theory_modelling | advanced-propulsion

Theory and Modelling

The Plasma&ElectroMagnetics Group conjugate a theoretical analysis with a numerical simulation approach of plasmas in order to grasp the physical phenomena involved in plasma source wheter being used for industrial applications, or for propulsion purposes, or - last but not least - using the plasma as the radiating element for a brand new concept of communication antenna.

The Group is working at the development of theoretical models and innovative and computationally-efficient numerical tools conceived for the study, design, and optimization of plasma sources. The expertise in plasma and electromagnetic modelling coming from Prof.A.Cardinali (ENEA-EURATOM) and Prof.V.Lancellotti (TU/e), respectively, helps us in providing the best solutions when deling with cutting-edge plasma science.

ADAMANT

ADAMANT (Advanced coDe for Anisotropic Media and ANTennas) is a full-wave numerical tool devised for the analysis and design of radiofrequency antennas which drive the discharge in helicon plasma sources. ADAMANT relies on a set of coupled surface and volume integral equations in which the unknowns are the surface electric current density on the antenna conductors and the volume polarization current within the plasma. The latter can be inhomogeneous and anisotropic whereas the antenna can have arbitrary shape. The set of integral equations is solved numerically through the Method of Moments with subsectional surface and volume vector basis functions. This approach allows the accurate evaluation of the current distribution on the antenna and in the plasma as well as the antenna input impedance, a parameter crucial for the design of the feeding and matching network. ADAMANT has been validated against other well-established numerical approaches for several examples. The numerical accuracy of the computed solution versus the number of basis functions in the volume region is also assessed.

Thanks to its approach and the unstructured mesh, ADAMANT can be employed to solve a wide range of plasma and EM problems, such as laboratory experiments of plasma physics, industrial plasma sources, plasma fusion scenarios, EM-biological interaction. Besides, ADAMANT can be used for the evaluation of radiating electromagnetic fields scattered by conducting antennas in free space.

SPIREs

SPIREs (plaSma Padova Inhomogeneous Radial Electromagnetic solver) is a Finite-Difference Frequency-Domain (FDFD) electromagnetic solver in one dimension for the rapid calculation of the

electromagnetic fields and the deposited power of a large variety of cylindrical plasma problems. The two Maxwell wave equations have been discretized using a staggered Yee mesh along the radial direction of the cylinder, and Fourier transformed along the other two dimensions and in time. By means of this kind of discretization, we have found that mode-coupling of fast and slow branches can be fully resolved without singularity issues that flawed other well-established methods in the past. Fields are forced by an antenna placed at a given distance from the plasma. The plasma can be inhomogeneous, finite-temperature, collisional, magnetized and multi-species. Finite-temperature Maxwellian effects, comprising Landau and cyclotron damping, have been included by means of the plasma Z dispersion function. Finite Larmor radius effects have been neglected. Radial variations of the plasma parameters are taken into account, thus extending the range of applications to a large variety of inhomogeneous plasma systems.

The method proved to be fast and reliable, with accuracy depending on the spatial grid size. Two physical examples have been used for validation: fields in a forced vacuum waveguide with the antenna inside, and forced plasma oscillations in the helicon radiofrequency range.

F3MPIC

F3MPIC is a three-dimensional plasma Particle-in-Cell (PIC) code with an unstructured mesh of tetrahedral elements coupled with a 3D FEM electrostatic and electromagnetic (frequency domain) solver; the presence of oscillating current sources (e.g., antenna, electromagnetic emitters) can be readily taken into account.

The code evaluates the particles trajectories of a n-species plasmas with a Boris-Leapfrog scheme under the action of electromagnetic fields generated by the plasma itself and by other external sources. At each time step, charge densities on nodes of the unstructured mesh is obtained by means of appropriate weighting schemes. Particle tracking locates particles in the mesh, using a fast algorithm. The topology of the mesh graph is obtained by means of an efficient front advancing scheme to allow a low computational cost. Additionally, collisions between charge particles and neutrals rely on a Monte Carlo Collision (MCC) tool; in order to simulate the correct interaction between species with different macro-particle weight, the concept of time-varying-weight particle is implemented.

Different types of boundary conditions are implemented, both for particles and for the field solver: particle emitter, neutral injectors, particle exit port, floating and biased conductor and simple dielectric. A logical sheath boundary condition can be used thus avoiding small Debye length, which means small spatial resolutions, when high-density plasmas have to be simulated.

F3MPIC can manage geometries of arbitrary complexity, with an arbitrary number of plasma species, both charged and neutral. The geometry of the simulated device can be easily imported from a generic 3D-CAD tool.

F3MPIC was developed for the detailed design and optimization of helicon and general-purpose plasma thrusters. F3MPIC has been validated both numerically and experimentally during the HPHcom project; it is multiplatform (Linux, AIX, Mac OS X) and has been tested on High Performance Computing (HPC) facilities (CINECA, ENEA-Grid). F3MPIC can work either in the sequential or in the parallel version; most notably, a GPU version is now under testing.

RAYWh

RAYWh (RAY-tracing Whistler) is a three-dimensional Ray-Tracing solver for the electromagnetic propagation and power deposition in cylindrical plasma sources for space plasma thrusters, where actual magnetic confinement configurations along with plasma density profiles have been included. The propagation and absorption of whistler waves has been investigated solving the 3D Maxwell-Vlasov model equations by a WKB asymptotic expansion. The reduced set of equations for the wave phase (Ray-tracing equations) and for the square amplitude (Power damping equations) of the electric field has been solved numerically. The resulting ordinary differential equation systems is solved by means of Hamming's modified predictor-corrector method, a fourth order method using 4 preceding points for the computation of a new vector of the dependent variables, while we used a fourth order Runge-Kutta method suggested by Ralston to adjust the initial increment, and to compute the starting values for the non self-starting predictor-corrector method.

This approach allows a deep physical insight in the wave propagation and power deposition phenomena; specifically, RAYWh provides the evolution of the wave vector, and power deposition profiles inside the plasma source, where realistic density profiles and confinement magnetic field lines can be readily included without any approximation.

The helicon case with axial, and uniform magneto-static field has been used as a benchmark, with propagative and power deposition features in agreement with helicon theory.