ARIES-CS Project Meeting Minutes
3 - 4 December 2003
Princeton Plasma Physics Laboratory
Princeton, New Jersey
Documented by L. Waganer
Ref: Agenda and Presentation Links: Project Meeting
Welcome and Challenge - Rob Goldston challenged the ARIES team to look ahead to our future and help define the fusion development vision and pathway. He praised our effort to help define the Stellarator concepts in both near term experiments and commercial applications. The Stellarator concept may be a benefit because it can represent a steady-state, high-power source. Our efforts will help guide research and define the next steps in this endeavor.
Status of ARIES Design Study - Farrokh Najmabadi explained that our team has been investigating the parameter space and key issues for Compact Stellarators for a year. We have examined and assessed two configurations to the point of assessing both physics and engineering issues. We have identified some shortcomings and are proposing potential solutions. However, we need to keep examining a broad range of concepts to fully explore the Compact Stellarator design space.
The FY03 Advanced Design budget is smaller than last year, which entails a stretched out program. At present, there is no information on the FY04 budget.
Arrangements for Meetings and Conference Calls - The next ARIES meeting will be held at UCSD during the first week of March, either Mon/Tues or Thur/Fri. Les Waganer will poll the team as to their preferences. The second 2004 ARIES meeting will be held in June, either the week of 7th or 14th. Les will also solicit preferences on these dates.
The next ARIES conference call will be held on January 13. Les Waganer will send out the conference call number and time.
ARIES CS Assessment
Compact Stellarator Reactor Physics Basis
Recent Progress in Configuration Development for Compact Stellarator Reactors - Long-Poe Ku explained the main focus has been the study of flux surface quality, namely flux surface integrity, methods to improve surface quality, and novel approaches to quasi-axisymmetric (QA) configuration design. Specifically, he has been defining a figure of merit to minimize surface islands.
QA reactor configurations are being developed using the NCSX knowledge base. We require QA plasmas to satisfy certain MHD stability acceptance criteria at 4% ß with “good” QA:
Additionally, it is required all coils have:
Jim Lyon has studied several configurations that possess “good” plasma, attractive coils, and overall reactor performance with plasma radius of less than 8 m and thermal power of 2 GW. These reactors must also minimize the a-particle loss and maximize the plasma-coil separation subject to Bmax < Bcritical. Minimization of alpha particle loss is now incorporated into the configuration optimization. Configurations with a-energy losses of around 10% have been identified. These losses are localized with levels around a few MW/m2 (see figure in presentation), which require engineering assessment and design solutions.
Optimization of modular coils has led to configurations with coil aspect ratios of < 6, hence smaller reactors are possible. However, to make QA reactors competitive, the plasma ß must be increased and the coils simplified. Increasing ß raises two issues: 1) the integrity of the flux surfaces and equilibrium ß limit and 2) increased demand of plasma shaping for MHD stability. It is encouraging that experimental results appear to indicate that stellarator plasmas may be more resilient than the linear theory would indicate.
It is predicted that the integrity of the flux surfaces and the MHD stability establish the ß limit:
The effect of ß on flux surface integrity was illustrated with a case of three-field period plasma with A = 4.5, a-loss optimized configuration. Due to the low aspect ratio and relatively high iota, the axis shift is modest even at a ß of 8% according to VMEC calculations. But, the presence of low order rational surfaces and high shear, large islands and regions of poor surfaces exist. Several Poincaré plots illustrate these islands. Islands can be “healed” by zeroing out the resonant perturbations using an algorithm that calculates resonant normal field. An illustration showed the positive results of hand adjusting boundary-shaping harmonics. Long-Poe questioned if there might be simpler optimization methods that would not be so computer intensive.
A possible approach was investigated to test the theory and find scaling constants. A three-field period, A = 6 configuration was used with one “tunable” term for adjusting the size of the vacuum island. Poincaré plots showed that indeed the vacuum and pressure driven islands were reduced or eliminated. However, Long-Poe suggested the need to resolve the sensitivity issue before devising a FOM for the configuration optimization.
An alternate solution would be to avoid having low-order rational surfaces in the plasma as much as possible. Such configurations would have steep, negative magnetic shear (externally generated) and low, positive shear at full ß and full current. Long-Poe illustrated this concept with a 3-field period A = 6 configuration comparing a N3JJ design (island avoidance at 0% ß) and N3JB design (island avoidance at 6% ß). Both have reasonably good QA, but improvements are needed at certain mode numbers.
