Page 5 - Suppressed ion-scale turbulence in a hot high-β plasma
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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13860
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tokamaks, with predominant toroidal magnetic field, the GTC code has been adapted to the FRC geometry with purely poloidal magnetic field, using Boozer coordinates36 and a reformulated Poisson solver. FRC plasma equilibria produced with the LamyRidge code24 are first transformed from cylindrical coordinates to magnetic flux coordinates and further to Boozer coordinates. The modified GTC code has been extensively tested for convergence, as described in detail elsewhere20. Linear growth rate calculations based on local (flux tube) simulations (krooky) are reported here. In these calculations, modes that may exist very close to the null field radius R are neglected due to difficulties simulating the region of vanishing magnetic field. We note also that in the present study our local simulations separate the FRC Core and SOL plasma domains. The potential coupling between these domains will be investigated in future work.
It is important to point out that FLR effects, important due to the high bulk ion temperature, are retained in the gyrokinetic approximation via toroidal gyro-averaging. Gyro-particles sampling different locations within the gyro-ring are implemen- ted via Bessel functions J0(kyri) where ri 1⁄4 mini>/eB signifies the gyro-particle gyroradius at the instantaneous perpendicular velocity ni>. For the local simulations described here, no radial gyro-averaging is performed as kr ky. It is well known that the parameter r* (the ratio of the ion gyroradius to the characteristic radial system dimension) is important for the transport scaling obtained with nonlinear gyrokinetic simulations in toroidal devices37–39. In particular, Bohm-like transport scaling has been obtained with global simulations for small system sizes (large r*), in contrast to the gyro-Bohm scaling obtained via local (flux tube) simulations. The results discussed here are obtained via linear, local simulations, carried out for fixed radial plasma parameter profiles. As such they represent an upper limit of the instability growth rate. When profile relaxation is not included, growth rates calculated via linear gyrokinetic simulations have been observed to be much less sensitive to radial system size39 and r*. Once nonlinear simulations become available, possible scaling differences between local and global gyrokinetic simulations in FRC geometry, characterized by relatively large r*, will need to be investigated, and results will be compared to fully kinetic calculations.
GTC linear stability calculations for the FRC core have been carried out for toroidal wavenumbers kyrer0.3. The most important result of these calculations is that no unstable low frequency drift modes (oooci) have been detected for realistic normalized density and ion/electron temperature gradients (here oci is the ion cyclotron frequency). In addition, GTC calculations have also confirmed that interchange modes (k|| 1⁄4 0) are stable. Therefore, in agreement with experimental data, no unstable ion modes are revealed in the FRC core. Core stability is attributed to FLR effects, the radial gradient in the magnetic field (rB directed oppositely to rp), and the short field-line connection length (short-circuit effect). The latter effect restricts the k|| spectrum such that even the lowest parallel wavenumbers in the drift wave spectrum are subject to electron Landau damping. To confirm the role of this effect, calculations have been carried out for an artificially elongated FRC configuration, and instability has been recovered for elongation factors above five. In addition, further efforts are presently under way to resolve the electron mode physics at high normalized wavenumber, and to assess the stability of high frequency, short scale modes up to the Lower Hybrid frequency range.
Extensive GTC linear stability calculations have also been carried out for the FRC SOL. The parameters used in the SOL simulation are R1⁄40.27m, Rs1⁄40.38m, ne1⁄42 1019m 3, Ti 1⁄4 200 eV, Ti/Te 1⁄4 5. Zeff 1⁄4 1.5 is used for the effective charge state, as indicated experimentally via visible Bremsstrahlung
–4 –2 0 2 4 ∆t (ms)
Figure 5 | Radial propagation delay of turbulent structures in the scrape-off layer. The correlation delay of turbulent density fluctuations between two radially spaced Doppler backscattering probing locations28–31 is measured. The statistical distribution of the radial correlation delay of density fluctuations in the scape-off layer (SOL) is depicted. Positive correlation delay corresponds to a radial outward propagation of turbulent structures. The statistically averaged correlation delay DtB1 ms indicates an average radial velocity of turbulent structures ntrB1 1.5 104 m s 1. Shot numbers for the data are indicated. The error bar represents the typical standard deviation (s.d.) of the measurements.
mode turbulence. In contrast, the FRC SOL spectrum measured here via DBS shows substantial fluctuation levels at higher kyrs, illustrating that fluctuations with sub-ion-Larmor-radius scales are important also outside the FRC separatrix. Notably, the core and SOL spectra roughly overlap at high kyreZ0.17 and both decay roughly exponentially.
Figure 4b shows the same data plotted versus the toroidal wavenumber normalized by the ion sound gyro-radius. Marked differences between the SOL and FRC core spectra are now obvious at high normalized wavenumber. This discrepancy may indicate that, as expected, electron-range modes and electron- range physics dominate at high toroidal wavenumber both in the FRC core and in the SOL.
We have examined the radial cross-correlation of SOL density fluctuations/turbulent structures to confirm that the observed SOL turbulence is indeed responsible for radial plasma transport. Figure 5 shows the probability distribution of the radial correlation delay, obtained from a pair of DBS channels probing two closely spaced radii (the channel spacing varies from DrB1.5 cm early in the discharge to DrB1 cm at later times). Data from nine FRC shots with similar parameters and similarly well-centred plasma have been averaged. Outward propagation of turbulent structures is clearly observed, with an average propagation delay of DtB1 ms, and provides strong evidence for fluctuation-driven convective radial particle/energy transport. The average radial propagation velocity of turbulent structures can be estimated as ntrBDr/DtB1–1.5 104 m s 1. The peak in the correlation delay around Dt 1⁄4 0 is related to macroscopic plasma movement or ‘wobble’ due to residual large-scale n 1⁄4 1 MHD mode activity.
Gyrokinetic stability analysis. FRC plasmas present a consider- able challenge for microstability analysis due to the large ion Larmor radii and high b. In particular, rigorous stability calculations for the FRC core plasma would require a fully kinetic approach, as bulk thermal ion gyroradii are comparable to the local temperature and density gradient lengths. Modelling efforts using a fully kinetic code are presently underway. As an initial step, the linear instability growth rate of modes driven by the radial density gradient and electron/ion temperature gradients have been calculated with the Gyrokinetic Toroidal Code34,35 (GTC). Originally designed to investigate and predict turbulence properties and radial thermal/particle transport fluxes in
NATURE COMMUNICATIONS | 7:13860 | DOI: 10.1038/ncomms13860 | www.nature.com/naturecommunications 5
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