P.W. Terry2

1University of California Los Angeles, Los Angeles, California 90095, USA 2University of Wisconsin-Madison, Madison, Wisconsin 53706, USA e-mail: brower@ucla.edu Abstract: Density fluctuations in the large-density-gradient region of improved confinement MST RFP plasmas exhibit multiple features that are characteristic of the trapped-electron-mode (TEM), strong evidence that drift wave turbulence emerges in RFP plasmas when magnetic transport associated with global tearing instability is reduced. In standard RFP plasmas, core transport is governed by magnetic stochasticity stemming from multiple long-wavelength tearing modes that arise from current profile peaking. Using inductive current profile control, these tearing modes are reduced and global confinement is increased to that expected for a comparable tokamak plasma. The improved confinement is associated with substantial increases in the local density and temperature gradients, and we present evidence for the onset of drift wave instability. These fluctuations have moderate frequencies (50-150 kHz), propagate in the electron diamagnetic drift direction, and normalized perpendicular wavelengths

€

k⊥ρs ≈ 0.2 . The fluctuation amplitude increases with the local density gradient and electron beta, and appear only when the density gradient exceeds a critical threshold value. Gyrokinetic analysis (GENE code) provides supporting evidence for the appearance of microinstability in these plasmas. 1. Introduction Drift wave turbulence underlies key transport phenomena in toroidal, magnetically confined plasmas [1,2]. While long-studied for the tokamak and stellarator configurations, the distinguishing features of the reversed field pinch (RFP) allow further development of gyrokinetic models that build on the RFP’s features of high-beta, large magnetic shear (tending to add stability), and relatively weak toroidal field. Since the RFP is poloidal-field-dominated, the role of ballooning is considerably weaker. Standard RFP behavior tends to be governed by tearing magnetic fluctuations driven by the gradient in the current density. However, tokamak-like improved confinement occurs with application of inductive current profile control, and large-scale electromagnetic fluctuations are largely suppressed [3,4]. In this environment, gyro-scale instabilities are anticipated to be important and could ultimately limit confinement [5,6]. The  role  of  drift  waves  is  rapidly  emerging  for  the  RFP,  and  this  provides   a   complementary   environment   to   other   configurations   for   exploring   basic  understanding   of   turbulence-­‐driven-­‐transport   physics   and   improving confidence in predictive capability for future burning plasmas. Herein  we  describe  detailed measurements of high-frequency density fluctuation spectral features and temporal-spatial dynamics   in  the  MST-­‐RFP.   Comparison   with   modeling   results   from   the   gyrokinetic   GENE   code[7]  provide   evidence   that   these   fluctuations   are   consistent   with   expectations   for   TEM  turbulence   and   may   indeed   be   playing   a   role   in   governing   the   overall   plasma  confinement.    

EX/P5-17 2

Measurements reported here were carried out on the Madison Symmetric Torus (MST) reversed-field pinch [8] with major radius R0=1.5 m, and minor radius a=0.52 m. Results are for low to moderate current (200-400 kA) deuterium plasmas with line-averaged

electron density

€

n e ~1×1019 m−3 , and electron

temperature up to

€

Te ~1.5 keV . Energy confinement comparable with tokamak quality can be achieved in MST at high beta and low toroidal magnetic field. Magnetic fluctuations normally present in the RFP are reduced using inductive pulsed poloidal (or parallel) current drive (PPCD) [3,9]. During PPCD, a programmed ramp of the toroidal field winding current is used to generate poloidal induction targeted to the outer region of the plasma. This results in dramatically improved particle and energy confinement leading to tokamak-like confinement in the reversed-field pinch, i.e., confinement time increases ten-fold (to ∼10 ms), which is comparable to a tokamak plasma having the same plasma current, density, heating power, size and shape [10]. PPCD acts to broaden the current density profile (reducing the gradient) by driving parallel electric field in the plasma

edge which reduces the m=1 tearing modes and suppresses sawteeth. A multi-chord far-infrared (wavelength λ=432 µm) laser-based heterodyne

interferometry system is used to measure both equilibrium and fluctuating electron density [11,12] on MST. The diagnostic consists of 11 vertically-viewing, single-pass chords with separation ~0.08 m, covering nearly the entire plasma cross section. Each chord measures a density induced phase shift according to the relation , where λ is the laser wavelength (432 µm), ne the electron density and dl the path length in the plasma, all in MKS units. From this we see that the line-integrated fluctuating electron density can be written as

. Adjacent

chords are displaced 5 degrees toroidally allowing the toroidal mode number to be determined via use of cross-correlation techniques. The interferometer has bandwidth up to 1 MHz and is sensitive to wavenumbers <1-2 cm-1.

