Page 9 - Suppressed ion-scale turbulence in a hot high-β plasma

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13860
ARTICLE
the short field line connection length contribute to stability. Due to the short connection length, drift wave parallel wavenumbers are constrained to k840.02 cm 1, and the corresponding mode spectrum is subject to electron Landau damping. In addition, low ky interchange modes (k8 1⁄4 0) are also found to be stable in the FRC core. These findings may have general implications for ion and electron thermal confinement in hot ion, high beta plasmas, including collisionless astrophysical plasmas.
Low levels of ion-scale turbulence have also been observed
in high confinement mode (H-mode) plasmas in spherical
49
tokamaks and in certain H-mode plasmas in larger aspect
ratio devices. However, in tokamaks the observed reduction in
ion-scale core turbulence results from strong shear in the toroidal
radial thermal and particle loss from the confined FRC region, and hence advancing towards long-pulse FRC operation with reduced fuelling and auxiliary heating/current drive sustainment requirements.
Methods
The C-2 field-reversed configuration. The C-2 FRC plasma is created via injecting and merging of two preformed, compact high-b plasmoids into a central confinement chamber with radius R 1⁄4 0.7 m and length L 1⁄4 4.5 m (Fig. 1a),
with an external solenoidal magnetic field Be 1⁄4 0.05–0.14 T, as described in detail elsewhere17,18,23. The injected plasmoids are produced in the formation sections (Fig. 1a) with an ion temperature of 25–50 eV before merging, and are accelerated to high axial (parallel) velocity. The axial plasmoid velocity at the transition from the formation sections to the central confinement chamber isB2.5 105 m s 1, corresponding to a (directional) parallel energy of B1 keV that is transformed into thermal energy upon merging, likely via shock heating. Typical line-averaged deuterium plasma densities of the merged FRC plasma in the experiments described here are 2–4 1019 m 3, and the ion and electron temperatures in the FRC core are TiB400–600 eV and TeB80–130 eV. Toroidally injected neutral beams (hydrogen, beam voltage VB 1⁄4 20 kV and total beam power, PBB4 MW) are applied to heat and sustain the FRC plasma and to extend the FRC pulse length toB5 ms. The absorbed neutral beam power is 2.3–2.7 MW throughout the first 2 ms of the discharge and slowly declines afterwards as the FRC gradually contracts and NBI shine-through increases. As Ti4Te, NBI beams predominantly heat electrons (via collisional exchange) and electron thermal transport dominates the beam power absorption. Fast ion lifetimes are consistent with classical slowing- down via Coulomb collisions18. With high neutral beam power deposition
(Pabs 1⁄4 2.5 MW) the global FRC energy confinement time is doubled compared to no-beam reference cases18. The (closed flux surface) FRC plasma in C-2 is surrounded by an (open fieldline) mirror-confined SOL plasma with primary mirror ratio LmB3. In addition to the primary mirror, secondary mirror plugs are installed (shown in Fig. 1) with a mirror ratio Lp 1⁄4 7–10. The SOL plasma is terminated axially on (floating or biased) metallic electrodes located in divertor chambers at a distance of 8.8 m from the machine axial midplane. In the SOL the thermal ion Larmor radius, averaged along the field line length, is riB2–3 cm. Closer to the null field radius in the FRC core the thermal ion Larmor radius is substantially larger and can reach riZ10 cm. The electron Larmor radius is almost always much smaller than the radial temperature/density scale lengths (reB2 10 2–10 1cm).
Plasma guns. Annular washer plasma guns25 (inner diameter 0.11 m, outer diameter 0.13 m, located on axis in the divertor chambers as indicated in Fig. 1a) are used to produce a warm plasma with TeB30 eV, TiB100 eV in the divertor. The local magnetic field at the gun location is B0.5 T, produced by an internal solenoid integrated with the plasma gun assembly. The washer guns have anode- cathode voltages ofB0.5–1.0 kV, with typical discharge current B10 kA. The plasma guns are electrically floating with respect to the vacuum chamber, producing a negative (inwards pointing) radial electric field transmitted to the SOL region just outside the FRC separatrix26,27. In a different biasing approach applied more recently, the co-axial endplate inside the gun annular anode is biased negatively at 0.5–1.0 kV with respect to the innermost annular divertor biasing electrode, with an arc discharge initiated simultaneously between the plasma gun cathode and anode.
