Numerical Simulations

THOR will explore which plasma processes in turbulent fluctuations at kinetic scales are responsible for the heating and acceleration of different plasma species. Our knowledge about those processes as of today is mainly coming from numerical simulations and therefore the numerical simulation support is critical for the THOR mission. The numerical simulations clearly demonstrate the ne
ed to resolve the kinetic scales physics, some examples being plasma heating in turbulence, ion acceleration at shocks, the heating of ion species with different mass.
The THOR team includes many scientists developing and running different plasma simulation codes addressing the physics of turbulence and shocks. Below is a list of numerical codes accessible to the THOR team and used in the mission preparation as well as during Study Phase to define the measurement strategy for fields and particle distribution functions.
For example, three-dimensional velocity distributions as obtained from direct numerical simulations of plasma turbulence are used to simulate the response of a virtual top-hat analyzer which mimics the real measurements of particle instruments on board THOR. In the picture below, an example of this kind of analysis is shown: in the box on the left we report the original proton velocity distribution (VD) from a kinetic simulation in the Cartesian velocity plane and in the spacecraft frame. This VD is then moved into energy-angular coordinates and sampled by a top-hat simulator. Results obtained by the virtual CSW instrument on board THOR (middle panel) are compared with the response of the particle instrument on board the WIND satellite (right panel).

Several numerical tools are available (see table below) to support the science of THOR. In the following some examples are given from both global simulations, designed to describe the global interaction of the Earth with the solar wind, and local simulations, which, instead, focus on a limited portion of space and allow for a deeper investigation of the system dynamics at very short (kinetic) scales.

Generation of the Earth's magnetosphere in 3D PIC simulations

Turbulence generation in a 3D-3V local Vlasov simulation

Departure from Maxwellian equilibrium

At kinetic scales, the particle velocity distribution deviates from the Maxwellian shape of thermodynamic equilibrium. In this movie the evolution of the proton velocity distribution is followed in time, as detected by the CSW instrument (results from HVM simulations of turbulence in the solar wind). The response of CSW has been simulated through a virtual top-hat analyzer, using the real angular and energy resolutions and geometric factor. More significant deformations are recovered when the PVI signal gets large values, that is when discontinuities and coherent structures are recovered in the current density. Moreover, variations in the shape of the proton velocity distribution occur on a short time scale.

Particle heating occurring close to thin current sheets

Particle heating occurs in the form of thin filaments localized in space close to regions where strong current sheets are generated during the development of the turbulent cascade

Heavy ions (alpha particles) exhibit differential kinetic behavior and preferential heating with respect to protons. In this movie, the contour map of total temperature of protons (left) and alphas (right) are followed in time, along the development of the turbulent cascade in the solar wind.

Differential ion heating

Available numerical codes

A list of the numerical tools which are employed to provide support during Study Phase to the science and to the measurement strategy of the THOR spacecraft is reported in the table below. Details on each numerical code can be found by clicking on the name of each code. Examples of scientific videos are also available from some kinetic simulations.










(Multi-solver pseud-spectr fram.)



(explicit PIC)