Clarification of symmetry breaking mechanism in intrinsic rotation of tokamak plasmas

Intrinsic rotation of tokamak plasmas is considered to be generated by non-diffusive stress (i.e. residual stress) induced by asymmetric $k_{\vert \vert } $ turbulence spectrum. To study the symmetry breaking mechanisms in intrinsic rotation, we have performed numerical simulations of intrinsic rotation by ITG turbulence using the gKPSP code, a delta-f global PIC code for tokamak. It is found that not only distortion of turbulence spectrum by $E\times B$ shear but also spatial diffusion of wave momentum driven by turbulence intensity gradient play an important role in the symmetry breaking mechanism, as expected from a theory [1]. It is hard to recognize individual contribution of $E\times B$ shear and turbulence intensity gradient to the residual stress because their evolution is strongly coupled with the prey-predator feature [2]. To clarify their role, a comprehensive analysis including their nonlinear coupling is performed. The key symmetry breaking mechanism is identified for various physics situations. \\[4pt] [1] P.H. Diamond, et al., Phys. of Plasmas 15, 012303 (2008). \\[0pt] [2] P.H. Diamond, et al., PRL 72, 2565 (1994).