Figure 2. Interferometrically measured electron density fluctuations at r/a~0.86 for standard (black) and improved confinement (red) 200 kA MST plasmas.

 Figure   1.   Evolution   of   density   fluctuation  spectra   (r/a~0.86)   for   improved  confinement  (PPCD)  200  kA  RFP  plasma.    

EX/P5-17 3

2. Experimental Results For improved confinement PPCD plasmas on MST, the measured magnetic fluctuations associated with tearing modes are  reduced by a factor of 2-3. Density fluctuations associated with the tearing modes (<30 kHz) are also greatly suppressed, and a new spectral feature emerges with a broad peak around 50 kHz (laboratory frame of reference), as shown in Fig. 1. The inductive programming is initiated at 10 ms, and the PPCD-enhanced plasma performance from tearing mode suppression begins at ~14 ms and lasts through 24 ms. For these 200 kA plasmas, maximum confinement and plasma pressure occur near the end of the PPCD phase. Spectral changes are more clearly seen in Fig 2, where the density fluctuations

exhibit a large decrease in the tearing mode range as well as for frequencies >70 kHz. However, a distinct spectral feature appears in the region about 40-60 kHz, where the density fluctuation amplitude increases. By examining the cross-phase between two toroidally displaced chords (separation ~15 cm), one can gain information on the mode number of the density fluctuations, as shown in Fig. 3. For fluctuations with frequency ~50 kHz, the toroidal mode number is n~25, which corresponds to normalized wavenumber

€

k⊥ρs ≈ 0.2 . These ion-gyroradius-scale fluctuations propagate in the electron diagmagnetic drift direction (plasma frame). The local Doppler shift is modest and determined from measurements of the plasma flow in the edge region. Line-integrated measurements of the spatial distribution of the density fluctuation amplitude along 11 discrete vertical chords shows a peak in the edge region where the electron density gradient is steepest, as shown in Fig. 4(a). At maximum (end of PPCD), the line-integrated density fluctuation amplitude is 0.018 x1019 m-2, or about 5% when normalized by the local edge density. As the density gradient grows in time from 15 to 20 ms during PPCD, shown in Fig. 4(b), the density fluctuation spectral feature centered at ~50 kHz also appears

Figure 3. Density fluctuation toroidal mode number versus frequency.

Figure 4. (a) Line-integrated density fluctuation (x) and density (red line) profiles, and (b) density gradient temporal evolution for 200 kA PPCD plasma.

EX/P5-17 4

and grows (Fig. 1). A similar high-frequency spectral feature appears during PPCD in higher current 400 kA

plasmas. For the example shown in Fig. 5, at the onset of PPCD (14-15 ms) we observe increased fluctuations at ~100 kHz and this spectral features downshifts to ~50 kHz by the end of the PPCD phase at 19 ms. The toroidal mode number is n~25, similar to the 200 kA case. Density profile measurements indicate that the peak in the density gradient shifts inward from 0.76 to 0.72 r/a, as seen in Fig. 6. This is unlike the 200 kA case where the shape of the density profile is more stationary. Nevertheless, the maximum in the profile of the line-integrated density fluctuation shifts inward, seeming to track the shift in the density gradient as shown in Fig. 7. At t= 14.5 ms (Fig. 7a), the maximum density fluctuation of

0.009x1019 m-2 occurs at the outermost measurement chord at x= 0.43m. Later in the PPCD pulse at t=18 ms (Fig. 7b), the maximum fluctuation 0.0075x1019 m-2 is observed at both the x=0.36 and 0.43 m chords. This strongly suggests the fluctuation amplitude is correlated with the density gradient. Direct evidence of a density-gradient drive for the density fluctuations is provided in Fig. 8. The high-frequency mode is observed only above a critical gradient, R/Ln~15, where

€

Lne = ne ∂ne ∂r( ) is the electron density gradient scale length. Above the critical gradient, the mode amplitude correlates inversely with Ln. The critical-gradient threshold, wavelength, and direction of propagation all point to electron drift wave turbulence that onsets in high-performance PPCD plasmas in MST.

Figure 6. Temporal evolution of electron density gradient during PPCD pulse.

Figure 5. Fig.  1.  Evolution  of  density  fluctuation  spectra   (r/a~0.86)   for   improved   confinement  (PPCD)  400  kA  RFP  plasma.    

