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A new simulation method that improves the conservation properties of δ f particle simulation for the collisionless Boltzmann equation is presented. When the distribution function is divided into a reference distribution specifi ed in advance and a variation distribution, the time evolution of the variation distribution is described by an advection termin the phase space and a source term associated with the reference distribution. The time evolution of the Klimontovich distribution function of the δ f method was investigated. It is shown that the errors in the Monte Carlo estimate of the source term in the δ f method deteriorate the conservation properties. In the new simulation method, errors in the Monte Carlo estimate of the source term are corrected with a complementary fl uid model. An example of the complementary fl uid model is presented for bump-on-tail instability. The simulation results are compared with those of the conventional δ f method. It is demonstrated that particle, momentum, and energy are well conserved with the new simulation method.

The interaction between toroidal Alfv?n eigenmode (TAE) and energetic ions in the Large Helical Device (LHD) is investigated using a reduced version of the MEGA code that implements a realistic equilibrium magnetic field with the HINT code and corresponding TAE profile with the AE3D code. In simulations, the linear growth rate of TAE amplitude is proportional to energetic ion density; consequently, the nonlinear saturation level of the TAE amplitude is enhanced by the increase in the energetic ion density. Energy transfer analysis is performed to clarify destabilization and saturation mechanisms of the TAE and to identify resonant energetic ions. An analysis of test particles in the electromagnetic field perturbed by the TAE shows that the magnitude of fluctuations in the energetic ion orbits is proportional to the square root of the TAE amplitude. Our results qualitatively reproduce the radial transport of energetic ions by the TAE in the LHD.

The magnetohydrodynamic (MHD) simulation code MHD Infrastructure for Plasma Simulation (MIPS) was benchmarked on ballooning instability in the Large Helical Device (LHD) plasma. The results were compared to the results of linear analysis by using the CAS3D code. Both the linear growth rates and the spatial profiles were found to be in good agreement. An extended MHD model with finite ion Larmor radius effects was implemented into the MIPS code. Ballooning instabilities were investigated using the extended MHD model, and the results were compared with those using the MHD model. Ion diamagnetic drift was found to reduce the growth rate of the short-wavelength modes; hence, modes with a diamagnetic drift frequency comparable to the ideal MHD growth rate are the most unstable. The most unstable toroidal mode number of ballooning instability in the LHD is reduced to |n| ? 5 for hydrogen plasma with ion number density ni ? 1019 m?3.