Computer-generated planar holograms are a powerful approach for designing planar lightwave circuits with unique properties. Digital planar holograms in particular can encode any optical transfer function with high customizability and is compatible with semiconductor lithography techniques and nanoimprint lithography. Here, we demonstrate that the integration of multiple holograms on a single device increases the overall spectral range of the spectrometer and offsets any performance decrement resulting from miniaturization. The validation of a high-resolution spectrometer-on-chip based on digital planar holograms shows performance comparable with that of a macrospectrometer. While maintaining the total device footprint below 2 cm 2 , the newly developed spectrometer achieved a spectral resolution of 0.15 nm in the red and near infrared range, over a 148 nm spectral range and 926 channels. This approach lays the groundwork for future on-chip spectroscopy and lab-on-chip sensing.

The turbulent particle flux in tokamaks has an inward component, the pinch flux, which is independent of the density gradient. It is proposed that this flux represents a tendency of the particle distribution to approach turbulent equipartition, which means that the phase space density is constant on hypersurfaces defined by those invariants that are not destroyed by the turbulence. For tokamaks the two first adiabatic invariants give the peaked density profile n∼1/q of trapped particles. Sharp gradients are predicted near the separatrix of divertor plasmas. The physical mechanism of the pinch is as follows. When a parcel of trapped particles is displaced inward by the turbulent fluctuations, their parallel velocity must increase in order to keep the longitudinal invariant J constant. This is equivalent to adiabatic compression, and increases the density. The turbulence is assumed to be caused by thermally driven electrostatic modes.

In general, turbulent transport drives a plasma toward a state of turbulent equipartition, in which Lagrangian invariants are uniformly distributed. Different invariants decay with different rates, and in tokamaks the frozen-in law of particles in the poloidal magnetic field survives longer than the corresponding law for the toroidal field, assuming that the trapped particles dominate the turbulent transport. Therefore, the plasma profiles depend on the safety factor q(r), and the condition for convection of trapped particles is that the shear dq/dr is positive. There are two ways to suppress this convection and thereby enhance confinement. The first one is to reverse the magnetic shear. The energy of typical trapped particles then increases outward instead of inward, which suppresses instabilities. The second method is to eliminate the trapped ions by poloidal rotation, and thereby create a transport barrier.

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