EX/P5-17 5

3. Highlights of Gyrokinetic Modeling The gyrokinetic GENE code has been used to study the linear and nonlinear fluctuation characteristics expected for MST discharges with PPCD. Gyrokinetic simulations have shown that modes familiar from tokamaks, TEM, ITG (Ion Temperature Gradient driven) and MTM (microtearing modes), can also be present in RFP plasmas but with modified characteristics [5]. Analysis of the equilibrium for the 200 kA discharge described above is summarized here. Both the TEM and ITG modes can be unstable, depending on the strength of the density gradient. The linear growth rates are shown in Fig. 9. The TEM dominates for equilibria with high R/Ln~30 while the ITG mode dominates for low R/Ln~18. There is no instability in the core region, r/a < 0.75, where the pressure gradient is small. The growth rates peak around kyρs = 0.4 with positive values in the range 0.2 < kyρs < 1.0, where ρs is the ion sound gyroradius. Given that the observed fluctuations propagate in the electron diamagnetic drift direction and have a large gradient-threshold, the instability observed in MST is very likely a density-gradient-driven TEM. The modeling shows that the phase relationship for trapped versus passing particles is consistent with this type of TEM. A somewhat weaker dependence on the ion temperature gradient scale length, LT, is consistent with the 200 kA equilibrium, which has Ln = LT. The growth rate decreases sharply with the ion-to-electron temperature ratio. Nonlinear simulations have also been performed using GENE. The heat flux in the nonlinear simulations is shown in Fig. 10, for varying density gradient (ωn=R/Ln) at r/a=0.86. The

Figure 8. Density fluctuation amplitude dependence on inverse density scalelength.

Figure 7. Line-integrated density fluctuation (x) and density (red line) profiles, at (a) t=14.5 ms and (b) t=18 ms, for 400 kA PPCD plasma.

EX/P5-17 6

linear growth rates are plotted as well for comparison. The electron heat flux dominates the ion heat flux and is almost entirely due to electrostatic fluctuations. There is a clear critical gradient for the onset of the electron heat flux, R/Ln~24, which is roughly 20% larger than for the linear growth rate, R/Ln~20. A nonlinear upshift in the critical density gradient for TEM turbulence has been previously observed in gyrokinetic simulations of tokamak plasmas [13] and interpreted as analogous to the Dimits shift observed in ITG turbulence [14]. As for the Dimits shift, zonal flows play an important

role in the suppression of transport fluxes, and it has been found that both magnetic shear and the electron temperature gradient can affect the characterization of zonal flows in TEM turbulence [15]. While tearing modes are greatly reduced with PPCD, the residual magnetic fluctuations associated with tearing are finite [16]. Such residual magnetic fluctuations have a significant impact on the behavior of the microturbulence by interrupting zonal flows. This is modeled in GENE by including a resonant radial magnetic perturbation within the domain of the simulation. The strength of the perturbation induces a small radial displacement, but it is not sufficient to induce full magnetic stochasticity. The impact of residual magnetic fluctuations on the nonlinearly saturated microturbulence include (1) generation of electromagnetic heat flux, and (2) an increase in the electrostatic heat flux by more than a factor of 10. The time evolution of the transport fluxes

Figure 9. GENE code simulation results showing TEM and ITG turbulence growth rate is positive (unstable) outside the RFP reversal surface, r/a>0.75 in high (~30) R/Ln (blue) and low (~18) R/Ln (red) plasmas.

Figure 10. Linear growth rate (red) and nonlinear electron heat flux (blue) as a function of ωn=R/Ln at r/a=0.8. Straight line fits have been applied to find the critical density gradient. Onset for nonlinear fluxes occurs at R/Ln~24, roughly 20% greater than the linear threshold of R/Ln~20.

