If successfully matched, the wave induces a current on the strap at the end of the transmission line. Later, the match with the antenna is adjusted against the plasma, one of the many reasons for that.
RF-sheath and potential rectification
More details on conjugate-T can be found in Section 4 of Chapter Four [18] with detailed mathematical calculations and applications for internal. The consequence at the level of plasma-facing components at the RF period scale is the appearance of a direct current due to privileged electron drift.
Physical sputtering yield
Thus, to compensate for this current, the DC potential of the coil must be adjusted and biased by an additional potential Vb:. For a deeper understanding of the topic, the reader is strongly encouraged to refer to the excellent tutorial [49] and reviews of key experiments [26–50].
Poor coupling efficiency and near-field effects
For a deeper understanding of the topic, the reader is highly recommended to refer to the excellent tutorial [49] and reviews of key experimental and modeling results [51]. and section 3.3 of this chapter). This behavior was also experimentally observed at WEST during scanning of the radial position of the ICRF antenna, where the drift potential measured by the alternating probe did not directly decrease when the antenna was retracted, but first passed the maximum for an intermediate position (cf. Fig. 4 in [50] or Fig. 6.23 in [22] in open access).
![Figure 14 in [54] or Figure 6.27 of [22] in open access)](https://thumb-ap.123doks.com/thumbv2/1libvncom/9200917.0/14.918.129.785.238.751/figure-figure-open-access.webp)
Abnormal wave absorption and far-field effects
The beauty of ICRH: assets and technological perspectives 1 Assets
Technological perspectives
However, operating the ICRF system with optimal settings is not only challenging in terms of control, but mostly limiting in terms of power density. Active limiters would then consist of applying a fraction of the power sent on the straps directly to the limiters. Summary of the key components of an ICRF system and a selection of the main phenomena that can occur in different locations.
Conclusion
Although this is already quite important in today's experimental tokamaks, it will be a critical aspect on future fusion reactors, which aim to maximize the surface area of the tritium breeding blanket to produce fuel and extract the energy radiated by the plasma to generate electricity. Summary and results of the investigation of the implementation of the hybrid matching option of the ITER ICRH system.
DOI: 10.1063/1.3273845
Design and operation of antennas at the ion cyclotron and lower hybrid range frequencies for nuclear fusion reactors. Optimization of discharges with ion cyclotron range of frequencies using local gas injection in OOS. Spatial Proximity Effects on the Generation of Sheath RF Voltages by Evanescent Slow Waves in the Ion Cyclotron Range of Frequencies.
Circuit model of ITER-like antenna for JET and simulation of its control algorithms. Proof-of-Concept of Charge-Resistant Cyclotron Ion Resonance Frequency Antenna in Tore Supra Plasmas. Experiments on helicons in DIII-D-investigation of the physics of a reactor-related non-inductive current technology.
High-harmonic fast-wave power flow along magnetic field lines in the scraping layer of NSTX.
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Introduction
The dream of harnessing energy from controlled nuclear fusion has been proposed for decades. The power ratio Q between the fusion output power and the input power is proportional to the fusion product nTτE, where and Tar are the central ion density and temperature [1]. Although remarkable progress has been made to achieve the required n,T and τE, they have not been achieved in the same reactor configuration simultaneously.
Two external sources are commonly used to provide the heating power, the resonant absorption of radio frequency electromagnetic waves and the injection of energetic neutral particle beams. By construction, the entry and exit of charged particles from magnetic isolation systems is prevented, except when necessary, as in the case of divertors. In the transverse displacement electromagnetic filter developed for the PTOLEMY (Princeton Tritium Observatory for Light, Early Universe, Mass-Yield-Neutrino) experiment, a compact configuration of electromagnetic fields simultaneously transports and decelerates energetic electrons from the high magnetic field of the β-de skin endpoint. Ethical energy and magnetic fields decrease by several orders of magnitude [5, 6].
A new method for accelerating low-energy charged particles into a region with a strong magnetic field by operating the PTOLEMY filter in reverse is designed. This chapter presents the principles of this acceleration method and describes its possible application using the diagnostic port of the International Thermonuclear Experimental Reactor (ITER) [7].
Basics of charged particle beam injection
Static accelerating fields avoid the bulk of these losses, but are primarily suitable for charged particle beams. In the following sections, charged particle injection of nonrelativistic ions is reexamined as a transport mechanism that drives charged ions from the outside of the reactor volume to the surface of the plasma.
Magnetic orbital angular momentum beam acceleration
- Guiding-center drifts in adiabatic field conditions
- Drifts and work
- Balanced drift
- Performance
- Injection
Only the gradient-Bdrift is orthogonal to the direction of the magnetic field gradient, so the first step is to create a component of EBdrift that exactly opposes the gradient-Bdrift. To introduce the work, the electric field is tilted by adding an additional component, E⊥, that is orthogonal to the direction of the magnetic field gradient. The lattice displacement is along the direction of the magnetic field gradient and directs the beam guiding center to cross the equipotential lines and accelerates the particles.
