skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information
  1. Calculation of collisionless pitch-angle scattering of runaway electrons with synchrotron radiation via high-order guiding-centre equation

    Recently, the collisionless pitch-angle scattering for relativistic runaway electrons (REs) in toroidal geometries such as tokamaks was discovered through a full orbit simulation approach (Liu et al., Nucl. Fusion, vol. 56, 2016, p. 064002), and it was then theoretically investigated that a new expression for the magnetic moment, including the second-order corrections, could essentially reproduce the so-called collisionless pitch-angle scattering process (Liu et al., Nucl. Fusion, vol. 58, 2018, p. 106018). In this paper, with synchrotron radiation, extensive numerical verification of the validity of the high-order guiding-centre theory is given for simulations involving REs by incorporating such an expression formore » the magnetic moment into our particle tracing code. A high-order guiding-centre simulation approach with synchrotron radiation (HGSA) is applied. Synchrotron radiation plays an essential role in the life cycle of REs. The energy of REs first increases and then becomes saturated until the electric field acceleration is balanced by the radiation dissipation. Unfortunately, the process cannot be simulated accurately with the standard guiding-centre model, i.e. the first-order guiding-centre model. Remarkably, it is found that the HGSA can effectively produce the fundamental process of REs. Since the time scale of the energy saturation of REs is close to seconds, the computational cost becomes significant. In order to save costs, it is necessary to estimate the time of energy saturation. An analytical estimate is derived for the time it takes for synchrotron drag to balance an accelerating electric field and the provided formula has been numerically verified. Finally, test calculations reveal that HGSA is favourable for exploiting the dynamics of REs in tokamak plasmas.« less
  2. A theory of self-organized zonal flow with fine radial structure in tokamak

    The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown here to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters;more » the results are presented in several figures and two movies that show the spatiotemporal evolutions as well as the spectrum analysis—frequency-wave number spectrum, auto power spectrum, and Lissajous diagram. This approach reveals that the zonal flow in tokamak is a local traveling wave. For the quasi-stationary process, the cycle of ITG wave energy is composed of two consecutive phases in distinct spatiotemporal structures: a pair of Cavitons growing and breathing slowly without long range propagation, followed by a sudden decay into many Instantons that carry negative wave energy rapidly into infinity. A spotlight onto the motion of Instantons for a given radial position reproduces a Blob-Hole temporal structure; the occurrence as well as the rapid decay of Caviton into Instantons is triggered by zero-crossing of radial group velocity. A sample of the radial profile of zonal flow contributed from 31 nonlinearly coupled rational surfaces near plasma edge is found to be very similar to that observed in the JET Ohmic phase [J. C. Hillesheim et al., Phys. Rev. Lett. 116, 165002 (2016)]. The theory predicts an interior asymmetric dipole structure associated with the zonal flow that is driven by the gradients of ITG turbulence intensity.« less
  3. The accurate particle tracer code

    The Accurate Particle Tracer (APT) code is designed for systematic large-scale applications of geometric algorithms for particle dynamical simulations. Based on a large variety of advanced geometric algorithms, APT possesses long-term numerical accuracy and stability, which are critical for solving multi-scale and nonlinear problems. To provide a flexible and convenient I/O interface, the libraries of Lua and Hdf5 are used. Following a three-step procedure, users can efficiently extend the libraries of electromagnetic configurations, external non-electromagnetic forces, particle pushers, and initialization approaches by use of the extendible module. APT has been used in simulations of key physical problems, such as runawaymore » electrons in tokamaks and energetic particles in Van Allen belt. As an important realization, the APT-SW version has been successfully distributed on the world’s fastest computer, the Sunway TaihuLight supercomputer, by supporting master–slave architecture of Sunway many-core processors. Here, based on large-scale simulations of a runaway beam under parameters of the ITER tokamak, it is revealed that the magnetic ripple field can disperse the pitch-angle distribution significantly and improve the confinement of energetic runaway beam on the same time.« less
  4. Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems

    Here, an explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as discrete differential form fields on a fixed mesh. With the assistance of Whitney interpolating forms, this scheme preserves the gauge symmetry of the electromagnetic field, and the pressure field is naturally derived from the discrete internal energy. The whole system is solved using the Hamiltonian splitting method discovered by He et al. [Phys. Plasmas 22, 124503 (2015)], which was been successfully adopted in constructing symplectic particle-in-cell schemes.more » Because of its structure preserving and explicit nature, this algorithm is especially suitable for large-scale simulations for physics problems that are multi-scale and require long-term fidelity and accuracy. The algorithm is verified via two tests: studies of the dispersion relation of waves in a two-fluid plasma system and the oscillating two-stream instability.« less

Search for:
All Records
Author / Contributor
000000017484401X

Refine by:
Resource Type
Availability
Publication Date
Author / Contributor
Research Organization