Electromagnetic Interaction of the Blanket and the Plasma

1. Electromagnetic Interaction of the Blanket and the Plasma Investigators • M. Kotschenreuther, L. Zheng, J. Wiley • IFS: University of Texas Institute for Fusion Studies

2. Reactor Blankets- even more than Neutronics, Thermo-Hydraulics, Structural Mechanics, … • Reactor blankets are also expected to aid in tokamak plasma MHD stability • Attractive reactors with low current drive and high beta need wall stabilization • Usually thought of as an after-thought: “just” add a conducting shell • However, there is considerable metallic conductivity in the engineering blanket itself • In principle, this could either: • Enhance the stability of the plasma • Interfere with the stabilizing effect of the nominal shell

3. Blanket Effects on Plasma Stability are Substantial Initial calculations find: • The conductivity in the blanket often suffices to eliminate the need for a dedicated conducting shell for kink modes • Expect this to improve breeding ratio • Simplify reactor design • The conductivity in the blanket or neutron shield interferes with stability by: • Neutron shield of steel can also electromagnetically shield necessary feedback signals from the plasma • Must laminate the shield to reduce eddy currents • The blanket puts conductivity “too close” to the plasma- preventing stabilization from plasma rotation • Plasma rotation is thus not viable for stabilizing low n MHD wall modes in a reactor- feedback MUST be used • Ferritic effects on plasma stability are not large • Since ambient magnetic field is well beyond saturation

4. Blanket Types and Characteristics • Have considered following types of blankets so far: • Stationary “Pool” blankets of liquid LiPb- no insulators • E.g., He or water cooled • Flowing LiPb in insulated poloidal channels with steel structure • Have considered toroidally segmented blanket modules- • Assumed 16 blanket segments here • Each segment is assumed electrically isolated • How much electrical connection is there between segments, e.g., welded to vacuum vessel at back?

5. Blanket Models • Blanket is a very complex electrical structure- two models are being developed: • Use simplified average response model here • Isolated eddy currrents inside insulated LiPb channelsare included • Eddy currents from steel structure are included • Note: overall impact of LiPb currents often exceeds steel currents • Assume all structures have spatial scale less than inductive field so can average and obtain smooth PDE’s • Straightforward analysis is then possible using standard methods, but still accounting for blanket complexity • Approximations marginal because channels are not that small • Detailed finite element model of the blanket • Very similar code already developed at IFS for other EM response applications • Modification for present application – several months • Very detailed analysis possible • In both models, PbLi flow is assumed unperturbed (so far)

6. Coupling to the Plasma • For realistic plasma equilibria- use AEGIS • Benchmarked against GATO for elongated, triangular geometries • Committed to results by IAEA (November) for average response model • Results from finite element model probably on roughly same time scale • Today- simplified circular cross section geometry for initial results • Model commonly used within plasma community for first investigations of resistive wall mode effects • Several conclusions expected to be robust and apply to more realistic cases

7. Consider Stabilization of Resistive Wall Kink Modes • Use same gross parameters as ARIES AT • Same shell (1 cm W for kinks) • Same distance of shell from plasma • Plasma instabilities with same stabilization distance for ideal shell (toroidal mode numbers n=1-4) • Note: ARIES analysis (RS,AT,ST) – ignored effects of blanket conductivity • We immerse this shell in a flowing LiPb blanket • Similar to ARIES ST: poloidal channels 0.25m x 0.25 m • 0.75 m thick • RESULTS: • Addition of blanket reduces resistive instability growth rate by ~ 3 times • Without W shell, blanket alone gives instability growth rate ~1.5 - 2 times less than shell alone • A dedicated kink mode shell is unnecessary • Breeding ratio and design simplicity improved • Reduced growth rates can enhance prospects for feedback stabilization • The eddy currents in the PbLi contribute more than steel

