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Simulations of the Rotating Positron Target in the Presence of OMD Field*

Simulations of the Rotating Positron Target in the Presence of OMD Field*. S. Antipov+, W. Liu, W. Gai Argonne National Lab +also Illinois Institute of Technology. *Collaboration with the ILC e+ Team. Problem formulation. z.

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Simulations of the Rotating Positron Target in the Presence of OMD Field*

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  1. Simulations of the Rotating Positron Target in the Presence of OMD Field* S. Antipov+, W. Liu, W. Gai Argonne National Lab +also Illinois Institute of Technology *Collaboration with the ILC e+ Team

  2. Problem formulation z Conducting disk (target) rotates in a constant magnetic field of arbitrary distribution. Eddy currents are produced. Find their distribution, induced magnetic field etc depending on rotational frequency and geometry

  3. Equation for induced field • To incorporate the fact, that disk is spinning we add an effective emf in Ohms law and get a non-standard equation: Velocity, B0-external, B-induced magnetic field

  4. Set of equations for simulation Source for approximate models and simulations

  5. Simulation of SLAC/LLNL experiment

  6. The experiment geometry Single pole disk Courtesy SLAC/LLNL Artificial subdomain to improve mesh quality

  7. Input data Material: copper Diameter: 9 inch Thickness: 0.9 inch Magnet position: 0.47 inch off-center Distance between the disk and the magnet: 0.1, 0.05 and 0.01 inch External field, produced in simulation Measured field map, 1.14mm probe+/-0.36mm large error bars B0z-field Thickness of the disk is 0.9 inch. It is hard to measure (and simulate) magnetic field near the face of magnet (divergence) – 20% error bars

  8. Results: color – induced magnetic field (z) y x Arrows: Eddy currents Arrows: Force field

  9. Copper disk Parameter – distance between the magnet and the disk simulation exp

  10. Higher frequencies With a single magnet the roll off is almost flat

  11. ILC target geometry simulation

  12. ILC target geometry Upper solenoid is not pictured Outer domain Full domain 1m Solenoid positioned at 0.95m 1.4cm Typical simulation result: streamlines of solenoidal magnetic field (in simulation we consider returning flux – principal difference from the setup with magnet) Color: induced magnetic field (produced by eddy currents) at some frequency of rotation, ω. 6cm

  13. Results: simulation with the magnet

  14. Results: simulation with the solenoid

  15. Results: power vs RPMs

  16. Parametric studies of the ring configuration of the ILC target

  17. Simulation geometry Upper solenoid is not pictured Outer domain Full domain 1m Solenoid positioned symmetrically over the ring dr=1.5/3/6 cm 1.4cm Typical simulation result: streamlines of solenoidal magnetic field (in simulation we consider returning flux – principal difference from the setup with magnet) Color: induced magnetic field (produced by eddy currents) at some frequency of rotation, ω. 3/6/12cm

  18. Simulation geometry Target ring magnet system artificial domain full domain Color: external magnetic field. Max field inside the target – 5Tesla

  19. Results: induced field Low RPM Near roll off RPM High RPM Color – induced magnetic field, main component (into the screen) Disc rotates counter clockwise

  20. Frequency study of total field Total z-field Tesla rpms: 100 980 1735 3367 (critical) m Inside target

  21. Bx and By components, a deflection force on the beam. tesla Color – By Arrows {Bx, By} The level of transverse (to the beam) components is one order lower than the z-component Plotted 5mm from the surface of the target at 980rpms

  22. Results for σ=3e6 @980rpm, 5Tesla Ring width Magnet aperture

  23. Results for σ=1.5e6 @910rpm, 5Tesla Ring width Magnet aperture

  24. Results for σ=3e6, dr=1.5cm, 5Tesla

  25. Transient Temperature Analysis of A Target Chamber Wanming Liu, Wei Gai HEP, ANL

  26. Energy deposition (Calculated with EGS4) Beryllium window of 0.375mm thickness Undulator: K=1 u=1cm, 100m long with 150GeV 3nC drive electron beam e e-,e + and g g e+ • ~0.32mJ per bunch deposited in upstream window • ~8.4mJ per bunch deposited in downstream window • For 100m long K=0.92, lu=1.15cm undulator with 150GeV 3nC e- drive beam, • ~0.265mJ per bunch deposited in upstream window • ~5.9mJ per bunch deposited in downstream window.

  27. Energy deposition distribution from EGS4 Simulation Downstream window Upstream window sr is ~3.5mm

  28. How we solve transient response Under cylindrical coordinate system, the partial differential equation for this problem is given as: (1) The Green’s function of (1) with an infinite body is given as (2) Since the pulse length is very short, only 1ms, the effect of boundary around the window has nearly no effect to transient thermal response of window for a short time. Using the Green’s function for infinite body is accurate enough for our problem here. To simplify the calculation, we approximate the deposit energy profile using a Gaussian function as: (3) where Q0 is the total deposit energy in window per bunch and d is the thickness of window.

  29. Since the bunch length is only ~1ps, we can simply replace it with a d(t). Then we have (4) and now the solution becomes (5) If one care about the long term response, we can simply replace the Green’s function in (5) with the Green’s function for a boundary value problem T=0 at r=b. A more accurate result could be obtained by using the energy distribution profile directly instead of fitting it into a Gaussian function.

