The TCV tokamak is augmenting its unique historical capabilities (strong shaping, strong electron heating) with ion heating, additional electron heating compatible with high densities, and variable divertor geometry, in a multifaceted upgrade program designed to broaden its operational range without sacrificing its fundamental flexibility. The TCV program is rooted in a three-pronged approach aimed at ITER support, explorations towards DEMO, and fundamental research. A 1 MW, tangential neutral beam injector (NBI) was recently installed and promptly extended the TCV parameter range, with record ion temperatures and toroidal rotation velocities and measurable neutral-beam current drive. ITER-relevant scenario development has received particular attention, with strategies aimed at maximizing performance through optimized discharge trajectories to avoid MHD instabilities, such as peeling-ballooning and neoclassical tearing modes. Experiments on exhaust physics have focused particularly on detachment, a necessary step to a DEMO reactor, in a comprehensive set of conventional and advanced divertor concepts. The specific theoretical prediction of an enhanced radiation region between the two X-points in the low-field-side snowflake-minus configuration was experimentally confirmed. Fundamental investigations of the power decay length in the scrape-off layer (SOL) are progressing rapidly, again in widely varying configurations and in both D and He plasmas; in particular, the double decay length in L-mode limited plasmas was found to be replaced by a single length at high SOL resistivity. Experiments on disruption mitigation by massive gas injection and electron-cyclotron resonance heating (ECRH) have begun in earnest, in parallel with studies of runaway electron generation and control, in both stable and disruptive conditions; a quiescent runaway beam carrying the entire electrical current appears to develop in some cases. Developments in plasma control have benefited from progress in individual controller design and have evolved steadily towards controller integration, mostly within an environment supervised by a tokamak profile control simulator. TCV has demonstrated effective wall conditioning with ECRH in He in support of the preparations for JT-60SA operation.

Integrating the plasma core performance with an edge and scrape-off layer (SOL) that leads to tolerable heat and particle loads on the wall is a major challenge. The new European medium size tokamak task force (EU-MST) coordinates research on ASDEX Upgrade (AUG), MAST and TCV. This multi-machine approach within EU-MST, covering a wide parameter range, is instrumental to progress in the field, as ITER and DEMO core/pedestal and SOL parameters are not achievable simultaneously in present day devices. A two prong approach is adopted. On the one hand, scenarios with tolerable transient heat and particle loads, including active edge localised mode (ELM) control are developed. On the other hand, divertor solutions including advanced magnetic configurations are studied. Considerable progress has been made on both approaches, in particular in the fields of: ELM control with resonant magnetic perturbations (RMP), small ELM regimes, detachment onset and control, as well as filamentary scrape-off-layer transport. For example full ELM suppression has now been achieved on AUG at low collisionality with n  =  2 RMP maintaining good confinement . Advances have been made with respect to detachment onset and control. Studies in advanced divertor configurations (Snowflake, Super-X and X-point target divertor) shed new light on SOL physics. Cross field filamentary transport has been characterised in a wide parameter regime on AUG, MAST and TCV progressing the theoretical and experimental understanding crucial for predicting first wall loads in ITER and DEMO. Conditions in the SOL also play a crucial role for ELM stability and access to small ELM regimes.

The presence of non-axisymmetric perturbations in an axisymmetric magnetic field equilibrium renders the Guiding Center (GC) particle motion non-integrable and may result in particle, energy and momentum redistribution, due to resonance mechanisms. We analyse these perturbations in terms of their spectrum, as observed by the particles in the frame of unperturbed GC motion. We calculate semi-analytically the exact locations and strength of resonant spectral components of multiple perturbations. The presented Orbital Spectrum Analysis (OSA) method is based on an exact Action-Angle transform that fully takes into account Finite Orbit Width (FOW) effects. The method provides insight into the particle dynamics and enables the prediction of the effect of any perturbation to all different types of particles and orbits in a given, analytically or numerically calculated, axisymmetric equilibrium.

Charged particle motion in axisymmetric toroidal magnetic fields is analysed within the context of the canonical Hamiltonian guiding centre theory. A canonical transformation to variables measuring the drift orbit deviation from a magnetic field line is introduced and an analytical transformation to action-angle variables is obtained, under a zero drift width approximation. The latter is used to provide compact formulas for the orbital spectrum of the drift motion, namely the bounce/transit frequencies as well as the bounce/transit averaged toroidal precession and gyration frequencies. These formulas are shown to have a remarkable agreement with numerically calculated full drift width frequencies and significant differences from standard analytical formulas based on a pendulum-like Hamiltonian description. The analytical knowledge of the orbital spectrum is crucial for the formulation of particle resonance conditions with symmetry-breaking perturbations and the study of the resulting particle, energy and momentum transport.

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