Interpretation of dispersion relations for bounded systems

Constructing normal modes for bounded systems from infinite dispersion relation roots for interpretation of plasma wave and instability studies on finite cylinder

Low-frequency macroscopic instabilities of fully ionized magnetoplasma

Studies are described of low-frequency quasi-static instabilities in a fully ionized plasma. The plasma is assumed to be immersed in a uniform magnetic field, and is either uniform or has a number density gradient perpendicular to the magnetic field. A moment equation description of the ion and electron dynamics is used; collisions are assumed to have a strong effect on electron motion along the magnetic field. Before considering specific modes, a stability analysis is developed which allows a classification of wave growth characteristics to be made for a bounded system from solutions to the dispersion relation for an infinite system. Also, a method is given for calculating the normal mode frequencies and wave profiles by using the reflection coefficients at the boundaries. For wave propagation perpendicular to the magnetic field, the flute wave is studied in cylindrical geometry. The destabilizing effect of a radial electric field is considered by solving a differential equation

Axisymmetric Tandem Mirror Magnetic Fusion Energy Power Plant with Thick Liquid-Walls

A fusion power plant is described that utilizes a new version of the tandem mirror device including spinning liquid walls. The magnetic configuration is evaluated with an axisymmetric equilibrium code predicting an average beta of 60%. The geometry allows a flowing molten salt, (flibe-Li{sub 2}BeF{sub 4}), which protects the walls and structures from damage arising from neutrons and plasma particles. The free surface between the liquid and the burning plasma is heated by bremsstrahlung radiation, line radiation, and by neutrons. The temperature of the free surface of the liquid is calculated, and then the evaporation rate is estimated from vapor-pressure data. The allowed impurity concentration in the burning plasma is taken as 1% fluorine, which gives a 17% reduction in the fusion power owing to D/T fuel dilution, with F line-radiation causing minor power degradation. The end leakage power density of 0.6 MW/m{sup 2} is readily handled by liquid jets. The tritium breeding is adequate with natural lithium. A number of problem areas are identified that need further study to make the design more self-consistent and workable; however, the simple geometry and the use of liquid walls promise the cost of power competitive with that from fission and coal

Progress on coupling UEDGE and Monte-Carlo simulation codes

Our objective is to develop an accurate self-consistent model for plasma and neutral sin the edge of tokamak devices such as DIII-D and ITER. The tow-dimensional fluid model in the UEDGE code has been used successfully for simulating a wide range of experimental plasma conditions. However, when the neutral mean free path exceeds the gradient scale length of the background plasma, the validity of the diffusive and inertial fluid models in UEDGE is questionable. In the long mean free path regime, neutrals can be accurately and efficiently described by a Monte Carlo neutrals model. Coupling of the fluid plasma model in UEDGE with a Monte Carlo neutrals model should improve the accuracy of our edge plasma simulations. The results described here used the EIRENE Monte Carlo neutrals code, but since information is passed to and from the UEDGE plasma code via formatted test files, any similar neutrals code such as DEGAS2 or NIMBUS could, in principle, be used

2-D electric fields and drifts near the magnetic separatrix in divertor tokamaks

A 2-D calculation is presented for the transport of plasma in the edge region of a divertor tokamak solving continuity, momentum, and energy balance fluid equations. The model uses anomalous radial diffusion, including perpendicular ion momentum, and classical cross-field drifts transport. Parallel and perpendicular currents yield a self-consistent electrostatic potential on both sides of the magnetic separatrix. Outside the separatrix, the simulation extends to material divertor plates where the incident plasma is recycled as neutral gas and where the plate sheath and parallel currents dominate the potential structure. Inside the separatrix, various radial current terms - from viscosity, charge-exchange and poloidal damping, inertia, and {triangledown}B - contribute to the determining the potential. The model rigorously enforces cancellation of gyro-viscous and magnetization terms from the transport equations. The results emphasize the importance of E x B particle flow under the X-point which depends on the sign of the toroidal magnetic field. Radial electric field (E{sub y}) profiles at the outer midplane are small with weak shear when high L-mode diffusion coefficients are used and are large with strong shear when smaller H-mode diffusion coefficients are used. The magnitude and shear of the electric field (E{sub y}) is larger both when the core toroidal rotation is co-moving with the inductive plasma current and when the ion {triangledown}B-drift is towards the single-null X-point