As the configuration N3JB is improved (to avoid islands at 6% ß) with respect to QA and MHD stability, this solution leads to increased elongation and triangularity (without introducing higher order terms in plasma shaping). When another design, N3JM, is adjusted to minimize the negative shear at full current, full ß results in a nearly “up-turn” vacuum iota near the plasma edge.
Two-field period configurations with similar characteristics may exist for iota < or = 0.5, but the width of regions free of low-order rational surfaces may be too narrow to make good configurations.
Long-Poe concluded that:
Physics Assessment of a Two-Field Period Reactor – Paul Garabedian explained that the high-resolution NSTAB calculations predict the LHD experimental stellarator is linearly stable. However, the experiment shows its plasma is nonlinearly stable at a ß of 3.2%. There is a similar situation between theory and experimental results for the W7-AS experiment. Paul has correlated those results to design a quasiaxially symmetric stellarator with two field periods. He showed a diagram of a MHH2 stellarator with A = 3.5, which was designed with the NSTAB equilibrium code. The large separation distances between coils would suggest maintenance ports would be feasible.
Paul showed Poincaré maps of the ß = 3.2% MHH2 flux surfaces at four cross sections of the torus. For a standard pressure profile (p = p0(1-s)), the global m = 1, n = 1 mode is linearly unstable, but nonlinearly stable. Paul also presented four cross-sections of flux surfaces for a wall-stabilized MHH2 equilibrium case at ß = 4.5% with the pressure p = p0 (1-s1.5)1.5 and hybrid net current bring the rotational transform into the interval 0.61 > i >0.51. Other similar flux plots were presented with different ß values and pressure profiles. Paul showed the line tracing calculation to display the control surface for the coils, the plasma shape, and the magnetic lines computed at a finite ß in the scrape off layer. The extent of the magnetic field lines outside the separatrix indicates there are good possibilities for a divertor.
Paul showed an exterior view of the MHH2 modular coils that suggested there is adequate room for maintenance ports. These smooth coils should produce robust flux surfaces that do not deteriorate when changes are made in the vertical and toroidal fields.
Paul showed similar coil and flux plots for the PG3, two-field period plasma with an aspect ratio of 4.5. This configuration also has smooth coil surfaces and good plasma surfaces. He showed a field plot of the LHD R = 3.6 configuration at m = 4, n = 3 island that indicates an equilibrium limit on ß may have been reached. This configuration may be non-linearly unstable at ß= 0.04 and stable at ß = 0.032.
Numerical implementations of the local ballooning criterion depend on the chosen boundary conditions. These calculations show that the ß limits for LHD experiment have been exceeded by a significant margin.
Experimental Stellarator High- ß Plasmas – Mike Zarnstorff showed the progress of ß values that have been achieved in Stellarators and Helitrons. The LHD has progressed to < ß > values of 3.0% and 3.2% with pellets. The W7AS has achieved a < ß > value of 3.4%. A plot of <ß> versus normalized flat top time showed many cases of < ß > greater than 3% and a typical Asdex Upgrade shot has a value of 3.3%. When compared to tokamak cases, the tokamaks are limited by Greenwald limits and q = 2, whereas the stellarators are not limited by these parameters (no MHD limits). On the other hand, ß values in stellarators may be limited by deterioration of equilibrium where the axis shift of ~ 1/2 of the plasma radius.
Mike presented a set of charts that illustrated that ß may be sensitive to the control coil current. The low ß phase approximately agrees with vacuum calculations. High ß phases optimizes with much higher control coil current, which may indicate the importance of islands to confinement. The preliminary PIES calculations indicate all stellarator plasmas are mainly stochastic at high ß. He showed a series of field plots at different control coil currents. Divertor type configurations are seen at higher positive coil currents. High ß configurations are seen at more negative control coil currents. PIES calculations at Icc = 0 show many island structures, whereas with Icc = -2.5 MA, the island structures are much reduced. A plot of high-ß campaigns after 2000 are compared to runs prior to 2000 showed an improved level of ß.
Mike illustrated that linear stability calculations (CAS3D) indicate the 2/1 mode should be unstable, even at low ß values. Mike quoted results from Watanabe that compared observed pressure gradient and low-n unstable regions based on linear ideal MHD mode analysis by the TERPSHICORE code in the dß/dp-ß diagram. The gradient seems to avoid low-n unstable regions. The final goal of this work is to obtain a criterion that the low-n mode is effective by using D1 or g.
Mike compared observed pressure gradient and low-n unstable regions based on linear ideal MHD mode analysis using TREPSHICORE code the dß/dp-ß diagram in the edge regions. Experiments values exceeded the Mercier limits but seemed to be limited by the low-n unstable limit.
