Universality in turbulence heating in magnetized plasma, entropy cascade in phase-space

Eiichirou Kawamori^1*

¹Institute of Space and Plasma Sciences,, National Cheng Kung University, Tainan, Taiwan

* Presenter:Eiichirou Kawamori, email:kawamori@isaps.ncku.edu.tw

The heating of the solar corona, adjacent to the solar photosphere with a temperature of around 6,000K, to approximately 100 eV by magnetized plasma turbulence, the heating and acceleration of the solar wind by magnetized plasma turbulence, and the entropy paradox of turbulence in magnetically confined fusion plasmas are all known as the heating problem of magnetized plasma turbulence. For example, a specific question regarding the turbulent heating of the solar corona is how Alfvén waves or kinetic Alfvén waves, which act as the driving source of turbulence, undergo processes (such as resonance, linear phase mixing, Landau damping, shock wave dissipation, and others) to cause energy dissipation (i.e., heating). Simply put, the turbulent heating problem involves determining at which scale ions are accelerated, at which scale energy dissipation occurs, and how energy is transported between these scales.
The solar corona, the solar wind, and magnetically confined fusion plasmas are collisionless (or more precisely, weakly collisional) plasmas, and their dynamics are described by the Vlasov-Fokker-Planck-Maxwell equations. According to Boltzmann's H-theorem, entropy generation (heating) occurs only through particle collisions. In the Fokker-Planck equation, the collision term is described as friction and diffusion in velocity space, meaning that in weakly collisional plasmas, entropy generation occurs when either ∂f/∂v or ∂²f/∂v² becomes large, where f is the ion velocity distribution function and v is the ion velocity vector. In other words, heating occurs when fine-scale structures form in velocity space. Furthermore, the spatial scales dominated by collisions are much smaller than the ion gyroradius scale [1].
On the other hand, energy injection in turbulence typically occurs on macroscopic scales. These facts suggest that the energy transport mechanism in magnetized plasma turbulence involves energy injected at macroscopic scales cascading into smaller scales in both real and velocity space in the form of entropy (strictly speaking, in the form of free energy F = E − TS, where E is internal energy, T is temperature, and S is entropy), and being dissipated. This picture is known as the entropy cascade, and it is described by gyrokinetics on scales where k⊥ρi ≳ 1, where k⊥ is the wavenumber perpendicular to the magnetic field lines of the turbulent fluctuations and ρi is the ion gyroradius at thermal velocity. The entropy cascade is believed to be a universal feature of magnetized plasma turbulence, occurring at the gyroradius scale regardless of whether the turbulence is two-dimensional or three-dimensional, electrostatic or electromagnetic. Since the entropy cascade is a dynamic process in ion phase space, its identification requires measurements in phase space.
In this study, we used the Ring-averaged ion distribution function probe [2] to measure the ring-averaged ion velocity distribution function in two-dimensional electrostatic turbulence in a laboratory magnetized plasma and, for the first time, determined the phase space distribution of Gibbs entropy in an actual magnetized plasma. In the experiment, we measured the phase space distribution of Gibbs entropy in drift-wave turbulence, with the turbulence driving wave's k⊥ controlled in the range of k⊥ρi ~ 0−10. Through this measurement, we identified the presence of an inertial subrange of entropy and electrostatic fluctuation energy in phase space and confirmed that a dual cascade—consisting of a forward cascade of entropy and a backward cascade of electrostatic fluctuation energy—occurs through nonlinear phase mixing in phase space [3].

References:
1. Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Plunk, G. G., Quataert, E. & Tatsuno, T. Gyrokinetic turbulence: a nonlinear route to dissipation through phase space. Plasma Phys. Control. Fusion 50, 124024 (2008).
2. Kawamori, E., Chen, J., Lin, C. & Lee, Z. “Ring-averaged ion velocity distribution function probe for laboratory magnetized plasma experiment” Review of Scientific Instruments 88, 103507 (2017).
3. Eiichirou Kawamori & Yu-Ting Lin, “Evidence of entropy cascade in collisionless magnetized plasma turbulence”. Communications Physics, Vol. 5 Article No.338 (2022).

Keywords: Plasma turbulence, entropy, phase space, cascade, scaling law