The profile of the transverse magnetic field in the CST simulation for the trajectory shown in Figure 1. The color (orientation) of the arrow indicates the magnitude (direction) of the field at the tail position. Simulation of the injection of deuterium ions in a 1/R magnetic field in a tokamak using the accelerating structure of Figure 1.
Upon exiting the accelerator, the energetic ion continues to drift toward the plasma confinement region under the 1/R magnetic field gradient-B drive of the tokamak.
Energy efficiency
The relatively hot thermal temperature of the 1 MeV deuterium ions will thermalize through Coulomb interactions with the plasma. For example, injection of 4 MeVα particles through the ITER diagnostic port can be an effective way to study the effects of fusion final-state ion interactions on the plasma. Charge neutralization can be achieved by instrumenting ion (electron) injection ports at the top (bottom) of the tokamak.
Gradient-Bdrift will move ions down (for a given orientation of the azimuthal toroidal magnetic field) and electrons (or negative ions) up. Such a magnet is compact and can be installed in an anti-dipole coil in the upper diagnostic port of ITER, as shown in The anti-dipole creates a zero-field region for the ion source and reduces the Lorentz forces on the primary reactor coils.
The details of this magnet and the field cage are beyond the scope of this chapter.
Conclusions
This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In particular, we are interested in coupled models for fluid flow interacting with the flow of porous media and fluid structure interaction (FSI) models. For coupled models for fluid flow interacting with porous media flow, we present discrete preconditioner techniques, two-level and multilevel methods, two-level and multilevel algorithms based on Newton-type linearization, and time-stepping methods.
For example, in fluid dynamics, there are two-phase flow models, fluid-structure interaction models, fluid heat transfer models, etc. Applications include the environmental engineering problem of groundwater contamination through rivers and the geoscience problem of surface flows percolating through turbulent porous media. For example, blood flow interacting with the ship's wall, compressible fluids interacting with the wings of the aircraft, and the collision and shock response of the ship's structure to the water flow.
To deal with the problems caused by the coupling of different submodels and nonlinearity [4–8], we discuss some decoupling techniques that have proven to be very successful and efficient.
Decoupled algorithms for the coupled models of fluid flow interacting with porous flow
- Coupled models for fluid flow interacting with porous media flow
- Decoupled algorithms in the preconditioning steps
- Decoupling and linearization by two-level and multi-level algorithms
- Decoupled algorithms by partitioned time schemes
By multiplying test functions by (3) and (8), integrating by dividing and plugging in the interface boundary conditions, we have the weak form of the linked Navier-Stokes/Darcy model: findu¼ðu,ϕÞ∈X,p∈Q such that. For the suitability of the coupled Navier-Stokes/Darcy model, we refer to the recent results in [5, 6, 34]. We also propose another preconditioner of the block triangular type:. by preserving the divergence operator.
The number of iterations based on the two preconditioners is independent of mesh refinement. Furthermore, the theory of the two-network algorithm guarantees that the approximation properties are good. As an illustration of the effectiveness of the multilevel algorithm [41], we present the numerical results in Table 2.
Furthermore, the Aubin-Nitsche duality argument can lead to an analysis of the L2error problem (19).
FSI models and decoupled algorithms
- Partitioned algorithms for FSI models
- Multirate time step approach for FSI models
- Numerical experiment
Numerical experiments suggest that the version with a larger time step size in the fluid solver (cf. Figure 3) results in better accuracy. We comment here that the multirateβ scheme is nothing but the β scheme itself when the time-step ratio¼1. We then perform numerical experiments to investigate the effects of the time-step ratio. Figure 6 illustrates that a larger time step size in the fluid part results in a more accurate numerical solution than that obtained by using a larger step size in the structure part.
This cuts off the possibility of using a larger time step size in the structure part. To further investigate the stability and convergence of the multirateβ scheme, in the right part of Figure 7, we reduce the mesh size to beh¼0:01 while fixing the time step size. The numerical results confirm that the multirate β scheme is still stable even though the time-step ratio is reasonably large.
Comparison of the β scheme and the multirateβ schemes with two different time step ratios (h¼0:1 and Δt¼10 5 are fixed).
Concluding remarks
A two-grid mixed Stokes-Darcy model method for coupling fluid flow to porous media flow. Stability and convergence analysis of extensions of the kinematically coupled scheme for fluid-structure interaction. A two-grid separation algorithm for the mixed Stokes-Darcy model with the Beavers-Joseph interface condition.
Two new decoupling algorithms for the stable Stokes-Darcy model based on two-grid discretizations. Convergence analysis of an iterative subdomain method for the finite element approximation of the coupling of Stokes and Darcy equations. Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer Series in Computational Mathematics.
Long-term stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblems.