Pressure driven MHD does not limit the LHD experimental operation. The LHD experiment observes saturated m/n modes at moderate ß, but does not limit access to higher ß. The 2/1 mode disappears for ß >2.3%. Some correlation exists between observed mode and theoretical linear-stability threshold. Typically, it exhibits lower collisionality than the W7-AS experiment. The question is: why do these conditions saturate?
Mike showed some possible divertor locations based upon vacuum magnetic field plots. He also said that initial non-linear two-fluid flow diagrams (finite gyro-radius and self-generated flows to stabilize equilibrium) with fixed boundary conditions suggest a possible higher ß limit for NCSX.
Assessment of ß Limits for Compact Stellarators – Alan Turnbull summarized his findings:
Alan showed the NCSX equilibrium plots scaled to ARIES-CS conditions. These are show at Nfp f from 0º to 330º. He also showed a sequence of conditions using fixed boundary higher ß equilibria that was constructed from VMEC by uniformly scaling pressure. The ß limit is ~ 6% for intermediate walls of the order twice the minor radius.
Alan noted several improvements that would increase the calculation reliability. For an aw < 1.7, one could analytically extract logarithmic singularity more carefully and possibly resort to using the Greens Function method. For aw > 2.7, use corrected logic in wall construction to eliminate crossover sections and resort to alternative definitions of the conformal wall (constant normal distance in the toroidal plane projection and constant normal distance in the helical plane projection).
Alan summarized his progress in 2003 and his plans for 2004. He believes the relevance of ideal MHD ß limits are not well understood in compact stellarators. Modern stellarator experiments seem to observe ß limits that are governed by a soft limit of degrading confinement. LHD and W7AS have exceeded the predicted ß limits by a factor of 2. He suggests:
But Mike asked the question: Should predictions based on nested flux surface equilibria be ignored? He suggested that resolution requires testing global MHD stability using actual discharge equilibria. If nested surface calculations are not valid, can the stability problem be formulated in terms of finding non-linear stable equilibria?
IPP Stellarator Reactor Perspective – Yuri Igitkhanov summarized the basic design features of the HELIAS reactor concept. It has an optimized magnetic field to provide good magnetic features to the plasma, divertor islands can be used for diverters, parallel currents are smaller than diamagnetic currents, small Shafranov shift, small neoclassical losses, and good alpha particle confinement. It has steady state operation, one set of modular coils, zero toroidal current, and low average neutron load of 1 MW/m2. He stated the design criteria:
The HELIAS reactor can be configured as a 3, 4, or 5 field period system. Yuri showed the bootstrap currents for both a W7-AS machine and a HSR machine.
The machine parameters for the 3, 4, and 5 field period machines are compared. The coil stresses and strains are shown for one coil configuration. He showed the stress distribution in one of the coil support structures. He also highlighted the critical coil issues along with more detailed coil information for the HELIAS reactor HSR4/18. He summarized the ignition experiment design information for the machine with a thermal power of 1300-1700 MWth. This machine has a major radius of 18 m, a = 2.1 m, B0 of 5.0 T, Bmax = 10 T, and a fusion power of 3000 MW. Yuri illustrated the general configuration of the blanket, shielding, and coil systems. The divertor is on the outer plasma edges and utilizes the 4/4 islands to create the divertor action. There are 8 target plates for a length of 15 m and a wetted area of 40 m2. More details were provided for the modular coils.
Beta Limits in Stellarators – Henry Strauss described his M3D extended MHD physics code to address ideal and resistive MHD in stellarators. It uses a 2-fluid drift model (from Sugiyama and Park) and gyro kinetic energetic ion theory. It uses a massively parallel computer system for the extensive computations and employs finite element unstructured mesh discretization.
He discussed ideal stability, with tokamaks at the lowest mode (n = 1), which has the lowest ß threshold, stellarators has the highest mode number, which is unstable. The 2-fluid flow is more important in stellarators than tokamaks. Ideal ballooning stability depends on the toroidal mode number, n. He described nonlinear internal modes defined by the M3D code using pressure isosurfaces and velocity stream function.
Stellarators tend to be resistive interchange unstable and are unstable to resistive ballooning for all beta conditions. M3D calculations, however, show that two-fluid effects stabilize resistive ballooning modes. Henry then explained how 2-fluid flow stabilization, resistive ballooning mode, and island growth occurs and are modeled with M3D. The M3D code may be more unstable than the TERPSICORE and newer code. Henry mentioned island growth depends both on ße, per data provided by L. Sugiyama, and on the Hall parameter, H. Henry also discussed the influence of the free boundary modes.
He examined the NCSC Li383 configuration at 5% ß. He noted it has a cold halo region, 5/3 islands in the plasma and halo, and a double-tearing mode.
