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Register a new userA Scale-Separated Approach for Studying Coupled Ion and Electron Scale Turbulence
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Multiple space and time scales arise in plasma turbulence in magnetic confinement fusion devices because of the smallness of the square root of the electron-to-ion mass ratio $(m_e/m_i)^{1/2}$ and the consequent disparity of the ion and electron thermal gyroradii and thermal speeds. Direct simulations of this turbulence that include both ion and electron space-time scales indicate that there can be significant interactions between the two scales. The extreme computational expense and complexity of these direct simulations motivates the desire for reduced treatment. By exploiting the scale separation between ion and electron scales,and expanding the gyrokinetic equations for the turbulence in $(m_e/m_i)^{1/2}$, we derive such a reduced system of gyrokinetic equations that describes cross-scale interactions. The coupled gyrokinetic equations contain novel terms which provide candidate mechanisms for the observed cross-scale interaction. The electron scale turbulence experiences a modified drive due to gradients in the ion scale distribution function, and is advected by the ion scale $E times B$ drift, which varies in the direction parallel to the magnetic field line. The largest possible cross-scale term in the ion scale equations is sub-dominant in our $(m_e/m_i)^{1/2}$ expansion. Hence, in our model the ion scale turbulence evolves independently of the electron scale turbulence. To complete the scale-separated approach, we provide and justify a parallel boundary condition for the coupled gyrokinetic equations in axisymmetric equilibria based on the standard twist-and-shift boundary condition. This approach allows one to simulate multi-scale turbulence using electron scale flux tubes nested within an ion scale flux tube.
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Multiscale interaction between the magnetic island and turbulence has been demonstrated through simultaneous two-dimensional measurements of turbulence and temperature and flow profiles. The magnetic island and turbulence mutually interact via the coupling between the electron temperature ($T_e$) gradient, the $T_e$ turbulence, and the poloidal flow. The $T_e$ gradient altered by the magnetic island is peaked outside and flattened inside the island. The $T_e$ turbulence can appear in the increased $T_e$ gradient regions. The combined effects of the $T_e$ gradient and the the poloidal flow shear determine two-dimensional distribution of the $T_e$ turbulence. When the reversed poloidal flow forms, it can maintain the steepest $T_e$ gradient and the magnetic island acts more like a electron heat transport barrier. Interestingly, when the $T_e$ gradient, the $T_e$ turbulence, and the flow shear increase beyond critical levels, the magnetic island turns into a fast electron heat transport channel, which directly leads to the minor disruption.
Radiative diagnostics of high-energy density plasmas is addressed in this paper. We propose that the radiation produced by energetic particles in small-scale magnetic field turbulence, which can occur in laser-plasma experiments, collisionless shocks, and during magnetic reconnection, can be used to deduce some properties of the turbulent magnetic field. Particles propagating through such turbulence encounter locally strong magnetic fields, but over lengths much shorter than a particle gyroradius. Consequently, the particle is accelerated but not deviated substantially from a straight line path. We develop the general jitter radiation solutions for this case and show that the resulting radiation is directly dependent upon the spectral distribution of the magnetic field through which the particle propagates. We demonstrate the power of this approach in considering the radiation produced by particles moving through a region in which a (Weibel-like) filamentation instability grows magnetic fields randomly oriented in a plane transverse to counterstreaming particle populations. We calculate the spectrum as would be seen from the original particle population and as could be seen by using a quasi-monoenergetic electron beam to probe the turbulent region at various angles to the filamentation axis.
We show that zonal flow can be preferentially excited by intermediate-scale toroidal electron temperature gradient (ETG) turbulence in tokamak plasmas. Previous theoretical studies that yielded an opposite conclusion assumed a fluid approximation for ETG modes. Here, we carry out a gyrokinetic analysis which ultimately yields a nonlinear Schr{o}dinger equation for the ETG dynamics with a Navier-Stokes type nonlinearity. For typical tokamak parameters, it is found that zonal flow generation plays an important role in the intermediate-scale ETG turbulence. This finding offers an explanation for recent multi-scale gyrokinetic simulations.
Turbulence plays a very important role in determining the transport of energy and particles in tokamaks. This work is devoted to studying the chaotic diffusion in multi-scale turbulence in the context of the nonlinear wave-particle interaction. Turbulent waves with different scales of characteristic wavelengths can interact with the same group of charged particles when their phase velocity is close to the velocities of the charged particles. A multi-wavenumber standard mapping is developed to model the chaotic diffusion in multi-scale turbulence. The diffusion coefficient is obtained by calculating the correlation functions analytically. It is found that the contribution of the largest scale turbulence dominates the deviation from the quasi-linear diffusion coefficient. Increasing the overlap parameters of the smaller scale turbulence by just the increasing the wavenumber cannot make the diffusion coefficient to be the quasi-linear diffusion coefficient for a finite wave amplitude. Especially, in two-scale turbulence, the diffusion coefficient is mostly over the quasi-linear diffusion coefficient in the large wavenumber (of the smaller scale turbulence) limit. As more scales of components are added in the turbulence, the diffusion coefficient approaches the quasi-linear diffusion coefficient. The results can also be applied to other resonance-induced multi-scale turbulence in Hamiltonian systems with 1.5 or 2 degrees of freedom.
Based on in-situ measurements by Wind spacecraft from 2005 to 2015, this letter reports for the first time a clearly scale-dependent connection between proton temperatures and the turbulence in the solar wind. A statistical analysis of proton-scale turbulence shows that increasing helicity magnitudes correspond to steeper magnetic energy spectra. In particular, there exists a positive power-law correlation (with a slope $sim 0.4$) between the proton perpendicular temperature and the turbulent magnetic energy at scales $0.3 lesssim krho_p lesssim 1$, with $k$ being the wavenumber and $rho_p$ being the proton gyroradius. These findings present evidence of solar wind heating by the proton-scale turbulence. They also provide insight and observational constraint on the physics of turbulent dissipation in the solar wind.
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