Most of the visible universe is in a plasma state, and usually the flows in these plasmas are turbulent. E.g., the origin of planetary, stellar, and cosmic magnetic fields, the physics of accretion disks, the acceleration and propagation of high-energy cosmic rays, as well as many other space and astrophysical processes are intimately related to turbulent dynamics.

Meanwhile, plasma turbulence also plays a crucial role in countless laboratory experiments of basic or applied plasma science. A prominent example is the small-scale turbulence observed in magnetic confinement fusion devices which determines their energy confinement time and thus influences their performance.

From a more fundamental point of view, turbulence is a paradigmatic example of nonlinear dynamics in open systems with many degrees of freedom. Here, the system typically establishes a quasistationary self-organized state far from thermodynamic equilibrium. For this to happen, a permanent input, redistribution, and output of energy is required. Various fundamental aspects of this prototypical nonlinear process are only poorly understood at present.

It undoubtedly belongs to the most important unsolved problems of classical physics.

For the description of weakly collisional astrophysical plasmas, the magnetohydrodynamic (MHD) model is often used. However, there are also key open questions which require a more fundamental treatment, as is provided by multi-fluid or kinetic descriptions. In the latter case, the problem can often be reduced to a so-called gyrokinetic description of magnetized plasmas, provided that one deals with low-frequency phenomena (compared with the ion gyrofrequency) satisfying a certain ordering. For many astrophysical systems, such an approach – which greatly reduces the complexity of the problem, mainly due to the removal of irrelevant space and time scales – is suitable.

Gyrokinetics has been developed since the late 1970s in the magnetic fusion community, and since the mid 1990s, various codes have been written which solve the coupled nonlinear integro-differential equations of gyrokinetics on massively parallel computers. We will apply both gyrokinetics and kinetics to astrophysical plasmas, a line of study which is still in its very early stages, but which is very promising. On the other hand, some astrophysical problems present new challenges which are expected to feed back into the fusion community, e.g., regarding numerical methods or mechanisms of energetic particle physics. The present collaboration represents a framework to pursue this dual goal.

Regarding gyrokinetic simulations of plasma turbulence in fusion plasmas, there has been much progress in recent years as far as the core region of tokamaks is concerned. However, there have been only few studies of gyrokinetics for stellarators and for the edge region of tokamaks, although they involve some important outstanding physics problems. These topics are bound to be an excellent area of collaboration between IPP and PPPL, given that both institutions have particular strengths and interests in these research areas.

Stellarators are characterized by non-axisymmetric 3D magnetic field configurations, and non-axisymmetric perturbations are of growing interest in tokamaks as well, of particular importance near the plasma edge where additional symmetry-breaking field coils may be used to try to suppress Edge Localized Modes. The edge region of fusion devices is very important as power loads on the wall are often near the physical limitations. Moreover, it controls the formation of a transport barrier whose height is a critical boundary condition for core turbulence and thus also for predicting the overall fusion gain.

In the Princeton-Max Planck Center for Plasma Physics, there are presently five projects directly dedicated to plasma turbulence, while most other projects in the areas of magnetic reconnection, energetic particles, and plasma astrophysics are also linked to and will benefit from a deeper understanding of this phenomenon. Involving a critical mass of scientists with a strong background in plasma physics, astrophysics, and applied mathematics, the area of plasma turbulence is well positioned for frontier research based on fruitful interactions between these neighboring fields.

The research presently conducted in the area of plasma turbulence focuses on the following five projects:

- Development and application of a 6D kinetic code for astrophysical and laboratory plasmas
- Deeper understanding of 3D geometric effects in stellarator and tokamak turbulence
- Development of a new gyrokinetic edge and stellarator code based on Discontinuous Galerkin methods
- Application of the gyrokinetic GENE code to astrophysical problems
- Turbulent transport of energetic particles in astrophysical and laboratory plasmas