DYnamics of a turbuleNt plasmA and Magnetic inductiOn – DYNAMO

The innovative experiment developed consists in a slightly magnetized plasma column created by a radiofrequency inductive source. The plasma column rotation is controlled by driving an electron current from the polarization of a highly emissive cathode: the interaction of the radial current driven from the cathode with the axial magnetic field confining the plasma leads to the rotation of the plasma column. Alternative driving schemes based on the DC or radiofrequency biasing of grids will also be tested.
The plasma velocity is probed by a set of electrostatic proves as well as by dedicated modern and specific optical diagnostics such as laser induced fluorescence using tunable laser diodes. Fluctuations of flows and plasma parameters are probed from arrays of electrostatic probes as well as ultra-high speed imaging of the fluctuations of the light emitted by the plasma. These allow in particular to probe the dynamics of drift waves excited in the plasma column.
Numerical simulations are driven using MHD codes based on spectral methods implementing immersed boundary methods to account for complex geometries, but also dedicated finite differences codes.
The experimental development strongly benefits from various national and international collaborations.

The first set of results concerns the implementation and use of dedicated instrumentation and of the experimental device (in a laboratory with no strong existing technical expertise in plasma physics). A set of electrostatic has been developed for space and time resolved measurements of plasma parameters (Langmuir probes, Mach probes, emissive probes, 5-tip probe for turbulence studies). The stability of the plasma source allowed to study the validity of the use of emissive probes in turbulent plasmas, using a controlled time-modulation of the plasma (this led to a published article and a submitted article including detailed modeling).
A laser induced fluorescence system probing the velocity distribution function of Ar+ ions has been developed in collaboration. This system nows allows for systematic ion distribution velocity scans and has been brought to the Univ of Wisconsin, allowing for the measurement of ion temperature and flows in a large volume non-magnetized flowing plasma device. In spring 2015, fluctuations measurements using ultra-high speed velocity of the plasma emitted light showed the ability to probe dynamical features of drift-waves. The implementation of these experimental diagnostics led to the publication of a reference article on the device.
These developments enable to analyze the various terms leading to the rotation of the plasma column, and to determine the relative contributions of the drift terms and of the Lorentz force (this has been presented in conferences; an article is in preparation).
The numerical simulations tools have been benchmarked on referenced cases and a systematic study as a function of the control parameters is currently led. Results from the simulations have been systematically compared to the experiment and used to support the experimental development (this has been presented in conferences; an article is in preparation).

On the short-term views, two mains topics will be addressed. On the one hand, a systematic study of the modification of the plasma potential in the presence of a radial current injected by highly emissive cathodes and driving the rotation of the plasma column will be led. The dedicated instrumentation implemented will provide a dataset which will be compared to numerical simulations and used for modeling how the plasma potential can be controlled (preliminary results show that the Lorentz force seems to play no leading role in the flow drive). On the other hand, the influence of controlled plasma flows on the dynamics of drift-waves will be carried out, using high speed imaging and dedicated instrumentation. In particular, the stabilizing or the destabilizing features of the controlled flows on drift waves will be addressed.
On the mid-term views, a second plasma cell will be developed to allow for the drive of a strong axial shear of plasma rotation. The development of this second cell will be based on the results previously obtained.
On the long-term views, several alternative plasma flow drive schemes will be tested; in particular using biased grids. The influence of plasma expansion (for example as occurs in the presence of a strongly diverging magnetic field) on the flow dynamic will be addressed. This will open the way to the identification of the most efficient schemes for the next generation of large-scale unmagnetized plasma experiments dedicated to study instabilities driven by flows.

1. N. Plihon et al., Flow dynamics and magnetic induction in the von-Karman plasma experiment, Journal of Plasma Physics, 81, 345810102 (2015)
2. G. Bousselin et al., How plasma parameters fluctuations influence emissive probe measurements, Physics of Plasmas, 22, 053511 (2015)
3. F. Palermo, W. Bos, N. Plihon, Stirring a conducting fluid in a cylinder using the Lorentz force, Physical Review E, soumis 2015
4. J. Cavalier et al., Strongly emissive plasma-facing material under space-charge limited regimes : Application to emissive probes, Phys. Plasmas, soumis 2016
5. N. Plihon et al., Stochastic reversal dynamics of two interacting magnetic dipoles: A simple model experiment, Phys. Rev. E, 94, 012224 (2016)

The coupling between magnetic and velocity fields in electrically conducting fluids is ubiquitous in nature. In astrophysical bodies, part of the kinetic energy can be converted into magnetic energy via the dynamo instability. The dynamic of fusion plasma is dominated by this coupling. The media are usually in a fully turbulent state and a unified description of the flow dynamics is lacking. The analysis of the magnetohydrodynamic (MHD) equations shows three important dimensionless numbers: the magnetic Prandtl number Pm (ratio of the kinetic viscosity over the magnetic viscosity), the kinetic Reynolds number Re (which defines the intensity of the turbulence) and the magnetic Reynolds number Rm (which quantifies nonlinear effects for the magnetic field). Two of them are independent, since Rm = PmRe.

The DYNAMO proposal consists in a systematic characterization of the influence of Pm and Re on the coupled magnetic field/velocity field dynamics in a plasma in the presence of controlled flows. The use of a plasma (ionized gas) as a conducting media is motivated by its unique ability to have Pm variation, over several orders of magnitude, as a function of the physical parameters. Our experimental setup will provide Pm in the range 1e-7 to 10.
The proposal will focus on
1. The influence of Re and Pm on turbulent MHD processes (such as magnetic induction) and plasma turbulence
2. The influence of large-scale flows on plasma (drift-wave) turbulence
The first point will bridge current state-of-the-art experimental investigations in liquid metals, at very low Pm values (1e-6), and cutting-edge numerical simulations, at moderate Pm values (0.1). These results will serve as a basis for dynamo modeling.
The second point is an original approach of plasma turbulence, where the fluctuations will be excited from large-scale controlled motions of the plasma. This aspect is complementary to the usual and very well–documented approach in plasma physics, where fluctuations are excited by non-linear interactions of unstable (drift-wave) modes at small scales.

Our proposal is aimed at providing models for the coupled dynamics from analysis of a dedicated innovative experiment and cutting-edge numerical simulations. In the experiment, a plasma flow will be created and controlled at large scale, giving an independent external control of Pm and Re numbers. Numerical simulations (based on volume-penalization methods) will support and complement the experimental developments. Physical modeling of the dynamical velocity/magnetic field coupling will benefit both from numerical simulations and experimental data.
The scientific program will be the following:
1. Plasma flow control: development and modeling of plasma acceleration schemes for a von-Karman type plasma flow, characterization of transport coefficient evolution, understanding of plasma potential shaping
2. Interaction of drift-wave turbulence with flows. The influence of rotation, axial and azimuthal sheared flows on drift-wave modes and turbulence will be characterized
3. Influence of Pm and Re on plasma turbulence and magnetic induction mechanisms from large scale imposed magnetic fields and gradients of velocity. Expected results are of primary interest for astrophysical dynamo modeling and understanding of next-generation plasma dynamo experiments. Statistical methods from neutral fluid turbulence will be applied for analysis of turbulent spectra, energy dissipation, intermittency and anisotropy. The results will be relevant for turbulence control of fusion plasmas and astrophysics issues.

Dedicated time-resolved instrumentation (electrostatic probes and optical measurements) for the magnetic and velocity fields will be implemented.

Finally, the development of this innovative tool (drive of a controlled plasma flow) is of broader interest and open new opportunities for studies on non-linear (magneto)-hydrodynamic in flowing plasmas (instabilities, turbulence…).