Below you can see examples of PhD projects at PPFE.

### “Turbulence and Transport in Plasmas”

General introduction

Turbulence is the main player in defining the confinement properties of plasma fusion devices. In hot magnetically confined plasmas the cross-field transport mediated by low frequency turbulence is far dominating the classical collision mediated transport.

The section for Plasma Physics and Fusion Energy (PPFE) develops theoretical models for the fundamental understanding of turbulence and transport. These models are implemented numerically and we use high performance supercomputers (HPC) to simulate the complex behaviour of fusion plasma in time and space. Our results are used in interpreting and enhancing fusion experiments in Europe and worldwide.

We participate in the European coordinated programme for fusion research in close collaboration with other European and international research groups. The PhD students will participate in the international collaborations and have wide opportunities for research visits at the collaborating laboratories. A PhD education within plasma physics and fusion research provides a very promising carrier outlook. The international fusion experiment, ITER, will need several hundreds of plasma and fusion scientists within few years from now.

**Specific projects:**

**1) Self-organisation and generation of large scale flows in plasma turbulence**

In magnetically confined plasma the low frequency turbulence is strongly anisotropic with scale lengths along the magnetic field significantly larger than the scales across the magnetic field. Thus, the turbulence may be considered quasi-two-dimensional and is known to mix and homogenize quantities, which are only advected by the turbulent velocity fluctuations (Lagrangian conserved quantities). The project shall exploit the importance of the Lagrangian invariants and the ensued self-organization for the dynamical evolution of the turbulence and the associated transport. Particularly, the mixing and homogenization of the of the so-called potential vorticity - a Lagrangian invariant - plays a key role for the generation and evolution of large scale flows which control the transport and are potentially important for achieving a high confinement regime in fusion devices. The project will contain theoretical investigations and numerical solutions of dynamical model equations – coupled nonlinear partial differential equations.

**2) Global modelling of turbulence and transport in magnetically confined plasma**

The edge of magnetically confined plasma is characterised by a transition from closed to open magnetic field lines. We are developing models capable of describing the global evolution of the plasma in this region, which is of key importance for the overall plasma performance. It controls the plasma exhaust and thereby sets the condition for the plasma confinement. The project foresees a throughout investigation of the turbulent transport of particles, energy and momentum employing a newly developed four field model, and further development of this model towards predictive capacity. The project will include implementing and solving the model numerically on HPC’s and involves extensive data analysis applying modern statistical methods. The results shall be benchmarked against experimental investigations within our international network.

**Contact:** Professor Jens Juul Rasmussen, jjra@fysik.dtu.dk, Senior Scientist Anders H. Nielsen, ahnie@fysik.dtu.dk or Head of Section Volker Naulin, vona@fysik.dtu.dk

### “Collective Thomson Scattering (CTS)”

General introduction

The ion dynamics, and specifically the dynamics of the fast ions produced in the fusion reactions, plays a key role in the harvesting of fusion energy from fusion power plants in the near future. The fast ions carry a significant amount of free energy which needs to be transferred to the background plasma without driving plasma instabilities. Furthermore, energetic particles may interact with plasma instabilities which may lead to redistribution of the fast ions and thus the internal plasma heat source redistribution.

In the section for Plasma Physics and Fusion Energy we operate a CTS system on the tokamak ASDEX Upgrade which is capable of diagnosing the distribution function of the fast ions together with the properties of the thermal ion distribution. The diagnostic operates by launching a MW microwave beam into the plasma which scatters off plasma fluctuations generated by the ions. From the scattering spectrum key information regarding the state of the plasma ions may be inferred.

We participate in the European coordinated programme for fusion research in close collaboration with other European and international research groups. The PhD students will participate in the international collaborations and have wide opportunities for research visits at the collaborating laboratories. A PhD education within plasma physics and fusion research provides a very promising carrier outlook. The international fusion experiment, ITER, will need several hundreds of plasma and fusion scientists within few years from now.

**Specific projects:**

**1) E****xperimental investigations of energetic alpha particle dynamics in tokamak plasmas **

In the deuterium-tritium fusion reaction so-called alpha particles are produced with a birth energy of 3.5 MeV which is 2 orders of magnitude higher than the energy of the thermal ions. Alpha particles are therefore a necessary ingredient of any fusion plasma. These alpha particles are expected to interact with plasma instabilities such as sawtooth oscillations, fishbones and toroidal Alfven eigenmodes. Especially for ITER, the next step fusion experiment, the dynamics of the alpha particles needs to be well understood as a large fraction of heating will originate from these particles. In this project alpha particles will be generated in the tokamak ASDEX Upgrade by means of neutral beam injection and ion cyclotron resonance heating. Previously, measurements of energetic hydrogen and deuterium ions by collective Thomson scattering have shown a strong interaction with the sawtooth instability. Here the dynamics of the alpha particles will be characterized, both temporal and spatially, by collective Thomson scattering.

**Contact:** Scientist Stefan Kragh Nielsen, skni@fysik.dtu.dk

**2)****Velocity-space tomography of energetic particle physics**

In this project we develop methods to measure 2D fast-ion velocity distribution functions in magnetized fusion plasmas in tokamaks. Such distribution function are almost never Maxwellian. This is done by first understanding the velocity-space sensitivity of the available diagnostics and then formulating a tomography problem that can be solved by standard tomography methods. The velocity-space tomography method based on the available diagnostics is becoming a standard tool to analyse fast-ion measurements at ASDEX Upgrade and has just been demonstrated at JET, the largest tokamak in the workd. A measured 2D fast-ion velocity distribution function at the tokamak JET looks like this:

The coordinate axes are the velocities parallel and perpendicular to the local magnetic field. The ITPA Energetic Particle Physics Group has started a set of Joint Experiments to make such measurements at all major machines worldwide: JET, ASDEX Upgrade, DIII-D, EAST, TCV, K-STAR, MAST Upgrade, NSTX Upgrade, LHD, Wendelstein 7-X. Eventually the velocity-space tomography method is developed to study energetic alpha particles from fusion reactions in ITER. Many projects within this endeavor are available. We develop new methods and tailor the methods to work on each of these machines. We further study energetic particle physics relying on the 2D images of the velocity distribution function, focusing on magnetohydrodynamic instabilities that are today not well understood.

**Contact:** Assistant Professor Mirko Salewski, msal@fysik.dtu.dk