Validation of thermal conductivity in magnetized plasmas using particle-in-cell simulations

The validity of three thermal conductivity models for magnetized plasmas developed by Braginskii [Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1], by Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], and by Ji and Held [Phys. Plasmas 13, 042114 (2013)] was evaluated by one-dimensional collisional particle-in-cell (PIC) simulations. Although the accuracy of Braginskii model had been improved in Epperlein-Haines and Ji-Held models, they still have potential source of error: Epperlein and Haines numerically solved the first-order Fokker-Planck equation and fit their results with similar to 15% error, while Ji and Held analytically solved the same equation ignoring the high order terms of Sonine polynomial expansion of distribution function. The results of the PIC simulations in this study showed that Ji-Held model gives a more accurate thermal conductivity than Braginskii and Epperlein-Haines models within the Hall parameter range 0 < chi < 0.9 with an ion charge state Z = 4. In the simulation, slower electrons contributed to thermal conduction in transverse direction compared to that in no magnetic field because of the short energy transport distance of cyclotron motion. Moreover, since collisional slowdown produces net heat flux in transverse direction along temperature gradient, slow and collisional electrons were much more effective for thermal conduction in this direction. The validity of Ji-Held model can be understood as a result of the good description of slow electrons, since higher order terms describe lower velocity part of distribution function, which is relevant to thermal conduction in magnetic fields. Published by AIP Publishing.