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Using radiofrequency (rf) for heating and levitation of alloy samples is greatly simplified by a passive element, the slotted cold crucible (similar to Faraday shield for rf plasma ion sources), which if properly designed can shape and concentrate the axial (non static) magnetic field profile. The effect is better represented and verified in 3D simulations (very time consuming) as shown here, even if some simplified 1D and 2D models may help understanding. Boundary conditions at large radius are discussed. Moreover, the sensitivity to important parameters (levitated weight vs frequency and power, sizes of crucible, sample conductivity, radius of sample to skin depth ratio) are demonstrated in a schematized 3D geometry, easily parametrized. Finally complete 3D simulation of a realistic design (adequate for clean alloy melting) are also reported.

A magnetized plasma strongly interacts with microwaves, when their angular frequency $\omega$ is around the electron cyclotron resonance (ECR) one, that is $\Omega=e\vert \mathrm{B}^{s}\vert /m_{e}$ , with $\mathrm{B}^{s}$ the static flux density. The case of small ion sources with $\mathrm{B}^{s}\cong 0.5$ to 1 T, where wavelength and plasma chamber radius are comparable, is studied with full wave equations, assuming a collision rate $v$ and a plasma of given density. Wave initially launched in the TE mode from a waveguide (TE 11 for a circular waveguide), aligned with the axis $z$ of a cylindrical plasma chamber and of $\mathrm{B}^{s}$ , are partially converted to $E_{z}$ waves; use of azimuthal symmetry to consider only the $m=1$ component is discussed. Large reflections are sometimes observed as a function of ratio of plasma angular frequency $\omega_{p}(z)$ and $\omega$ , possibly due to model simplification (density constant in $x$ and $y$ ). Extension to off-axis waveguides (perhaps rectangular or coaxial) is mentioned.

In the vast literature on waves and plasma interaction, the skin depth, the stochastic heating and the radiofrequency (rf) magnetic field effects emerge as important factors in simulations, still relying on effective collision rate models: a closed form and universal graph are given for stochastic heating. A simulation code based on iteration between plasma and rf calculations is recalled, and typical results are shown, for a simple induction ion source design.

Powerful radiofrequency (rf) and microwave generator are of widespread in particle accelerators and sources, for the lower voltages required by rf accelerators as compared to electrostatic ones (which have a better power efficiency). Large accelerator projects request efficiency optimization, especially promising in the case of klystrons, where efficiency is determined by the intermediate cavity tunings, and for large tube ratings (multiMW), by the self electrostatic potential of the electron beam itself. Tubes with many electron beamlets are an option to mitigate this effect. Also modern developments in computational physics offer the possibility to study and improve the klystron bunching mechanism more directly, and general features and trends are discussed. The gyrotron and applications to ion sources are also summarized.