7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Vlasov simulation in 6-dimensional phase space for cosmological neutrinos andits application to astrophysical magnetized plasma
Kohji Yoshikawa1
1
Center for Computational Sciences, University of Tsukuba
e-mail (speaker): kohji@ccs.tsukuba.ac.jp

Kinetic simulation is a versatile method for simulatingcollective behavior of a huge number of particles under acertain Hamiltonian such as self-gravitating systems andmagnetized plasma in astrophysical context. So far, thesekinetic simulations have been performed with particlebased methods such as gravitational N-body simulationsof dark matter in galaxies and galaxy clusters, andparticle-in-cell (PIC) simulations of astrophysicalmagnetized plasma, in which matter distribution in a sixdimensional phase space is sampled in a Monte-Carlomanner by a finite number of discrete super-particles andtheir dynamics is numerically solved by integrating theequation of motion of each super-particle.
Although the particle-based numerical methods havebeen successful and primary options both in selfgravitating and magnetized plasma systems, there exist
several intrinsic drawbacks in particle-based methods
originating from the statistical sampling of matter
distribution by super-particles. Such statistical samplingof matter distribution in the phase space introduces thewell-known shot noise and critically compromises thenumerical results, especially, for example, in simulating“hot” component with a large velocity dispersion, where
the sampling of matter distribution is relatively sparse.
Furthermore, matter in the high velocity tail, which is notwell sampled in the particle-based methods, playsimportant roles in several important kinetic processes
such as collisionless damping in the self-gravitating
systems.
As a remedy for these shot noise in the particle-based
methods, we, for the first time, implement a completely
new approach (dubbed as Vlasov simulation/approachhereafter) that simulate the dynamics of matter bysolving collisionless Boltzmann (Vlasov) equation basedon a finite volume method.[1] This approach is free fromthe numerical problems described above by representing

the matter distribution as a continuum medium in the sixdimensional phase space and enables us to perform
completely noiseless simulations even when the velocity
distribution has a broad and extended tail. Of course, thisapproach does not suit to all situations and the particlebased methods can be a better option for relatively “cold”
matter with small extent of matter distribution in thevelocity space. Therefore, a hybrid of N-body andVlasov approaches is a desirable option which takes best
advantage of both the particle-based and Vlasov
approaches in a complementary manner.
Here, we present a Vlasov simulation of cosmologicalneutrinos which is combined with the particle-based Nbody simulation of dark matter in the large-scale
structure in the universe, as an example of such hybrid
simulation of N-body and Vlasov simulations.[2] Thishybrid approach to simulate the cosmological neutrinos
exhibits clear advantages over the conventional particlebased N-body counterparts in terms of the shot noise
seen in the particle-based simulations and the effective
spatial resolution (see Figure 1).
Vlasov approach is also beneficial to simulation ofmagnetized plasma not only because it is not affected by
the numerical shot noise but also because it is free fromthe constraints of the PIC method on the spatial
resolution which must be chosen to be less than theDebye length, enabling us to perform a consistent
simulation up to the MHD scale.
This research is supported by the Grant-in-Aid for
Scientific Research byt the JSPS KAKENHI grant No.
JP21H01079.
References[1] K. Yoshikawa et al. ApJ, 762, 116 (2013)[2] K. Yoshikawa et al. ApJ, 904, 159 (2020)

Figure 1. Density and velocity maps of neutrinos simulated with Vlasov and N-body simulations.