T. M. Tran

TDA - A three-dimensional axisymmetric code for free-electron-laser (FEL) simulation

Abstract A particle simulation code, TDA, which models the single-pass amplification process in a free-electron-laser (FEL) is developed and tested. The code allows for the treatment of the fully three-dimensional electron dynamics, thus taking into account the transverse betatron motion as well as the longitudinal bunching of the electrons. The paraxial wave equation that governs the growth and the diffraction of the self-consistent radiation field (assumed to be axisymmetric), is discretized in the radial direction by the finite difference method. The benchmark study indicates that the single-pass gain, as well as the optical guiding phenomena can be well described by the code with a reasonable number simulation particles ( N ≈ 1000) and a radial mesh number not exceeding 64. A detailed discussion of the numerical method is presented.

A global collisionless PIC code in magnetic coordinates

A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), delta f scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-1 line magnetic coordinates and a field-aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Another feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 109 marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests. (c) 2007 Elsevier B.V. All rights reserved.

Finite element approach to global gyrokinetic Particle-In-Cell simulations using magnetic coordinates

We present a fully-global linear gyrokinetic simulation code (GYGLES) aimed at describing the unstable spectrum of the ion-temperature-gradient modes in toroidal geometry. We formulate the Particle-In-Cell method with finite elements defined in magnetic coordinates, which provides excellent numerical convergence properties. The poloidal mode structure corresponding to k(parallel to) = 0 is extracted without approximation from the equations, which reduces drastically the numerical resolution needed. The code can simulate routinely modes with both very long and very short toroidal wavelengths, can treat realistic (MHD) equilibria of any size, and runs on a massively parallel computer

Experimental study from linear to chaotic regimes on a terahertz-frequency gyrotron oscillator

Basic wave-particle interaction dynamics from linear to chaotic regimes is experimentally studied on a frequency tunable gyrotron generating THz radiation in continuous mode (200W) at 263GHz which will be used for dynamic nuclear polarization nuclear magnetic resonance spectroscopy applications. In the studied system, the nonlinear dynamics associated to the waveparticle interaction is dominated by longitudinal mode competition of a given transverse TEm;p cavity-mode. This study covers a wide range of control parameter from gyro-traveling wave tube (gyro-TWT) to gyro-backward wave oscillator (gyro-BWO) like interactions for which extensive theoretical studies have been performed in the past on a simplified system. Besides the common route to chaos characterized by period doubling, other routes have been identified among which some are characterized by line-width frequency-broadening on the side-bands. The complex nonlinear dynamics is in good agreement with the theory and the experimental results are discussed on the basis of the prediction obtained with the nonlinear time-dependent selfconsistent codes TWANG and EURIDICE both based on a slow-time scale formulation of the self-consistent equations governing the wave-particle dynamics. VC

Long global gyrokinetic simulations: Source terms and particle noise control

In global gyrokinetic simulations it takes a long time for the turbulence to reach a quasisteady state, and quantitative predictions about the quasisteady state turbulence have been difficult to obtain computationally. In particular, global particle-in-cell gyrokinetic simulations have been inefficient for long simulations due to the accumulation of noise. It is demonstrated that a simple Krook operator can effectively control noise; it also introduces an unphysical dissipation, which damps the zonal flows and can significantly affect simulation results even when the relaxation time is very long. However, it is possible to project out the effects of the Krook operator on the zonal flows. This permits noise accumulation to be controlled while preserving the physics of interest; simulations are then run to determine the level of quasisteady state transport and the variation across the ensemble of turbulent dynamics. Convergence is demonstrated both in the number of computational particles and the unphysical relaxation time.

Nonlinear low noise particle-in-cell simulations of electron temperature gradient driven turbulence

In this Letter, it is shown that global, nonlinear, particle-in-cell (PIC) simulations of electron temperature driven turbulence recover the same level of transport as flux-tube codes when the level of statistical noise, associated with the PIC discretization, is sufficiently small. An efficient measure of the signal-to-noise ratio, applicable to every PIC code, is introduced. This diagnostic provides a direct measure of the quality of PIC simulations and allows for the validation of analytical estimates of the numerical noise. Global simulations for values of rho(*)(e)< 1/450 (normalized electron gyroradius) show no evidence of a gyro-Bohm scaling. (c) 2007 American Institute of Physics.

