Aug 29, 2006S. Kahn T HTS Solenoid1 A Proposal for a 50 T HTS Solenoid Steve Kahn Muons Inc. August 29, 2006

Aug 29, 2006S. Kahn T HTS Solenoid2 Alternating Solenoid Lattice for Cooling We plan to use high field solenoid magnets in the near final stages of cooling. The need for a high field can be seen by examining the formula for equilibrium emittance: The figure on the right shows a lattice for a 50 T alternating solenoid scheme previously studied. From R. Palmer

Aug 29, 2006S. Kahn T HTS Solenoid3

Aug 29, 2006S. Kahn T HTS Solenoid4 A Proposal for a High Field Solenoid Magnet R&D The availability of commercial high temperature superconductor tape (HTS) should allow significantly higher field that can produce smaller emittance muon beams. HTS tape can carry significant current in the presence of high fields where Nb 3 Sn or NbTi conductors cannot. We would like to see what we can design with this commercially available HTS tape.

Aug 29, 2006S. Kahn T HTS Solenoid5 Comparison of J E for HTS Conductors We have chosen to use Bi2223 since it is available as a reinforced tape from AMSC The conductor can carry significant current at very high fields. NbTi and Nb 3 Sn can not.

Aug 29, 2006S. Kahn T HTS Solenoid6 Properties of American Superconductor’s High Temperature Superconductor Wire 6% more current per turn 10 % more turns per radial space New and Improved High Strength Plus Tape High Strength Tape used for calculations

Aug 29, 2006S. Kahn T HTS Solenoid7 Cross Sections of AMSC HTS Tape High Strength Tape High Compression Tape High Current Tape React and Wind

Aug 29, 2006S. Kahn T HTS Solenoid8 Some Mechanical Properties of Oxford BSSCO-2212 Young’s Modulus E~51-63 GPa Ultimate Strength~130 MPa Strain Degradation at 0.4% Wind and React

Aug 29, 2006S. Kahn T HTS Solenoid9 Why Do We Want to Go to Liquid Helium? The parallel field orientation is the most relevant for a solenoid magnet. Previous calculations had used the perpendicular field. (We can view this not as a mistake, but as a contingency).

Aug 29, 2006S. Kahn T HTS Solenoid10 Current Carrying Capacity for HTS Tape in a Magnetic Field Scale Factor is relative to 77ºK with self field

Aug 29, 2006S. Kahn T HTS Solenoid11 A Vision of a Very High Field Solenoid Design for 50 Tesla. Inner Aperture Radius: 2.5 cm. Axial Length chosen:0.7 meter Use stainless steel ribbon between layers of HTS tape. –We will vary the thickness of the SS ribbon. –The SS ribbon provides additional tensile strength HTS tape has 300 MPa max tensile strength. SS-316 ribbon: choose 660 MPa (Goodfellow range for strength is MPa) Composite strength =  SS  SS + (1-  SS )  HTS (adds like parallel springs). We use the J eff associated to 50 Tesla. –We operate at 85% of the critical current. All parameters used come from American Superconductor’s Spec Sheets.

Aug 29, 2006S. Kahn T HTS Solenoid12 Constraining Each Layer With A Stainless Steel Strip Instead of constraining the forces as a single outer shell where the radial forces build up to the compressive strain limit, we can put a mini-shell with each layer. Suggested by R. Palmer, but actually implemented previously by BNL’s Magnet Division for RIA magnet. (See photo)

Aug 29, 2006S. Kahn T HTS Solenoid13 Using Stainless Steel Interleaving for Structural Support of 40 Tesla Magnet Case 1: Use constant thickness interleaving between layers for structural support. –The high strength HTS tape comes with ~2.7 mils stainless steel laminated to the tape. Additional SS is wound between the layers. –The effective modulus of the HTS/SS combination increases with increased SS fraction. Figure shows strain vs. radial position for a 40 Tesla magnet. –The maximum strain limit for the material is 0.4%. This is achieved with 5 mil SS interleaving. The use of constant thickness SS interleaving is not effective for magnets with fields much above 40 Tesla.