Henry concluded that the ideal mode ß limit is determined by intermediate modes. Resistive ballooning is stabilized by 2-fluid flow. Equilibrium islands depend on H and ße. Free boundary can be modeled in vacuum conditions as a resistive halo.
Discussion of Physics Basis – Hutch Nielsen posed the question “What should we use to set the ß limit?” Then he enumerated four possible solutions:
Additionally there are the metrics of island structures at the plasma edge, robustness of island structures, and thermal heat flux peaking.
Jim Lyon thought there was too much emphasis on determining the plasma ß value and the limiting cause.
The group thought a good reactor should have good alpha confinement, “simple” coils (simply meaning relatively easy to construct with moderate bend radii), and no criteria weighting associated with achieving linear MHD stability. Long-Poe Ku disagreed with no linear MHD stability criteria. Other criteria should be a minimum coil-to-coil distance, coil-to-plasma distance, and coil bend radii. We should examine lower order rational surface terms.
The divertor physics and engineering should be explored more as it may drive the design approach. We should try to optimize the physics issues and assess the engineering impacts.
Reactor Integrated Systems AssessmentNCSX and NHH2 Reactor Assessments – Jim Lyon summarized the NCSX-R, MHH2-R, and QPS-r key configuration parameters and discussed the similarities and differences. He highlighted the desirable features for reactor: low cost, smaller physical size, adequate coil-to-coil distance, and higher ß (related to B0). Farrokh Najmabadi stressed the systems code should be used to optimize on cost, not size. From this meeting, Jim now has cost algorithms for the coils. Laila and Rene have provided blanket geometry that can be used with existing material cost algorithms.
Jim examined the relationship between machine major radius and maximum field. He also described how to maximize B/ B0 for coil aspect ratio and coil size (d). He discussed the importance of ß limits, confinement multiplier (H-ISS95), and alpha particle losses. For each of the three reactor configurations, Jim employed a strawman base case for the comparison.
Jim questioned what the maximum ß limit he should use. The group suggested using ß limits by Long-Poe Ku for NCXS machines and Paul Garabedian for MHH2 machines. It was also recommended he use Bmax of 8 T with NbTi coils to assess the impact.
Reactor Engineering Assessment
ARIES-CS Engineering Approach – René Raffray described the process to examine the generic compact stellarator design configurations to determine the key issues and applicable design windows and engineering constraints. This led to a matrix of blanket/shield designs for several maintenance concepts. René and the engineering team is defining and evaluating these options to determine the main design drivers and engineering parameter windows. All combinations have been assessed except for the He-cooled solid breeder with ferritic steel and He-cooled divertor combination, which is in work.
René described the engineering definition and analysis of the NCSX-R three-field period reactor with field-period based maintenance approach. Groundrules were discussed, configuration defined, maintenance scheme outlined, and power core elements conceptually defined. It was suggested the conceptual tube and coil arrangement be more representative of the actual modular coil geometry to determine if this concept is acceptable. René explained the procedure to remove the blanket segments from a 120º sector. Presently, a minor amount of sculpting of the reduced-size blanket and shield is needed to accomplish the removal, but this is highly dependent on the coil and plasma geometry. Details of the blanket cooling routing and thermal performance were described.
In the case of a two-field period MHH2 reactor, the modular maintenance approach through several ports is more feasible. More room is available between adjacent coils for the port openings as shown by a matrix of available port sizes. The key features of the modular maintenance approach were discussed. An example blanket employing SiC/SiC as the structure and Pb-17Li as the breeder and coolant was described. The unique coolant routing chosen allowed the exit coolant temperature (1100º) to exceed the maximum structure temperature (900º), so this configuration allows a very high thermal conversion efficiency (~55%).
Next year, the Engineering Group will optimize the configuration to assess and select the best scheme and configuration. This configuration will be further analyzed and optimized regarding heat load and specified geometry.
Discussion of Engineering Approach and Constraints – The group thought we should continue with both the NCSX and MHH2 reactor configurations. Ku should do a calculation to define the alpha loss for both configurations based on the last closed magnetic surface and the first wall (last closed surface plus 5 cm).
Wrap Up of Physics and Engineering Action Items
MHH2 Modular Coil Parameters – Long-Poe Ku analyzed the MHH2 coils as Paul Garabedian had defined them. He showed the distance from the plasma to the coil winding surface as viewed on the plane of the normalized toroidal and poloidal angles for R = 3.5m. Two minimum distance regions were slightly below 0.65m. Long-Poe compared the LCMS (Last Closed Magnetic Surface) and concluded the magnetic fields from VMEC free boundary reconstruction capture the essence of the original coil design.