Simulation of Large Parallel Plasma Flows in the Tokamak SOL Driven by Cross-Field Transport Asymmetries

Large-Mach-number parallel plasma flows in the single-null SOL of different tokamaks are simulated with multi-fluid transport code UEDGE. The key role of poloidal asymmetry of cross-field plasma transport as the driving mechanism for such flows is discussed. The impact of ballooning-like diffusive and convective transport and plasma flows on divertor detachment, material migration, impurity flows, and erosion/deposition profiles is studied. The results on well-balanced double null plasma modeling that are indicative of strong asymmetry of cross-field transport are presented

A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas

A high-order finite volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm is based on a general fourth-order reconstruction scheme for an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. The method provides density conservation and high-order-accurate evaluation of the FPO independent of the choice of the velocity coordinates. As an example, a linearized FPO in constant-of-motion coordinates, i.e. the total energy and the magnetic moment, is developed using the present algorithm combined with a cut-cell merging procedure. Numerical tests include the Spitzer thermalization problem and the return to isotropy for distributions initialized with velocity space loss cones. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Rosenbluth potentials

Recent progress of plasma exhaust concepts and divertor designs for tokamak DEMO reactors

The power exhaust concept and an appropriate divertor design are common critical issues for tokamak DEMO design activities which have been carried out in Europe, Japan, China, Korea and the USA. Conventional divertor concepts and power exhaust studies for recent DEMO designs (Pfusion = 1 – 2 GW, Rp = 7 – 9 m) are reviewed from the viewpoints of the plasma physics issues and the divertor engineering design. Radiative cooling is a common approach for the power fusion scenario. Requirements on the main plasma radiation fraction (frad main = Prad main/Pheat) and the plasma performance constrain the divertor design concept. Different challenges contribute to optimizing the future DEMO designs: for example, (i) increasing the main plasma radiation fraction for ITER level Psep/Rp designs and simplifying the divertor geometry, and (ii) extending ITER divertor geometry with increasing divertor radiation (Prad div) for larger Psep/Rp ≥ 25MWm− 1 designs. Power exhaust simulations with large Psep = 150 – 300 MW have been performed using integrated divertor codes considering an ITER-based divertor geometry with longer leg length (1.6 – 1.7 m), as in a common baseline design. Geometry effects (ITER like geometry or more open one without baffle) on the plasma detachment profile and the required divertor radiation fraction (frad div = Prad div/Psep) were key aspects of these studies. All simulations showed that the divertor plasma detachment were extended widely across the target plate with a reduction in the peak heat load of qtarget ≤ 10 MWm− 2 for the large frad div = 0.7 – 0.8, while the peak qtarget location and value were noticeably different in the partially detached divertor. Simulation results also demonstrated that radial diffusion coefficients of the heat and particle fluxes were critical parameters for DEMO divertor design, and that effects of plasma drifts on outboard enhanced asymmetry of the heat flux, suggested the need for longer divertor leg to ensure the existence of a detached divertor operation with qtarget ≤ 10 MWm− 2 . Integrated design of the water cooled divertor target, cassette body (CB) and cooling pipe routing has been developed for each DEMO concept, based on the ITER-like tungsten monoblock (W-MB) with Cu-alloy cooling pipes. Engineering design adequate under higher neutron irradiation condition was required. Therefore, inlet coolant temperature (Tcool) was increased. In current designs, it still shows a large potential variation between 70 ◦C and 200 ◦C. The influence of thermal softening on the Cu-alloy (CuCrZr) pipe was fostered near the strike point when the high qtarget of ~10 MWm− 2 was studied. Improved technologies for high heat flux components based on the ITER W-MB unit have been developed for EU-DEMO. Different coolant conditions (low- and high Tcool) were provided for Cu-alloy and reduced activation ferritic martensitic (RAFM) steel heat sink units, respectively. The high-Tcool coolant was also considered for the CB and supporting structures. Appropriate conditions for the high-Tcool coolant, i.e. 180 ◦C/ 5 MPa (EU-DEMO) and 290 ◦C/ 15 MPa (JA-DEMO, CFETR and K-DEMO), will be determined in the future optimizations of the divertor and DEMO design