Coupled wake boundary layer model of wind-farms

We present and test the coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a wind-farm. The model couples the traditional, industry-standard wake model approach with a "top-down" model for the overall wind-farm boundary layer structure. This wake model captures the effect of turbine positioning, while the "top-down" portion of the model adds the interactions between the wind-turbine wakes and the atmospheric boundary layer. Each portion of the model requires specification of a parameter that is not known a-priori. For the wake model, the wake expansion coefficient is required, while the "top-down" model requires an effective spanwise turbine spacing within which the model's momentum balance is relevant. The wake expansion coefficient is obtained by matching the predicted mean velocity at the turbine from both approaches, while the effective spanwise turbine spacing depends on turbine positioning and thus can be determined from the wake model. Coupling of the constitutive components of the CWBL model is achieved by iterating these parameters until convergence is reached. We illustrate the performance of the model by applying it to both developing wind-farms including entrance effects and to fully developed (deep-array) conditions. Comparisons of the CWBL model predictions with results from a suite of large eddy simulations (LES) shows that the model closely represents the results obtained in these high-fidelity numerical simulations. A comparison with measured power degradation at the Horns Rev and Nysted wind-farms shows that the model can also be successfully applied to real wind-farms.Comment: 25 pages, 21 figures, submitted to Journal of Renewable and Sustainable Energy on July 18, 201

Spectral behaviour of free electron masers

VI+122hlm.;24c

Spectral dynamics of a collective free electron maser

A study of the nonlinear spectral dynamics of a Free Electron Maser (FEM) is reported. In the FEM for fusion applications [1], the electron beam is modulated by a step-tapered undulator consisting of two sections with different strengths and lengths. The sections have equal periodicities and are separated by a field-free gap. The microwave beam is guided in a rectangular corrugated waveguide. The electron energy is rather low and the current density is large, therefore, the FEM operates in the collective (Raman) regime. The dynamics of the spectrum is calculated with a code that is based on a multifrequency model in the continuous beam limit with a 3D description of the electron beam. Space-charge forces are included. They strongly influence the behaviour of the generated spectrum. In the saturated regime the gain is still relatively high because of the large outcoupled power fraction. It is discussed that quite robust parameter regions exist, where single-peaked frequency spectra are excited

Spectral Dynamics of a Free-Electron Maser with a Step-Tapered Undulator

The spectral behavior of a high-power, high-gain free-electron maser (FEM) is investigated. The maser has a step-tapered undulator consisting of two sections with different strengths and lengths and equal periodicities. The sections are separated by a field-free gap. The configuration is enclosed within a low quality cavity. The millimeter wave beam is guided within a rectangular corrugated waveguide. The purpose of this undulator setup is to enhance the efficiency at high output power. The associated high gain in the Linear as well as in the nonlinear regime provides a unique oscillator. The spectral dynamics of this device is analyzed with a multipass, multifrequency code. The radiation field of the code is described as a sum over discrete frequency components. The linear gain curve of the step-tapered undulator is not the sum of the curves of two single undulators and has a completely different spectrum. The gain of the FEM is so high that nonlinear interaction occurs within a few passes. In the fully nonlinear regime the gain is still relatively high. The power spectrum evolves towards a state in which the power at the resonance of the second undulator section is suppressed. In the final state, where the frequency spectrum hardly changes from pass to pass, the power spectrum exhibits two peaks at frequencies that are determined by the first section of the undulator. The main peak is related to its resonance frequency, while the second peak is a lower sideband. The dependence of the sideband on the gap length, the relative polarization of both sections, and the reflection coefficient is investigated

Investigation of Multifrequency Generation in the Fem

The FOM Fusion FEM project involves the construction and operation of a 1-MW, 100 ms pulse, rapid tunable FEM in the 130-250 GHz range for fusion applications. The undulator of the FEM consists of two sections with different strengths and different lengths separated by a gap without undulator field. The design provides arbitrary focussing. Single frequency codes predict a much higher output power for the two-section undulator than for a one-section undulator. However, the different undulator strengths lead to different resonance conditions and therefore, in principle, multiple frequencies can be generated. This problem of multi-frequency generation due to the two-section undulator is under investigation. First results are presented in this paper. The longitudinal mode structure of the FEM is simulated in a multi-pass, multi-frequency code. In this code the electrons are described fully 3D, non-wiggler averaged and in the long pulse limit. AC longitudinal space-charge forces are included. The radiation field is considered to have the known transverse radial dependence of a HE11-mode, due to the rectangular corrugated waveguide of the FEM. A multi-pass calculation in the single-frequency limit is presented, where the field grows into saturation

Spectral Dynamics of the Fem

The FOM Fusion FEM project involves the construction and operation of a 1-MW, 100 ms pulse, rapidly tunable FEM in the 130-250 GHz range for fusion applications. The undulator is a novel step-tapered undulator, consisting of two sections with different strengths and lengths and equal periodicities, and separated by a fieldfree gap. The purpose of this novel proposal is to enhance the efficiency at high output power. The associated high gain in the linear and in the non-linear regime provide a unique oscillator. The spectral dynamics of the high-current FEM with a low-quality cavity is calculated with a multi-pass, multi-frequency code. In this code the electrons are described 3D. The equations in the model are not averaged over a wiggler period. The continuous beam limit is considered. The radiation field is described as a sum over discrete frequencies. The millimeter wave field has the transverse radial dependence of the HE(11)-mode in the rectangular corrugated waveguide. The linear gain curve of the step-tapered undulator has a completely different spectrum than the single undulator. Furthermore the gain of the FEM is so high that non-linear interaction already occurs within a few passes. In the fully non-linear regime the gain is still relatively high and the output power reaches the required high level. Already in an early phase the spectral dynamics is strongly influenced by non-linear competition between the various maser modes. This non-linear mode competition is investigated, in particular the evolution of the sidebands is analized. It is observed that the spectral signal at the resonant frequency of the second undulator is suppressed. This suppression is observed for several gap lengths, Furthermore the spectrum can change with the variation of the gap length from quasi-stable to chaotic