Spectrum Cascade in Electrostatic Plasma Turbulence

为了研究具有磁切变的圆柱形等离子体中电阻漂移波和交换湍流的特性，我们扩展了Hasegawa-Wakatani方程，使其包含平均磁曲率。在三维非线性模拟中，线性不稳定波动在电阻率、粘度和粒子扩散等耗散作用下趋于饱和。对于饱和稳态湍流能，计算了熵谱和交叉螺旋谱，并与解析理论进行了比较。模拟中的一个重要参数是电阻率。当它是可忽略的小时，密度和势涨落之间施加玻尔兹曼关系，模型方程简化为Hasegawa-Mima方程。然后能量反向级联而熵级联正常。当电阻率极大时，动能、内能、熵和横螺旋度分别保持在无耗散极限。然后动能反级联而内能正级联。数值结果与解析理论吻合较好。

In order to study characteristics of resistive drift wave and interchange turbulence in a cylindrical plasma with magnetic shear, we extended Hasegawa-Wakatani equations to include the average magnetic curvature. In the three-dimensional nonlinear simulation the linearly unstable fluctuations saturate under the effect of dissipation due to resistivity, viscosity and particle diffusion. For the saturated stationary turbulence energy, enstrophy and cross-helicity spectra are calculated and compared with the analytic theory.An important parameter in the simulation is resistivity. When it is negligibly small, the Boltzmann relation is imposed between the density and potential fluctuation and the model equations reduced to Hasegawa-Mima equation. Then the energy cascades inversely and the enstrophy cascades normally. When the resistivity is extremely large, kinetic energy, internal energy, enstrophy and cross-helicity conserve separately in the dissipationless limit. Then the kinetic energy cascades inversely and the internal energy cascades normally. We obtain good agreement between the numerical results and the analytic theory.