EX/P5-17 7

for particles and heat are shown in Fig. 11 for cases with and without the addition of a magnetic perturbation. Heat diffusivities in nonlinear simulations settle to very low values of order χe ~ 10-4 m2/s once zonal flows are established, but the flux is substantially increased to experimentally-relevant values of ~20 m2/s as the zonal flows are weakened by the imposed δbr that approximates residual tearing mode activity. The nonlinear up-shift of the critical gradient is also reduced by the residual magnetic fluctuation. Including the magnetic perturbation increases the thermal transport from negligible levels to values close to what is observed experimentally. If the magnetic perturbations are not included in the nonlinear analysis, the onset for nonlinear fluxes, shown in Fig. 10, increases to R/Ln~80, a factor of ~4

greater than the linear threshold. 4. Summary Measurements of density fluctuations together with gyrokinetic modeling using GENE are consistent with the appearance of density-gradient-driven trapped electron modes in improved-confinement MST plasmas. Measured mode characteristics, including the propagation direction, wavenumber, and critical-gradient onset, are consistent with TEM turbulence. Very strong zonal flows are predicted for TEM turbulence in the RFP, which causes a large nonlinear up-shift in the critical gradient and very low transport

fluxes. However, small magnetic fluctuations imposed in the GENE simulations affect the zonal flows and increase the saturated fluxes to experimental levels. The critical gradient for the nonlinear case with residual magnetic fluctuations is only marginally larger than for linear stability. These gradients are similar in magnitude to that measured in MST. If further reduction in tearing can be affected, the prospect for very low turbulent transport in the RFP is excellent. Acknowledgements Work supported by U.S. DOE, Office of Science, Office of Fusion Energy Sciences under Award Numbers DE-FC02-05ER54814, DE-FG02-85ER53212, and DE-FG02-01ER54615.

Figure 11. GENE calculated particle (blue) and heat (green) transport in plasmas with (solid) and without (dashed) an approximation of the radial magnetic perturbations, δbr, associated with a suppressed global magnetic tearing mode during PPCD.

EX/P5-17 8

References [1] A.J. Wootton, et al., Phys. Fluids B2, 2879(1990). [2] P.C. Liewer, Nuclear Fusion 25, 543(1985). [3] J.S. Sarff, et al., Nuclear Fusion 43,1684-1692 (2003). [4] L. Lin, W.X. Ding, D.L. Brower, Nuclear Fusion 56, 126020(2016). [5] D. Carmody, et al., Phys. Plasmas 22, 012594 (2015). [6] P.W. Terry, D. Carmody, H. Doerk, W. Guttenfelder, D.R. Hatch, C.C. Hegna, A. Ishizawa, F. Jenko, W.M. Nevins, I. Predebon, M.J. Pueschel, J.S. Sarff and G.G. Whelan, Nucl. Fusion 55, 104011 (2015). [7] F. Jenko, W. Dorland, M. Kotschenreuther, and B. N. Rogers, Phys. Plasmas 7, 1904 (2000). [8] R. N. Dexter, D.W. Kerst, T.W. Lovell, S. C. Prager, and J. C. Sprott, Fusion Technol. 19, 131 (1991). [9] J.S. Sarff, et al., Phys. Rev. Lett. 72, 3670 (1994). [10] B.E. Chapman et al, PPCF 52, 124048 (2010). [11] W. X. Ding, L. Lin, J.R. Duff, D. L. Brower, Rev. Sci. Instrum. 85, 11D406(2014). [12] D.L Brower, W.X. Ding, S. D. Terry et al. Rev. Sci. Instrum.74, 1534(2003). [13] D.R. Ernst, P.T. Bonoli, P.J. Catto, W. Dorland, et al., Phys. Plasmas 11, 2637(2004). [14] A. M. Dimits, G. Bateman, M. A. Beer, B. I. Cohen, W. Dorland, G. W. Hammett, C. Kim, J. E. Kinsey, M. Kotschenreuther, A. H. Kritz, L. L. Lao, J. Mandrekas, W. M. Nevins, S. E. Parker, A. J. Redd, D. E. Shumaker, R. Sydora, and J. Weiland, Phys. Plasmas 7, 969 (2000). [15] J. Lang, Y. Chen, and S. E. Parker, Phys. Plasmas 14, 082315 (2007). [16] J. S. Sarff, A. F. Almagri, J. K. Anderson, T. M. Biewer, A. P. Blair, M. Cengher, B. E. Chapman, P. K. Chattopadhyay, D. Craig, D. J. Den Hartog, F. Ebrahimi, G. Fiksel, C. B. Forest, J. A. Goetz, D. Holly, B. Hudson, T. W. Lovell, K. J. McCollam, P. D. Nonn, R. O’Connell, S. P. Oliva, S. C. Prager, J. C. Reardon, M. A. Thomas, M. D. Wyman, D. L. Brower, W. X. Ding, S. D. Terry, M. D. Carter, V. I. Davydenko, A. A. Ivanov, R. W. Harvey, R. I. Pinsker, and C. Xiao, Nuclear Fusion 43, 1684 (2003).