Physical properties of plasma ion dynamics in various equilibria of field-reversed configuration

T. Takahashi, M. Ubukata, N. Iwasawa, Y. Kondoh

Gunma University, Kiryu, Gunma 376-8515, Japan

The tilt mode stability is the major physical issue of Field-Reversed Configurations (FRCs). Although the ideal MHD predicts the FRC plasmas are unstable against the mode, however, the several experimental measurements show their resilient feature. Since the averaged beta value of FRC is near unity and thus ion Larmor radius is comparable to the scale length, the fluid limit breaks and the velocity distributions become important to expect an FRC's global behavior. In the FRCs, depending on the velocity, there are three types of particle trajectories. A faster ion with large canonical angular momentum exhibits betatron orbit encircling the geometric axis. A fast but with a smaller canonical angular momentum than the betatron particle draws a figure-8 orbit. The direction of gyration is changed due to the field reversal. These two peculiar trajectories may cause a kinetic stability of FRCs, and therefore the properties of ion dynamics should be investigated. On this viewpoint, Hayakawa et al. studied the stochasticity or adiabaticity of ion motion in the deuterium-helium 3 fueled fusion plasma.[1] The existence of adiabatic and trapped particle in the curved magnetic line region was shown in [1], and it may offer a stabilizing flow to the tilt mode activity. However, only Hill's vortex model was employed for the equilibrium of FRC, and how the equilibrium field affects the particle orbit is still unclear.
In the present study, the internal equilibrium of FRC is calculated by solving the Grad-Shafranov equation analytically and numerically. The radial part of flux function is expanded in the power series, and the axial one is expanded in the cosine series. Unknown expansion coefficients are determined numerically by the boundary condition (i.e., the flux function at the separatrix). This method is effective to express various internal equilibria with different separatrix shape and current profile. In order to reduce the calculation time, with this semi-analytical method the flux function is calculated only at the grid mesh points. In the orbit calculation code, the flux function and the magnetic fields at an arbitrary position are obtained from the interpolation method.
The surface of section plot is used to classify the stochastic and adiabatic motion. The relations between stochasticity and the adiabatic invariant and azimuthal drift velocity are shown in the present paper.

References

[1]Y. Hayakawa, T. Takahashi, Y. Kondoh, Nucl. Fusion, 42 (2002) 1075