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Radial basis functions are typically used when discretization sche-mes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in solving many types of differential equations. However, the weights of the interpolated solution, used in the linear superposition of basis functions to interpolate the solution, and the actual value of the solution are completely different. In fact, these weights mix the value of the solution with the geometrical location of the nodes used to discretize the equation. In this paper, we used nodal radial basis functions, which are interpolants of the impulse function at each node inside the domain. This transformation allows to solve a linear hyperbolic partial differential equation using series expansion rather than the explicit computation of a matrix inverse. This transformation effectively yields an implicit solver which only requires the multiplication of vectors with matrices. Because the solver requires neither matrix inverse nor matrix-matrix products, this approach is numerically more stable and reduces the error by at least two orders of magnitude, compared to other solvers using radial basis functions directly. Further, boundary conditions are integrated directly inside the solver, at no extra cost. The method is naturally conservative, keeping the error virtually constant throughout the computation.

This paper shows analytically and numerically that a vortex plate coupled to a neutral density filter can deliver a true optical derivative when placed at the focal plane of a $2f$ lens pair. This technique turns spatial variations in intensity into an intensity, which square root is the spatial derivative of the initial intensity variation. More surprisingly, it also turns any spatial variations in phase into an intensity, which square root is the spatial derivative of the initial phase variation. Since the optical derivative drops the DC component of the signal, it is possible to measure the full electron plasma turbulence spectrum optically, without using any interferometer.

Intense magnetic fields modify the properties of extremely dense matter via complex processes that call for precise measurements in very harsh conditions. This endeavor becomes even more challenging because the generation of mega-gauss fields in a laboratory is far from trivial. This paper presents a unique and compact approach to generate fields above 2 mega-gauss in less than 150 ns, inside a volume close to half a cubic centimeter. Magnetic insulation, keeping plasma ablation close to the wire surface, and mechanical inertia, limiting coil motion throughout the current discharge, enable the generation of intense magnetic fields where the shape of the conductor controls the field topology with exquisite precision and versatility, limiting the need for mapping exactly magnetic fields.

A robust and portable power supply has been developed specifically for charging linear transformer drivers, a modern incarnation of fast pulsed power generators. It is capable of generator +100 kV and -100 kV at 1 mA, while withstanding the large voltage spikes generated when the pulsed-power generator is triggered. The three-stage design combines a zero-voltage switching circuit, a step-up transformer using ferrite cores, and a dual Cockcroft-Walton voltage multiplier. The zero-voltage switching circuit drives the primary of the transformer in parallel with a capacitor. With this driver, the tank circuit naturally remain in its resonant state, allowing for maximum energy coupling between the zero-voltage switching circuit and the Cockcroft-Walton voltage multiplier across a wide range of loading conditions.

The plasma beta, ratio of kinetic to magnetic pressure, inside a tokamak should stay below the Troyon limit to avoid major plasma instabilities. However, this paper argues that Troyon limit occurs only when current profiles cannot sustain high beta equilibria. This paper shows that plasmas with peak beta on the order of unity are stable to ideal MHD modes. While the theoretical (ideal-MHD) stability of unity beta equilibrium has been resolved, the experimental existence of high beta equilibria in tokamaks remains an unsolved problem of plasma physics.

The Hall term has often been neglected in MHD codes as it is difficult to compute. Nevertheless setting it aside for numerical reasons led to ignoring it altogether. This is especially problematic when dealing with tokamak physics as the Hall term cannot be neglected as this paper shows.

Linear transformer drivers (LTD) allow to greatly reduce the size of pulsed-power drivers while increasing their efficiency and repetition rate. However, limitations on the capacitors voltage and current exist, mostly driven by technological imperatives. As a result, LTD required to be connected in series and in parallel to form a practical pulsed-power generator. The High Amperage Driver for Extreme States (HADES) proposed here can generate 250 GW of power, i.e. a 1 MA on current with a rise time of 150 ns into a 20nH load. The key feature of the driver is its size. The machine footprint is less than 5m2 and its height is less than 1.6m. This reduction in footprint, compared to other 1 MA LTD based-systems, comes from a compact transmission line geometry which allow to connect LTDs is series and in parallel efficiently. This paper summarizes this design and describes HADES operation and maintenance.