Maintenance Studies for 3-Field Period and 2-Field Period Configurations – René Raffray told the group of the analytical studies to refine and verify the clearances for the field-period maintenance approach for the three-field period maintenance approach. CAD cross-sections were defined at every 7.5º to determine the size of the blanket module to be removed and the available space for blanket module removal. Results indicated there was some interference in a few local areas. Small changes in plasma geometry, coil geometry, or thickness of blanket and shield would be required for clearance. Specific recommendations were provided.
The two-field period maintenance scheme uses the modular replacement approach through several ports between adjacent modular coils. The vacuum vessel is located between the high temperature shield and the coils. The core elements were shown at two cross-sections. The coils would be wound onto a continuous (no openings other than ports) structural element. It was recommended the next design effort would be to define the coil support structure that conforms to the coils rather than showing a generic torus. René showed a design approach for the external cryostat that incorporates concrete in the outer radius to provide additional shielding. However, more shielding will be necessary to adequately shield the ports and the upper dome. The maintenance ports radially bridge between the cryostat and the vacuum vessel. Additional definition of the biological shielding will be necessary when the core design is finalized.
René also proposed a sector maintenance approach based on a per-coil basis, such as that used for ARIES-AT. It would only be possible if each coil could be extracted radially. Perhaps it is possible on the two-field period MHH2 coil set. Xueren Wang will use his CAD model of the two-field coil set to determine if the coils (and associated other structures) can be moved independently of the other coils. If individual coils could not be independently removed, there may exist a combination of a few coil sets that might be independently removed (a la SPPS).
Neutronic Implications on Radial Build – Laila El-Guebaly summarized the candidate blanket concepts being considered for the Compact Stellarator. She highlighted a new candidate that has been added since the last meeting – a FS structure, He/LiPb-cooled blanket with a He/B-H2O cooled shield. All of these candidate systems can meet the tritium breeding requirement if the blanket covers most of the FW area and the blanket is installed behind the divertor plates or baffles. There will probably be a non-uniform thickness blanket and a local shield of WC could be used to minimize the radial build. Water would be a cost effective shielding material, if it does not pose a safety problem with other materials. The low-temperature shield will contain low-grade heat for ≤ 1% of total nuclear heating.
The distance from the plasma to the middle of the winding pack (D) varies widely for the various blanket concepts, from 1.25 cm to 1.97 cm. On the other hand, the WC shield-only region has much less variability – less than 10 cm from 1.05 to 1.15 cm.
Laila used the LiPb/FS/He/B-H2O concept with a water-cooled internal vacuum vessel for further analysis. She provided the radial thickness as a function of the neutron wall loading and compositions for the blanket and the shield-only regions. She recommended four alternate blanket and shield arrangements for the baseline system. Laila examined several attributes of the LiPb/SiC blanket system that might prove advantageous.
ARIES-CS Magnet Engineering Attributes – Leslie Bromberg showed the critical current plot for a range of applied magnetic fields. The high critical temperature superconductors have the capability for very high current density and no need for quench protection. Therefore the coil cross-sectional area is determined from structural and cooling considerations. The superconductor strain limitations are similar to the structural strain limitations. He recommended allowing 20% of the area for cooling. The coil thickness is constant with the value determined by the outer thickness.
Leslie provided the cost data on NbTi, Nb3Sn, and YBCO high temperature superconductors. If the field remains low, NbTi can be used. Nb3Sn can be used in high field applications, but winding it in the stellarator configuration can be difficult (aka costly). It might be appropriate to use either the YBCO or MgB2 . Leslie also suggested operating at a 15 K temperature with gaseous helium coolant might be more cost effective. Leslie will interact with Jim Lyon to select the proper superconductor and the appropriate costing algorithms.
UCSD Coil Design Codes – T. K. Mau said that UCSD wants to develop the capability to do detailed magnetic coil and plasma-facing component design codes. They are obtaining the capability to run:
In the immediate future, TK will create VMEC equilibrium file, perform coil optimization using VMEC/COILOPT, and use ORBIT-3D to assess alpha particle loss for the MHH2 configuration. In the longer term, TK will use VMEC/MFBE and field line tracing codes to assess thermal and fast alpha heat flux in the design of PFCs and create an interface between VMEC equilibrium and EC ray tracing code for plasma heating analysis.
New Action Items
Farrokh Najmabadi and Hutch Neilson discussed their list of action items. Farrokh edited his final list and will distribute it to the team for compliance (see below).
Action Item List
Systems Studies (Lyon)