Avalanchelike bursts in global gyrokinetic simulations

Highly variable flux surface averaged heat fluxes are resolved in gyrokinetic simulations of ion temperature gradient (ITG) turbulence, even in large systems. Radially propagating fronts or avalanches are also seen. Their propagation lengths in gyroradii and relative amplitude remain constant as simulation size is increased, so the avalanches appear to result from local dynamics, rather than global relaxation events. For the Cyclone [Dimits et al., Phys. Plasmas 7, 969 (2000)] case, the avalanche propagation direction is found to depend on the sign of the shearing rate. A mechanism for avalanche propagation based on the advection of turbulence tilted by the shear flows is proposed: The Cyclone linear ITG dispersion relation explains the propagation direction of tilted vortices. It also explains why there is no such preferred direction in a simulation with reduced magnetic shear. The paper explores several models for these bursts. First, certain types of models based on nonlinear heat diffusion equations a...

Operation of a quasi-optical gyrotron with a Gaussian output coupler

The operation of a 92 GHz quasi‐optical gyrotron having a resonator formed by a spherical mirror and a diffraction grating placed in −1 order Littrow mount is presented. A power of 150 kW with a Gaussian output pattern was measured. The Gaussian content in the output was 98% with less than 1% of depolarization. By optimizing the magnetic field at fixed frequency, a maximum efficiency of 15% was reached.

First principles based simulations of instabilities and turbulence

It is now widely believed that low frequency turbulence developing from smallscale instabilities is responsible for the phenomenon of anomalous transport generally observed in magnetic confinement fusion experiments. The microinstabilities are driven by gradients of equilibrium density, ion and electron temperatures and magnetic field strength. Gyrokinetic theory is based on the Vlasov-Maxwell equations and, consistent with the ordering, averages out the fast particle gyromotion, reducing the phase space from 6 to 5 dimensions. Solving the resulting equations is a non-trivial task. Difficulties are associated with the magnetic confinement geometry, the strong disparities in space and time scales perpendicular and parallel to B, the different time scales of ion and electron dynamics, and the complex nonlinear behaviour of the system. The main numerical methods are briefly presented together with some recent developments and improvements to the basic algorithms. Recent results are shown, with emphasis on the roles of zonal E x B flows, of parallel nonlinearity and of toroidal coupling on the saturation of ion temperature gradient (ITG) driven turbulence in tokamaks.

Gyrokinetic simulations of turbulent transport: size scaling and chaotic behaviour

Important steps towards the understanding of turbulent transport have been made with the development of the gyrokinetic framework for describing turbulence and with the emergence of numerical codes able to solve the set of gyrokinetic equations. This paper presents some of the main recent advances in gyrokinetic theory and computing of turbulence. Solving 5D gyrokinetic equations requires state-of-the-art high performance computing techniques involving massively parallel computers and parallel scalable algorithms. The various numerical schemes that have been explored until now, Lagrangian, Eulerian and semi-Lagrangian, each have their advantages and drawbacks. A past controversy regarding the finite size effect (finite ρ∗) in ITG turbulence has now been resolved. It has triggered an intensive benchmarking effort and careful examination of the convergence properties of the different numerical approaches. Now, both Eulerian and Lagrangian global codes are shown to agree and to converge to the flux-tube result in the ρ∗ → 0 limit. It is found, however, that an appropriate treatment of geometrical terms is necessary: inconsistent approximations that are sometimes used can lead to important discrepancies. Turbulent processes are characterized by a chaotic behaviour, often accompanied by bursts and avalanches. Performing ensemble averages of statistically independent simulations, starting from different initial conditions, is presented as a way to assess the intrinsic variability of turbulent fluxes and obtain reliable estimates of the standard deviation. Further developments