  30. Transient Response on downstream window. 100m undulator with K=1,lu=1cm

  31. Result for downstream windows,100m undulator with K=0.92,lu=1.15cm Melting point is 1560K for beryllium Downstream Windows melt in ~0.1ms. The smallest energy deposition among these windows is 0.265mJ for 0.375mm beryllium window, which is about 1/22 of the corresponding downstream window. The peak temperature rise on upstream window will be about 493K.

  32. Modeling and Prototyping of Flux Concentrator and ILC AMD Design

  33. Outline • Circuit model of Flux concentrator • Modeling of Brechna’s flux concentrator • Prototype experiment • ILC AMD design based on flux concentrator

  34. Introduction of flux concentrator • Work as a pulsed transformer. • The induced current generated by the primary coil tends to shift the primary coil flux into the smaller vacuum region inside the central bore and relieves the magnetic pressure on the primary coil. Simple transformer model 1: primary winding, 2: core, 3: radial slot, 4: bore. Cross-sectional and side view of a general flux concentrator.

  35. Circuit model of flux concentrator (1) Geometry division The flux concentrator modeling is started by dividing flux concentrator into thin disks along the longitudinal direction, and then each disk is subdivided into concentrating rings. These rings are interconnected with each other at the slot end. Each concentrating ring is modeled as a resistance and a inductance, and interconnection line along slot is modeled a resistance.

  36. Circuit model of flux concentrator (2) Equivalent circuit

  37. Modeling of Brechna’s flux concentrator(1) Geometry structure Primary coil This structure of flux concentrator is from Brechna’s paper. We will calculate its transient response and on-axis field profile using our equivalent circuit model. H. Brechna, D. A. Hill and B. M. Bally, “150 kOe Liquid Nitrogen Cooled Flux-Concentrator Magnet”, Rev. Sci. Instr., 36 1529, 1965.

  38. Modeling of Brechna’s flux concentrator(2) Comparison of transient response Results from circuit model (Source R =0.12 Ω) Measurement results

  39. Modeling of Brechna’s flux concentrator(3) Field profile along central axis Magnetic field is calculated at 20ms when a pulse is applied. Coil + flux concentrator Coil only

  40. Prototype experiment (1) Geometric structure

  41. Prototype experiment (2) Experimental setup Pulsed voltage is produced using a DC power supply and IGBT switch circuit. Pulsed magnetic field is measured using a magnetic sensor based on hall effect. Whole structure including coil and flux concentrator disk is placed in a cooler cooled by liquid nitrogen. Temperature is around 150ºK.

  42. Prototype experiment (3) Measurement data Two sets of data are measured, one works at room temperature (293ºK), and another is cooled by liquid nitrogen (around 150 ºK). After cooling by liquid nitrogen, current raise 21%, and magnetic field increase 45%.

  43. Prototype experiment (4) Comparison of magnetic fields Magnetic field produced by coil can be calculated from measured current, and magnetic field from flux concentrator is obtained by reduction coil field from measured total B field. After cooling by liquid nitrogen, magnetic field produced by coil increase 21% at pulse end, magnetic field from flux concentrator increase 100%, and total magnetic field raise 45%. Working at room temperature Cooling by liquid nitrogen

  44. Prototype experiment (5)Comparing test data with modeling results Working at room temperature Cooling by liquid nitrogen Test Model

  45. ILC AMD design (1)Geometric structure Target Flux concentrator Coils (DC)

  46. ILC AMD design (2) Transient response and field profile Transient response at target exit Distribution of on-axis magnetic field (4ms after pulse is applied.) Target exit

  47. ILC AMD design (3) Typical operating parameters Parameters of flux concentrator Parameters of DC coil

  48. ILC AMD design (4)The effect of the fluctuation of B field in FC As shown before, there is no flattop during the pulse duration(5ms) of the pulsed magnetic field. To investigate the effect of such fluctuating field, magnetic field distributions at different time near the peak of the pulse are applied in the end to end simulation. The results of positron yield and polarization are compared here in the following table. The field on target varies by about 8% during 4-5ms near the peak of pulse, but the yield varies less than 2% and the polarization barely changed.

  49. Summary • We developed a circuit model based on frequency domain analysis to calculate transient response of a flux concentrator and its field profile. • The circuit model was applied to calculate Brechna’s flux concentrator, and a good agreement is achieved. • We designed a prototype flux concentrator with 50ms pulse width. Transient response of the flux concentrator were measured both at room temperature (293ºK) and at low temperature (around 150ºK), cooling by liquid nitrogen. The magnetic field increases 45% after cooling. The magnetic field from flux concentrator raise 100%. The circuit model gave a good prediction to the measured data. • ILC AMD based on pulsed flux concentrator technique were designed using the equivalent circuit model. The designed AMD has a peak magnetic field at target exit equal to 5 Tesla. The peak power input to flux concentrator is about 5MW. The average power input to the entire AMD is around 200KW (flux concentrator + DC coil). • There is no flattop during the pulse duration for the magnetic field. But simulation results show that during 4ms to 5ms, even though the magnetic field has a variation of about 8%, the positron yield fluctuates less than 2% and the polarization barely changes. According to the result, this design will work even though the time constant is relatively big.

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