Transient Coupled Field Solution for a Pion / Muon Collector Mike Yaksh Yaksh Magnetic Solutions 1
Some background on Pion/Muon Collection An axial magnetic field is generated by current flowing in circumferential direction in a circular section (1) Magnetic field on the order of 14T are required Requires megampere current to generate the magnetic field Pulse durations are in the range of Micro-seconds Pion / Muon physics are discussed in Reference (1) Current direction Field direction A coaxial design for the collector is used in this effort (1) Design of Pulsed High-Field Magnets for Pion / Muon Collection, Turchi, P. Kauffman, M., Yaksh, M. 18th IEEE International Pulsed Power Conference 2
3 Preliminary evaluation to confirm Muon collector behavior model was targeted to have in excess of one million nodes for a transient evaluation The current pulse shape could vary from sine to more complicated shapes. Short durations would give rise to the field being concentrated at the surface For expediency, a simple test case using target collector dimensions was evaluated to observe impact of mesh density on power verses time. Commonly used 2-3 elements 1 µsec at the surface was more than 0.16 mm sufficient field penetratio n Amp time history 6 µsec 0.6 mm field penetrati on
Initial design efforts for the coaxial collector Initial design efforts focused on defining a design to obtain magnetic fields at the center in excess of 14T A magnetic model was constructed for each design considered. Initial design considered a large center conduction ring connected to the coaxial section Models generated in WorkBench Inflation layers were modeled to capture the skin effect Model size: > 1 million nodes Applied current: 1.8 Mega-Amps 10μsec equivalent pulse using AC analysis collector model 4
Mesh Details for the midsectiontypical Mesh was generated in WorkBench A thin layer of elements are modeled on the inner and outer surface of the conductor 6.1 mm 5 Each layer in this region was 0.2 mm thick
6 Development effort for the collector Maximum field at the interior was 4T < 14T Current flow was not concentrated at the inner surface Introduction of lobes was thought to generate sufficient resistance to force the current inward Additional iterations were made to force the current towards the inner surface Lobe geometry changes Additional parts outside the collector Each iteration required model regeneration Current Density
Final design met the design objective Midsection ring radial thickness was reduced to move the current flow closer to the inner diameter Exterior lobes were added to increase mass to dampen out the shock of the 10 μsec pulse Maximum field at the center was in excess of 14 T Current Density 7
Coupled Field Transient Solution The transient Methodology solution consists of three collector model solutions performed in sequence Magnetic field solution Thermal solution Structural dynamics solution To transfer data between fields, the transients is comprised of a series of restarts for each field solution The process is repeated and in each solution, the initial conditions are the results of the previous analysis. Initial collector conditions are ambient, no current, no motion X 8
Coupled Field Transient Solution Methodology Typical cycle in the transient evaluation Magnetic solution Amperage time history Update nodal coordinat es Temperature s(1) Thermal solution Heat generatio ns Temperature (2) Forces Structural solution 9 (1) Temperatures to the magnetic model are for the properties (2) Temperatures to the structural model are for properties and thermal expansion to account for thermal
Magnetics Results: Centerline flux density (T) B(x) @ 0.83µsec B(x) @ 2.5µsec B(x) @ 5µsec B(x) @ 7.5µsec B(x) @ 10µsec Maximum B vs. time 10
The current flow seems to concentrate nearer the edge where the current enters the mid section. Current density Direction Directio of current flow n of current flow Directi on of current flow 11 Two views of the current density @ 0.83 µsec Two views of the current density @ 5µsec
Thermal solution post processing The temperature ( C) increase is observed primarily in the mid conductor section. Maximum temperatures occur in the corners. Temperature increase is minimal due to the short duration of the pulse. 5 µsec 10 µsec 12
Detailed view of the midsection at the end of the pulse The temperature ( C) increase is limited to the surface which indicates that the penetration of the heat into the interior is limited. This is consistent with the short duration and the limited penetration of the heat generation. 13
Structural solution post processing The displacement magnitude (m) for the center section at 5µsec is shown below. The maximum displacement is observed to be on the order of.006 mm. The maximum displacements occur along the edge of the center section To observe the effect of the transient behavior of the center section, the displacement magnitude at the corner edge was plotted verses time. Since the time frame is short, the momentum induced into the conductor allows the motion to continue after the current is removed. Displacement magnitude (m) 14
Equivalent stress @ 5µsec The maximum stresses occur in the corners and the edges. The peak stress of 965 MPa shown in the legend corresponds to the lowest yield stress for Cu-Be. This indicates that local yielding will take place at the corners. The stresses away from the corners are limited to be being less than 40% of yield indicating that the 15
Conclusion Using WorkBench to generate models, a design was identified that met the target objective of 14T field at the center of the collector Using a coupled field approach to the transient solution, the interaction of the magnetic, thermal and structural fields were simulated. Temperatures remain low due to the short duration Structural response indicate local yielding at the corner, but the overall response remains elastic This methodology allow other designs to be evaluated using longer duration and different current time histories ANSYS overall objective is to allow MAXWELL to be integrated into the coupled field solution methodology. 16