8. Deleterious Effects of the Shield on Feedback Stabilization • The neutron shield can also shield the plasma from feedback signals of coils outside the shield • Unless the shield (0.65) is laminated: • Feedback gain requirements are increased by ~ 3-4 for mode numbers 1-2 • Implies a considerable increase in feedback power • Also, potential for feedback driven instabilies • Need to include finite feedback bandwidth to assess this • Lamination of the shield to the same degree as the blanket (0.25 m channels) greatly reduces problem • With sufficient lamination, feedback stabilization of plasma resisitive wall modes (n=1-2) appears possible without an added stabilizing shell

9. Serious Effects of the Blanket on Stabilization by Plasma Rotation • Plasma rotation is another method to stabilize plasma modes • An alternative to feedback, but required plasma rotation is regarded as too high from analysis which ignore the blanket • It is deleteriously effected by placing conductors too close to the plasma • The blanket/steel first wall has sufficient conductivity close to the plasmas to increase rotation requirements significantly n=1 ~ 100% increase n=2 ~ 50- 100 % increase n=3 ~ 10-20% increase n=4 ~ 10 – 20 % reduction • Plasma rotation appears to not be a feasible option for stabilizing n = 1-2 modes: feedback MUST be used

10. Effects of the Blanket on Stabilization of Axisymmetric modes (Vertical Instability) Axisymmetric stability is difficult to assess in a circular model, but some qualitative results seem robust • A toroidally segmented blanket has much less effect on axi-symmetric modes than on kink modes • Without a strong electrical connection between segments, a flowing Pb blanket/shield will not substantially affect shell requirements or feedback for the vertical mode • A pool PbLi blanket may significantly reduce shell/feedback requirements • With strong electrical connection in the back, a flowing PbLi blanket might also reduce shell/feedback requirements • Satisfactory analysis of blanket effects on the axi-symmetric instability require the 3-D finite element approach (more so than kink modes)

11. Finite Element Model of the Blanket • A finite element code to solve the full Maxwell’s equations with arbitrary conductivity and permeability has already been developed at the IFS (for RF applications) • By eliminating the displacement current term, it can be fairly easily adapted for the low frequency blanket electromagnetic response • Already efficiently parallelizable • Algorithm: discontinuous Galerkin method • Very well suited to problems with discontinuous conductivities/permeabilities (as in blankets with insulator/metal/vacuum interfaces) • High order accuracy: fast convergence and fewer spurious eigenvalues found in practice • Time scale for applications to this problem: a few months • The code could also potentially calculate eddy currents in fast disruptions, or static magnetic perturbations from ferritics

12. Potential Plasma Performance Optimizations • By utilizing the conductivity in metal breeder blankets, it may be possible to moderately increase plasma elongation • Increasing elongation even from 1.8 to 2.2 can increase beta by almost 2 (ARIES RS to ARIES AT) • Increasing elongation from 2.2 to 2.5 can increase beta to perhaps another 50%- still very useful (work by Chuck Kessel and M.K.) • A more modest improvement than in APEX, but significant • Increased elongation would also modestly improve confinement • Thus, even conventional blankets can be utilized to improve plasma performance in novel ways • Such optimizations have never been considered before because no suitable 3D code was available for analyzing the coupled plasma/blanket interaction • The tools discussed would provide such a tool

13. Conclusions • The blanket has very significant electromagnetic interactions with the plasma • Cases analyzed have sufficient conductivity that an additional stabilizing shell for kink modes is unnecessary- aiding breeding • Blanket interactions quite negatively affect the viability of plasma rotation stabilization for modes n = 1-2, implying feedback is needed • Satisfactory feedback performance probably requires some degree of lamination of the shield • Blanket effects may possibly reduce the requirement for the axisymmetric stabilizing shell-further improving breeding • More quantitative results with realistic geometry and possibly a finite element treatment of the blanket expected before year end • The blanket might also assist in attaining higher elongation and bettter wall stabilization which can improve reactor plasma performance