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

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

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

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?

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 channels are 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)

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

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

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

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

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)

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

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

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