Additional details on diagnostics. A six-channel Doppler Backscattering (DBS)28,29 system is used for measurements of the density fluctuation level, and of the toroidal E B velocity (Fig. 2a,b). Six collinear microwave beams, at tunable frequencies 26 GHzofo65 GHz, are launched via two lensed horn antennas and quasi-optically transmitted to the plasma at an oblique angle z in the toroidal plane30. A polarizer/beam combiner and an adjustable parabolic mirror are used to combine the different frequency bands and focus the combined Gaussian beams into the plasma. Frequencies in the range 26–40 GHz are launched in X-mode polarization, and frequencies above 40 GHz are launched in O-mode polarization. The backscattered radiation is detected via the same horn antennas (monostatic beam optics), at an oblique angle in the toroidal plane. Figure 2a,b illustrate the beam path and scattering geometry for one frequency. The rms density fluctuation level (0.5rkyrsr40), toroidal E B velocity and turbulence decorrelation rate near the FRC midplane are evaluated from the intensity and Doppler shift of the backscattered signals.
Backscattering by plasma density fluctuations occurs preferentially near the plasma cutoff layer28, according to the selection rules kS 1⁄4 kI 1⁄4 ky/2 and
oS 1⁄4 oI ntky, where the indices I and S denote the incident and backscattered wave, nt 1⁄4 nE B þ nph is the toroidal turbulence advection velocity (vph is the turbulence phase velocity in the plasma frame and can be neglected here), and ky is the probed resonant density fluctuation toroidal wavenumber. Variation of the toroidal launch angle allows acquiring the density fluctuation level versus toroidal wavenumber. The toroidal wavenumber resolution is primarily determined by the toroidal plasma curvature and the width of the Gaussian probing beams52. The
rotation, leading to long-wavelength turbulence quench via E B 48
shear, in combination with magnetic shear . In contrast, there is only weak E B flow shear in the FRC core in our experiment, and the observed absence of ion-scale turbulence is due to effects directly suppressing linear instability growth as discussed above.
There is another important difference between FRCs and tokamak plasmas with respect to the minimum achievable ion thermal transport. In tokamaks, due to toroidicity, neoclassical ion transport is the irreducible minimum. At the same magnetic field and collisionality, neoclassical transport still substantially exceeds classical transport. FRCs, on the other hand, potentially can achieve classical ion transport due to axisymmetry.
FRC instability and transport physics is substantially different from tokamaks, and global FRC energy confinement in the presence of classical ion transport is determined by the electron channel, opening the prospect of radically different FRC electron thermal confinement scaling compared to conven- tional tokamaks. The electron energy confinement scaling observed in the MAST and NSTX spherical tokamaks, however, has already shown a favourable scaling with decreasing collision- ality49–51. The confinement time varies approximately inversely with the normalized electron collisionality which scales as 1/T2e.
Ion and electron-scale turbulence with higher density
fluctuation levels is observed experimentally in the SOL region
just outside the FRC separatrix, where an exponential wave-
number spectrum is measured. Linear gyrokinetic simulations
show unstable SOL modes in the wavenumber range
1.5rkyrsr20 propagating in the electron diamagnetic direction,
with frequencies well above the ion and electron transit
frequencies, and below the ion diamagnetic frequency.
Benchmarking calculations demonstrate directly the stabilizing
effects of both finite Larmor radius (FLR) and the magnetic field
gradient for the SOL modes, with FLR effects reducing the growth
rate by more than one order of magnitude. Collisions are also
found to reduce the linear instability growth rate substantially in
the SOL. Experimentally, the SOL turbulence amplitude increases
nonlinearly at a critical density gradient R/L B4, somewhat n
above the linear instability threshold as calculated from linear gyrokinetic simulations. The critical gradient is sufficiently large so that the SOL in a reactor-relevant FRC plasma would remain reasonably narrow and not unduly increase the required device radius.
For the first time to the best of our knowledge, evidence for sustained turbulence reduction/gradient control via E B flow shear has been found in FRC geometry. In contrast to tokamak edge and core transport barriers, the FRC transport barrier is localized just outside the separatrix on open magnetic field lines, which terminate in the divertor and are actively biased in a controlled fashion. The prospect of active control of turbulence and radial transport across the FRC separatrix, via manipulating the E B shear by electrostatic biasing in the divertor far away from the hot core plasma, opens up the possibility of reducing
NATURE COMMUNICATIONS | 7:13860 | DOI: 10.1038/ncomms13860 | www.nature.com/naturecommunications 9