Aug 29, 2006S. Kahn T HTS Solenoid14 A Slightly More Aggressive Approach We can vary the amount of stainless steel interleafing as a function of radius. –At small radius where we have smaller stress, we could use a smaller fraction of stainless steel. (See previous slide) –In the middle radial region we would use more stainless where the tensile strength is largest. Following this approach we can build a 50 Tesla solenoid. –I will show you results for two cases: Case 2: 40 Tesla solenoid with SS interleaving varied to achieve 0.4% strain throughout. Case 3: 50 Tesla solenoid with SS interleaving varied to achieve 0.4% strain throughout. A 60 Tesla solenoid may be achieved by increasing the current as the field falls off with radius by using independent power supplies for different radial regions.

Aug 29, 2006S. Kahn T HTS Solenoid15 Varying SS Interleaving to Achieve Maximum Strain The thickness of the stainless steel interleaving is varied as a function of radius so as to reach the maximum allowable strain through out the magnet. –This minimizes the outer solenoid radius (and consequently the conductor costs). –This also brings the center of current closer to the axis and reduces the stored energy. –This is likely to increase the mechanical problems.

Aug 29, 2006S. Kahn T HTS Solenoid16 Case Comparisons The tables on the left summarize the parameters and results of the three cases presented. –The analysis assumes the solenoid length is 70 cm –The top table shows the dimensional parameters: Inner/outer radius Conductor length and amp-turns. –The bottom table shows the results from the magnetic properties: Stored energy Radial and Axial Forces

Aug 29, 2006S. Kahn T HTS Solenoid17 Comments on Stored Energy The 70 cm length was chosen to be consistent with the range of ~100 MeV muon. It is also the minimum solenoid length where there is some “non-fringing” central field. The stored energy of the 50 Tesla magnet (case 3) is 20 Mega- Joules (for 70 cm). –This can be compared to 7 Mega-Joules for the 10 m long LHC 2-in-one dipole. The LHC quench protection system actually handles a string of dipoles in a sextant (?). There are differences between HTS and NbTi that need to be considered for quench protection. –HTS goes resistive at a slower rate than NbTi. –A quench propagates at a slower velocity in HTS than for NbTi. –We will have to design a quench protection for the HTS system to determine how to protect the magnet in case of an incident.

Aug 29, 2006S. Kahn T HTS Solenoid18 What about Axial Forces? There is a significant contribution to the axial forces from the fringing radial fields at the ends. –In the 50 Tesla solenoid shown we will see a fringing field of 9 Tesla –We have seen that there is a total axial compressive force at the center of ~30 Mega-Newtons.

Aug 29, 2006S. Kahn T HTS Solenoid19 More on Compressive Forces The top figure shows the Lorentz force density at the end of the solenoid as a function of radius for the three cases. –The axial pressure on the end is P=J  B r  t where t is the tape width. This peaks at 10 MPa. The lower figure shows the Lorentz force density along the length for the peak radial position. –It is largest at the end and falls to zero at center as expected. These stresses are not large. Do we have to worry about compressive strain along the axial direction? –The maximum allowable compressive strain for the tape is 0.15%.

Aug 29, 2006S. Kahn T HTS Solenoid20 Formulate R&D Plan Initial measurements of material properties. –J C measurements under tensile and compressive strain. –Modulus measurements of conductor. –Thermal cycling to 4  K. Formulate and prepare inserts for high field tests. –Design insert for test in 30 Tesla magnet. This magnet has a reasonable size aperture. –At 30 Tesla, some part of the insert should be at the strain limit. Initial testing of insert can be performed with FNAL T solenoid. –Can increase current in lower field magnet so that J  B can still be significant for testing. –Program for conductor tests at 45 Tesla. 45 Tesla magnet has limited aperture (3.1 cm). It has a warm aperture. Formulate and simulate a quench protection scheme.